diff --git a/changes/BDClusters_AtmIssues.ipynb b/changes/BDClusters_AtmIssues.ipynb new file mode 100644 index 00000000..516e7669 --- /dev/null +++ b/changes/BDClusters_AtmIssues.ipynb @@ -0,0 +1,719 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "e99bddf5-2499-461b-9102-d8d450c3890f", + "metadata": {}, + "source": [ + "# New Additions!" + ] + }, + { + "cell_type": "markdown", + "id": "11bed8fe-4a9a-4499-8721-a34b6a9297cf", + "metadata": {}, + "source": [ + "### First Import Necessary Packages" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "01b7a3c9-8d7a-483f-a25a-161817f55e9f", + "metadata": {}, + "outputs": [], + "source": [ + "from spisea import synthetic, evolution, atmospheres, reddening, ifmr\n", + "from spisea.imf import imf, multiplicity\n", + "import numpy as np\n", + "import pandas as pd\n", + "import pylab as py\n", + "from scipy.interpolate import RegularGridInterpolator\n", + "import pdb\n", + "import matplotlib.pyplot as plt\n", + "from astropy.table import vstack\n", + "%matplotlib inline\n", + "%load_ext autoreload\n", + "%autoreload" + ] + }, + { + "cell_type": "markdown", + "id": "230b1ba3-eeca-4207-9125-08115cf15341", + "metadata": {}, + "source": [ + "## 1: BD objects in isochron" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "bc90dc34-0747-4b24-805f-6e8abf081565", + "metadata": {}, + "outputs": [], + "source": [ + "# Create isochrone object \n", + "logAge = np.log10(5*10**9.)\n", + "filt_list = ['wfc3,ir,f153m'] # Only 1 filter for plotting purposes\n", + "my_ifmr = ifmr.IFMR_Raithel18()\n", + "my_iso = synthetic.IsochronePhot(8, 0, 10,\n", + " evo_model = evolution.MergedBaraffePisaEkstromParsec(), #our new evolution model for BDs\n", + " filters=filt_list)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "3bfb0efe-bf1a-4666-945b-057c64e6cccd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " L Teff ... phase m_hst_f153m \n", + " W K ... \n", + "---------------------- ------------------ ... ----- -----------------\n", + "5.2116102444796556e+23 2793.830151362531 ... 1 9.517653682370574\n", + " 5.890768137510784e+23 2838.5725586841204 ... 1 9.39108220785009\n" + ] + } + ], + "source": [ + "bd_idx = np.where(my_iso.points['mass'] < 0.08)\n", + "print(my_iso.points[bd_idx])" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "998eaa3e-103d-40bf-85ba-125ad4a5ed75", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Brown dwarf (mass < 0.08 M_sun): F153M = 9.518 mag\n" + ] + } + ], + "source": [ + "# Create sample BD case\n", + "# Identify a brown dwarf with mass < 0.08 M_sun\n", + "bd_idx = np.where(my_iso.points['mass'] < 0.08)[0]\n", + "if len(bd_idx) > 0:\n", + " f153m = np.round(my_iso.points[bd_idx[0]]['m_hst_f153m'], decimals=3)\n", + " mass = my_iso.points[bd_idx[0]]['mass']\n", + " print('Brown dwarf (mass < 0.08 M_sun): F153M = {0} mag'.format(f153m))\n", + "else:\n", + " print('No brown dwarf with mass < 0.08 M_sun found.')" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "dca63ebb-6c40-4f76-abb6-b709ccb71466", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Make a mass-magnitude diagram from the isochrone and plot a brown dwarf\n", + "py.figure(1, figsize=(6,6))\n", + "py.clf()\n", + "py.plot(my_iso.points['mass'], my_iso.points['m_hst_f153m'], 'r-', label='generated isochron')\n", + "py.plot(my_iso.points['mass'][bd_idx[0]], my_iso.points['m_hst_f153m'][bd_idx[0]], 'b*', ms=15, label='BD mass')\n", + "py.title('Generated Isochron Containing Brown Dwarf Masses')\n", + "py.xlabel('Mass')\n", + "py.ylabel('F153M')\n", + "py.gca().invert_yaxis()\n", + "py.legend()\n", + "py.show()" + ] + }, + { + "cell_type": "markdown", + "id": "44b18dc0-a450-497c-9ef8-a23c31263718", + "metadata": {}, + "source": [ + "## 2. BD Objects in Cluster (Primary and Companions)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "6d32d779-8e93-44e1-9375-7ff6e4f5f246", + "metadata": {}, + "outputs": [], + "source": [ + "# Create IMF objects \n", + "imf_multi = multiplicity.MultiplicityUnresolved()\n", + "kc_imf = imf.CombinedWeidnerKroupaKirkpatrick_2024(multiplicity=imf_multi)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "76787edf-ced9-478a-8572-c3b5e327febe", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/mambaforge3/envs/astro/lib/python3.11/site-packages/numpy/core/fromnumeric.py:3464: RuntimeWarning: Mean of empty slice.\n", + " return _methods._mean(a, axis=axis, dtype=dtype,\n", + "/opt/mambaforge3/envs/astro/lib/python3.11/site-packages/numpy/core/_methods.py:192: RuntimeWarning: invalid value encountered in scalar divide\n", + " ret = ret.dtype.type(ret / rcount)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Found 8211 companions out of stellar mass range\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/mambaforge3/envs/astro/lib/python3.11/site-packages/numpy/core/fromnumeric.py:3464: RuntimeWarning: Mean of empty slice.\n", + " return _methods._mean(a, axis=axis, dtype=dtype,\n", + "/opt/mambaforge3/envs/astro/lib/python3.11/site-packages/numpy/core/_methods.py:192: RuntimeWarning: invalid value encountered in scalar divide\n", + " ret = ret.dtype.type(ret / rcount)\n" + ] + } + ], + "source": [ + "# Make cluster\n", + "cluster_mass = 10**6\n", + "kc_cluster = synthetic.ResolvedCluster(my_iso, kc_imf, cluster_mass, ifmr=my_ifmr)\n", + "\n", + "# Get outputs\n", + "kc_out = kc_cluster.star_systems\n", + "kc_comp = kc_cluster.companions" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "9ca75682-5e3a-4178-b9a1-0db1ecc9b4a6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Locate BHs, NSs, WDs, and BDs\n", + "p2_bh = np.where(kc_out['phase'] == 103)[0]\n", + "c_bh = np.where(kc_comp['phase'] == 103)[0]\n", + "p2_ns = np.where(kc_out['phase'] == 102)[0]\n", + "c_ns = np.where(kc_comp['phase'] == 102)[0]\n", + "p2_wd = np.where(kc_out['phase'] == 101)[0]\n", + "c_wd = np.where(kc_comp['phase'] == 101)[0]\n", + "p2_bd = np.where(kc_out['phase'] == 90)[0]\n", + "c_bd = np.where(kc_comp['phase'] == 90)[0]\n", + "\n", + "# Define bins for histograms\n", + "bh_bins = np.linspace(14, 100, 20)\n", + "wd_bins = np.linspace(0.4, 10, 20)\n", + "bd_bins = np.linspace(0.01, 0.08, 8)\n", + "ns_bins = np.linspace(0, 30, 20)\n", + "\n", + "# Create subplots\n", + "plt.figure(figsize=(14,6))\n", + "\n", + "# Plot BHs\n", + "plt.subplot(2, 2, 1)\n", + "plt.hist(kc_out[p2_bh]['mass'], histtype='step', bins=bh_bins, label='Primary Black Holes', color='blue')\n", + "plt.hist(kc_comp[c_bh]['mass'], histtype='step', bins=bh_bins, label='Companion Black Holes', color='orange')\n", + "plt.title(\"Black Holes by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot WDs\n", + "plt.subplot(2, 2, 2)\n", + "plt.hist(kc_out[p2_wd]['mass'], histtype='step', bins=wd_bins, label='Primary White Dwarves', color='blue')\n", + "plt.hist(kc_comp[c_wd]['mass'], histtype='step', bins=wd_bins, label='Companion White Dwarves', color='orange')\n", + "plt.title(\"White Dwarves by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot BDs\n", + "plt.subplot(2, 2, 3)\n", + "plt.hist(kc_out[p2_bd]['mass'], histtype='step', bins=bd_bins, label='Primary Brown Dwarves', color='blue')\n", + "plt.hist(kc_comp[c_bd]['mass'], histtype='step', bins=bd_bins, label='Companion Brown Dwarves', color='orange')\n", + "plt.title(\"Brown Dwarves by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot NSs\n", + "plt.subplot(2, 2, 4)\n", + "plt.hist(kc_out[p2_ns]['mass'], histtype='step', bins=ns_bins, label='Primary Neutron Stars', color='blue')\n", + "plt.hist(kc_comp[c_ns]['mass'], histtype='step', bins=ns_bins, label='Companion Neutron Stars', color='orange')\n", + "plt.title(\"Neutron Stars by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Adjust space between subplots\n", + "plt.subplots_adjust(hspace=0.5)\n", + "\n", + "# Show the plots\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "8f03eedf-780a-47cc-bcb5-1bd767ff4135", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "287.8044158821004\n", + "287.80301331492325\n", + "2321.1831860770926\n", + "2321.183556796764\n" + ] + } + ], + "source": [ + "print(np.min(kc_out[p2_bd]['Teff']))\n", + "print(np.min(kc_comp[c_bd]['Teff']))\n", + "print(np.max(kc_out[p2_bd]['Teff']))\n", + "print(np.max(kc_comp[c_bd]['Teff']))" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "fbbd559a-4f0d-426e-9c6c-798debb699dc", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from astropy.io import fits\n", + "from astropy.table import Table\n", + "\n", + "# plotting 1200K star from Meisner vs. BTSettl 3000K\n", + "bt_file = '/System/Volumes/Data/mnt/g/lu/models/cdbs/grid/BTSettl_rebin/btm05/lte033-3.0-0.5a+0.2.BT-Settl.spec.fits'\n", + "m_file = '/System/Volumes/Data/mnt/g/lu/models/cdbs/grid/Meisner2023/mp00/spec_jwst_t1200_g4.5_p0_kg_g1.25.fits'\n", + "p_file = '/System/Volumes/Data/mnt/g/lu/models/cdbs/grid/Phillips2020/spec_T1200_lg4.5_CEQ.fits' # Phillips 1200K star for reference\n", + "\n", + "b_hdu_list = fits.open(bt_file)\n", + "m_hdu_list = fits.open(m_file)\n", + "p_hdu_list = fits.open(p_file)\n", + "\n", + "b_data = Table(b_hdu_list[1].data)\n", + "m_data = Table(m_hdu_list[1].data)\n", + "p_data = Table(p_hdu_list[1].data)\n", + "\n", + "b_w = np.array(b_data['Wavelength'])\n", + "b_f = np.array(b_data['Flux'])\n", + "m_w = np.array(m_data['Wavelength'])\n", + "m_f = np.array(m_data['Flux'])\n", + "p_w = np.array(p_data['Flux'])\n", + "p_f = np.array(p_data['Wavelength'])\n", + "\n", + "plt.figure()\n", + "plt.plot(b_w, b_f, label = 'BTSettl')\n", + "plt.plot(m_w, m_f, label = 'Meisner')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "dcb9ce22-afd5-4f75-a033-3f205e2e8613", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "90.9000015258789\n", + "0.0\n", + "2000.3333534194462\n", + "1.524743e-33\n", + "\n", + "\n", + "1600000.0\n", + "557203.6\n", + "299949.9969872583\n", + "1.1996874e-15\n" + ] + } + ], + "source": [ + "print(np.min(b_w))\n", + "print(np.min(b_f))\n", + "print(np.min(m_w))\n", + "print(np.min(m_f))\n", + "print('\\n')\n", + "print(np.max(b_w))\n", + "print(np.max(b_f))\n", + "print(np.max(m_w))\n", + "print(np.max(m_f))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "a3e80ffe-ef8d-4fc8-8c2a-463c12c5e42d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize = (8,6))\n", + "\n", + "plt.subplot(1, 2, 1)\n", + "plt.plot(b_w, b_f)\n", + "plt.title('BTSettl Flux vs. Wavelength for 3000K star')\n", + "plt.xlabel('Wavelength (A)')\n", + "plt.ylabel('Flux (erg/cm$^2$/A)')\n", + "plt.xlim(0, 1e5)\n", + "\n", + "plt.subplot(1, 2, 2)\n", + "plt.plot(m_w, m_f)\n", + "plt.title('Meisner Flux vs. Wavelength for 1200K star')\n", + "plt.xlabel('Wavelength (A)')\n", + "plt.ylabel('Flux (erg/cm$^2$/A)')\n", + "plt.xlim(0, 1e5)\n", + "\n", + "plt.tight_layout()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "f48f74a1-3b51-4cc1-98ef-fdbf0e4f175c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Where did Phillips peak for 1200K star?\n", + "plt.figure(figsize = (8,6))\n", + "\n", + "plt.subplot(1, 2, 1)\n", + "plt.plot(p_f, p_w)\n", + "plt.title('Phillips Flux vs. Wavelength for 1200K star')\n", + "plt.xlabel('Wavelength (A)')\n", + "plt.ylabel('Flux (erg/cm$^2$/A)')\n", + "plt.xlim(0, 1e5)\n", + "\n", + "plt.subplot(1, 2, 2)\n", + "plt.plot(m_w, m_f)\n", + "plt.title('Meisner Flux vs. Wavelength for 1200K star')\n", + "plt.xlabel('Wavelength (A)')\n", + "plt.ylabel('Flux (erg/cm$^2$/A)')\n", + "plt.xlim(0, 1e5)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "d2aaf035-d3b8-4667-862c-6c430d78df63", + "metadata": {}, + "source": [ + "It becomes clear that the Meisner model peaks at fluxes much, much smaller than expected, and much, much smaller than those given by the Phillips model for a star under the same conditions (Teff = 1200K, metallicity = 0, log g = 4.5) and unit scalings. This implies that there might be some conversion factor that we are missing, due to conditions and the fact that both papers use the ATMO model for their model generation." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "5419c340-4abc-44a9-9ec3-c77bb35d1b2f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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0bt0avXr1KtZ+/fr1g6OjI7Zt2wYAePLkCQ4dOoSxY8fKP6Ctra0RFBSE1q1b47PPPkPz5s3h5OSERYsWITc3t1Txent74/bt23j06BECAgLg7u4u//D28vJCeHg40tLSEBAQACMjI7z++usAgPPnz6N3794AgE2bNuHMmTMIDQ3FwoULAUChi3nixInIysrCnj17ALxIpuPi4hS6ChMSEiCEgL29vdK1//fffwv9HSzpvq/+HgIvrtvLMScnJ8Pe3l6pnqqyohT1e18ST548gRBCZeLu5OQE4EXsLytOkl9aQghMnjwZO3fuhI+PD9566y2F7QWv/dWYgBd3sr48kL1WrVoq62VmZiInJ0dp0LuBgQEOHTqEXr164aOPPsKvv/5arJglEgn++ecf9OnTB99++y3atm0LW1tbzJgxo1jd7n5+fhg2bBhq166NnTt3IiQkRP4lNisrS6m+Lt9/0i7eXViIfv36yb/xq5KTk4PPP/8cu3btQmpqKtzc3PDNN9+Ues6nos5XQCqVKo0xKCvjx4/Hl19+ifXr12P58uVq6xUMRFc3sLSoKR8mTJiACRMmIDMzE6dOncKiRYvwxhtv4Pbt2yW6jdrGxgbAizmcirNfYd96tcXU1BQAlAYLq/vQj4iIwJdffol27dohNDQUq1evxpw5c4o8T0FLxE8//YTU1FTs3r0b2dnZSoOAW7RogT179kAIgStXrsDHxwdLly6FmZkZ5s+fX+LX5+3tjdWrVyMwMBCBgYHo37+/fFtBQnXq1Cn5gPiCBGzPnj0wNjbG33//LX+PAKhs0W3WrBnat2+Pbdu24YMPPsC2bdvg5OQkT9KAF9e+YAxYQRLyMlVl2thXnVq1aqkcBxYfH1/iY2lTjRo1YGBgoHCzQoGCm0gK/o4K6OrvpCDB2rZtG7Zs2aI0vhL47w7Fq1evKvxuFZS9fAdjwe92fHy8wv/Mq1evKhzrZaampjh48CAGDx6MadOmQSaTYfr06UXG7uzsLJ/m5vbt2/j999+xePFi5OTkFNkqtnPnTtSvXx979+5VeG/V3VBQFv+nSDvYkqWBCRMm4MyZM9izZw+uXLmCoUOHom/fvmonz9OWwMBA2NnZwdXVFe+9957KCfh0pXbt2vjkk08wcOBAjBs3Tm29N954A8nJycjPz1dq5fHw8EDjxo2LdT4LCwv069cPCxcuRE5OjtJ8OUXp06cPjIyMcO/ePZVxlMfUCwV3FF25ckWh/NChQ0p1MzMzMXToULi4uCAgIADTpk3D/Pnzce7cuWKda8KECcjKyoKvry98fHzg6emJJk2aqKwrkUjQqlUr/PDDD6hevTouXrxYshf2/7p27QpDQ0Ps27cP165dU/jSYW1tjdatW+O3337DgwcPFLoKJRIJjIyMFLrBnj9/jh07dqh9befOncPp06fx119/Ydy4cQr7vvHGGxBCIDY2VuV1b9GihdrXoMm+6nh5eSEiIkKpS7agNe5lr7aC6ZKFhQU6dOgAPz8/hXPKZDLs3LkTderUgaurq87jEELgvffew7Zt27BhwwalLwMFateujfbt22Pnzp3Iz8+Xl//777+4desWhgwZIi976623IJFIlO6+8/HxgZmZGfr27avyHKampjhw4AD69euHGTNm4McffyzRa3F1dcXnn3+OFi1aKPwdqbuuEokEJiYmCslTfHy8yrsLqWJhS1Yp3bt3D76+voiJiZE3qc+dOxdHjx7Ftm3bijXRXWn069cPQ4cOhbOzMyIjI/HFF1+ge/fuCAsLK9W369JYuXJlkXXeffdd7Nq1C/3798fMmTPRvn17GBsbIyYmBgEBAXjrrbcwePBglfu+9957MDMzQ+fOneHo6Ij4+HisWLEC1tbWaNeuXYlidXFxwdKlS7Fw4ULcv38fffv2RY0aNZCQkIDz58/DwsKiWHcQalO7du3QuHFjzJ07F3l5eahRowb279+P06dPK9WdMmUKoqKi5LF+//33CAkJwbvvvovw8HBUr1690HM1adIEnp6eWLFiBaKjo7Fx40aF7X///TfWrl2LQYMGoUGDBhBCwM/PD6mpqQrdkj169EBQUFCx7pwsmHrhwIEDMDAwkI/HKuDl5SWfaPPlJGvAgAFYvXo1Ro4ciffffx/JyclYtWqV2t/rESNGYM6cORgxYgSys7OVZtXv3Lkz3n//fUyYMAEXLlxA165dYWFhgbi4OJw+fRotWrSQz6f0Kk32VWfWrFnYunUr+vXrh6VLl8Le3h67d+/GzZs3AShOddCiRQv4+flh3bp1cHd3h4GBgU6/EKxYsQK9evWCt7c35s6dCxMTE6xduxYRERHw9fXVqOXkwoUL8ulK0tPTIYTAvn37ALz4WyhoYZ4xYwa2bNmCiRMnokWLFgpTUkilUrRp00b+/JtvvkGvXr0wdOhQTJ06FYmJiZg/fz7c3NwUkrPmzZtj0qRJWLRoEQwNDdGuXTscP34cGzduxLJly9TOkVVwzv379+Ptt9/GrFmzIJPJMHv2bJV1r1y5gmnTpmHo0KFo1KgRTExMcPLkSVy5ckWhNbigZW3v3r1o0KABTE1N0aJFC7zxxhvw8/PD1KlT8c477yA6OhpfffUVHB0ddf6lnXSsfMbbVzwAxP79++XPf//9dwFAWFhYKDyMjIzkd6wV3MlT2OOjjz4q1vnUefTokTA2Nla6i09bXr67sDCq7prJzc0Vq1atEq1atRKmpqaiWrVqokmTJuKDDz4Qd+7ckdd79e7C3377TXh7ewt7e3thYmIinJycxLBhw8SVK1eKjEvdHXoHDhwQ3t7ewsrKSkilUuHs7CzeeecdceLECXmdcePGCQsLi2K+M8V/b169u1AIIW7fvi169+4trKyshK2trZg+fbo4fPiwQuybNm0SAMS2bdsU9r17966wsrISgwYNKlacGzduFACEmZmZSEtLU9h28+ZNMWLECNGwYUNhZmYmrK2tRfv27YWPj49CvYI76Ipr3rx5AoDw8PBQ2nbgwAEBQJiYmIjMzEyFbVu3bhWNGzcWUqlUNGjQQKxYsUJs2bJF5d2YQggxcuRIAUB07txZbSxbt24VHTp0EBYWFsLMzEw0bNhQjB07Vly4cEFe59W7C0uyr5eXl2jevLnSvqqOGRERIXr27ClMTU1FzZo1xaRJk8Rvv/0mAIjLly/L66WkpIh33nlHVK9eXUgkEvl7r+7uQCFe/M9YtGiR2vehqP2Dg4NF9+7d5a+1Y8eO8rtQCxT3d/5lL9+19+rj5d9tZ2dntfVUXZvjx4+Ljh07yt/LsWPHioSEBKV6OTk5YtGiRaJevXrCxMREuLq6ip9++kllnKr+/rOzs8XAgQMFALFq1SqVrzEhIUGMHz9eNGnSRFhYWIhq1aqJli1bih9++EHhLtAHDx6I3r17C0tLS6XXtXLlSuHi4iKkUqlo2rSp2LRpk1i0aJHS311hnxukfyRCvDTLH6klkUiwf/9+DBo0CMCLyS1HjRqFa9euKXRRAEC1atXg4OCA3Nxc3Lt3r9Dj1qhRQ+XA11fPV5hGjRph8uTJ+PTTT4v9eohIP7z//vvw9fVFcnIyTExMyjscItIidheWUps2bZCfn4/ExES1d9gZGxurHf+iLcnJyYiOjubdJkQVwNKlS+Hk5IQGDRrg6dOn+Pvvv7F582Z8/vnnTLCIKiEmWYV4+vSpwrIkkZGRuHTpEmrWrAlXV1eMGjUKY8eOxffff482bdogKSkJJ0+eRIsWLZTuetH0fPXq1cPTp0+xePFivP3223B0dMSDBw/w2WefwcbGRu34JiLSH8bGxvjuu+8QExODvLw8NGrUCKtXr8bMmTPLOzQi0gF2FxYiMDBQ5cK148aNg4+PD3Jzc7Fs2TJs374dsbGxqFWrFjw9PbFkyZJS3X1U1PmeP3+OQYMGITw8HKmpqXB0dIS3tze++uorlZP1ERERUflhkkVERESkA5wni4iIiEgHmGQRERER6QAHvr9CJpPh0aNHsLS05NIFREREFYQQAhkZGXByclKY3Lc8Mcl6xaNHjziInIiIqIKKjo5GnTp1yjsMAEyylBQsXBwdHQ0rK6tyjoaIiIiKIz09HXXr1pV/jusDJlmvKOgitLKyYpJFRERUwejTUB/96LQkIiIiqmSYZBERERHpAJMsIiIiIh1gkkVERESkA0yyiIiIiHSASRYRERGRDjDJIiIiItIBJllEREREOsAki4iIiEgHmGQRERER6YBeJ1mnTp3CwIED4eTkBIlEggMHDhRa38/PD7169YKtrS2srKzg6emJY8eOlU2wRERERC/R6yQrMzMTrVq1wi+//FKs+qdOnUKvXr1w5MgRhIWFwdvbGwMHDkR4eLiOIyUiIiJSJBFCiPIOojgkEgn279+PQYMGlWi/5s2bY/jw4fjyyy+LVT89PR3W1tZIS0urkgtEP8/Jh5mJYXmHQUREVCL6+Pmt1y1ZmpLJZMjIyEDNmjXV1snOzkZ6errCo6o6dfsxmn55FKv9b5d3KERERBVepU6yvv/+e2RmZmLYsGFq66xYsQLW1tbyR926dcswQv3y5cEIAMBP/9wp50iIiIgqvkqbZPn6+mLx4sXYu3cv7Ozs1NZbsGAB0tLS5I/o6OgyjJKIiIgqK6PyDkAX9u7di0mTJuGPP/5Az549C60rlUohlUrLKDIiIiKqKipdS5avry/Gjx+P3bt3Y8CAAeUdDhEREVVRet2S9fTpU9y9e1f+PDIyEpcuXULNmjVRr149LFiwALGxsdi+fTuAFwnW2LFj8eOPP6Jjx46Ij48HAJiZmcHa2rpcXkNFUiFuMyUiIqog9Lol68KFC2jTpg3atGkDAJgzZw7atGkjn44hLi4OUVFR8vobNmxAXl4ePvroIzg6OsofM2fOLJf4iYiIqOrS65asbt26obBpvHx8fBSeBwYG6jYgIiIiomLS65YsIiIiooqKSRbJVYy5/4mIiCoGJllEREREOsAki4iIiEgHmGQRERER6QCTLCIiIiIdYJJFcoLTkRIREWkNkywiIiIiHWCSRURERKQDTLKIiIiIdIBJFhEREZEOMMkiIiIi0gEmWUREREQ6wCSLiIiISAeYZJEcF4gmIiLSHiZZRERERDrAJIuIiIhIB5hkEREREekAkyySS32WW94hEBERVRpMskjuaXZeeYdARERUaTDJIiIiItIBJllEREREOsAki4iIiEgHmGQRERER6QCTLCIiIiIdYJJFREREpANMsoiIiIh0gEkWERERkQ4wySIiIiLSASZZRERERDrAJIuIiIhIB5hkEREREekAkywiIiIiHWCSRURERKQDTLKIiIiIdIBJFhEREZEOMMkiIiIi0gEmWUREREQ6wCSLiIiISAeYZBEA4HlOfnmHQEREVKkwySIAwOWY1PIOgYiIqFJhkkVERESkA0yyCAAgRHlHQEREVLkwySIiIiLSASZZBACQSMo7AiIiospFr5OsU6dOYeDAgXBycoJEIsGBAweK3CcoKAju7u4wNTVFgwYNsH79et0HWgmwu5CIiEi79DrJyszMRKtWrfDLL78Uq35kZCT69++PLl26IDw8HJ999hlmzJiBP//8U8eREhERESkyKu8ACtOvXz/069ev2PXXr1+PevXqYc2aNQCApk2b4sKFC1i1ahXefvttHUVJREREpEyvW7JKKiQkBL1791Yo69OnDy5cuIDc3FyV+2RnZyM9PV3hQURERKSpSpVkxcfHw97eXqHM3t4eeXl5SEpKUrnPihUrYG1tLX/UrVu3LEIlIiKiSq5SJVkAIHnlNjnx/yO6Xy0vsGDBAqSlpckf0dHROo9RHwlw5DsREZE26fWYrJJycHBAfHy8QlliYiKMjIxQq1YtlftIpVJIpdKyCE+vPcvm2oVERETaVKlasjw9PeHv769Qdvz4cXh4eMDY2LicoqoYvjwYUd4hEBERVSp6nWQ9ffoUly5dwqVLlwC8mKLh0qVLiIqKAvCiq2/s2LHy+lOmTMHDhw8xZ84c3LhxA1u3bsWWLVswd+7c8gi/QnmUllXeIRAREVUqet1deOHCBXh7e8ufz5kzBwAwbtw4+Pj4IC4uTp5wAUD9+vVx5MgRzJ49G7/++iucnJzw008/cfoGIiIiKnMSITjX98vS09NhbW2NtLQ0WFlZlXc4ZcZl/mGF5w9WDiinSIiIiEpOHz+/9bq7kIiIiKiiYpJFREREpANMsghn76qeqJWIiIhKj0kWYeTmc+UdAhERUaXDJIuIiIhIB5hkEREREekAkywiIiIiHWCSRURERKQDTLKIiIiIdIBJVhUX8+RZeYdARERUKTHJquJinjxXWX40Iq6MIyEiIqpcmGSRSt8evVXeIRAREVVoTLKIiIiIdIBJFhEREZEOMMmq4iRqykWZRkFERFT5MMkiIiIi0gEmWUREREQ6wCSripNI1HUYEhERkSaYZBERERHpAJMsIiIiIh1gkkUqRSZllncIREREFRqTLCIiIiIdYJJFREREpANMsoiIiIh0gElWFVfYDA6J6VllFwgREVElwySL1LoYlVreIRAREVVYTLJIrTUnbpd3CERERBUWkywiIiIiHWCSVcVxUR0iIiLdYJJFREREpANMsoiIiIh0gElWFVfYFA5ERERUekyySK2cfFl5h0BERFRhMcmq4oRQv+3+Yy4STUREVFpMsoiIiIh0gElWFXc1Nq28QyAiIqqUmGRVcbcTMso7BCIiokqJSRYRERGRDjDJIiIiItIBJllVnIyzNBAREekEkywiIiIiHWCSRURERKQDTLKqOIFCZiMlIiKiUmOSVcUlpGeXdwhERESVEpOsKi7o9uPyDoGIiKhS0vska+3atahfvz5MTU3h7u6O4ODgQuvv2rULrVq1grm5ORwdHTFhwgQkJyeXUbREREREL+h1krV3717MmjULCxcuRHh4OLp06YJ+/fohKipKZf3Tp09j7NixmDRpEq5du4Y//vgDoaGhmDx5chlHTkRERFWdXidZq1evxqRJkzB58mQ0bdoUa9asQd26dbFu3TqV9f/991+4uLhgxowZqF+/Pl5//XV88MEHuHDhQhlHTkRERFWd3iZZOTk5CAsLQ+/evRXKe/fujbNnz6rcp1OnToiJicGRI0cghEBCQgL27duHAQMGqD1PdnY20tPTFR5VhRC8s5CIiEhXtJJk5ebmIjo6Grdu3UJKSoo2DomkpCTk5+fD3t5eodze3h7x8fEq9+nUqRN27dqF4cOHw8TEBA4ODqhevTp+/vlntedZsWIFrK2t5Y+6detqJf6K4J8bieUdAhERUaVV6iTr6dOn2LBhA7p16wZra2u4uLigWbNmsLW1hbOzM9577z2EhoZqHKBEIlF4LoRQKitw/fp1zJgxA19++SXCwsJw9OhRREZGYsqUKWqPv2DBAqSlpckf0dHRGsdcUcQ8eVbeIRAREVVaRqXZ6YcffsDy5cvh4uKCN998E/Pnz0ft2rVhZmaGlJQUREREIDg4GL169ULHjh3x888/o1GjRiU6h42NDQwNDZVarRITE5VatwqsWLECnTt3xieffAIAaNmyJSwsLNClSxcsW7YMjo6OSvtIpVJIpdISxUZERERUlFIlWWfPnkVAQABatGihcnv79u0xceJErF+/Hlu2bEFQUFCJkywTExO4u7vD398fgwcPlpf7+/vjrbfeUrnPs2fPYGSk+JIMDQ0BcPwRERERla1SJVl//PFHserduHEDU6dOLc0pAABz5szBmDFj4OHhAU9PT2zcuBFRUVHy7r8FCxYgNjYW27dvBwAMHDgQ7733HtatW4c+ffogLi4Os2bNQvv27eHk5FTqOIiIiIhKqlRJVmHS0tKwa9cubN68GZcvX0Z+fn6pjzV8+HAkJydj6dKliIuLg5ubG44cOQJnZ2cAQFxcnMKcWePHj0dGRgZ++eUXfPzxx6hevTq6d++Ob775RuPXVRmxbY+IiEh3JEJL/WgnT57E1q1b4efnB2dnZ7z99tt4++230aZNG20cvsykp6fD2toaaWlpsLKyKu9wdGrbmUgs+et6oXUerFQ//QUREZG+0MfPb41asmJiYuDj44OtW7ciMzMTw4YNQ25uLv788080a9ZMWzGSjqi+R5OIiIi0odRTOPTv3x/NmjXD9evX8fPPP+PRo0eFzkdF+ofdhURERLpT6pas48ePY8aMGfjwww9LfOcgERERUWVX6pas4OBgZGRkwMPDAx06dMAvv/yCx48fazM2IiIiogqr1EmWp6cnNm3ahLi4OHzwwQfYs2cPateuDZlMBn9/f2RkZGgzTiIiIqIKReO1C83NzTFx4kScPn0aV69exccff4yVK1fCzs4Ob775pjZiJCIiIqpwtLJAdIHGjRvj22+/RUxMDHx9fbV5aCIiIqIKpdRJ1meffYbz58+r3GZoaIhBgwbh0KFDpQ6MiIiIqCIrdZIVFxeHN954A46Ojnj//fdx+PBhZGdnazM2IiIiogqr1EnWtm3bkJCQgN9//x3Vq1fHxx9/DBsbGwwZMgQ+Pj5ISkrSZpxEREREFYpGY7IkEgm6dOmCb7/9Fjdv3sT58+fRsWNHbNq0CbVr10bXrl2xatUqxMbGaiteIiIiogpBqwPfmzZtinnz5uHMmTOIiYnBuHHjEBwczEHwREREVOVotHZhYWxtbTFp0iRMmjRJV6cgIiIi0lslbsl6/vy5yu6/a9euaSUgIiIiosqgREnWvn374Orqiv79+6Nly5Y4d+6cfNuYMWO0HhwRERFRRVWiJGvZsmW4ePEiLl++jK1bt2LixInYvXs3AEAIoZMAiYiIiCqiEo3Jys3Nha2tLQDAw8MDp06dwpAhQ3D37l1IJBKdBEhERERUEZWoJcvOzg5XrlyRP69Vqxb8/f1x48YNhXKqGGRsfCQiItKZEiVZO3bsgJ2dnUKZiYkJfH19ERQUpNXASPfuJGSUdwhERESVVom6C+vUqaOyPCsrC8bGxvj7778hk8kUtr355pulj450Kp9NWURERDqj8TxZR48exZgxY5CcnKy0TSKRID8/X9NTEBEREVU4Gs/4Pm3aNAwbNgxxcXGQyWQKDyZY+o33KhAREemOxklWYmIi5syZA3t7e23EQ2WIs24QERHpjsZJ1jvvvIPAwEAthEJERERUeWg8JuuXX37B0KFDERwcjBYtWsDY2Fhh+4wZMzQ9BekIuwuJiIh0R+Mka/fu3Th27BjMzMwQGBioMCmpRCJhkqXH2F1IRESkOxonWZ9//jmWLl2K+fPnw8BA495HIiIiokpB46woJycHw4cPZ4JFRERE9BKNM6Nx48Zh79692oiFylg++wuJiIh0RuPuwvz8fHz77bc4duwYWrZsqTTwffXq1ZqegnSEM74TERHpjsZJ1tWrV9GmTRsAQEREhMI2CW9fIyIioipK4yQrICBAG3EQERERVSocrU5ERESkAxonWStWrMDWrVuVyrdu3YpvvvlG08MTERERVUgaJ1kbNmxAkyZNlMqbN2+O9evXa3p4KmNt6lUv7xCIiIgqBY2TrPj4eDg6OiqV29raIi4uTtPDk5aIYk7XMKh1bR1HQkREVDVonGTVrVsXZ86cUSo/c+YMnJycND08aUFiRhY8V5zE98dvFVm3poVJGURERERU+Wl8d+HkyZMxa9Ys5Obmonv37gCAf/75B/PmzcPHH3+scYCkufWB9xGfnoWfT97Fx70by8s5wQYREZHuaJxkzZs3DykpKZg6dSpycnIAAKampvj000+xYMECjQMkzcnUdBVyKlIiIiLd0TjJkkgk+Oabb/DFF1/gxo0bMDMzQ6NGjSCVSrURH+kQV9UhIiLSnVKPyfrss89w/vx5+fNq1aqhXbt2cHNzY4KlZ4o76J2IiIi0p9RJVlxcHN544w04Ojri/fffx+HDh5Gdna3N2EjHmHoRERHpTqmTrG3btiEhIQG///47qlevjo8//hg2NjYYMmQIfHx8kJSUpM04SQdSn+UolXG5SSIiIu3QaAoHiUSCLl264Ntvv8XNmzdx/vx5dOzYEZs2bULt2rXRtWtXrFq1CrGxsdqKl0pBXYtV8B0mwkRERLqi1bULmzZtinnz5uHMmTOIjo7GuHHjEBwcDF9fX22ehoiIiEjv6WyBaDs7O0yaNAkHDx7E3LlzS32ctWvXon79+jA1NYW7uzuCg4MLrZ+dnY2FCxfC2dkZUqkUDRs2VLm2IhEREZEuaTyFw5w5c1SWSyQSmJqaolGjRnjzzTdRs2bNEh977969mDVrFtauXYvOnTtjw4YN6NevH65fv4569eqp3GfYsGFISEjAli1b8NprryExMRF5eXklPndlkpMnk/8skwkYGKgfeCXhFKVERERaoXGSFR4ejosXLyI/Px+NGzeGEAJ37tyBoaEhmjRpgrVr12LOnDk4ffo0mjVrVqJjr169GpMmTcLkyZMBAGvWrMGxY8ewbt06rFixQqn+0aNHERQUhPv378uTOhcXF01fYoX3KC1L/nNOvgymBoblGA0REVHVoHF34VtvvYWePXvi0aNHCAsLw8WLFxEbG4tevXphxIgRiI2NRdeuXTF79uwSHTcnJwdhYWHo3bu3Qnnv3r1x9uxZlfscOnQIHh4e+Pbbb1G7dm24urpi7ty5eP78udrzZGdnIz09XeFR2XCeLCIiorKncUvWd999B39/f1hZWcnLrKyssHjxYvTu3RszZ87El19+qZQsFSUpKQn5+fmwt7dXKLe3t0d8fLzKfe7fv4/Tp0/D1NQU+/fvR1JSEqZOnYqUlBS147JWrFiBJUuWlCi2ykxw9iwiIiKt0LglKy0tDYmJiUrljx8/lrcKVa9eXb6uYUlJXpm4SQihVFZAJpNBIpFg165daN++Pfr374/Vq1fDx8dHbWvWggULkJaWJn9ER0eXKk599vL7xUYtIiKisqGV7sKJEydi//79iImJQWxsLPbv349JkyZh0KBBAIDz58/D1dW1RMe1sbGBoaGhUqtVYmKiUutWAUdHR9SuXRvW1tbysqZNm0IIgZiYGJX7SKVSWFlZKTyqMg58JyIi0g6Nk6wNGzagR48eePfdd+Hs7Ix69erh3XffRY8ePbB+/XoAQJMmTbB58+YSHdfExATu7u7w9/dXKPf390enTp1U7tO5c2c8evQIT58+lZfdvn0bBgYGqFOnTglfWeXx8pgszuhORERUNjRKsnJzczFw4EB88sknSE5Olt9pmJycjI0bN8LCwgIA0Lp1a7Ru3brEx58zZw42b96MrVu34saNG5g9ezaioqIwZcoUAC+6+saOHSuvP3LkSNSqVQsTJkzA9evXcerUKXzyySeYOHEizMzMNHmpVUZpx2Tl5cuw+NA1HLumerwcERFRVaPRwHdjY2NERERAIpGgWrVqaNmypbbiAgAMHz4cycnJWLp0KeLi4uDm5oYjR47A2dkZwItFqqOiouT1q1WrBn9/f0yfPh0eHh6oVasWhg0bhmXLlmk1ropMV2Oy9oXFwOfsA/icfYAHKwfo5iREREQViMZ3F44dOxZbtmzBypUrtRGPkqlTp2Lq1Kkqt/n4+CiVNWnSRKmLkZRdiUnV6vHiXpqLi4iIiLSQZOXk5GDz5s3w9/eHh4eHvIuwwOrVqzU9BenAgfBHKstLO/A9J/+/WeWf5+TDzIQTnhIRUdWmcZIVERGBtm3bAngxyPxl6qZaIP1V2jFZz7L/W7oo5H4SujdRfQcoERFRVaFxkhUQEKCNOKiMxTx5ptXjvbweYlSydo9NRERUEWk8hQPpv9hU5YlY7z5+qqJm6W0780D+c56MM54SERFpJckKDg7G6NGj4enpidjYWADAjh07cPr0aW0cnjR0/3Fmieq3rVddo/NlZOUVXYmIiKiS0zjJ+vPPP9GnTx+YmZkhPDwc2dnZAICMjAx8/fXXGgdIFc+P/9wp7xCIiIjKncZJ1rJly7B+/Xps2rQJxsbG8vJOnTrh4sWLmh6eygFvWCAiItKcxknWrVu30LVrV6VyKysrpKamanp40pHC0iimWERERJrTOMlydHTE3bt3lcpPnz6NBg0aaHp40rLiTNHAhiwiIiLNaZxkffDBB5g5cybOnTsHiUSCR48eYdeuXZg7d67amdqJiIiIKjuN58maN28e0tLS4O3tjaysLHTt2hVSqRRz587FtGnTtBEjaVFkUiaaO1kXOu6qtLO+ExER0X80TrIAYPny5Vi4cCGuX78OmUyGZs2aoVq1ato4NGnZufspaO5kjcxsTrNARESkS6XqLoyKilIqMzc3h4eHB9q3b6+UYBXMnUXlb+nf1wEAyU9z1FdiQxYREZHGSpVktWvXDu+99x7Onz+vtk5aWho2bdoENzc3+Pn5lTpAKnslzbGe5+TrJA4iIqKKrFTdhTdu3MDXX3+Nvn37wtjYGB4eHnBycoKpqSmePHmC69ev49q1a/Dw8MB3332Hfv36aTtu0lQhmVRJ7y7cHvJAo1CIiIgqo1K1ZNWsWROrVq3Co0ePsG7dOri6uiIpKQl37ryY6XvUqFEICwvDmTNnmGDpKy0uL/iAC0ITEREp0Wjgu6mpKYYMGYIhQ4ZoKx6qgK7GppZ3CERERHpHKwtEUwXEwe1EREQ6xSSrqlLTXSgEYMAp34mIiDTGJIuUMMciIiLSHJMsUlCaBCsiNl37gRAREVVwTLJICZfVISIi0pzGSdaJEyfUbtuwYYOmhycNCaF68JVQMyhLTfUSy8mTaedAREREFZTGSdaAAQPw8ccfIyfnv2VaHj9+jIEDB2LBggWaHp40cCMuHR2+/qdczv08Jx95+Uy0iIio6tI4yTp16hT++usvtGvXDteuXcPhw4fh5uaGp0+f4vLly9qIkUrpk32XkZiRXeL9tDHwvcu3J9Fu+QnkMtEiIqIqSuMkq0OHDggPD0fLli3h7u6OwYMH4+OPP8bJkydRt25dbcRIpZSUoXoR6Lx8GXLzVfcLauvOwvSsPDx5losHSZnaOSAREVEFo5WB77du3UJoaCjq1KkDIyMj3Lx5E8+ecamV8hafnqWyPLOIBZ0lWpzDQabF5XuIiIgqEo2TrJUrV8LT0xO9evVCREQEQkND5S1bISEh2oiRylBJB75fe5RW6PZ8ZllERFRFaZxk/fjjjzhw4AB+/vlnmJqaonnz5jh//jyGDBmCbt26aSFE0jZtTjYaeOtxodv/vvJIeycjIiKqQDROsq5evYp+/foplBkbG+O7777D8ePHNT086cDfl+MK3V6SHKyohG1t4L0SHI2IiKjy0DjJsrGxUbvNy8tL08OTDny2/6rabRIJFO4ILGoahj3no7UWFxERUWVipOkBli5dWuj2L7/8UtNTUBkSAkjJ/O+uxMycfFibqc/Fo1J4gwMREZEqGidZ+/fvV3iem5uLyMhIGBkZoWHDhkyyKiDZS6PfDQ24xA4REVFpaJxkhYeHK5Wlp6dj/PjxGDx4sKaHp3Lw8g2BhtocJU9ERFSF6GSBaCsrKyxduhRffPGFLg5POibT1gKGREREVZhOkiwASE1NRVpa4XMokX6ScW4rIiIijWncXfjTTz8pPBdCIC4uDjt27EDfvn01PTyVgyYOVniQ/GJAuwATLiIiotLQOMn64YcfFJ4bGBjA1tYW48aNw4IFCzQ9PJUDC6nGvxZERERVnsafppGRkdqIg8pRh/o1cS4yRWfHP34tHr2bO+js+ERERPpIZ2OyqHzl5BU+iejLzE0M1W7Txhj493eEaX4QIiKiCqZULVlz5swpdt3Vq1eX5hSkoT8vxhS7rgDwdts6CI9+gl7N7BF0u/D1CImIiKhopUqyVM2NpYqEcyyVm/TnucWuKwTw/bBWEELwmhEREWlJqZKsgIAA3L9/Hy4uLjAwYI+jPipJL19BXVUJFu8tJCIiKp1SZ0iNGjVCUlKS/Pnw4cORkJCglaCobIlXBl6xLYuIiEhzpU6yXv1gPnLkCDIzMzUOiLSjJAPWZ/dyVXg+pG0dLUcDzNl7SevHJCIi0md639e3du1a1K9fH6ampnB3d0dwcHCx9jtz5gyMjIzQunVr3QZYCdSpYabwvE296vKfX02mS8svPFYrxyEiIqooSp1kSSQSpTE82h40vXfvXsyaNQsLFy5EeHg4unTpgn79+iEqKqrQ/dLS0jB27Fj06NFDq/EQERERFVepJyMVQmD8+PGQSqUAgKysLEyZMgUWFhYK9fz8/Eod3OrVqzFp0iRMnjwZALBmzRocO3YM69atw4oVK9Tu98EHH2DkyJEwNDTEgQMHSn3+qkLCUVhERERaV+oka9y4cQrPR48erXEwL8vJyUFYWBjmz5+vUN67d2+cPXtW7X7btm3DvXv3sHPnTixbtqzI82RnZyM7O1v+PD09vfRBV1CFNUDy7kIiIqLSKXWStW3bNm3GoSQpKQn5+fmwt7dXKLe3t0d8fLzKfe7cuYP58+cjODgYRkbFe2krVqzAkiVLNI5X32iysLOupsriPFxERFSV6P3A91c/lNV9UOfn52PkyJFYsmQJXF1dlbars2DBAqSlpckf0dHRGsesD86XYC3C6mbGpTrHzn8flqj+puD7pToPERFRRaTxAtG6YmNjA0NDQ6VWq8TERKXWLQDIyMjAhQsXEB4ejmnTpgEAZDIZhBAwMjLC8ePH0b17d6X9pFKpfFxZZRJ4q/hL4xgaqG9dKuzmws8PRJQkJGw8dR/vd21Yon2IiIgqKr1tyTIxMYG7uzv8/f0Vyv39/dGpUyel+lZWVrh69SouXbokf0yZMgWNGzfGpUuX0KFDh7IKvcLT3UB4dhUSEVHVobctWcCLhajHjBkDDw8PeHp6YuPGjYiKisKUKVMAvOjqi42Nxfbt22FgYAA3NzeF/e3s7GBqaqpUTkRERKRrep1kDR8+HMnJyVi6dCni4uLg5uaGI0eOwNnZGQAQFxdX5JxZpCHeXkhERFQqettdWGDq1Kl48OABsrOzERYWhq5du8q3+fj4IDAwUO2+ixcvxqVLl3QfZCVT2hsAOzWspd1AiIiIKjC9T7Ko4jAzNix0O2dvICKiqoRJFikvj/TSzyWZb4tJFBER0X+YZBERERHpAJMs0iIJbKqpn3OMDV1ERFSVMMkiJS93HxY2GalqvB2RiIgIYJJFWiSRKI/velliRrbabURERJUNkyzSGgmAzpzGgYiICACTLFJB8e7CkjEy5K8UERERwCSLtKjzazawNjMu7zCIiIj0ApMs0poR7euVYqA8ERFR5cQki5S8PHZdlCBrMjTgJA1EREQFmGRRoeLSslSWP8nMUSqTAHi/awNUk+r1uuNERERlgkkWFSo86onKcpmKFi6JBHCwNsXlRb3h3dhW16ERERHpNSZZpERhMtJS7GdoIIGZSeGLRRMREVV2TLKoUKUdyM4B8EREVNUxyaoi6ttYlOn5VHUnEhERVSVMsqqIfm4OpdpP3d2FTKGIiIgKxySriihkScFClTaZYkMWERFVdUyyqggJSpdlqUuWbidkFL6fmvJ8GbMvIiKqGphkVRFCyx18V2LSCt3es6mdynLf81FajYOIiEhfMcmqhFJUTBRa1oa618XGMe5K5RfVzLtFRERU2TDJqoQOXorV2rHUtX8V1floYCCBdxPl1iy/i9qLjYiISJ8xyaqEXk2ArEzVL3NT1IB4dXcX3kl8qvB8SJvaSnWMuJYhERFVYUyyKqHFf11XeD7W00Vt3dKkQWnPc7EvLEbxOCqyNVVlREREVQWTrErm7istTADwZmsntfUNSpEIJaQrLxrNRisiIiJFTLIqGVWD3k0M1V/morsLi3dewxJkWUcj4otdl4iIqKJiklXJqBpDZSCRlH4NwmJO/VCSrsEpO8NKFwwREVEFwiSrklGVEhWW/5Rm3JSqhM3WUlri4xAREVVmTLIqGVULM9tbmaqtr62hVCPb11NZvn50Wy2dgYiIqGJhklXZqGhlMjEyUD/flZbGZBkbqj5QXzfH4h2AiIiokmGSVcnkl3DwVWnXNFQ6DqdrICIiUsAkq5LZcz5aZXkNc2OV5UW2ZGkaEBERURXFJKuSOXw1TmW5panqJOtZTn6hxyvtXYlERERVHZMsKlRxp3BQt/wOERFRVcUkiwqlKncqbuJVoFtjWy1FQ0REVHEwyaIS+3x/hFJZYWnXuE4uOouFiIhIXzHJohK78PBJieob8s5DIiKqgphkEREREekAk6xKrlcze43218aAdg6JJyKiqohJViW3YbR7mZyHNxcSEREpYpJVyRkYaDYeKvVZrpYi0Ux2Xj4ysvQjFiIiouIwKu8ASHvSnqtPQmqYm5TqmJtPR+LzN5oVWa+k0zrIZKLYCWBGVi5aLD4uf97EwRL7p3aGmYlhic5JRERUltiSVYnk5MnUbuut4dgsTaga1+UbGoVL0anIlxWdnH1xQHHKiJvxGWjz1XE1tYmIiPQDk6wqQtNuQ02oSqMW7o/AoF/P4Pvjt4rcP/D2Y6WyrFwZbsanayE6IiIi3WCSVYkkpGeVdwgltjbwXpF11A2q77smWMvREBERaY/eJ1lr165F/fr1YWpqCnd3dwQHq/9g9fPzQ69evWBrawsrKyt4enri2LFjZRht+dp9Pkrn59gbquYcOry7sLCxZkRERPpKr5OsvXv3YtasWVi4cCHCw8PRpUsX9OvXD1FRqj/oT506hV69euHIkSMICwuDt7c3Bg4ciPDw8DKOvPL69M+rKsuNDNX/KtlYSHUVDpKfZuvs2ERERJrQ6yRr9erVmDRpEiZPnoymTZtizZo1qFu3LtatW6ey/po1azBv3jy0a9cOjRo1wtdff41GjRrhr7/+KuPIy0d5zlVV00L93Yst6ljr7Lzz9l3R2bGJiIg0obdJVk5ODsLCwtC7d2+F8t69e+Ps2bPFOoZMJkNGRgZq1qyptk52djbS09MVHlQyDWwtdHbsomac/+dmos7OTUREpAm9TbKSkpKQn58Pe3vFqQfs7e0RHx9frGN8//33yMzMxLBhw9TWWbFiBaytreWPunXrahR3ebqTkFEu59XlfYvFmOFBK0v/EBERaZveJlkFJBLFj3AhhFKZKr6+vli8eDH27t0LOzs7tfUWLFiAtLQ0+SM6OlrjmMtLRlaewvN33OuUUyTaczfxaZF17j0uug4REVFZ09sZ321sbGBoaKjUapWYmKjUuvWqvXv3YtKkSfjjjz/Qs2fPQutKpVJIpbobmF2WZK+06NhZls3rKk7SWxoh95IxYtO/RdZ7mPwMr9lZ6iQGIiKi0tLbliwTExO4u7vD399fodzf3x+dOnVSu5+vry/Gjx+P3bt3Y8CAAboOU688eZaj8Lw4uU9J8qOyXjtw7h+XVZZ/5N1Q4fmk3y6URThEREQlorctWQAwZ84cjBkzBh4eHvD09MTGjRsRFRWFKVOmAHjR1RcbG4vt27cDeJFgjR07Fj/++CM6duwobwUzMzODtbXu7nDTF0lPX0mytDxaKvCW8szruqRurNXHvRrDzckaH+66WKbxEBERlYTetmQBwPDhw7FmzRosXboUrVu3xqlTp3DkyBE4OzsDAOLi4hTmzNqwYQPy8vLw0UcfwdHRUf6YOXNmeb2EclWcVqqSjBl/tTuygKGWugvvJj5Fj+8DcSA8ttB6BgYS9GvhqJVzEhER6Ypet2QBwNSpUzF16lSV23x8fBSeBwYG6j6gCqSsVis0LMa6iNO7v4afT94ttE7P1UEAgFl7L2FQm9oq6zRztCp5gEREROVAr1uySEM6GpD+KiPDos9T3Vz9ZKUAkF7M8V7qXlJmdp7qDUREROWESVYlpq1uvALquhatTI2LsW/h/ZJtl/orlanaQ91hDl56VGQMREREZYlJViVWjF48rbCpVngrFQB0fs1G7ba5f1xGnopZR+PSsgo95ucDmsp/Dr5TtoPyiYiIisIkqxLr4mqrleN4fReAoNuPkZmjuktucpcGRR6jaSFjqfaFxZQqrhHt68l//l9E8VYBICIiKit6P/CdiiciNk3hebfGtmhdt7pCWd2aZohOea5QVpwexYfJzzBu63mYmxiq3O5Wu+ymx6j1UquZsSG/IxARkf7ip1Ql8c3RmwrPezZVnhX/0Eeva3SOZzn5Gu1fEu2Xn1BZvmJIC/nPxsUYcE+l9yj1OdeFJCLSAJOsSiL4TpLC89rVzZTq1LAoeuyUvkjMyFZZXqeGufxnXS3nU5XdSchAVPIz7AuLQaeVJ/H5gYjyDomIqMJid2El1dypaswn9ZF3Q/wacK+8w6gU0p7lotcPpxTKdp2LwvLBLdTsQUREhWFLViVVkVqtNNG+fi0AhQ+sp+J5lPZcZTm7DImISoctWZVUZexIs7OUKpUVDMbPyi278WKVlYGa7tdWS45jqEddvGZXTeGOTiIiKhyTrErKqJh33hmV1WRaWjCnl6tSmZnxiyQrMimzrMOpdNQNcUvPysOW05EAwCSLiKgE2F1YxRW13I0+ece9jlLZy60vATcTyzKcSuXPsBj8UsTakgDw5cEITNkRhrRnxVsGiYioKmOSRWXG0dpUo/1Vtc6ZGP1XNsEnFCH3kjU6R1X01+VH+PiPyzh0ueilibaHPMTRa/H45tjNIusSEVV1TLKozOhi/LSlqWKP94hN/2r/JJXcdN/wEu9zOz5DB5EQEVUuHJNVCdyISy/vEIpFqFzyWTP2VsqtY0IIzqFVDA+TM/GklN1+Fx4+QVZuPkyNVa8CQERETLIqhfgiFlIujKqZ4UuiXk3zoiuVsTyZ4GzwRYhLew6v7wI1OkbQ7cf4PTQak16vj06FLABORFRVMcmqBJ48y1F4PqGzS5H7dKhfE4Pb1MabrZ00Ovd7XYteHLqAJt2Fvu91LHbd+LQs1NXD5E+fvLMuRONjzP3jMjKy8vDPzUQ8WDlAC1EREVUuHJNVCcz5/bLCczenohdstrWU4t329WBuolmerWruKl2wsyr+ebp8G1Csejfj0+Ey/zB2/vtQ5faAW4m4//hpsc9bUcSnZSE2VfXEowVcapnjwcoBuL2sH6RGqv9NZGTl6SI8IqJKg0lWJVSW83Orm8BSFX2aNzwxPQt91wQDgMr1+cIePsGEbaHo/n1QWYemc8uP3Ch0ewNbC/hMaA/gxd2bh6a9jmpSNnoTEZUUk6xK6DW7amV2rlrVij/PlibdhRYlbHG7k5ABl/mH4XMmUuX214to7boakyr/+cT1hBKdW5V8mcD4beex8n/lO/XBiesJ+EvNVA3rR7vj7vJ+OPlxN7jYWMjLGztY4syn3Qs9LpfeISJSxiSrEmpdt3qZnattvRrFrqvJ7PIOJZxjq2Ch48V/XVcoz8mTYee/D5GTJyv2sSZvv1Cic+fly3A0Ih5JT7PlZUcj4hF46zHWB5XvYtaFvZa+bg5qVwqwNjcu/Li/XUBufvHfUyKiqoBJFpWac62SDS53q12+izjLZAKun/9PZffgq1RNAZGSmYPfzj7Ak8wcpW3RKc/Qc3UQ9oZGYcvpSEzZGQaPZSewI+QBIpMy8dHui1p5DZoorLXpw24Ni9x/mvdrarf9czMRg349U6q4iIgqKw60qKK00blzdGbXEtUvyfitlw1uU7tU+72qwWdHNNr/gx0XEPrgCfyvJ2Dn5A4IfZCC5YdvYOlbzbHmxB3cTXyKT/+8qrDPFwevaXRObYlMyoT3qkC12z/t26TIYxTVEHntUTruPX6KhrZl111NRKTP2JJFpWZmUrKJKBcOaFqq82iaZJ28mYBZe4o3q/n1R+m4FZ+hcrHk0AdPAACn7yYBAIauD8Gl6FSM2Pgvnmbr9512Xx4suvWuKK3rVS+yTo/vg/T+vSAiKitMsiq4ijTg2LmWRdGVVGjsYFnodvsipneY6HMBBy4Vvi7f7L2X8OHOMPT/KRh91pxCbn7x39fMnHycj0wpdv3yWFw5+E6SxsfwbmyHX0e2LbLeiiLuXiQiqiqYZFVwCenZRVeq4FQtnfOyv6a/jp9GtNHoHPvDY/G/iHj587wiBnF/uu9Kqc/VaunxUu9bGulZhSd1xZ31XyKRYEBLR/hMaFdovXMlSDiJiCozjsmq4Ng1A9hZmuLNVk5Ie56LL4oxqL04vj12q9Dtey9Ea3T8slxfsfUS5aSuhrkxzn3WE0+e5RSZxL6qW2O7QrffTax8E7gSEZUGW7IquH/vJ5fLeVvVKXpWeVWsTHWX1/dt7qC1Y+XLdNsNG3ArUafHLyCEwKsvxd25BsK/7A0TI4MSJ1gFdk7qoIXoiIgqNyZZFdyr0xF4udqWyXnXvKtZ95wu2OpwiZ/HGdrtlv34laWQdOXXgLtKZX9+2Enj477eqPAFoSvSWEEiIl1hklXJTC3GfEfaULeGWZmcZ2SHemVynqK0W35Cq8d78ixX54lITp4Mq47fVigrznxYxdXARv2NDDfjM7R2HiKiiopJViVTw6LwZW5a1H7RzfeOe52yCEdjS99sXqL6b7R01FEk2newiDseNdXtO+Wlg4ozH1Zx7ZjcAVO7NcS5z3ogcG43hW2p5XAHJRGRvuHA90qmqKVr9n3oiZgnz8ttwsiSDPbe/V4Htcu8qLNmeGv8fSWupGGVi1l7L6GhbTW0KOX4tsIMXX8Wj9KytH7cl9WuboZ5apK2Cw9S4Nmwlk7PT0Sk79iSVYFl5eYrPB/Q0hH1C+nCAQCpkWG5zsi9eZxHseu2rFO9xMc3MjTA3vc7lni/8jLwl9OQaXmQ/dGIOPnEqQUsTAyxY1J7rZ7nVS93H37vf5vjsoioymOSVYHdiEuX/9zcyQq/jmxbZtMClPY87VxqFv8cpToD0KFBLWwaW/xkrrzt+PehUtnznHy4zD8Ml/mHEXzncZHHuBKTiuWHr2OiTyim7FReJ/Ha0r7o0ki3N0XkvDK3WP0FR5Cdl6+mNhFR5cckqwJ7edzLq61alYEm+WJpp5goD4sOKa5vmJcvQ9Mvj8qfj9lyXv5zZFImJvqEIuzhfy1VSU+z8eYvZ7ApOBInbypPDVFWLXtWpsZKZe9tD6swv5sxT56h34/B+F3DOdCIiAowyarALsekyn/W8bROWvWRd/HucNOkt8m0kHUVZ3R/rfQHLgPBd1UvgRNyLxneqwJx8mYi3l53FiH3knE+MgVD14cUejyPErQeauKH4a2VEuNTtx+jyRdH4XcxBgBwPjIFLvMP4wf/21gfdA/XH6WrOFLh/gyLQfdVgQqTnm4Ovo8tpyPlzyNi03D2pffxSWYO3t0YAr+LMYhOeQYhBFKf5eDLgxFwmX8YfdecwvLDN3AjLh3z9l3BAr8ruBmfjtjU5/JjCCFwMz69yNUAiIgKcOB7BXYpOlX+cxn1EmqFZwMb/BpwT6fnUNWqAgCjO9bDnN6NYWVmjGWHy36NvTm9XLHa/7ZS+Yr/3UA1EyMIQOX2fJnAiE3/KpS9+lwdwyJuhtCWxg6WCF3YEx7LlKe7mPP7ZQxpWwfDNrxICH/85w4AYOX/bgIAVgxpgSFta0NqVPii4xlZufj4jxdzjH3mdxW/T/HE3cSn8mu569xDdG1kC5+zDwAA2ya0g3djO7T5yh8A8O/9F0v+VDc3VmgJvhmfoTDthO/5aPie/69F6/MBTfFbyANEp7xIugLmdity/CMREZOsCszM+L8PpAqUYxWbpo1zFiaGyMxR7KoqWKdvrKdLuSRZM3o0UplEbQi6X+h+EbFppTqf/+yupdqvtAwKyfYPhMeq3bbA7yr+uZGIj7wbok29GgBezPP15cEIxKY+R5dGNjh8NR6XX/picf5BChYfuiZPqADg/uNM3H+cKX8+YVsomqhYYLykU0y8+rvivSoQ15b0wZ7QaPRuZo+6Nc3lMZ+++xjtXGrCUk2iT0RVB5OsCkoIgQsvjcspqwHv2lDcUE2NNOvN/mNKJ6z2v4UTN/4bp9S+/ouuMxMNj13W4tNLNx1DI3vlBEOXCntfZ+29VOi+J24k4MSNBJXbgu+o7kJ9OcFSR1cTozZfdAwAsObEbczq6Yq8fBlW/H/LXOfXamHX5IpzlysR6UbF+qQhueiU5wpLvZRlilXD3FijLqii5vJaN6otLn7Rq8RzZL2qmZMVNo9rB4eX1uczNyn77xVD3eugq6stPvBqUOpj/FaMZOJVqlpwdK2a1Ahbx1ecOzu1ISMrD1/9fV2eYAHAmbvJ+PrIDTxKfY7AW4nou+YU5uy9BJf5h3FaTcJIRJUPW7IqqAsPUxSel2VD1tn5PTTa38OlJtq71MT5B4qvwdHaFL2b2aNfC+3O2l7N1AhQMb56rKcztocoT5+gbRM610czJyv5838X9EDHFf+U6Bhn75VsIfAjM7rA1b585kPr3sQeVxf3xtGIeDxMfoZfVKyfWBVsPHUfG0/91w1c0KI2ess5AMDXg1tgcJvaSHuei+0hD3AjLh0Btx5jTi9XfODVAHcSnqK5kxUkEonCnGNpz3Ox5XQkRnVwhoP1iy8QV2JSYVNNiifPcpCbL9C6bnV5/XyZkD8epT1HTXMTmEsNixz/RkSakwjOGKggPT0d1tbWSEtLg5WVVdE7lJNJPqH456Xb9RvbW+KYFsffuMw/rHbbg5UDdHKeyBX9ddLteTM+HbP3XsacXq7o1cxe7fl1YU4vV8zo0UipXNfn1eY10tSrr1Xd4H/6j5GBBHkygX5uDriT+FR+J6WxoQS5+f/9yx7mUQeTXm+APmtOKey/Y1J7SI0M5TcaqDOyQz0Mda+DCw+eYIynM0yNmXhRxaWPn99syaqg/lExH1JFVMvCBMmZOQB0N66siYMV/jezi06OXRh35xp4r4vqLsJ5fRvj26O3tHo+eyspEtKz9e6ut38+9kKP74NgbyVFyPweMDCQwMXGAjN8w8s7NL2V9/9zsvwvIl6h/OUECwB+vxCD3y/EKO3/8txqhdl9Lgq7z0UBAFKe5Wh1bUsiYpJVId17/FSprHYNM62e48NuDbEuUHmaBVtLqVbPU7emuTzJKg/LB7th4f4IrR930cBmmNC5vtrtU7u9BjNjQyz567pWznfxi16oaWGC6JRnWr9GmmpoW02pZe3NVk6ITnmG745pN9Gk0lsXeE/+N//14BYY0b4ufvznDi5GpWLjGHdEpTzDyZuJ6N3MHt/734arnSWe5eRh578P4ft+R8zeewk5+TJsG98er9m96KpOfZYDazNjLD98A79fiMbCAU3h4VITtaubIfRBCtq51GTrGVVq7C58hT42N77q++O38PPJF+Ncapgbo0P9WljyVnPYvzTAW1Npz3PRaslxhbINY9zRrbGtVsdyDPr1jHy+r/Lq4tJm193lL3vjUkwqXn/Nplg3B2wOvq92KonNYz0w+/dLyMjKU7v/nvc7opmTldp5wfSd+1f+5ZZkz+zRCFtPR8KzYS0M86iLydsvAAAW9GuiMIi9Z1N7tXc9knZ85N0QwXeS8DgjGxM714eLjcWLO4EFsOPfB+jW2A5utRVXcZDJBCSS0reA33/8FDaW0gr7t1PehBB6d1e7Pn5+631L1tq1a/Hdd98hLi4OzZs3x5o1a9Cli/qun6CgIMyZMwfXrl2Dk5MT5s2bhylTppRhxP8JfZACAwng7qy9GbczsnLlzfsA8HojW/w8oo3Wjl/A2swYXw1ywxcH/mvl6dPcQevn0Ye/0bDPe+KLgxE4cjW+6MqF+GF4K1ibG8PLtfhrBE7u0gBSY0OF97mRXTX8/oEnaliYFJpgze3tio4NamkUc3kL+6IXNgTdU0hqysKI9vUwu5crZvdylZedmOOFiw+fYKhHHbSoY415+65g0cDm6N7EDj+euI0/L8YqzAD/kXdDhUl1rc2Mkfa8ZPNv0Qsvv4/Ljyh/6Vh1XP0Yvtdfs8H5BymQyQTyZAL1apqjW2NbuNpb4vMDyq3UbrWtEBH7350wOya1R+eGNjBQ8aUoJ0+G2NTnCLiZiFZ1rdHYwQpPMnPw2f6rMDSQIDM7D0+e5aJHEzucf5CCBjbV8OfFGPRoYofTd5PwjnsdPM7IRqu61WFpaoQvD15DO5camNylAfaGRuPkzUR0algLHs414NnQBsmZ2Vjgd1Xp797EyACO1qaQCYFn2fnyLyamxgbIyi18BYImDpYqpzEpzr6aqF3dTOHvpWdTe1x7lIa4NMXpaFrWscaVmBfzADZ3ssK1QlaB6OfmgHORKUjJzMGP77bGo9Qs/HLyDqqZGiEhPRuy7Ge6eTEa0OuWrL1792LMmDFYu3YtOnfujA0bNmDz5s24fv066tWrp1Q/MjISbm5ueO+99/DBBx/gzJkzmDp1Knx9ffH2228X65zayoRjnjzD698EAAD+nv660rew0vr26E2sfakbb1BrJ6x5V/tJVoFb8RmYuSccc3q5orcOkiz/6wl4b/sFvNHSEb+MbKv14xdXvkzg9wvRWOB3FcCLGb4zs/PxwwnFf+7dGtviakwanmbnITvvxT+oQ9M6o2Wd6hqdPyUzB79fiEbIvWSsGd4aNSxMACi2ss3u6YpRHeuhupkx7j5+isb2lnr3TbK00rNy0XLx8SLrrRzSAvP//xoV182v+iIjKw+2llLEPHmG2tXNSv2+3YxPh6FEgvSsXLStVwOJGdno8PU/GNDSEb+ObIvE9CzUsDCBgUSCD3ZckM/RVru6GerbWOC0miWTdOUd9zro1cwewXce44OuDVGnxovXvuhgBH4rgztricqSLPsZotcM06uWLL1Osjp06IC2bdti3bp18rKmTZti0KBBWLFihVL9Tz/9FIcOHcKNG/99E5oyZQouX76MkJDC77IpUJwkKy9fhoSMbOTnC+QLgXyZDHkygbx8AZkQyM0XeHvdWbXn2DDGHY3sqsHIwAB5MtmL26vFi/3z///b2POcfCRnZiP5aQ5kQqCRvSXWBtzFuUjFaQ+2T2yPriVoOdFHCelZsK0mVflNsrztDY3Cp3+++FA/McdLPtZEJhPIzMlDNamRThOdy9GpeOvXMwBeJAtVYfxK2MMUGBoYIOBmIuLTsrD3QjRmdH8N03s0grGhAfJlAgnpWQh7+AQ9m9pDamSAEzcSkJ0nQy0LE1iZGcPV3hIyIWBoIIGxhvOtaUKIF3/TBXO+hT1MwaJD17BoYHPk5stw9m4yZvVshLuPnyIvX8DR2hTuy06gbb3q2DW5I8ZuPYfIpGf4aURrXItNh7WZMcylhhjQwhHZeTJ5l/76Me6oW8McEbFpeKOlI24nPEUTB0u1f1PZefnYEHQfDtamaOZohTd+Pg0AGNDCEYevxpXNm0OkZUyySiAnJwfm5ub4448/MHjwYHn5zJkzcenSJQQFBSnt07VrV7Rp0wY//vijvGz//v0YNmwYnj17BmNj5b737OxsZGf/N6lneno66tatW+hFik55hi7fBmjy8jR286u+iHnyDK/Zlf2Ek1VNvkyU2fp/qmg69oSoNHLzZfIE9VJ0KpIysmFsZIA1J27jrVZOGOPpAuD/E0khIDUyRGzqcxgbSmBnaYqs3HxkZOXhyNU4DPWoI58IOCE9CzfjM9C1kQ0kEgkS0rOwLvAeJnR2gXMtC/kxd56LQkJaFrq62uLkzURM7lIfRgYSRMSmw8TIABIJ4HcxBimZL+6KfPIsFxZSQ5y7n4KHyc+w9Uwk1o9ui75ujniU+hwOVqZIfZ6L4DuPAQButa3x5s+nlZbeAoCeTe3Q0LYaDAwkSH2Wiz7N7fHX5TikZ+VicJvaeJ6Tj4Z21XA5OhXtXGpitf9tdG9ih/9FxGF0R2fcTXyKN1o64szdZJibGOJ2Qgba16+JB0mZeM3OEucik9GpoQ3audTArYQMSCBBQkYWIIDXG9kgMSMbBhLAztIU2Xn5OBeZguaOVrC1lCr8H7j2KA3PcvLRzqUm8vJlChM4P8/Jh5GhBPkyAamRgcJ+Wbn5yJMJWJgY4ml2HnLzBWpamCAn78WX/tjUZ2hgU00hSS+4ieHV/0Nxac9hW00qP7dMJpCT/6Kb1dzEEI9Ss9DcyQomhgby/2MxT54hL1/AxcYCKZk5yJPJUMtCivTnuTCXGv5/XQny8mUwkEggkbxY9SL9eR5qWpjgVnwGpvtexOA2dTDW0xl1a5ojXybwNCMdtWrWYJJVHI8ePULt2rVx5swZdOrUSV7+9ddf47fffsOtW8p3Jbm6umL8+PH47LPP5GVnz55F586d8ejRIzg6Kk9yuXjxYixZskSpvLCLFJf2HF7fBcLIQAJDiQSGhpIXPxtIYGRggKfZeUWOzagmNZJ/0y7Yt2B/QwMJTI0NUMtCiprVTCCEQNjDJ0hIf5EMarP7kYiIqDLgwPdSeDVrLuqOBlX1VZUXWLBgAebMmSN/XtCSVRhHazPcXtav0DpERERUteltkmVjYwNDQ0PExyve8ZWYmAh7e3uV+zg4OKisb2RkhFq1VN+FJZVKIZXq17xCREREVPHp7QLRJiYmcHd3h7+/v0K5v7+/Qvfhyzw9PZXqHz9+HB4eHirHYxERERHpit4mWQAwZ84cbN68GVu3bsWNGzcwe/ZsREVFyee9WrBgAcaOHSuvP2XKFDx8+BBz5szBjRs3sHXrVmzZsgVz584tr5dAREREVZTedhcCwPDhw5GcnIylS5ciLi4Obm5uOHLkCJydnQEAcXFxiIr6b2LO+vXr48iRI5g9ezZ+/fVXODk54aeffir2HFlERERE2qK3dxeWF328O4GIiIgKp4+f33rdXUhERERUUTHJIiIiItIBJllEREREOsAki4iIiEgHmGQRERER6QCTLCIiIiIdYJJFREREpANMsoiIiIh0gEkWERERkQ7o9bI65aFgAvz09PRyjoSIiIiKq+BzW58WsmGS9Yrk5GQAQN26dcs5EiIiIiqp5ORkWFtbl3cYAJhkKalZsyYAICoqSm8uUlWVnp6OunXrIjo6Wm/WoaqqeC30C6+H/uC10B9paWmoV6+e/HNcHzDJeoWBwYthatbW1vyD0RNWVla8FnqC10K/8HroD14L/VHwOa4P9CcSIiIiokqESRYRERGRDjDJeoVUKsWiRYsglUrLO5Qqj9dCf/Ba6BdeD/3Ba6E/9PFaSIQ+3etIREREVEmwJYuIiIhIB5hkEREREekAkywiIiIiHWCSRURERKQDTLJesnbtWtSvXx+mpqZwd3dHcHBweYdUoaxYsQLt2rWDpaUl7OzsMGjQINy6dUuhjhACixcvhpOTE8zMzNCtWzdcu3ZNoU52djamT58OGxsbWFhY4M0330RMTIxCnSdPnmDMmDGwtraGtbU1xowZg9TUVIU6UVFRGDhwICwsLGBjY4MZM2YgJydHJ69d361YsQISiQSzZs2Sl/FalJ3Y2FiMHj0atWrVgrm5OVq3bo2wsDD5dl6LspOXl4fPP/8c9evXh5mZGRo0aIClS5dCJpPJ6/B66MapU6cwcOBAODk5QSKR4MCBAwrb9e19v3r1Kry8vGBmZobatWtj6dKlJV8XUZAQQog9e/YIY2NjsWnTJnH9+nUxc+ZMYWFhIR4+fFjeoVUYffr0Edu2bRMRERHi0qVLYsCAAaJevXri6dOn8jorV64UlpaW4s8//xRXr14Vw4cPF46OjiI9PV1eZ8qUKaJ27drC399fXLx4UXh7e4tWrVqJvLw8eZ2+ffsKNzc3cfbsWXH27Fnh5uYm3njjDfn2vLw84ebmJry9vcXFixeFv7+/cHJyEtOmTSubN0OPnD9/Xri4uIiWLVuKmTNnyst5LcpGSkqKcHZ2FuPHjxfnzp0TkZGR4sSJE+Lu3bvyOrwWZWfZsmWiVq1a4u+//xaRkZHijz/+ENWqVRNr1qyR1+H10I0jR46IhQsXij///FMAEPv371fYrk/ve1pamrC3txfvvvuuuHr1qvjzzz+FpaWlWLVqVYleM5Os/9e+fXsxZcoUhbImTZqI+fPnl1NEFV9iYqIAIIKCgoQQQshkMuHg4CBWrlwpr5OVlSWsra3F+vXrhRBCpKamCmNjY7Fnzx55ndjYWGFgYCCOHj0qhBDi+vXrAoD4999/5XVCQkIEAHHz5k0hxIs/ZgMDAxEbGyuv4+vrK6RSqUhLS9Pdi9YzGRkZolGjRsLf3194eXnJkyxei7Lz6aefitdff13tdl6LsjVgwAAxceJEhbIhQ4aI0aNHCyF4PcrKq0mWvr3va9euFdbW1iIrK0teZ8WKFcLJyUnIZLJiv052FwLIyclBWFgYevfurVDeu3dvnD17tpyiqvjS0tIA/LfodmRkJOLj4xXeZ6lUCi8vL/n7HBYWhtzcXIU6Tk5OcHNzk9cJCQmBtbU1OnToIK/TsWNHWFtbK9Rxc3ODk5OTvE6fPn2QnZ2t0E1T2X300UcYMGAAevbsqVDOa1F2Dh06BA8PDwwdOhR2dnZo06YNNm3aJN/Oa1G2Xn/9dfzzzz+4ffs2AODy5cs4ffo0+vfvD4DXo7zo2/seEhICLy8vhYlN+/Tpg0ePHuHBgwfFfl1cIBpAUlIS8vPzYW9vr1Bub2+P+Pj4coqqYhNCYM6cOXj99dfh5uYGAPL3UtX7/PDhQ3kdExMT1KhRQ6lOwf7x8fGws7NTOqednZ1CnVfPU6NGDZiYmFSZa7pnzx5cvHgRoaGhStt4LcrO/fv3sW7dOsyZMwefffYZzp8/jxkzZkAqlWLs2LG8FmXs008/RVpaGpo0aQJDQ0Pk5+dj+fLlGDFiBAD+bZQXfXvf4+Pj4eLionSegm3169cv1utikvUSiUSi8FwIoVRGxTNt2jRcuXIFp0+fVtpWmvf51Tqq6pemTmUVHR2NmTNn4vjx4zA1NVVbj9dC92QyGTw8PPD1118DANq0aYNr165h3bp1GDt2rLwer0XZ2Lt3L3bu3Indu3ejefPmuHTpEmbNmgUnJyeMGzdOXo/Xo3zo0/uuKhZ1+6rD7kIANjY2MDQ0VPrmkJiYqJTtUtGmT5+OQ4cOISAgAHXq1JGXOzg4AECh77ODgwNycnLw5MmTQuskJCQonffx48cKdV49z5MnT5Cbm1slrmlYWBgSExPh7u4OIyMjGBkZISgoCD/99BOMjIwUvpG9jNdC+xwdHdGsWTOFsqZNmyIqKgoA/y7K2ieffIL58+fj3XffRYsWLTBmzBjMnj0bK1asAMDrUV707X1XVScxMRGAcmtbYZhkATAxMYG7uzv8/f0Vyv39/dGpU6dyiqriEUJg2rRp8PPzw8mTJ5WaU+vXrw8HBweF9zknJwdBQUHy99nd3R3GxsYKdeLi4hARESGv4+npibS0NJw/f15e59y5c0hLS1OoExERgbi4OHmd48ePQyqVwt3dXfsvXs/06NEDV69exaVLl+QPDw8PjBo1CpcuXUKDBg14LcpI586dlaYyuX37NpydnQHw76KsPXv2DAYGih99hoaG8ikceD3Kh769756enjh16pTCtA7Hjx+Hk5OTUjdioYo9RL6SK5jCYcuWLeL69eti1qxZwsLCQjx48KC8Q6swPvzwQ2FtbS0CAwNFXFyc/PHs2TN5nZUrVwpra2vh5+cnrl69KkaMGKHyFt06deqIEydOiIsXL4ru3burvEW3ZcuWIiQkRISEhIgWLVqovEW3R48e4uLFi+LEiROiTp06lfbW6OJ4+e5CIXgtysr58+eFkZGRWL58ubhz547YtWuXMDc3Fzt37pTX4bUoO+PGjRO1a9eWT+Hg5+cnbGxsxLx58+R1eD10IyMjQ4SHh4vw8HABQKxevVqEh4fLp0rSp/c9NTVV2NvbixEjRoirV68KPz8/YWVlxSkcNPHrr78KZ2dnYWJiItq2bSufeoCKB4DKx7Zt2+R1ZDKZWLRokXBwcBBSqVR07dpVXL16VeE4z58/F9OmTRM1a9YUZmZm4o033hBRUVEKdZKTk8WoUaOEpaWlsLS0FKNGjRJPnjxRqPPw4UMxYMAAYWZmJmrWrCmmTZumcDtuVfNqksVrUXb++usv4ebmJqRSqWjSpInYuHGjwnZei7KTnp4uZs6cKerVqydMTU1FgwYNxMKFC0V2dra8Dq+HbgQEBKj8jBg3bpwQQv/e9ytXroguXboIqVQqHBwcxOLFi0s0fYMQQkiEKOn0pURERERUFI7JIiIiItIBJllEREREOsAki4iIiEgHmGQRERER6QCTLCIiIiIdYJJFREREpANMsoiIiIh0gEkWEVU4ixcvRuvWrcs7DDmJRIIDBw6UeL9bt27BwcEBGRkZJdqvXbt28PPzK/H5iKhsMckiIpXWr18PS0tL5OXlycuePn0KY2NjdOnSRaFucHAwJBIJbt++XdZhliltJ3cLFy7ERx99BEtLS6VtjRs3homJCWJjY5W2ffHFF5g/f758vT0i0k9MsohIJW9vbzx9+hQXLlyQlwUHB8PBwQGhoaF49uyZvDwwMBBOTk5wdXUtj1ArpJiYGBw6dAgTJkxQ2nb69GlkZWVh6NCh8PHxUdo+YMAApKWl4dixY2UQKRGVFpMsIlKpcePGcHJyQmBgoLwsMDAQb731Fho2bIizZ88qlHt7ewMAdu7cCQ8PD1haWsLBwQEjR45EYmIiAEAmk6FOnTpYv369wrkuXrwIiUSC+/fvAwDS0tLw/vvvw87ODlZWVujevTsuX75caLzbtm1D06ZNYWpqiiZNmmDt2rXybQ8ePIBEIoGfnx+8vb1hbm6OVq1aISQkROEYmzZtQt26dWFubo7Bgwdj9erVqF69OgDAx8cHS5YsweXLlyGRSCCRSBQSoKSkJAwePBjm5uZo1KgRDh06VGi8v//+O1q1aoU6deoobduyZQtGjhyJMWPGYOvWrXh19TNDQ0P0798fvr6+hZ6DiMoXkywiUqtbt24ICAiQPw8ICEC3bt3g5eUlL8/JyUFISIg8ycrJycFXX32Fy5cv48CBA4iMjMT48eMBAAYGBnj33Xexa9cuhfPs3r0bnp6eaNCgAYQQGDBgAOLj43HkyBGEhYWhbdu26NGjB1JSUlTGuWnTJixcuBDLly/HjRs38PXXX+OLL77Ab7/9plBv4cKFmDt3Li5dugRXV1eMGDFC3h165swZTJkyBTNnzsSlS5fQq1cvLF++XL7v8OHD8fHHH6N58+aIi4tDXFwchg8fLt++ZMkSDBs2DFeuXEH//v0xatQotfECwKlTp+Dh4aFUnpGRgT/++AOjR49Gr169kJmZqZDoFmjfvj2Cg4PVHp+I9ECJlpMmoipl48aNwsLCQuTm5or09HRhZGQkEhISxJ49e0SnTp2EEEIEBQUJAOLevXsqj3H+/HkBQGRkZAghhLh48aKQSCTiwYMHQggh8vPzRe3atcWvv/4qhBDin3/+EVZWViIrK0vhOA0bNhQbNmwQQgixaNEi0apVK/m2unXrit27dyvU/+qrr4Snp6cQQojIyEgBQGzevFm+/dq1awKAuHHjhhBCiOHDh4sBAwYoHGPUqFHC2tpa/vzV8xYAID7//HP586dPnwqJRCL+97//qXxPhBCiVatWYunSpUrlGzduFK1bt5Y/nzlzphg1apRSvYMHDwoDAwORn5+v9hxEVL7YkkVEanl7eyMzMxOhoaEIDg6Gq6sr7Ozs4OXlhdDQUHkrS7169dCgQQMAQHh4ON566y04OzvD0tIS3bp1AwBERUUBANq0aYMmTZrIu7qCgoKQmJiIYcOGAQDCwsLw9OlT1KpVC9WqVZM/IiMjce/ePaUYHz9+jOjoaEyaNEmh/rJly5Tqt2zZUv6zo6MjAMi7Mm/duoX27dsr1H/1eWFePraFhQUsLS3lx1bl+fPnMDU1VSrfsmULRo8eLX8+evRo+Pn5ITU1VaGemZkZZDIZsrOzix0jEZUto/IOgIj012uvvYY6deogICAAT548gZeXFwDAwcEB9evXx5kzZxAQEIDu3bsDADIzM9G7d2/07t0bO3fuhK2tLaKiotCnTx/k5OTIjztq1Cjs3r0b8+fPx+7du9GnTx/Y2NgAeDFuy9HRUWUXWcH4qJcV3GG3adMmdOjQQWGboaGhwnNjY2P5zxKJRGF/IYS8rIB4ZSxUYV4+dsHxC7v7z8bGBk+ePFEou379Os6dO4fQ0FB8+umn8vL8/Hz4+vriww8/lJelpKTA3NwcZmZmxY6RiMoWkywiKpS3tzcCAwPx5MkTfPLJJ/JyLy8vHDt2DP/++6/8DrmbN28iKSkJK1euRN26dQFA4e7EAiNHjsTnn3+OsLAw7Nu3D+vWrZNva9u2LeLj42FkZAQXF5ci47O3t0ft2rVx//59jBo1qtSvs0mTJjh//rxC2auxm5iYID8/v9TneFmbNm1w/fp1hbItW7aga9eu+PXXXxXKd+zYgS1btigkWREREWjbtq1WYiEi3WB3IREVytvbG6dPn8alS5fkLVnAiyRr06ZNyMrKkg96r1evHkxMTPDzzz/j/v37OHToEL766iulY9avXx+dOnXCpEmTkJeXh7feeku+rWfPnvD09MSgQYNw7NgxPHjwAGfPnsXnn3+uMmEDXsxftWLFCvz444+4ffs2rl69im3btmH16tXFfp3Tp0/HkSNHsHr1aty5cwcbNmzA//73P4XWLRcXF0RGRuLSpUtISkrSqKuuT58+CAkJkSdtubm52LFjB0aMGAE3NzeFx+TJkxEWFqZwh2VwcDB69+5d6vMTke4xySKiQnl7e+P58+d47bXXYG9vLy/38vJCRkYGGjZsKG+1srW1hY+PD/744w80a9YMK1euxKpVq1Qed9SoUbh8+TKGDBmi0OUlkUhw5MgRdO3aFRMnToSrqyveffddPHjwQOH8L5s8eTI2b94MHx8ftGjRAl5eXvDx8UH9+vWL/To7d+6M9evXY/Xq1WjVqhWOHj2K2bNnK4ybevvtt9G3b194e3vD1tZWoykU+vfvD2NjY5w4cQIAcOjQISQnJ2Pw4MFKdRs1aoQWLVpgy5YtAIDY2FicPXtW5RxbRKQ/JKIkgw6IiKqQ9957Dzdv3tTZVAlr167FwYMHSzyp6CeffIK0tDRs3LhRJ3ERkXZwTBYR0f9btWoVevXqBQsLC/zvf//Db7/9pjCpqba9//77ePLkCTIyMlQuraOOnZ0d5s6dq7O4iEg72JJFRPT/hg0bhsDAQGRkZKBBgwaYPn06pkyZUt5hEVEFxSSLiIiISAc48J2IiIhIB5hkEREREekAkywiIiIiHWCSRURERKQDTLKIiIiIdIBJFhEREZEOMMkiIiIi0gEmWUREREQ6wCSLiIiISAf+D8eusxrBKYWMAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.plot(m_w, m_f)\n", + "plt.title('Meisner Flux vs. Wavelength for 1200K star')\n", + "plt.xlabel('Wavelength (A)')\n", + "plt.ylabel('Flux (erg/cm$^2$/A)')\n", + "plt.xlim(0, 1e5)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "51fcf941-7b85-4c8a-851d-8d73f315e365", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plotting new IMF\n", + "\n", + "mass_range = np.linspace(0.01, 120, 10000)\n", + "\n", + "def power_law(masses, index):\n", + " return masses**index\n", + "\n", + "plt.figure()\n", + "\n", + "# Define each mass range and plot with the corresponding index\n", + "mass_1 = mass_range[(mass_range >= 0.01) & (mass_range < 0.05)]\n", + "plt.plot(mass_1, power_law(mass_1, -0.6), label='Index = -0.6')\n", + "\n", + "mass_2 = mass_range[(mass_range >= 0.05) & (mass_range < 0.22)]\n", + "plt.plot(mass_2, power_law(mass_2, -0.25), label='Index = -0.25')\n", + "\n", + "mass_3 = mass_range[(mass_range >= 0.22) & (mass_range < 0.55)]\n", + "plt.plot(mass_3, power_law(mass_3, -1.3), label='Index = -1.3')\n", + "\n", + "mass_4 = mass_range[(mass_range >= 0.55) & (mass_range < 8)]\n", + "plt.plot(mass_4, power_law(mass_4, -2.3), label='Index = -2.3')\n", + "\n", + "mass_5 = mass_range[(mass_range >= 8) & (mass_range <= 120)]\n", + "plt.plot(mass_5, power_law(mass_5, -2.35), label='Index = -2.35')\n", + "\n", + "# Add labels and legend\n", + "plt.xlabel('Mass (M_sun)')\n", + "plt.ylabel('Relative Number Density of Stars')\n", + "plt.legend()\n", + "plt.yscale('log')\n", + "plt.xscale('log')\n", + "plt.title('CombinedWeidnerKroupaKirkpatrick_2024 IMF Function')\n", + "plt.grid()\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "60c949a3-f40e-402f-8923-3e914d58cb3b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Locate BHs, NSs, WDs, and BDs\n", + "p2_bh = np.where(kc_out['phase'] == 103)[0]\n", + "c_bh = np.where(kc_comp['phase'] == 103)[0]\n", + "k_bh = vstack([kc_out[p2_bh], kc_comp[c_bh]])\n", + "p2_ns = np.where(kc_out['phase'] == 102)[0]\n", + "c_ns = np.where(kc_comp['phase'] == 102)[0]\n", + "k_ns = vstack([kc_out[p2_ns], kc_comp[c_ns]])\n", + "p2_wd = np.where(kc_out['phase'] == 101)[0]\n", + "c_wd = np.where(kc_comp['phase'] == 101)[0]\n", + "k_wd = vstack([kc_out[p2_wd], kc_comp[c_wd]])\n", + "p2_bd = np.where(kc_out['phase'] == 90)[0]\n", + "c_bd = np.where(kc_comp['phase'] == 90)[0]\n", + "k_bd = vstack([kc_out[p2_bd], kc_comp[c_bd]])\n", + "\n", + "# Create subplots\n", + "plt.figure(figsize=(14,6))\n", + "\n", + "# Plot BHs\n", + "plt.subplot(2, 2, 1)\n", + "plt.hist(k_bh['mass'], histtype='step', bins=bh_bins, label='Progenitor Black Hole Masses', color='blue')\n", + "plt.hist(k_bh['mass_current'], histtype='step', bins=bh_bins, label='Current Black Hole Masses', color='orange')\n", + "plt.title(\"Black Holes by Mass Over Time\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot WDs\n", + "plt.subplot(2, 2, 2)\n", + "plt.hist(k_wd['mass'], histtype='step', bins=wd_bins, label='Progenitor White Dwarf Masses', color='blue')\n", + "plt.hist(k_wd['mass_current'], histtype='step', bins=wd_bins, label='Current White Dwarf Masses', color='orange')\n", + "plt.title(\"White Dwarves by Mass Over Time\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot BDs\n", + "plt.subplot(2, 2, 3)\n", + "plt.hist(k_bd['mass'], histtype='step', bins=bd_bins, label='Progenitor Brown Dwarf Masses', color='blue')\n", + "plt.hist(k_bd['mass_current'], histtype='step', bins=bd_bins, label='Current Brown Dwarf Masses', color='orange')\n", + "plt.title(\"Brown Dwarves by Mass Over Time\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot NSs\n", + "plt.subplot(2, 2, 4)\n", + "plt.hist(k_ns['mass'], histtype='step', bins=ns_bins, label='Progenitor Neutron Star Masses', color='blue')\n", + "plt.hist(k_ns['mass_current'], histtype='step', bins=ns_bins, label='Current Neutron Stars Masses', color='orange')\n", + "plt.title(\"Neutron Stars by Mass Over Time\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Adjust space between subplots\n", + "plt.subplots_adjust(hspace=0.5)\n", + "\n", + "# Show the plots\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "c397930b-0fa9-4592-b571-e3dfbf00b8f7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.scatter(kc_out[p2_bd]['mass'], kc_out[p2_bd]['Teff'])\n", + "plt.title('Brown Dwarf Assigned Teff vs. Mass')\n", + "plt.xlabel('Mass (M_$\\odot$)')\n", + "plt.ylabel('Effective Temperarture (K)')\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "4a03d8bd-18df-4d28-8106-19a9e14c12a4", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7747" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.min(k_ns['mass_current'])\n", + "np.max(k_ns['mass_current'])\n", + "len(k_ns['mass_current'])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6b514e4e-1ed0-457c-ad03-49bb64ec2236", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/changes/BD_Clusters.ipynb b/changes/BD_Clusters.ipynb new file mode 100644 index 00000000..637ffc12 --- /dev/null +++ b/changes/BD_Clusters.ipynb @@ -0,0 +1,588 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "38ea9963-fc45-4dbc-86b8-fa882b608583", + "metadata": {}, + "source": [ + "# Simulating Stellar Clusters with Brown Dwarfs" + ] + }, + { + "cell_type": "markdown", + "id": "4a8eebf3-dd6d-4331-943a-57f7b5f8833f", + "metadata": {}, + "source": [ + "#### Importing Necessary Packages" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "81f8a8a2-18b9-4ec5-a3a5-16a728e24163", + "metadata": {}, + "outputs": [], + "source": [ + "# Import necessary packages. \n", + "from spisea import synthetic, evolution, atmospheres, reddening, ifmr\n", + "from spisea.imf import imf, multiplicity\n", + "import numpy as np\n", + "import pandas as pd\n", + "import pylab as py\n", + "from scipy.interpolate import RegularGridInterpolator\n", + "import pdb\n", + "import matplotlib.pyplot as plt\n", + "from astropy.table import vstack\n", + "%matplotlib inline\n", + "%load_ext autoreload\n", + "%autoreload" + ] + }, + { + "cell_type": "markdown", + "id": "7ab56664-88f3-4ff1-8afc-baea7af1ef94", + "metadata": {}, + "source": [ + "## Creating Isochrone Extending to Substellar Range" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "7f0e899f-6cb7-48f1-acfc-1fd9c4df4135", + "metadata": {}, + "outputs": [], + "source": [ + "# Create isochrone object \n", + "filt_list = ['wfc3,ir,f153m'] # We won't be doing much with synthetic photometry here, so only need 1 filter\n", + "my_ifmr = ifmr.IFMR_Raithel18()\n", + "my_iso = synthetic.IsochronePhot(9, 0, 10,\n", + " evo_model = evolution.MergedPhillipsBaraffePisaEkstromParsec(), #our new evolution model for BDs\n", + " filters=filt_list)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "8a5bda53-583b-42ec-8448-399c8b98de64", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Brown dwarf (mass < 0.08 M_sun): F153M = 19.201 mag\n" + ] + } + ], + "source": [ + "# Creating a sample BD case for identification\n", + "bd_idx = np.where((my_iso.points['mass'] > 0.01) & (my_iso.points['mass'] < 0.08) )[0]\n", + "if len(bd_idx) > 0:\n", + " f153m = np.round(my_iso.points[bd_idx[0]]['m_hst_f153m'], decimals=3)\n", + " mass = my_iso.points[bd_idx[0]]['mass']\n", + " print('Brown dwarf (mass < 0.08 M_sun): F153M = {0} mag'.format(f153m))\n", + "else:\n", + " print('No brown dwarf with mass < 0.08 M_sun found.')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "3cf86905-d02a-4fd1-bb58-2f2432edcb4e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Make a mass-magnitude diagram from the isochrone and plot brown dwarfs\n", + "py.figure(1, figsize=(6,6))\n", + "py.clf()\n", + "py.plot(my_iso.points['mass'], my_iso.points['m_hst_f153m'], 'r-', label='generated isochron')\n", + "py.plot(my_iso.points['mass'][bd_idx], my_iso.points['m_hst_f153m'][bd_idx], 'b*', ms=15, label='BD mass')\n", + "py.title('Generated Isochron Containing Brown Dwarf Masses')\n", + "py.xlabel('Mass')\n", + "py.ylabel('Magnitude in F153M filter')\n", + "py.gca().invert_yaxis()\n", + "py.legend()\n", + "py.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8da89871-b687-44e2-a7e4-a6fc753f5222", + "metadata": {}, + "source": [ + "## Case 1: Cluster Without Companions" + ] + }, + { + "cell_type": "markdown", + "id": "db8bfa5e-1106-4cbf-969b-0816e91fc5aa", + "metadata": {}, + "source": [ + "For this stellar cluster, we will be using the MergedBaraffePisaEkstromParsec evolution model, IMFR_Raithel18 initial-final mass relation, and the Salpeter_Kirkpatrick_2024 initial mass function, all of which have been modified to describe substellar masses." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "e79ee070-7f0d-4d46-b477-d22bd4fcb810", + "metadata": {}, + "outputs": [], + "source": [ + "# Create IMF object without companions \n", + "k_imf = imf.Salpeter_Kirkpatrick_2024()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "79704dca-9b9e-4572-b49f-760511e06b08", + "metadata": {}, + "outputs": [], + "source": [ + "# Make cluster\n", + "cluster_mass = 10**6\n", + "k_cluster = synthetic.ResolvedCluster(my_iso, k_imf, cluster_mass, ifmr=my_ifmr)\n", + "\n", + "# Get outputs\n", + "k_out = k_cluster.star_systems" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "a192b379-25fb-43ac-a799-6ba4a98d5df9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Locate BHs, NSs, WDs, and BDs\n", + "p_bh = np.where(k_out['phase'] == 103)[0]\n", + "p_ns = np.where(k_out['phase'] == 102)[0]\n", + "p_wd = np.where(k_out['phase'] == 101)[0]\n", + "p_bd = np.where(k_out['phase'] == 90)[0]\n", + "\n", + "# Determine individual histogram bins\n", + "bh_bins = np.linspace(0.01, 16, 20)\n", + "wd_bins = np.linspace(0.4, 10, 20)\n", + "bd_bins = np.linspace(0.01, 0.08, 8)\n", + "ns_bins = np.linspace(8, 30, 20)\n", + "\n", + "# Plot BHs\n", + "plt.figure(figsize=(14,6))\n", + "plt.subplot(2, 2, 1)\n", + "plt.hist(k_out[p_bh]['mass_current'], histtype = 'step',\n", + " bins = bh_bins, label = 'Generated Black Holes')\n", + "plt.title(\"Generated Black Holes by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot WDs\n", + "plt.subplot(2, 2, 2)\n", + "plt.hist(k_out[p_wd]['mass'], histtype = 'step',\n", + " bins = wd_bins, label = 'Generated White Dwarves')\n", + "plt.title(\"Generated White Dwarves by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot BDs\n", + "plt.subplot(2, 2, 3)\n", + "plt.hist(k_out[p_bd]['mass_current'], histtype = 'step',\n", + " bins = bd_bins, label = 'Generated Brown Dwarves')\n", + "plt.title(\"Generated Brown Dwarves by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot NSs\n", + "plt.subplot(2, 2, 4)\n", + "plt.hist(k_out[p_ns]['mass'], histtype = 'step',\n", + " bins = ns_bins, label = 'Generated Neutron Stars')\n", + "plt.title(\"Generated Neutron Stars by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Adjust space between subplots\n", + "plt.subplots_adjust(hspace=0.5)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "7c9bbd80-1243-485d-a944-9bfafc5049fd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "BH max mass: 119.66334547857207\n", + "BH min mass: 15.0000788054688\n", + "\n", + "NS max mass: 119.69186137462842\n", + "NS min mass: 9.00041007150772\n", + "\n", + "WD max mass: 8.999600545649336\n", + "WD min mass: 2.3067911099815683\n", + "\n", + "BD max mass: 0.07999963770010694\n", + "BD min mass: 0.010000021076120833\n", + "\n" + ] + } + ], + "source": [ + "# Checking that objects are in the correct mass ranges\n", + "print(\"BH max mass: \" + str(np.max(k_out[p_bh]['mass'])))\n", + "print(\"BH min mass: \" + str(np.min(k_out[p_bh]['mass'])) + '\\n')\n", + "\n", + "print(\"NS max mass: \" + str(np.max(k_out[p_ns]['mass'])))\n", + "print(\"NS min mass: \" + str(np.min(k_out[p_ns]['mass'])) + '\\n')\n", + "\n", + "print(\"WD max mass: \" + str(np.max(k_out[p_wd]['mass'])))\n", + "print(\"WD min mass: \" + str(np.min(k_out[p_wd]['mass'])) + '\\n')\n", + "\n", + "print(\"BD max mass: \" + str(np.max(k_out[p_bd]['mass'])))\n", + "print(\"BD min mass: \" + str(np.min(k_out[p_bd]['mass'])) + '\\n')" + ] + }, + { + "cell_type": "markdown", + "id": "c5cf0b4c-2b80-4b0c-9adf-e3d590dd39a3", + "metadata": {}, + "source": [ + "It is worth noting [explain about big NS's after confirmation from Matt] ..... \n", + "white dwarfs capped at low end due to age of cluster" + ] + }, + { + "cell_type": "markdown", + "id": "4e0ca5d6-c984-45be-982a-4e76e6083dde", + "metadata": {}, + "source": [ + "## Case 2: Cluster With Companions" + ] + }, + { + "cell_type": "markdown", + "id": "f64318cd-f631-4a24-9abe-93c96fa17251", + "metadata": {}, + "source": [ + "For this cluster we are using the same isochrone as the one generated in Case 1, just changing our IMF to allow for systems with companions. We then record the number of progenitors in each mass bin for black holes, neutron stars, white dwarfs, and brown dwarfs. We can then view how they all evolve over time." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "104a64d0-6a52-4b26-a418-0df265902a92", + "metadata": {}, + "outputs": [], + "source": [ + "# Create IMF objects \n", + "imf_multi = multiplicity.MultiplicityUnresolved()\n", + "kc_imf = imf.Salpeter_Kirkpatrick_2024(multiplicity=imf_multi)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "6042a1ae-86c2-44d3-b718-fd678185a6e7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Found 19241 companions out of stellar mass range\n" + ] + } + ], + "source": [ + "# Make cluster\n", + "cluster_mass = 10**6\n", + "kc_cluster = synthetic.ResolvedCluster(my_iso, kc_imf, cluster_mass, ifmr=my_ifmr)\n", + "\n", + "# Get outputs\n", + "kc_out = kc_cluster.star_systems\n", + "kc_comp = kc_cluster.companions" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "f7f2111d-2cdb-4d3c-80fd-7b7025010841", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Locate BHs, NSs, WDs, and BDs\n", + "p2_bh = np.where(kc_out['phase'] == 103)[0]\n", + "c_bh = np.where(kc_comp['phase'] == 103)[0]\n", + "p2_ns = np.where(kc_out['phase'] == 102)[0]\n", + "c_ns = np.where(kc_comp['phase'] == 102)[0]\n", + "p2_wd = np.where(kc_out['phase'] == 101)[0]\n", + "c_wd = np.where(kc_comp['phase'] == 101)[0]\n", + "p2_bd = np.where(kc_out['phase'] == 90)[0]\n", + "c_bd = np.where(kc_comp['phase'] == 90)[0]\n", + "\n", + "# Define bins for histograms\n", + "bh_bins = np.linspace(14, 100, 20)\n", + "wd_bins = np.linspace(0.4, 10, 20)\n", + "bd_bins = np.linspace(0.01, 0.08, 8)\n", + "ns_bins = np.linspace(0, 30, 20)\n", + "\n", + "# Create subplots\n", + "plt.figure(figsize=(14,6))\n", + "\n", + "# Plot BHs\n", + "plt.subplot(2, 2, 1)\n", + "plt.hist(kc_out[p2_bh]['mass'], histtype='step', bins=bh_bins, label='Primary Black Holes', color='blue')\n", + "plt.hist(kc_comp[c_bh]['mass'], histtype='step', bins=bh_bins, label='Companion Black Holes', color='orange')\n", + "plt.title(\"Black Holes by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot WDs\n", + "plt.subplot(2, 2, 2)\n", + "plt.hist(kc_out[p2_wd]['mass'], histtype='step', bins=wd_bins, label='Primary White Dwarves', color='blue')\n", + "plt.hist(kc_comp[c_wd]['mass'], histtype='step', bins=wd_bins, label='Companion White Dwarves', color='orange')\n", + "plt.title(\"White Dwarves by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot BDs\n", + "plt.subplot(2, 2, 3)\n", + "plt.hist(kc_out[p2_bd]['mass'], histtype='step', bins=bd_bins, label='Primary Brown Dwarves', color='blue')\n", + "plt.hist(kc_comp[c_bd]['mass'], histtype='step', bins=bd_bins, label='Companion Brown Dwarves', color='orange')\n", + "plt.title(\"Brown Dwarves by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot NSs\n", + "plt.subplot(2, 2, 4)\n", + "plt.hist(kc_out[p2_ns]['mass'], histtype='step', bins=ns_bins, label='Primary Neutron Stars', color='blue')\n", + "plt.hist(kc_comp[c_ns]['mass'], histtype='step', bins=ns_bins, label='Companion Neutron Stars', color='orange')\n", + "plt.title(\"Neutron Stars by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Adjust space between subplots\n", + "plt.subplots_adjust(hspace=0.5)\n", + "\n", + "# Show the plots\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "fedb95f5-8f7a-41e8-b586-20ce6e497126", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "BH prim max mass: 119.81313623903503\n", + "BH prim min mass: 15.00991526273759\n", + "BH comp max mass: 117.87922107922613\n", + "BH comp min mass: 15.025589362143613\n", + "\n", + "NS prim max mass: 118.77258608698675\n", + "NS prim min mass: 9.000462873651996\n", + "NS comp max mass: 112.7083837457762\n", + "NS comp min mass: 9.001307704298794\n", + "\n", + "WD prim max mass: 8.999282260049943\n", + "WD prim min mass: 2.3066340801114324\n", + "WD comp max mass: 8.995879334368274\n", + "WD comp min mass: 2.306670656743985\n", + "\n", + "BD prim max mass: 0.07999996275188857\n", + "BD prim min mass: 0.010000063950493392\n", + "BD comp max mass: 0.07999976499332974\n", + "BD comp min mass: 0.010000270279172984\n", + "\n" + ] + } + ], + "source": [ + "# Checking that objects are in the correct mass ranges\n", + "print(\"BH prim max mass: \" + str(np.max(kc_out['mass'][p2_bh])))\n", + "print(\"BH prim min mass: \" + str(np.min(kc_out['mass'][p2_bh])))\n", + "print(\"BH comp max mass: \" + str(np.max(kc_comp['mass'][c_bh])))\n", + "print(\"BH comp min mass: \" + str(np.min(kc_comp['mass'][c_bh])) + '\\n')\n", + "\n", + "print(\"NS prim max mass: \" + str(np.max(kc_out[p2_ns]['mass'])))\n", + "print(\"NS prim min mass: \" + str(np.min(kc_out[p2_ns]['mass'])))\n", + "print(\"NS comp max mass: \" + str(np.max(kc_comp[c_ns]['mass'])))\n", + "print(\"NS comp min mass: \" + str(np.min(kc_comp[c_ns]['mass'])) + '\\n')\n", + "\n", + "print(\"WD prim max mass: \" + str(np.max(kc_out[p2_wd]['mass'])))\n", + "print(\"WD prim min mass: \" + str(np.min(kc_out[p2_wd]['mass'])))\n", + "print(\"WD comp max mass: \" + str(np.max(kc_comp[c_wd]['mass'])))\n", + "print(\"WD comp min mass: \" + str(np.min(kc_comp[c_wd]['mass'])) + '\\n')\n", + "\n", + "print(\"BD prim max mass: \" + str(np.max(kc_out[p2_bd]['mass'])))\n", + "print(\"BD prim min mass: \" + str(np.min(kc_out[p2_bd]['mass'])))\n", + "print(\"BD comp max mass: \" + str(np.max(kc_comp[c_bd]['mass'])))\n", + "print(\"BD comp min mass: \" + str(np.min(kc_comp[c_bd]['mass'])) + '\\n')" + ] + }, + { + "cell_type": "markdown", + "id": "3dd322a2-2d57-43f9-b9bd-5f0664dc571f", + "metadata": {}, + "source": [ + "All of our brown dwarf primary and companion progenitor objects are in the correct mass range! Now let's see how everything evolves over time!" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "698c9fd3-02f4-49c1-bef8-16e102f30f72", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Locate BHs, NSs, WDs, and BDs\n", + "p2_bh = np.where(kc_out['phase'] == 103)[0]\n", + "c_bh = np.where(kc_comp['phase'] == 103)[0]\n", + "k_bh = vstack([kc_out[p2_bh], kc_comp[c_bh]])\n", + "p2_ns = np.where(kc_out['phase'] == 102)[0]\n", + "c_ns = np.where(kc_comp['phase'] == 102)[0]\n", + "k_ns = vstack([kc_out[p2_ns], kc_comp[c_ns]])\n", + "p2_wd = np.where(kc_out['phase'] == 101)[0]\n", + "c_wd = np.where(kc_comp['phase'] == 101)[0]\n", + "k_wd = vstack([kc_out[p2_wd], kc_comp[c_wd]])\n", + "p2_bd = np.where(kc_out['phase'] == 90)[0]\n", + "c_bd = np.where(kc_comp['phase'] == 90)[0]\n", + "k_bd = vstack([kc_out[p2_bd], kc_comp[c_bd]])\n", + "\n", + "# Create subplots\n", + "plt.figure(figsize=(14,6))\n", + "\n", + "# Plot BHs\n", + "plt.subplot(2, 2, 1)\n", + "plt.hist(k_bh['mass'], histtype='step', bins=bh_bins, label='Progenitor Black Hole Masses', color='blue')\n", + "plt.hist(k_bh['mass_current'], histtype='step', bins=bh_bins, label='Current Black Hole Masses', color='orange')\n", + "plt.title(\"Black Holes by Mass Over Time\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot WDs\n", + "plt.subplot(2, 2, 2)\n", + "plt.hist(k_wd['mass'], histtype='step', bins=wd_bins, label='Progenitor White Dwarf Masses', color='blue')\n", + "plt.hist(k_wd['mass_current'], histtype='step', bins=wd_bins, label='Current White Dwarf Masses', color='orange')\n", + "plt.title(\"White Dwarves by Mass Over Time\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot BDs\n", + "plt.subplot(2, 2, 3)\n", + "plt.hist(k_bd['mass'], histtype='step', bins=bd_bins, label='Progenitor Brown Dwarf Masses', color='blue')\n", + "plt.hist(k_bd['mass_current'], histtype='step', bins=bd_bins, label='Current Brown Dwarf Masses', color='orange')\n", + "plt.title(\"Brown Dwarves by Mass Over Time\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Plot NSs\n", + "plt.subplot(2, 2, 4)\n", + "plt.hist(k_ns['mass'], histtype='step', bins=ns_bins, label='Progenitor Neutron Star Masses', color='blue')\n", + "plt.hist(k_ns['mass_current'], histtype='step', bins=ns_bins, label='Current Neutron Stars Masses', color='orange')\n", + "plt.title(\"Neutron Stars by Mass Over Time\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "# Adjust space between subplots\n", + "plt.subplots_adjust(hspace=0.5)\n", + "\n", + "# Show the plots\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "e63c4166-df0a-4314-9fa8-f2d5e505c1be", + "metadata": {}, + "source": [ + "We expect brown dwarfs to not change over time, which is consistent with evolutionary models imposed for these objects." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/changes/BD_Evolution.ipynb b/changes/BD_Evolution.ipynb new file mode 100644 index 00000000..ef60330e --- /dev/null +++ b/changes/BD_Evolution.ipynb @@ -0,0 +1,172 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "cf875d01-eefb-4ab5-8bc1-9d7ff0b68e6e", + "metadata": {}, + "source": [ + "## Attempting to Describe Brown Dwarf Evolution Using Known Relations" + ] + }, + { + "cell_type": "markdown", + "id": "edb00592-f126-4ae1-ab2b-13f7094e01ee", + "metadata": {}, + "source": [ + "We are trying to find a relation between age/mass and effective temperature of brown dwarf stars. To do this, we are looking at several evolutionary .csv files laid out in the [SPLAT evolutionary model for brown dwarves program](https://github.com/aburgasser/splat/tree/main/resources/EvolutionaryModels). Namely, we will be considering:\n", + "* [Baraffe 2003](https://github.com/aburgasser/splat/blob/main/resources/EvolutionaryModels/baraffe2003.csv)\n", + "* " + ] + }, + { + "cell_type": "markdown", + "id": "79e30b98-f4d3-44df-aa44-2cb7a223c747", + "metadata": {}, + "source": [ + "#### Importing Necessary Packages" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "910e4a29-8083-4dca-b1ac-3d574999efae", + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "205f6536-9dd1-444f-a194-c28610089e60", + "metadata": {}, + "source": [ + "#### Importing .csv Files for Analysis" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "620a1840-cf87-45c9-b65f-6b6b0e803192", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " age mass luminosity temperature gravity radius\n", + "0 0.001 0.0005 -5.370 628 2.645 0.176\n", + "1 0.001 0.0010 -4.715 942 2.996 0.166\n", + "2 0.001 0.0020 -4.137 1285 3.259 0.174\n", + "3 0.001 0.0030 -3.746 1553 3.372 0.187\n", + "4 0.001 0.0040 -3.482 1747 3.438 0.200\n", + ".. ... ... ... ... ... ...\n", + "230 10.000 0.0720 -4.472 1556 5.481 0.081\n", + "231 10.000 0.0750 -3.954 1997 5.415 0.089\n", + "232 10.000 0.0800 -3.602 2322 5.353 0.099\n", + "233 10.000 0.0900 -3.274 2624 5.289 0.113\n", + "234 10.000 0.1000 -3.082 2786 5.246 0.125\n", + "\n", + "[235 rows x 6 columns]\n" + ] + } + ], + "source": [ + "baraffe_2003 = pd.read_csv('/System/Volumes/Data/mnt/g3/scratch/caitlinbegbie/code/SPISEA/changes/bd_evo_csv/baraffe2003.csv')\n", + "print(baraffe_2003)" + ] + }, + { + "cell_type": "markdown", + "id": "fec3c4e4-52b4-46e9-8599-16170dc4eb3b", + "metadata": {}, + "source": [ + "#### Plotting Mass vs. Temperature" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "634c1991-bc5f-4bf1-bd2b-7ba90acc7af0", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/var/folders/hf/8_ckhzzx55xc7f3s404_kn_4000131/T/ipykernel_33945/3087070154.py:12: MatplotlibDeprecationWarning: The get_cmap function was deprecated in Matplotlib 3.7 and will be removed two minor releases later. Use ``matplotlib.colormaps[name]`` or ``matplotlib.colormaps.get_cmap(obj)`` instead.\n", + " age_colors = plt.cm.get_cmap('viridis', len(b_ages)) # Adjust colormap range\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Filter .csv files to only include BD masses\n", + "filtered_baraffe_2003 = baraffe_2003[(baraffe_2003['mass'] >= 0.01) & (baraffe_2003['mass'] <= 0.08)]\n", + "\n", + "# Define variables\n", + "b_masses = filtered_baraffe_2003['mass']\n", + "b_teffs = filtered_baraffe_2003['temperature']\n", + "\n", + "# Look at age span\n", + "b_ages = np.unique(filtered_baraffe_2003['age'])\n", + "\n", + "# Define age-based color map\n", + "age_colors = plt.cm.get_cmap('viridis', len(b_ages)) # Adjust colormap range\n", + "\n", + "# Plot each age group separately\n", + "for i, age in enumerate(b_ages):\n", + " age_data = filtered_baraffe_2003[filtered_baraffe_2003['age'] == age]\n", + " plt.scatter(age_data['mass'], age_data['temperature'], label=f'Age {age:.2f} Myr',\n", + " c=[age_colors(i / (len(b_ages)-1))], alpha=0.7) # Normalize 'i' for colormap range\n", + "\n", + "# Add colorbar and legend\n", + "plt.colorbar(label='Age (Myr)')\n", + "plt.xlabel('Mass')\n", + "plt.ylabel('Temperature')\n", + "plt.title('Mass vs Temperature Colored by Age')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "90980d47-aedc-484d-94b4-49f14ccc8b66", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/changes/BD_IMF.ipynb b/changes/BD_IMF.ipynb new file mode 100644 index 00000000..895870be --- /dev/null +++ b/changes/BD_IMF.ipynb @@ -0,0 +1,960 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "11fc535c-f15b-4386-a98d-5d8f4c1c1ebf", + "metadata": {}, + "source": [ + "## Plotting Studied Power-Law Functions for Brown Dwarf Stars (BDs)" + ] + }, + { + "cell_type": "markdown", + "id": "b35147ec-8425-4834-8d36-2d3802823277", + "metadata": {}, + "source": [ + "#### Importing Packages" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "de897cdf-e478-4d49-b16a-ea7a1e0d547d", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/caitlinbegbie/opt/anaconda3/lib/python3.9/site-packages/pandas/core/computation/expressions.py:21: UserWarning: Pandas requires version '2.8.4' or newer of 'numexpr' (version '2.8.1' currently installed).\n", + " from pandas.core.computation.check import NUMEXPR_INSTALLED\n", + "/Users/caitlinbegbie/opt/anaconda3/lib/python3.9/site-packages/pandas/core/arrays/masked.py:60: UserWarning: Pandas requires version '1.3.6' or newer of 'bottleneck' (version '1.3.4' currently installed).\n", + " from pandas.core import (\n", + "/Users/caitlinbegbie/opt/anaconda3/lib/python3.9/site-packages/scipy/__init__.py:146: UserWarning: A NumPy version >=1.16.5 and <1.23.0 is required for this version of SciPy (detected version 1.26.4\n", + " warnings.warn(f\"A NumPy version >={np_minversion} and <{np_maxversion}\"\n" + ] + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas as pd\n", + "from scipy.optimize import curve_fit\n", + "import math\n", + "from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score" + ] + }, + { + "cell_type": "markdown", + "id": "24c6f353-fbf2-412d-864d-6df254492717", + "metadata": {}, + "source": [ + "#### Defining a general power law function and mass range" + ] + }, + { + "cell_type": "markdown", + "id": "dc79ec2b-79ad-4e17-a010-701923320bf4", + "metadata": {}, + "source": [ + "All of the papers that we consider here are in agreement that the initial mass function (IMF) for brown dwarfs is best represented by a power law function, much like full-fledged stars and planets. The general power law equation is as follows:\n", + "\n", + "$ f(\\alpha) = M^{-\\alpha} $,\n", + "\n", + "Where M represents the mass of an object and $\\alpha$ represents the index of the function. \n", + "\n", + "We know that we can find a general power law to represent brown dwarfs in most star forming regions because, in a [2021 paper by M. J. Huston and K. L. Luhman](https://arxiv.org/pdf/2101.11497), a conclusion is made that there are not significant variations in the IMF of low mass stars and brown dwarfs based on star-forming conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "2f67bd3c-cc80-4294-88e5-f257100893f6", + "metadata": {}, + "outputs": [], + "source": [ + "def power_law(M, a):\n", + " return M ** (-1 * a)\n", + "# M represents a mass value, and a is the associated alpha value of a specified paper\n", + "\n", + "# By NASA JPL, BDs have a mass range of 13-80 Jupiter masses (0.0124 - 0.0764 solar masses)\n", + "BD_masses = np.linspace(0.0124, 0.0764, 1000)" + ] + }, + { + "cell_type": "markdown", + "id": "1a4b6339-52d4-41a8-b890-5993559be0de", + "metadata": {}, + "source": [ + "We chose this mass range for brown dwarf stars because 80 Jupiter masses is approximately the lower mass limit for hydrogen burning, which brown dwarfs characteristically do not do. In addition, 13 Jupiter masses is the lower mass limit for deuterium burning, which is what defines a brown dwarf star. This mass range is supported by [NASA JPL](https://www.jpl.nasa.gov/images/pia23685-what-is-a-brown-dwarf)." + ] + }, + { + "cell_type": "markdown", + "id": "cbbf169d-5f2d-4fa2-83e9-20b977e299a1", + "metadata": {}, + "source": [ + "#### Defining different $\\alpha$ values and errors based on specified papers" + ] + }, + { + "cell_type": "markdown", + "id": "f5bcb285-3f28-406d-8377-8ea9376fe53e", + "metadata": {}, + "source": [ + "To create a general power law function for brown dwarfs we wanted to consider a plethora of functions already found. To do this, we found seven papers over a span of 25 years surveying different star-forming regions. The papers considered were as follows:\n", + "\n", + "1. \"L Dwarfs and the Substellar Mass Function\" ([I. Neill Reid, et al. 1999](https://iopscience.iop.org/article/10.1086/307589/pdf))\n", + "2. \"The Substellar Mass Function: A Baysian Approach\" ([P. R. Allen, et al. 2005](https://iopscience.iop.org/article/10.1086/429548/pdf))\n", + "3. \"The low-mass content of the massive young star cluster RCW 38\" ([K. Mužić, et al. 2017](https://academic.oup.com/mnras/article/471/3/3699/4044705))\n", + "4. \"Looking Deep into the Rosette Nebula’s Heart: The (Sub)stellar Content of the Massive Young Cluster NGC 2244\" ([K. Mužić, et al. 2019](https://ui.adsabs.harvard.edu/abs/2019ApJ...881...79M/abstract))\n", + "5. \"The Field Substellar Mass Function Based on the Full-sky 20 pc Census of 525 L, T, and Y Dwarfs\" ([J. D. Kirkpatrick, et al. 2021](https://iopscience.iop.org/article/10.3847/1538-4365/abd107/pdf))\n", + "6. \"A Self-consistent Model for Brown Dwarf Populations\" ([R. E. Ryan, Jr., et al. 2022](https://iopscience.iop.org/article/10.3847/1538-4357/ac6de5/pdf))\n", + "7. \"A Volume-limited Sample of Ultracool Dwarfs. II. The Substellar Age and Mass Functions in the Solar Neighborhood\" ([W. Best, et al. 2024](https://iopscience.iop.org/article/10.3847/1538-4357/ad39ef/pdf))\n", + "\n", + "Below we list the indexes of the power laws found in the specified papers and their respective errors." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "384973ef-5396-4d20-af19-5899db1a5673", + "metadata": {}, + "outputs": [], + "source": [ + "#Neill Reid 1999\n", + "NR_a = 1.3\n", + "NR_aerr = 0.3 #made up because actual paper does not include errors or an exact numerical conclusion\n", + "\n", + "#Allen 2005\n", + "A_a = 0.3\n", + "A_aerr = 0.6 #error > actual value --> unconstrained\n", + "\n", + "#Mužić 2017 (RCW 38)\n", + "M1_a = 0.29\n", + "M1_aerr = 0.11\n", + "\n", + "#Mužić 2019 (NGC 2244)\n", + "M2_a = 1.03\n", + "M2_aerr = 0.02\n", + "\n", + "#Kirkpatrick 2021\n", + "K_a = 0.6\n", + "K_aerr = 0.1\n", + "\n", + "#Ryan 2022\n", + "R_a = 0.71\n", + "R_aerr = 0.11\n", + "\n", + "#Best 2024\n", + "B_a = 0.58\n", + "B_paerr = 0.16\n", + "B_naerr = 0.20\n", + "B_avgerr = 0.18" + ] + }, + { + "cell_type": "markdown", + "id": "38e02440-ed2d-4e91-8b1f-a8c54408da42", + "metadata": {}, + "source": [ + "#### Plotting curves together (w/o errors)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "4e520010-9702-45f2-877c-1fb5104fa7a1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#plotting different IMFs based on literature\n", + "plt.plot(BD_masses, power_law(BD_masses, NR_a), color = 'r', label = \"Neill Reid 1999\")\n", + "plt.plot(BD_masses, power_law(BD_masses, A_a), color = 'orange', label = \"Allen 2005\")\n", + "plt.plot(BD_masses, power_law(BD_masses, M1_a), color = 'y', label = \"Mužić 2017\")\n", + "plt.plot(BD_masses, power_law(BD_masses, M2_a), color = 'g', label = \"Mužić 2019\")\n", + "plt.plot(BD_masses, power_law(BD_masses, K_a), color = 'c', label = \"Kirkpatrick 2021\")\n", + "plt.plot(BD_masses, power_law(BD_masses, R_a), color = 'b', label = \"Ryan 2022\")\n", + "plt.plot(BD_masses, power_law(BD_masses, B_a), color = 'm', label = \"Best 2024\")\n", + "\n", + "#organizing the graph\n", + "plt.title(\"Brown Dwarf IMFs Based on Literature\")\n", + "plt.xlabel(\"Brown Dwarf Masses (solar masses)\")\n", + "plt.ylabel(\"M^-a\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "e10c5f12-486a-44c8-ab70-bee7cd9b7998", + "metadata": {}, + "source": [ + "Looking at the curves, it is clear that the Neill Reid conclusion of the $\\alpha$ value is outdated in comparison to the other papers. This is most likely due to outdated theory and information, as this paper was created in 1999 using simulations, versus actual data of brown dwarf stars. With this in mind, we will subtract it from our future considerations as the rest of the papers considered since then agree that $\\alpha$ should be less than 1. In addition, it is explained in the Mužić 2019 paper that NGC 2244 is unusually dense, which is leading to a larger index value than typical. For this reason, I omitted this paper as well from consideration. Lastly, in Allen 2005, the error for the function is larger than the actual $\\alpha$ value, hinting that the function is unconstrained and should not be considered. Thus, we omitted this paper as well.\n", + "\n", + "Below is the graph subtracting the Neill Reid, Allen, and Mužić 2019 conclusions." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "11fc4c9d-0be7-4d75-a35c-4b82fae451f0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#plotting different IMFs based on literature\n", + "plt.plot(BD_masses, power_law(BD_masses, M1_a), color = 'y', label = \"Mužić 2017\")\n", + "plt.plot(BD_masses, power_law(BD_masses, K_a), color = 'c', label = \"Kirkpatrick 2021\")\n", + "plt.plot(BD_masses, power_law(BD_masses, R_a), color = 'b', label = \"Ryan 2022\")\n", + "plt.plot(BD_masses, power_law(BD_masses, B_a), color = 'm', label = \"Best 2024\")\n", + "\n", + "#organizing the graph\n", + "plt.title(\"Brown Dwarf IMFs Based on Literature\")\n", + "plt.xlabel(\"Brown Dwarf Masses (solar masses)\")\n", + "plt.ylabel(\"M^-a\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "20d30430-4eb1-4c19-9179-3138a2814c6e", + "metadata": {}, + "source": [ + "#### Accounting for error in $\\alpha$" + ] + }, + { + "cell_type": "markdown", + "id": "64da7c68-85ef-40f6-a538-331d7f799572", + "metadata": {}, + "source": [ + "At this point we wanted to explore the individual functions and their errors to make sure that they seemed reasonable. Thus, we used the specified errors to find upper and lower bounds for each function and plotted the information." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "9d984c93-387a-4586-ba16-ac579562ca24", + "metadata": {}, + "outputs": [], + "source": [ + "#Mužić 2017 (RCW 38)\n", + "M1_aup = M1_a + M1_aerr\n", + "M1_alow = M1_a - M1_aerr\n", + "M1_outup = power_law(BD_masses, M1_aup)\n", + "M1_outlow = power_law(BD_masses, M1_alow)\n", + "\n", + "#Kirkpatrick 2021\n", + "K_aup = K_a + K_aerr\n", + "K_alow = K_a - K_aerr\n", + "K_outup = power_law(BD_masses, K_aup)\n", + "K_outlow = power_law(BD_masses, K_alow)\n", + "\n", + "#Ryan 2022\n", + "R_aup = R_a + R_aerr\n", + "R_alow = R_a - R_aerr\n", + "R_outup = power_law(BD_masses, R_aup)\n", + "R_outlow = power_law(BD_masses, R_alow)\n", + "\n", + "#Best 2024\n", + "B_aup = B_a + B_paerr\n", + "B_alow = B_a - B_naerr\n", + "B_outup = power_law(BD_masses, B_aup)\n", + "B_outlow = power_law(BD_masses, B_alow)" + ] + }, + { + "cell_type": "markdown", + "id": "7ac4acb4-f29b-4735-b58d-be7cd78d9f76", + "metadata": {}, + "source": [ + "#### Graphing Individual Power-Law Functions (Accounting for Error in $\\alpha$)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "ac20c536-15c8-4fc5-885e-190d3fd888d1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Setting up subplots\n", + "fig, ax = plt.subplots(nrows=2, ncols=2, figsize=(8,8))\n", + "plt.subplots_adjust(hspace=0.5, wspace=0.75)\n", + "\n", + "#Mužić 2017\n", + "ax[0,0].plot(BD_masses, power_law(BD_masses, M1_a), color='y')\n", + "ax[0,0].fill_between(BD_masses, M1_outup, M1_outlow, color='y', alpha=0.2, label=\"error in $\\\\alpha$\")\n", + "ax[0,0].set_title(\"Mužić Mass Function for BDs in RCW 38\")\n", + "ax[0,0].set_xlabel(\"Mass of Objects (Solar Masses)\")\n", + "ax[0,0].set_ylabel(\"$M^{-0.29 ± 0.11}$\")\n", + "ax[0,0].legend()\n", + "\n", + "#Kirkpatrick 2021\n", + "ax[0,1].plot(BD_masses, power_law(BD_masses, K_a), color='c')\n", + "ax[0,1].fill_between(BD_masses, K_outup, K_outlow, color='c', alpha=0.2, label=\"error in $\\\\alpha$\")\n", + "ax[0,1].set_title(\"Kirkpatrick Mass Function for BDs within 20 pc\")\n", + "ax[0,1].set_xlabel(\"Mass of Objects (Solar Masses)\")\n", + "ax[0,1].set_ylabel(\"$M^{-0.6 ± 0.1}$\")\n", + "ax[0,1].legend()\n", + "\n", + "#Ryan 2022\n", + "ax[1,0].plot(BD_masses, power_law(BD_masses, R_a), color='b')\n", + "ax[1,0].fill_between(BD_masses, R_outup, R_outlow, color='b', alpha=0.2, label=\"error in $\\\\alpha$\")\n", + "ax[1,0].set_title(\"Ryan Mass Function for BDs in Milky Way Disk\")\n", + "ax[1,0].set_xlabel(\"Mass of Objects (Solar Masses)\")\n", + "ax[1,0].set_ylabel(\"$M^{-0.71 ± 0.11}$\")\n", + "ax[1,0].legend()\n", + "\n", + "#Best 2024\n", + "ax[1,1].plot(BD_masses, power_law(BD_masses, B_a), color='m')\n", + "ax[1,1].fill_between(BD_masses, B_outup, B_outlow, color='m', alpha=0.2, label=\"error in $\\\\alpha$\")\n", + "ax[1,1].set_title(\"Best Mass Function for BDs within 25 pc\")\n", + "ax[1,1].set_xlabel(\"Mass of Objects (Solar Masses)\")\n", + "ax[1,1].set_ylabel(\"$M^{-0.58^{+ 0.16}_{-0.20~}}$\")\n", + "ax[1,1].legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cbc89037-9574-487a-9f75-e17fee2667db", + "metadata": {}, + "source": [ + "### Creating a General Power-Law Curve Fit" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "c594d201-d695-414d-9d23-05d6e1f2171b", + "metadata": {}, + "outputs": [], + "source": [ + "#Combine all of the power_law output data for all 5 papers\n", + "all_power = np.concatenate([power_law(BD_masses, M1_a), power_law(BD_masses, K_a), \n", + " power_law(BD_masses, R_a), power_law(BD_masses, B_a)])\n", + "all_err = np.concatenate([np.tile(M1_aerr, 1000), np.tile(K_aerr, 1000), \n", + " np.tile(R_aerr, 1000), np.tile(B_avgerr, 1000)])" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "5b054e0c-c0b6-4556-b649-a959fba74da0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4000 4000\n" + ] + } + ], + "source": [ + "#make sure all entries are appended\n", + "print(len(all_power), len(all_err))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "a1aaa018-16da-44e0-9473-2611ec50ab2c", + "metadata": {}, + "outputs": [], + "source": [ + "#create a mass array of the same size\n", + "all_masses = np.tile(BD_masses, 4)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "baafa6a8-0c11-4380-899a-a61834474854", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4000" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#make sure it is the right size\n", + "len(all_masses)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "56aa35b6-aa24-4695-9094-fe5857846bd5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#use scipy curve fit to create a general power law\n", + "popt, pcov = curve_fit(power_law, sorted_masses, sorted_powers, sigma = sorted_errors)#, absolute_sigma = True) #popt gives fit value for a\n", + "avg_a = popt\n", + "avg_aerr = np.sqrt(np.diag(pcov)) #gives the error in a\n", + "\n", + "#create an array with mass values using fitted a\n", + "avg_power = power_law(sorted_masses, avg_a)\n", + "\n", + "#plot combined mass and power law datasets\n", + "plt.figure()\n", + "plt.scatter(sorted_masses, sorted_powers, label = 'data')\n", + "plt.plot(sorted_masses, avg_power, color = 'r', label = 'curve fit')\n", + "\n", + "#label graph\n", + "plt.title(\"Power Law Curve Fit for BD Candidate Objects\")\n", + "plt.xlabel(\"Mass of Objects (Solar Masses)\")\n", + "plt.ylabel(\"$M^{-0.584 ± 0.002}$\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "011eac9f-7e9d-4e5d-8bfc-f0380920f575", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.5836496] [0.00202593]\n" + ] + } + ], + "source": [ + "#determine the index of the power law based on the curve fit\n", + "print(avg_a, avg_aerr)" + ] + }, + { + "cell_type": "markdown", + "id": "0c050ca1-499e-426a-b4ef-0e4e64fc80a2", + "metadata": {}, + "source": [ + "Based on the curve fit, our a value for BDs is 0.5836496 ± 0.00202593. The error is smaller than expected, which may take more looking into. " + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "de5f6d54-b675-447c-bef7-a979715eb5f0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#account for error in plot\n", + "avg_aup = avg_a + avg_aerr\n", + "avg_alow = avg_a - avg_aerr\n", + "power_outup = power_law(sorted_masses, avg_aup)\n", + "power_outlow = power_law(sorted_masses, avg_alow)\n", + "\n", + "plt.scatter(sorted_masses, sorted_powers, label = 'data')\n", + "plt.plot(sorted_masses, power_law(sorted_masses, avg_a), color= 'r', label = \"curve fit for power law\")\n", + "plt.fill_between(sorted_masses, power_outup, power_outlow, color = 'r', label = \"error in a\")\n", + "plt.title(\"Power Law Curve Fit for BD Candidate Objects\")\n", + "plt.xlabel(\"Mass of Objects (Solar Masses)\")\n", + "plt.ylabel(\"$M^{0.584 ± 0.002}$\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "83430453-9da9-49e6-a1b1-4f12db8b63a7", + "metadata": {}, + "source": [ + "#### Cleaning Up the Curve Fit" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "d1ef4b5a-06b7-4295-9c5a-7e9d231020ec", + "metadata": {}, + "outputs": [], + "source": [ + "#combining all mass and output data sets to fit\n", + "all_masses = np.array(all_masses)\n", + "all_power = np.array(all_power)\n", + "\n", + "#put combined mass data set into increasing order and reorder output array to match new indices \n", + "sorted_indices = np.argsort(all_masses)\n", + "sorted_masses = all_masses[sorted_indices]\n", + "sorted_powers = all_power[sorted_indices]\n", + "sorted_errors = all_err[sorted_indices]" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "d3af8ed8-a459-486c-9f44-c6a9f1008d59", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#use scipy curve fit to create a general power law\n", + "popt, pcov = curve_fit(power_law, sorted_masses, sorted_powers,sigma=sorted_errors, absolute_sigma=True) #popt gives fit value for a\n", + "avg_a = popt\n", + "avg_aerr = np.sqrt(np.diag(pcov)) #gives the error in a\n", + "\n", + "#create an array with mass values using fitted a\n", + "avg_power = power_law(sorted_masses, avg_a)\n", + "\n", + "#plot combined mass and power law datasets\n", + "plt.figure()\n", + "plt.scatter(sorted_masses, sorted_powers, label='raw data')\n", + "plt.plot(sorted_masses, avg_power, color='r', label='curve fit')\n", + "plt.title(\"Power Law Curve Fit for 0.006 - 0.6 Solar Mass Objects\")\n", + "plt.xlabel(\"Mass of Objects (Solar Masses)\")\n", + "plt.ylabel(\"M^(-a)\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "id": "400886ad-ad9a-47a9-8fa2-e513ef125d45", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.5836496] [7.20652905e-05]\n" + ] + } + ], + "source": [ + "print(avg_a, avg_aerr)" + ] + }, + { + "cell_type": "markdown", + "id": "9bc14680-1eb4-45ec-abed-4b399d7693a4", + "metadata": {}, + "source": [ + "#### Converting into a log function to match the curve fit" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "76bfab00-53a2-4a18-9cee-b4f11cfdde98", + "metadata": {}, + "outputs": [], + "source": [ + "#take the log of each of the values in sorted_powers\n", + "log_power = []\n", + "for n in sorted_powers:\n", + " log_power.append(math.log(n))\n", + "\n", + "#take the log of each of the values in sorted_masses\n", + "log_masses = []\n", + "for a in sorted_masses:\n", + " log_masses.append(math.log(a))\n", + "\n", + "#make sure both are arrays\n", + "log_power = np.array(log_power)\n", + "log_masses = np.array(log_masses)" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "527b824d-29a7-4715-810b-01b626eae7fa", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fitted parameters: m = -0.5450\n", + "RMSE: 0.5058\n", + "MAE: 0.4105\n", + "R-squared: 0.2151\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#define a linear model (no intercept since no coefficient in power law)\n", + "def linear_model(x, m):\n", + " return m * x\n", + "\n", + "#curve fit\n", + "params, covariance = curve_fit(linear_model, log_masses, log_power)\n", + "\n", + "#get the fitted values\n", + "power_fitted = linear_model(log_masses, *params)\n", + "\n", + "#calculate residuals\n", + "residuals = log_power - power_fitted\n", + "\n", + "#calculate error metrics\n", + "rmse = np.sqrt(mean_squared_error(log_power, power_fitted))\n", + "mae = mean_absolute_error(log_power, power_fitted)\n", + "r2 = r2_score(log_power, power_fitted)\n", + "\n", + "#output the results\n", + "print(f\"Fitted parameters: m = {params[0]:.4f}\")\n", + "print(f\"RMSE: {rmse:.4f}\")\n", + "print(f\"MAE: {mae:.4f}\")\n", + "print(f\"R-squared: {r2:.4f}\")\n", + "\n", + "#plot the results\n", + "plt.figure(figsize=(10, 6))\n", + "plt.scatter(log_masses, log_power, label='Data', color='blue', s=10)\n", + "plt.plot(log_masses, linear_model(log_masses, *params), label='Fitted line', color='red')\n", + "plt.legend()\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.title('Linear Fit of Multiple Linear Functions')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "23e78450-e261-4fe7-b307-41204c800ed3", + "metadata": {}, + "outputs": [], + "source": [ + "linpower_fit = []\n", + "for l in log_masses:\n", + " linpower_fit.append(linear_model(l, -0.5450))" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "2d6df51d-54d3-48d2-bfcd-49f0dceed8bc", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(log_masses, log_power, '.')\n", + "plt.plot(log_masses, linpower_fit)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "69324962-a5fb-44b7-a734-8d17dbe84c98", + "metadata": {}, + "source": [ + "#### Attempting a more accurate error" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "id": "40a444f8-9de7-4d39-8b40-2fa6272acf78", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-0.545\n" + ] + } + ], + "source": [ + "print(params[0])" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "cff2e9d0-e55a-4dbb-83e1-ccf940f84d97", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.15556349186104046\n" + ] + } + ], + "source": [ + "#find the difference between fit and upper/lower bounds\n", + "m = params[0]\n", + "up_diff = R_a - m\n", + "up_differr = R_aerr\n", + "low_diff = m - M1_a\n", + "low_differr = M1_aerr\n", + " #the errors in up_differr and low_differr are the same because m is a fixed value in this case\n", + "\n", + "#calculate error using sqrt function\n", + "fit_err = np.sqrt((up_differr)**2 + (low_differr)**2) #uncertainty formula\n", + "print(fit_err)" + ] + }, + { + "cell_type": "markdown", + "id": "b71d92d4-1658-46b1-b4a5-31aa601a29fa", + "metadata": {}, + "source": [ + "#### Replot our function with our new " + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "id": "93f528bc-5570-46b2-902c-1c8137fb9c46", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#calculate error margins with RMSE value\n", + "logerr_up = linear_model(log_masses, -0.5450 + fit_err)\n", + "logerr_low = linear_model(log_masses, -0.5450 - fit_err)\n", + "\n", + "#plot new errors with function\n", + "plt.figure(figsize=(10, 6))\n", + "plt.scatter(log_masses, log_power, label='Data', color='blue', s=10)\n", + "plt.plot(log_masses, linear_model(log_masses, *params), label='Fitted line', color='red')\n", + "plt.fill_between(log_masses, logerr_up, logerr_low, color='red', alpha=0.2, label='error margin')\n", + "plt.legend()\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.title('Linear Fit of Multiple Linear Functions')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "b90191d6-3b08-42c9-9b7e-b925f79c30cb", + "metadata": {}, + "source": [ + "This margin of error makes a lot more sense, as it encompasses many more values represented by the function. " + ] + }, + { + "cell_type": "markdown", + "id": "9412765c-6aba-4280-8c97-0f3c7a6f7daa", + "metadata": {}, + "source": [ + "#### Graphing our new error in power law space" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "id": "a1ff5709-854c-46db-8dc5-822cfd65b212", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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aP//8M+vWrWPt2rXMnz+fypUr061bN3bs2JGpbP/+/e3uq3379nHt2jWGDBli1+eoY8eOVK1a1S6+pk2b2u6nhIQEDh06xODBg/Hx8bG7zzJqT27XunVru+aLWrVq4ebmluk9JD9cXFxsMWXEefXqVU6ePGmLqVmzZnbxb9u2DUVR7Gpubn9dkpKSuHHjBo0bN0ZRFA4ePJjpugX5t96nTx9Onz7N3r17bf9m1SQF4ODgYOuTYrVaiYmJwWKxUL9+fbv3BQ8PD5KSknJ8f/fw8ODo0aOcOnUqT/EmJCTc9X0iY3/G+0qGwYMH2w1aefnll9FoNHbv13f66aefqFatGlWrVrX7+2/VqhWA7e//l19+wWq1Mnr06Ex9yVQq1V2fV35fj4IiHYrvUcOGDbPtUJwVvV6fqTre09MzUzvpqlWr+PDDDwkPD7drB83NTZWdLl26MGzYMFQqFa6urtSoUcPWCfX8+fMAVKlSJdNx1apV46+//rJ19GvatCkWi4WdO3cSHBzMtWvXaNq0KUePHrV7Y65evbotUcq4wTP+gO7k5uZm97NGo6F06dK2nxMTE+0+sB0cHLJt1shKTEwM48aN44cffrB1VMwQFxdn+39+nltOzyfjQ6Kg3fn6ZOjZsyfTpk3jt99+o0+fPiQmJvLnn3/y4osv2u6dvP4usvPII4/QunXrfD6DvMvuHtVqtZQvX962P0NQUFCeO1M2a9bMrkPxs88+S6VKlXjllVfYv3+/Xdk7R0nm9DdUtWpVuyanpk2bMmfOHE6fPs2ZM2dQqVQ0atTIljQMGjSIrVu30qRJk0wfLFk1c2b1HpIfGX9jGR+mGQnL1q1bKV26NAcPHuTDDz/E19eXKVOm2Pa5ubnZdUK+cOECo0eP5rfffssU1+1/b5D9vZxfderUoWrVqixduhQPDw8CAgKyvdcBFi5cyGeffcaJEyfsmjZv//0OGTKEH3/8kfbt2xMUFESbNm3o0aMH7dq1s5UZP348Xbp0oXLlytSsWZN27drx3HPPUatWrRzjdXV1vev7RMb+O5OgSpUq2f3s4uJCYGBgjk3Lp06d4vjx49m+f2a8P545cwa1Wk316tVzjC07+X09CookN/dZRp+HnGzdupWnnnqKZs2aMWvWLAIDA3F0dGT+/Pl2bcl5Vbp06QL5MKpfvz56vZ4tW7ZQpkwZ/Pz8qFy5Mk2bNmXWrFmYTCa2bt1qazMHbH0xFi1alOW3+9s7bEL6t+7b39SnTJnCuHHjbD+XLVs2131DAHr06MGOHTt46623CA0NtQ33bdeunV0/kfw8t6xUrFgRjUbDP//8k6v4sktas5sH587XJ8Njjz1GSEgIP/74I3369OH3338nJSXFri09r7+Lkur22oP8cnFx4dFHH+XXX3/NNCLtXs6fUYu2ZcsWzp49S926dW1fHL744gsSExM5ePAgH330UaZjs3sPUXLoZ5FbR44cwc/Pz5bglipVinLlyrFlyxZCQkJQFIVGjRrh6+vLa6+9xvnz59m6dSuNGze23Y9paWk8+eSTxMTE8M4771C1alWcnZ25fPkyYWFhmfplZXcv34s+ffowe/ZsXF1d6dmzZ7bnX7x4MWFhYXTt2pW33noLPz8/W3+pM2fO2Mr5+fkRHh7OX3/9xerVq1m9ejXz58+nX79+LFy4EEhPjM+cOcOvv/7K2rVr+fbbb5k6dSpz5szhhRdeyDbWatWqcfDgQUwmEzqdLssyhw8fxtHRMVMykx9Wq5VHHnmEzz//PMv9wcHB93wNyP/rUVAejHexB8zPP/+MXq/nr7/+srvZ58+fX2jXLFu2LICt+vl2J06cwMfHx/bGrtVqadiwIVu3bqVMmTK2b3dNmzbFZDKxZMkSrl69atcRMqMa3c/PL18JVr9+/eyagfLywXLz5k3Wr1/PuHHjGD16tG17VtWl+XluWXFycqJVq1Zs2LCBixcv3vUNw9PTEyDTqJ87ayNyo0ePHkyfPp34+HiWLVtGSEiIrQkO7v13kR/3UuOY4fZ7tHz58rbtqampREREFNpzsVgsQHqtRk7D7W+P786agpMnT9r2Q3rtS5kyZdi6dStnz5613WfNmjXjjTfe4KeffiItLe2u91lB2rlzJ2fOnMk0TLxp06Zs2bKFcuXKERoaiqurK7Vr18bd3Z01a9Zw4MABuy8e//zzD//++y8LFy6060B8v0bJQHpyM3r0aCIjI1m0aFG25ZYvX0758uVZsWKF3T2aMVLrdlqtls6dO9O5c2esVitDhgzhq6++YtSoUbZ5eLy8vBgwYAADBgwgMTGRZs2aMXbs2Bw/zDt16sTOnTv56aefMr32kD5icuvWrbRu3TrT+96pU6fsOsonJiYSGRlpmzMnKxUqVODQoUM88cQTOf5dVqhQAavVyrFjx3KcBiGnc+Tn9Sgo0uemGHJwcEClUtl9az937hy//PJLoV0zMDCQ0NBQFi5caPcBe+TIEdauXZvpj6Vp06bs3r2bjRs32t6YfXx8qFatGpMmTbKVydC2bVvc3NyYOHFiplEtkD4yJCfly5endevWtkeTJk1y/dwyvune+c122rRpWZbP63PLzpgxY1AUheeee86uSS3D/v37bd/6ypYti4ODg93IFEgf9pxXPXv2xGQysXDhQtasWZNpFMa9/i7yIyMpyO0MxVlp3bo1Wq2WL774wu53OXfuXOLi4rIcDXOvYmJi2LFjBwEBAfj5+eVYtn79+vj5+TFnzhy7puTVq1dz/PjxTPE1bdqUDRs2sGfPHtv9lJE8fPLJJ7YpIO6H8+fPExYWhlartQ3bvz3Oc+fOsWzZMlucarWaxo0b8/nnn2M2m+3+HrL6e1MUxW7YdGGrUKEC06ZN4+OPP6Zhw4bZlssq1t27d7Nz5067cneORFOr1bbmlYzf9Z1lXFxcqFixYpbDq2/34osv4ufnx1tvvZWp35TRaGTAgAEoimL3xSzD119/bfc3PHv2bCwWS47zlvXo0YPLly/zzTffZNqXkpJi62/YtWtX1Go148ePz1Tbdvvr5ezsnOXfdX5fj4IiNTfFUMeOHfn8889p164dffr04dq1a8ycOZOKFSvazY1R0D799FPat29Po0aNGDhwICkpKXz55Ze4u7tnmmOiadOmfPTRR1y8eNHuja1Zs2Z89dVXhISE2LWju7m5MXv2bJ577jnq1q1Lr1698PX15cKFC/zxxx80adKEGTNm5Dv269ev8+GHH2baXq5cOfr27UuzZs2YPHkyZrOZoKAg1q5daze/z708t+w0btyYmTNnMmTIEKpWrWo3Q/GmTZv47bffbDG7u7vTvXt3vvzyS1QqFRUqVGDVqlWZ+gflRt26dalYsSLvv/8+JpMp0/DOwv5dZCXjQ/r999+nV69eODo60rlz5zxNPOjr68vIkSMZN24c7dq146mnnuLkyZPMmjWLBg0aZPmtN6+WL1+Oi4sLiqJw5coV5s6dy82bN5kzZ85da58cHR2ZNGkSAwYMoHnz5vTu3ZurV68yffp0QkJCeP311+3KN23alCVLlth1TndwcKBx48b89ddftGjRolAmYDtw4ACLFy/GarUSGxvL3r17bfPsLFq0KFOfiIy/gZMnTzJx4kTb9mbNmrF69Wp0Op3dTNVVq1alQoUKjBgxgsuXL+Pm5sbPP/9cIH2C8uK11167a5lOnTqxYsUKnn76aTp27EhERARz5syhevXqdl9IXnjhBWJiYmjVqhWlS5fm/PnzfPnll4SGhlKtWjUAqlevTosWLahXrx5eXl7s27eP5cuX33W5B29vb5YvX07Hjh2pW7duphmKT58+zfTp07OcwC81NZUnnniCHj162P4WHn/8cZ566qlsr/fcc8/x448/8tJLL7Fx40aaNGlCWloaJ06c4Mcff+Svv/6ifv36tveQCRMm0LRpU5555hl0Oh179+6lVKlSfPzxx0D63/bs2bP58MMPqVixIn5+frRq1Srfr0eBKZIxWg+AjKF4e/fuzXJ/dkN4nZ2dM5XNGMZ4u7lz5yqVKlVSdDqdUrVqVWX+/PlZlsvLUPDbh0Bm5++//1aaNGmiGAwGxc3NTencubNy7NixTOXi4+MVBwcHxdXV1W545OLFixVAee6557I8/8aNG5W2bdsq7u7uil6vVypUqKCEhYUp+/bts5XJ7nXKTsaw36weTzzxhKIoinLp0iXl6aefVjw8PBR3d3ele/fuypUrVzINWb6X55ad/fv3K3369FFKlSqlODo6Kp6ensoTTzyhLFy40G6I5fXr15Vu3bopTk5Oiqenp/Liiy8qR44cyfV9dLv3339fAeyGxN4pN7+L7I4DlJ9++inbMlm9rhMmTFCCgoIUtVp912HhOQ0DnjFjhlK1alXF0dFR8ff3V15++WXl5s2bdmVyMz1AVte7/eHs7Kw0atRI+fHHH+3K3u35L1u2TKlTp46i0+kULy8vpW/fvsqlS5cylTt69KgCKNWqVbPb/uGHHyqAMmrUqEzHZPd3nJv3gYz3pIyHRqNRvLy8lEcffVQZOXKk3RDtO/n5+SmAcvXqVdu2bdu2KYDStGnTTOWPHTumtG7dWnFxcVF8fHyUQYMG2Yas5/Zezu9Q8Jzc+fpZrVZl4sSJStmyZRWdTqfUqVNHWbVqldK/f3+lbNmytnLLly9X2rRpo/j5+SlarVYpU6aM8uKLLyqRkZG2Mh9++KHSsGFDxcPDQzEYDErVqlWVjz76yG6odk4iIiKUQYMGKWXKlFEcHR0VHx8f5amnnso0ZFtR/vv82bx5szJ48GDF09NTcXFxUfr27Ws3lYeiZB4Krijp0xZMmjRJqVGjhqLT6RRPT0+lXr16yrhx42zTAGSYN2+e7X729PRUmjdvrqxbt862PyoqSunYsaPi6uqqALZr3evrca9UilIAvdCEEEIIUew0bdoUnU7H33//XdSh3FfS50YIIYR4QEVGRtpNb/CwkORGCCGEeMDs2LGDESNGcObMGZ544omiDue+k2YpIYQQ4gEzYMAAVq9eTe/evfn0008fmPmrckuSGyGEEEI8UKRZSgghhBAPFEluhBBCCPFAebga4W6xWq1cuXIFV1fXApkWXgghhBCFT1EUEhISKFWqVI5rkj2Uyc2VK1cKbHEwIYQQQtxfFy9ezHGm+IcyuclYNv7ixYu21W+FEEIIUbzFx8cTHBxs+xzPzkOZ3GQ0Rbm5uUlyI4QQQpQwd+tSIh2KhRBCCPFAkeRGCCGEEA8USW6EEEII8UB5KPvcCCGEyCwtLQ2z2VzUYYiHmKOjIw4ODvd8HkluhBDiIacoClFRUcTGxhZ1KELg4eFBQEDAPc1DJ8mNEEI85DISGz8/P5ycnGRyU1EkFEUhOTmZa9euARAYGJjvc0lyI4QQD7G0tDRbYuPt7V3U4YiHnMFgAODatWv4+fnlu4lKOhQLIcRDLKOPjZOTUxFHIkS6jHvxXvp/SXIjhBBCmqJEsVEQ96IkN0IIIQSwefNmtm/fDsCWLVvYtm1bro/98ssv2blzZ2GFJvJIkhshhBACqF69OoMHD2bXrl28/PLLVK9e3bYvLCyMrl27Znnc9OnT+emnn6hbt+59ilTcjSQ3QgghSpywsDBUKhUvvfRSpn1Dhw5FpVIRFhaWp3P6+voyatQoHn/8cT766CO8vLxs+6ZPn86CBQsyHbNr1y7mzZvHr7/+ik6ny/bcH3/8MQ0aNMDV1RU/Pz+6du3KyZMn7coYjUaGDh2Kt7c3Li4udOvWjatXr9qVefXVV6lXrx46nY7Q0NBM1xk7diwqlSrTw9nZOU+vRUknyY0QQogSKTg4mB9++IGUlBTbNqPRyNKlSylTpky+ztmrVy8sFkumWhp3d3c8PDwylX/sscc4dOgQnp6eOZ538+bNDB06lF27drFu3TrMZjNt2rQhKSnJVub111/n999/56effmLz5s1cuXKFZ555JtO5nn/+eXr27JnldUaMGEFkZKTdo3r16nTv3v3uT/4BIslNATMajUUdghBCPBTq1q1LcHAwK1assG1bsWIFZcqUoU6dOnZlQ0JCmDZtmt220NBQxo4dC8CCBQuyrPHI2H9ns5TVamXy5MlUrFgRnU5HmTJl+Oijj7KNdc2aNYSFhVGjRg1q167NggULuHDhAvv37wcgLi6OuXPn8vnnn9OqVSvq1avH/Pnz2bFjB7t27bKd54svvmDo0KGUL18+y+u4uLgQEBBge1y9epVjx44xcODAu72cDxRJbgpQamoqhw8ftk1AJIQQJY2iKKSlJRXJQ1GUPMf7/PPPM3/+fNvP8+bNY8CAAXk+T8+ePe1qO77//ns0Gg1NmjTJsvzIkSP55JNPGDVqFMeOHWPp0qX4+/vn+npxcXEAtqav/fv3Yzabad26ta1M1apVKVOmzD11VP7222+pXLkyTZs2zfc5SiKZxK8AKYpCYmIiV69exc/Pr6jDEUKIPLNak9m61aVIrt20aSIODnnrG/K///2PkSNHcv78eQC2b9/ODz/8wKZNm/J0HoPBYJtA7syZMwwdOpSJEyfy5JNPZiqbkJDA9OnTmTFjBv379wegQoUKPP7447m6ltVqZfjw4TRp0oSaNWsC6bNEa7XaTE1f/v7+REVF5em5ZDAajSxZsoR33303X8eXZJLcFDCLxUJsbCxWqxW1WirGhBCiMPn6+tKxY0cWLFiAoih07NgRHx+ffJ8vLi6OTp060bFjR956660syxw/fhyTycQTTzyRr2sMHTqUI0eO5GmoeX6sXLmShIQEWwL2MJHkphDEx8eTkJCAu7t7UYcihBB5olY70bRpYpFdOz+ef/55hg0bBsDMmTOzObc6U7PXnTPgpqWl0bNnT9zc3Pj666+zvV5GDU9+DBs2jFWrVrFlyxZKly5t2x4QEEBqaiqxsbF2tTdXr14lICAgX9f69ttv6dSpU56ayx4UktwUgoSEBKKjoyW5EUKUOCqVKs9NQ0WtXbt2pKamolKpaNu2bZZlfH19iYyMtP0cHx9PRESEXZnXX3+df/75h3379qHX67O9XqVKlTAYDKxfv54XXnghVzEqisIrr7zCypUr2bRpE+XKlbPbX69ePRwdHVm/fj3dunUD4OTJk1y4cIFGjRrl6hq3i4iIYOPGjfz22295PvZBIMlNIdDpdFy5coWQkBBpmhJCiELm4ODA8ePHbf/PSqtWrViwYAGdO3fGw8OD0aNH25WdP38+s2bNYuXKlahUKls/FxcXF1xc7Psg6fV63nnnHd5++220Wi1NmjTh+vXrHD16NNtRSUOHDmXp0qX8+uuvuLq62s7v7u6OwWDA3d2dgQMH8sYbb+Dl5YWbmxuvvPIKjRo14rHHHrOd5/Tp0yQmJhIVFUVKSgrh4eFA+gSEWq3WVm7evHkEBgbSvn37PL6aDwZJbgqBm5sbcXFxxMfHZzkvghBCiILl5uaW4/6RI0cSERFBp06dcHd3Z8KECXY1N5s3byYtLY2nnnrK7rgxY8bYhoPfbtSoUWg0GkaPHs2VK1cIDAzMckLBDLNnzwagRYsWdtvnz59vm2xw6tSpqNVqunXrhslkom3btsyaNcuu/AsvvMDmzZttP2cMeY+IiCAkJARI77C8YMECwsLC8r2qdkmnUvIz9q6Ei4+Px93dnbi4uLv+QeSFyWRi8+bNGAwGbty4Qa1atahQoUKBnV8IIQqa0WgkIiKCcuXK5dgUI8T9ktM9mdvPb2kzKSROTk5cuXKFtLS0og5FCCGEeKhIclNI3N3diY2NtU3UJIQQQoj7Q5KbQuLo6EhaWho3btwo6lCEEEKIh4okN4XIxcWFK1euYLFYijoUIYQQ4qEhyU0hcnV1JS4ujpiYmKIORQghhHhoSHJTiDSa9JH2spCmEEIIcf9IclNAUlPht9/ULFxoP/Tb1dWVq1evYjKZiigyIYQQ4uEiyU0BuXYNevbUsHRpBSIjdbbtrq6utuUYhBBCCFH4JLkpIKVLQ/Pm6fMhrlvnZ9uuVqvRaDT5XrJeCCGEEHkjyU0B6tMnfcK+tWv9uH3eZzc3N65fv05iYtGstCuEEA+jFi1aMHz48BzLnDt3DpVKZVujqTjYtGkTKpWK2NjYXJXPzfN82EhyU4C6drWi1aZx4YITx4872bY7OzuTlJQkTVNCCFFAwsLC6Nq1q9225cuXo9fr+eyzzwBYsWIFEyZMKILoMhs7diyhoaG5Ktu4cWMiIyNxd3cvlFgOHTpE7969CQ4OxmAwUK1aNaZPn56p3KZNm6hbty46nY6KFSuyYMECu/0ff/wxDRo0wNXVFT8/P7p27crJkyftynz99de0aNECNze3PCVs90qSmwLk5gaNGqWPjFq92stun5OTE5cvX8ZqtRZFaEII8UD79ttv6du3L7Nnz+bNN98EwMvLC1dX12yPSU1NvV/h5ZrZbEar1RIQEIBKpSqUa+zfvx8/Pz8WL17M0aNHef/99xk5ciQzZsywlYmIiKBjx460bNmS8PBwhg8fzgsvvMBff/1lK7N582aGDh3Krl27WLduHWazmTZt2pCUlGQrk5ycTLt27XjvvfcK5blkS3kIxcXFKYASFxdXoOc1Go3K+PH7FVAUL69UZdeufcq+femPHTt2KL///rsSHR1doNcUQoh7kZKSohw7dkxJSUkp6lDypH///kqXLl0URVGUSZMmKXq9XlmxYoVdmebNmyuvvfaa7eeyZcsq48ePV5577jnF1dVV6d+/vxIREaEAysGDBxVFURSLxaIMGDBAqVKlinL+/HlFURQFUGbNmqW0a9dO0ev1Srly5ZSffvrJ7lpvv/22UqlSJcVgMCjlypVTPvjgAyU1NVVRFEWZP3++Atg95s+fb3fuzp07K05OTsqYMWOUjRs3KoBy8+ZN2/m3bdumNG/eXDEYDIqHh4fSpk0bJSYmJsvnuWrVKsXNzU1ZvHhxrl/PIUOGKC1btrR7PjVq1LAr07NnT6Vt27bZnuPatWsKoGzevDnTvqyeU3Zyuidz+/ktNTcFrF69aNzdzcTEOLJnz38rlmq1WiwWC9evXy/C6IQQImeKopCUllYkD+X2zoq59M477zBhwgRWrVrF008/fdfyU6ZMoXbt2hw8eJBRo0bZ7TOZTHTv3p3w8HC2bt1KmTJlbPtGjRpFt27dOHToEH379qVXr14cP37ctt/V1ZUFCxZw7Ngxpk+fzjfffMPUqVMB6NmzJ2+++SY1atQgMjKSyMhIevbsaTt27NixPP300/zzzz88//zzmWIODw/niSeeoHr16uzcuZNt27bRuXPnLBdmXrp0Kb1792bJkiX07dv37i/gLXFxcXh5/dfisHPnTlq3bm1Xpm3btuzcuTPHcwB25ykqmqIO4EGj0Sg88cR1VqwoxZ9/etG4cbxtn6urK5cuXaJcuXJotdoijFIIIbKWbLXisnVrkVw7sWlTnB0ccl1+9erV/Prrr6xfv55WrVrl6phWrVrZmq0gvUMxQGJiIh07dsRkMrFx48ZM/V26d+/OCy+8AMCECRNYt24dX375JbNmzQLggw8+sJUNCQlhxIgR/PDDD7z99tsYDAZcXFzQaDQEBARkiqlPnz4MGDDA9vPZs2ft9k+ePJn69evbrgVQo0aNTOeZOXMm77//Pr///jvNmzfP1esBsGPHDpYtW8Yff/xh2xYVFYW/v79dOX9/f+Lj40lJScFgMNjts1qtDB8+nCZNmlCzZs1cX7uwSHJTCNq0ucqKFaXYuNGTpKQLODun97Nxc3Pj8uXLREdHExgYWMRRCiFEyVarVi1u3LjBmDFjaNiwIS4uLnc9pn79+llu7927N6VLl2bDhg2ZPrgBGjVqlOnn20dYLVu2jC+++IIzZ86QmJiIxWLBzc2N3Mgupgzh4eF07949xzLLly/n2rVrbN++nQYNGuTqugBHjhyhS5cujBkzhjZt2uT6uDsNHTqUI0eOsG3btnyfoyBJclMIqlVLpEwZIxcu6Nm0yYOOHdPXlsqY8+bKlSuS3AghiiUntZrEpk2L7Np5ERQUxPLly2nZsiXt2rVj9erVOXYghvTRq1np0KEDixcvZufOnbmuBcqwc+dO+vbty7hx42jbti3u7u788MMPtlFbd5NdTBmySrbuVKdOHQ4cOMC8efOoX79+rjojHzt2jCeeeILBgwfb1TwBBAQEcPXqVbttV69exc3NLVM8w4YNY9WqVWzZsoXSpUvf9br3g/S5KQQqFbRvn57Q/PGHt90+d3d3rl27Rnx8fFaHCiFEkVKpVDg7OBTJIz+jg8qWLcvmzZuJioqiXbt2JCQk5Ot5v/zyy3zyySc89dRTbN68OdP+Xbt2Zfq5WrVqQHqzTtmyZXn//fepX78+lSpV4vz583bltVptln1kcqNWrVqsX78+xzIVKlRg48aN/Prrr7zyyit3PefRo0dp2bIl/fv356OPPsq0v1GjRpmuuW7dOrsaLEVRGDZsGCtXrmTDhg2UK1cul8+o8ElyU0g6doxGpVLYs8eNK1f+61/j5ORESkqKdCwWQogCEhwczKZNm7h27Rpt27bN95fHV155hQ8//JBOnTplal756aefmDdvHv/++y9jxoxhz549DBs2DIBKlSpx4cIFfvjhB86cOcMXX3zBypUr7Y4PCQkhIiKC8PBwbty4kaf1BkeOHMnevXsZMmQIhw8f5sSJE8yePZsbN27YlatcuTIbN27k559/znFSvyNHjtCyZUvatGnDG2+8QVRUFFFRUXafSy+99BJnz57l7bff5sSJE8yaNYsff/yR119/3VZm6NChLF68mKVLl+Lq6mo7T0pKiq1MVFQU4eHhnD59GoB//vmH8PBwYmJicv3880OSm0JSqlQqDRqkf4P4/Xf72hsXFxcuXbqExWIpitCEEOKBU7p0aTZt2sSNGzfuKcEZPnw448aNo0OHDuzYscO2fdy4cfzwww/UqlWL7777ju+//57q1asD8NRTT/H6668zbNgwQkND2bFjR6aRWN26daNdu3a0bNkSX19fvv/++1zHVLlyZdauXcuhQ4do2LAhjRo14tdff0WjydyzpEqVKmzYsIHvv//eruP07ZYvX87169dZvHgxgYGBtsftfXXKlSvHH3/8wbp166hduzafffYZ3377LW3btrWVmT17NnFxcbRo0cLuPMuWLbOVmTNnDnXq1GHQoEEANGvWjDp16vDbb7/l+vnnh0rJz9i7Ei4+Ph53d3fi4uJy3eErN0wmE5s3b8ZgMODk5MSaNZ588EF5/P1T+e23f8gYBGCxWIiKiuKxxx7L1BtdCCHuJ6PRSEREBOXKlUOv1xd1OMWSSqVi5cqVmWZEFoUjp3syt5/fUnNTiFq2jMXNzcLVq1q7OW80Gg0qlYrIyMgijE4IIYR4MElyU4h0OoV27dLbFX/7zb5pysPDg6ioqHx3fhNCCCFE1iS5KWRPPZXe4WvTJg9iY/+bnMrZ2Znk5GSuXbtWVKEJIYTIBUVRpEmqhJHkppBVrZpClSrJmM1qVq/OumOx2WwuouiEEEKIB48kN/dBly7ptTe//urN7d23PTw8iI2NJTo6uogiE0IIIR48ktzcB+3axaDVWjl92oljx5xs2x0cHFCr1Vy+fDlfC8YJIYQQIjNJbu4DN7c0nnjiJgA//+xrt8/Ly4urV6/aVlMVQgghxL2R5OY+6dYtfebHv/7yIj7+v47Fer0ek8mUaQ0PIYQQQuSPJDf3Se3aSVSsmIzJpGbVKvuOxW5ubly6dAmj0VhE0QkhhBAPDklu7hOVCp59Nr32ZvlyX7uOxRmzLcp6U0IIIcS9k+TmPmrfPgYnpzQuXNCzd6+rbbtKpcLJyYnz58/ne9VYIYR4mISFhaFSqVCpVDg6OlKuXDnefvvtIq8BN5vNvPPOOzzyyCM4OztTqlQp+vXrx5UrV+zKxcTE0LdvX9zc3PDw8GDgwIEkJiba9m/atIkuXboQGBiIs7MzoaGhLFmyxO4c33zzDU2bNsXT0xNPT09at27Nnj177svzLO4kubmPnJ2tdOyYPux7+XL7jsWenp5ER0fLsHAhhMildu3aERkZydmzZ5k6dSpfffUVY8aMKdKYkpOTOXDgAKNGjeLAgQOsWLGCkydP8tRTT9mV69u3L0ePHmXdunWsWrWKLVu2MHjwYNv+HTt2UKtWLX7++WcOHz7MgAED6NevH6tWrbKV2bRpE71792bjxo3s3LmT4OBg2rRpw+XLl+/b8y2uZOHMQlw4MyunT+vp1asGDg4Kv//+D35+/03gd/nyZUqXLk2dOnVQqVQFFpcQQmSnpC6cGRYWRmxsLL/88ottW7du3YiIiODAgQOMHz+eH3/8kSNHjtgdFxoaSufOnZkwYQJ79+7lvffe4+DBg5jNZkJDQ5k6dSp169a1lVepVHzzzTf88ccf/PXXXwQFBfHZZ59lSlZysnfvXho2bMj58+cpU6YMx48fp3r16uzdu5f69esDsGbNGjp06MClS5coVapUlufp2LEj/v7+zJs3L8v9aWlpeHp6MmPGDPr165fr+IobWTizBKpY0UidOgmkpan45Rcfu31eXl5ERUXJsHAhRJFRFEhKKprHvXzVPnLkCDt27ECr1QLw/PPPc/z4cfbu3Wsrc/DgQVstCEBCQgL9+/dn27Zt7Nq1i0qVKtGhQ4dMa/6NGzeOHj16cPjwYTp06EDfvn2JiYnJdWxxcXGoVCo8PDwA2LlzJx4eHrbEBqB169ao1Wp2796d43m8vLyy3Z+cnIzZbM6xzMNCU9QBPIy6dbvOwYOurFjhw4ABUTg6pv9FGwwGrl+/TmRkpO2PQAgh7qfkZHBxKZprJyaCs3Puy69atQoXFxcsFgsmkwm1Ws2MGTMAKF26NG3btmX+/Pk0aNAAgPnz59O8eXPKly8PQKtWrezO9/XXX+Ph4cHmzZvp1KmTbXtYWBi9e/cGYOLEiXzxxRfs2bOHdu3a3TVGo9HIO++8Q+/evW01DVFRUfj5+dmV02g0ti+4Wfnxxx/Zu3cvX331VbbXeueddyhVqhStW7e+a1wPOqm5KQJPPBGLt7eZGze0rF/vYbfPw8ODS5cukZycXDTBCSFECdGyZUvCw8PZvXs3/fv3Z8CAAXTr1s22f9CgQXz//fcYjUZSU1NZunQpzz//vG3/1atXGTRoEJUqVcLd3R03NzcSExO5cOGC3XVq1apl+7+zszNubm65WvTYbDbTo0cPFEVh9uzZ+X6eGzduZMCAAXzzzTfUqFEjyzKffPIJP/zwAytXrixRzYuFRWpuioCjo0L37teYMyeIpUv9adv2JhldbFxdXTl//jxRUVG2bxdCCHG/ODml16AU1bXzwtnZmYoVKwIwb948ateuzdy5cxk4cCAAnTt3RqfTsXLlSrRaLWazmWeffdZ2fP/+/YmOjmb69OmULVsWnU5Ho0aNSE1NtbuOo6Oj3c8qlQqr1ZpjbBmJzfnz59mwYYNd/5CAgIBMyZHFYiEmJoaAgAC77Zs3b6Zz585MnTo12340U6ZM4ZNPPuHvv/+2S8QeZpLcFJFu3W4wb14gx445c+iQM6GhSUD6H42bmxsXLlygdOnStvZjIYS4H1SqvDUNFRdqtZr33nuPN954gz59+mAwGNBoNPTv35/58+ej1Wrp1asXBoPBdsz27duZNWsWHTp0AODixYvcuHHjnmPJSGxOnTrFxo0b8fa2n7i1UaNGxMbGsn//furVqwfAhg0bsFqtPProo7ZymzZtolOnTkyaNMluJNXtJk+ezEcffcRff/1l14fnYSfNUkXE09NC+/bpHdK+/97fbp+Hhwc3b97MVbWnEEKIdN27d8fBwYGZM2fatr3wwgts2LCBNWvW2DVJAVSqVIlFixZx/Phxdu/eTd++fe2Sn/zIqB3at28fS5YsIS0tjaioKKKiomw1QtWqVaNdu3YMGjSIPXv2sH37doYNG0avXr1sI6U2btxIx44defXVV+nWrZvtHLd3ZJ40aRKjRo1i3rx5hISE2MokFlXVWzEiyU0R6t07fT2pjRs9iIz8r4ZGrVaj1+s5d+6cTOonhBC5pNFoGDZsGJMnTyYpKb02vFKlSjRu3JiqVava1YoAzJ07l5s3b1K3bl2ee+45Xn311UwdffPq8uXL/Pbbb1y6dInQ0FACAwNtjx07dtjKLVmyhKpVq/LEE0/QoUMHHn/8cb7++mvb/oULF5KcnMzHH39sd45nnnnGVmb27Nmkpqby7LPP2pWZMmXKPT2HB4HMc3Of57m505Ahldizx43//S+K4cP/m3jJYrEQFRXFo48+mqkNVgghCkpJnecmtxRFoVKlSgwZMoQ33nijqMMRuSDz3DwA+vRJr7355RcfkpL++3VoNBocHBy4cOHCXTuuCSGEyOz69evMmDGDqKgo29w24uEgHYqLWOPG8ZQpY+TCBT2//+5Nr17/LZ7p7e1NVFQU0dHR+Pr65nAWIYQQd/Lz88PHx4evv/4aT0/Pog5H3EfFqubm448/pkGDBri6uuLn50fXrl05efKkXRmj0cjQoUPx9vbGxcWFbt26cfXq1SKK+N6p1f/V3ixZ4o/F8t++jJFSFy9e5CFsPRRCiHuiKArXr1+nT58+RR2KuM+KVXKzefNmhg4dyq5du1i3bh1ms5k2bdrYOoYBvP766/z+++/89NNPbN68mStXrth1sCqJOnWKxsvLTGSkjrVr7afN9vb2JjIykps3bxZRdEIIIUTJUqyapdasWWP384IFC/Dz82P//v00a9aMuLg45s6dy9KlS23TZs+fP59q1aqxa9cuHnvssaII+57p9Qq9el1j1qwgFi4MoH37GNukfnq9HovFwsWLF2W9ECGEECIXilXNzZ0yFpDM+FDfv38/ZrPZbt2MqlWrUqZMGXbu3JnteUwmE/Hx8XaP4qZ79+s4O6dx5oyB7dvte4B7eXlx+fJlYmNjiyY4IYQQogQptsmN1Wpl+PDhNGnShJo1awLpi41ptdpMi0r6+/tnu9gYpPflcXd3tz2Cg4MLM/R8cXVN45ln0jsTL1hgP/TbycmJ1NRULl68WBShCSGEECVKsU1uhg4dypEjR/jhhx/u+VwjR44kLi7O9iiuSUKfPtdwdLQSHu5KeLj9/OdeXl5cunTJVpslhBBCiKwVy+Rm2LBhrFq1io0bN1K6dGnb9oCAAFJTUzM1z1y9ejXHie50Oh1ubm52j+LI19dMx47RACxcaP98nJ2dMZlMxTYxE0IIIYqLYpXcKIrCsGHDWLlyJRs2bKBcuXJ2++vVq4ejoyPr16+3bTt58iQXLlygUaNG9zvcQvHcc1dRqRS2bvXg9Gn7mRk9PT2l9kYIIYS4i2KV3AwdOpTFixezdOlSXF1dbYuApaSkAODu7s7AgQN544032LhxI/v372fAgAE0atSoxI6UulPZsiZatYoFMve9cXFxwWg0Su2NEOKhFxYWhkqlsj28vb1p164dhw8fLrBrjB07ltDQ0LuW++abb2jatCmenp54enrSunVr9uzZY1dGURRGjx5NYGAgBoOB1q1bc+rUKdv+c+fOMXDgQMqVK4fBYKBChQqMGTPGttjmnU6fPo2rq2umPqgiXbFKbmbPnk1cXBwtWrSwWwRs2bJltjJTp06lU6dOdOvWjWbNmhEQEMCKFSuKMOqCN2BAJABr13px7pzObp/U3gghRLp27doRGRlJZGQk69evR6PR0KlTp/sex6ZNm+jduzcbN25k586dBAcH06ZNGy5f/m+9wMmTJ/PFF18wZ84cdu/ejbOzM23btsVoNAJw4sQJrFYrX331FUePHmXq1KnMmTOH9957L9P1zGYzvXv3pmnTpvftOZY0xSq5URQly0dYWJitjF6vZ+bMmcTExJCUlMSKFSseuIUlq1ZNoXnzWKxWFXPnBtrtc3FxISUlhQsXLhRRdEIIUTzodDoCAgIICAggNDSUd999l4sXL3L9+n/L2Fy8eJEePXrg4eGBl5cXXbp04dy5c7b9mzZtomHDhjg7O+Ph4UGTJk04f/48CxYsYNy4cRw6dMhWO7RgwYIs41iyZAlDhgwhNDSUqlWr8u2332K1Wm1dKBRFYdq0aXzwwQd06dKFWrVq8d1333HlyhV++eUXID1Rmz9/Pm3atKF8+fI89dRTjBgxIssv7x988AFVq1alR48eBfZaPmiKVXIj/jNo0BUA/vorc+2Nt7c3Fy9elHlvhBAFTlEU0pLSiuRxL8vMJCYmsnjxYipWrIi3tzeQXsPRtm1bXF1d2bp1K9u3b8fFxYV27dqRmpqKxWKha9euNG/enMOHD7Nz504GDx6MSqWiZ8+evPnmm9SoUcNWO9SzZ89cxZKcnIzZbLbN0RYREUFUVJTdHG3u7u48+uijOc7RFhcXl2ny1g0bNvDTTz8xc+bMvL5ED5ViNUOx+E9G7c3mzR7MnRvIhAnnbPucnZ25efMm58+fx93dHVXGdMZCCHGPrMlWtrpsLZJrN01sioOzQ67Lr1q1ChcXFwCSkpIIDAxk1apVqNXp39uXLVuG1Wrl22+/tb1Pzp8/Hw8PDzZt2kT9+vWJi4ujU6dOVKhQAYBq1arZzu/i4oJGo8lz68A777xDqVKlbMlMxjxs/v7+duVymqPt9OnTfPnll0yZMsW2LTo6mrCwMBYvXlxsR/0WF1JzU4zdrfbm0qVLsuaUEOKh1bJlS8LDwwkPD2fPnj20bduW9u3bc/78eQAOHTpk63jr4uKCi4sLXl5eGI1Gzpw5g5eXF2FhYbRt25bOnTszffp0IiMj7ymmTz75hB9++IGVK1ei1+vvfkAWLl++TLt27ejevTuDBg2ybR80aBB9+vShWbNm9xTjw0BqboqxqlVTaNYsli1bMtfeGAwGoqOjOX/+PJ6enlJ7I4QoEGonNU0Ti6ajqtopb9+3nZ2dqVixou3nb7/9Fnd3d7755hs+/PBDEhMTqVevHkuWLMl0rK+vL5Bek/Pqq6+yZs0ali1bxgcffMC6devyNQJ3ypQpfPLJJ/z999/UqlXLtj2j5ufq1asEBv7Xj/Lq1auZRmNduXKFli1b0rhxY77++mu7fRs2bOC3336z1eYoioLVakWj0fD111/z/PPP5znmB5UkN8Xc4MFX2LLFg7/+8mLgwEhCQky2fT4+Ply6dInSpUvb/lCFEOJeqFSqPDUNFScqlQq1Wm2bPqRu3bosW7YMPz+/HJtx6tSpQ506dRg5ciSNGjVi6dKlPPbYY2i1WtLS0nJ17cmTJ/PRRx/x119/Ub9+fbt95cqVIyAggPXr19uSmfj4eHbv3s3LL79sK3f58mVatmxJvXr1mD9/vq15LcPOnTvt4vn111+ZNGkSO3bsICgoKFdxPiykWaqYy6i9sVpVfPNNKbt9GVWeERERWK3WoghPCCGKjMlkss2Hdvz4cV555RUSExPp3LkzAH379sXHx4cuXbqwdetWIiIi2LRpE6+++iqXLl0iIiKCkSNHsnPnTs6fP8/atWs5deqUrd9NSEgIERERhIeHc+PGDUwmU5ZxTJo0iVGjRjFv3jxCQkJsMSUmJgLpSdfw4cP58MMP+e233/jnn3/o168fpUqVomvXrkB6YtOiRQvKlCnDlClTuH79uu08GapVq0bNmjVtj6CgINRqNTVr1sTT07MQX+mSR5KbEmDw4P/63pw8abDb5+vrS2RkJFevXi2K0IQQosisWbPGNh/ao48+yt69e/npp59o0aIFkL7o8JYtWyhTpgzPPPMM1apVY+DAgRiNRtzc3HBycuLEiRN069aNypUrM3jwYIYOHcqLL74IQLdu3WjXrh0tW7bE19eX77//Pss4Zs+eTWpqKs8++6zdHG23dwZ+++23eeWVVxg8eDANGjQgMTGRNWvW2L6krlu3jtOnT7N+/XpKly5tdx6RdyrlXsbelVDx8fG4u7sTFxdXoD3OTSYTmzdvxmAw4OTkVGDnBXjvvXKsXetFkyZxTJ9+2m7f1atXcXNz47HHHkOjkZZGIUTuGY1GIiIiKFeuXL47wApRkHK6J3P7+S01NyXEyy9fwcFBYft2dw4ccLHb5+3tzfXr17ly5UoRRSeEEEIUH5LclBDBwSaefjp91s0ZM4K4vb5No9Hg7OzM2bNnbVN5CyGEEA8rSW5KkBdeiESns3L4sAtbtrjb7fP09CQmJoZLly4VUXRCCCFE8SDJTQni42OhT5/0jsMzZwZx+whFtVqNh4cHZ8+eJSEhoYgiFEIIIYqeJDclTL9+V3Fzs3D2rIHVq+3XHHF3dycpKYlz587d0xotQgghREkmyU0J4+qaRv/+6fMezJ4dhNFoPzOxr68vFy5cIDo6uijCE0IIIYqcJDclUM+e1wgIMHH1qpbFi+0XYjMYDKSlpXH27Nlcz6wphBBCPEgkuSmB9HqFV165DMCCBQFcv+5ot9/Pz48rV67c8wJwQgghREkkyU0J1abNTWrVSsRodGDWLPtlGRwdHTEYDJw5c0aGhgshhHjoSHJTQqlU8Prr6cO+V63y5sQJ+2UZvLy8uHHjBufPny+K8IQQolApisLgwYPx8vJCpVIRHh5OixYtGD58eJ7PFRUVxZNPPomzszMeHh4FHusvv/xCxYoVcXBwyFd8BSm/r1FJI8lNCfbII0m0bRuDoqj4/PNgu4n91Go13t7eREREEBsbW2QxCiFEYVizZg0LFixg1apVREZGUrNmTVasWMGECRNsZUJCQpg2bdpdzzV16lQiIyMJDw/n33//LfBYX3zxRZ599lkuXrxoF19h2rRpEyqVKtP7/52v0YNKkpsS7pVXLqHTWTlwwJVNmzzs9rm6umI0Gjlz5oysGi6EeKCcOXOGwMBAGjduTEBAABqNBi8vL1xdXfN1rnr16lGpUiX8/PzyFU9qamqW2xMTE7l27Rpt27alVKlS+YqvIOX3NSppJLkp4QICzPTtmz6x37RppTMNDff39+fSpUtERUUVRXhCCFHgwsLCeOWVV7hw4QIqlYqQkBDAvsmlRYsWnD9/ntdffx2VSoVKpcryXCEhIfz888989913qFQqwsLCALhw4QJdunTBxcUFNzc3evTowdWrV23HjR07ltDQUL799ttsFx3dtGmTLZFo1aoVKpWKTZs22Y693bRp02zPI+M5du3alSlTphAYGIi3tzdDhw7FbDbbyphMJt555x2Cg4PR6XRUrFiRuXPncu7cOVq2bAmkz15/+/O6s1nq5s2b9OvXD09PT5ycnGjfvj2nTp2y7V+wYAEeHh789ddfVKtWDRcXF9q1a2c3YGXTpk00bNjQ1qzXpEmTIu8SIUtIPwDCwqJYtcqby5d1fPddAIMH/3fTabVadDodp06dwsvLS1b9FULkSFEUkpOTi+TaTk5O2SYht5s+fToVKlTg66+/Zu/evTg4OGQqs2LFCmrXrs3gwYMZNGhQtufau3cv/fr1w83NjenTp2MwGLBarbbEZvPmzVgsFoYOHUrPnj3ZtGmT7djTp0/z888/s2LFiixjaNy4MSdPnqRKlSr8/PPPNG7cGC8vL7tz5GTjxo0EBgayceNGTp8+Tc+ePQkNDbU9n379+rFz506++OILateuTUREBDdu3CA4OJiff/6Zbt26cfLkSdzc3DAYDFleIywsjFOnTvHbb7/h5ubGO++8Q4cOHTh27BiOjukjcZOTk5kyZQqLFi1CrVbzv//9jxEjRrBkyRIsFgtdu3Zl0KBBfP/996SmprJnz55c/R4LkyQ3DwAnJyuvv36JkSPLs2BBAB06RFO69H9VpN7e3ly8eJFz585RtWrVIoxUCFHcJScn4+LiUiTXTkxMxNnZ+a7l3N3dcXV1xcHBgYCAgCzLeHl54eDggKura7ZlIH3iU51Oh8FgsJVbt24d//zzDxEREQQHBwPw3XffUaNGDfbu3UuDBg2A9Kao7777Dl9f3yzPrdVqbc1cXl5eOcaRFU9PT2bMmIGDgwNVq1alY8eOrF+/nkGDBvHvv//y448/sm7dOlq3bg1A+fLl7Z4/pE8Nkl0n6YykZvv27TRu3BiAJUuWEBwczC+//EL37t0BMJvNzJkzhwoVKgAwbNgwxo8fD0B8fDxxcXF06tTJtr9atWp5ep6FQZqlHhCtW9+kYcN4UlPVfPppmSw7F589e5aYmJiiC1IIIUqA48ePExwcbEtsAKpXr46HhwfHjx+3bStbtmy2iU1BqFGjhl2NUGBgINeuXQMgPDwcBwcHmjdvnu/zHz9+HI1Gw6OPPmrb5u3tTZUqVeyep5OTky1xuTMOLy8vwsLCaNu2LZ07d2b69OnFYo41SW4eECoVvP32BTQaK9u3u2daNdzFxQWLxcKpU6ewWCxFFKUQorhzcnIiMTGxSB5OTk5F/fTzJDe1TFlRq9WZ1v+7vS9NhoxmoQwqlco2OCS7ZqbCkFUct8c/f/58du7cSePGjVm2bBmVK1dm165d9y2+rEhy8wAJCTHxv/+ld3ibMiU4y87FV65c4dKlS0URnhCiBFCpVDg7OxfJo6D7aWi12nwtQ1OtWjUuXrzIxYsXbduOHTtGbGws1atXv+e4fH19iYqKsksQwsPD83SORx55BKvVyubNm7Pcr9VqAXJ8/tWqVcNisbB7927btujoaE6ePJnn51mnTh1GjhzJjh07qFmzJkuXLs3T8QVNkpsHzMCBUfj7pxIZqWPBAvv2XY1Gg6urK6dOnSIhIaGIIhRCiPsjJCSELVu2cPnyZW7cuJHr41q3bs0jjzxC3759OXDgAHv27KFfv340b96c+vXr33NcLVq04Pr160yePJkzZ84wc+ZMVq9enadzhISE0L9/f55//nl++eUXIiIi2LRpEz/++COQ3mSmUqlYtWoV169fJzExMdM5KlWqRJcuXRg0aBDbtm3j0KFD/O9//yMoKIguXbrkKo6IiAhGjhzJzp07OX/+PGvXruXUqVNF3u9GkpsHjMFg5Y030r9tLFwYwPnzOrv9np6eJCYmcvr0aZn7RgjxQBs/fjznzp2jQoUKeeobo1Kp+PXXX/H09KRZs2a0bt2a8uXLs2zZsgKJq1q1asyaNYuZM2dSu3Zt9uzZw4gRI/J8ntmzZ/Pss88yZMgQqlatyqBBg0hKSgIgKCiIcePG8e677+Lv78+wYcOyPMf8+fOpV68enTp1olGjRiiKwp9//pmpKSo7Tk5OnDhxgm7dulG5cmUGDx7M0KFDefHFF/P8fAqSSrmz4e8hEB8fj7u7O3Fxcbi5uRXYeU0mE5s3b8ZgMBRp27GiwKuvVmTnTnfq1k1gzpx/Ud+WxppMJq5fv079+vUJCgoqsjiFEEXPaDQSERGR7VwtQtxvOd2Tuf38lpqbB5BKBe++ewG9Po0DB1z57Tdvu/06nQ69Xs/JkyeLbD4LIYQQorBIcvOACgpK5aWXrgDpMxffuGE/pZG3tzdxcXGcOnUqU699IYQQoiST5OYB1qvXNapXTyIxUcPkyWXs9qlUKvz8/Dh37lyxmJNACCGEKCiS3DzANBr44IPzODgobNjgycaNHnb79Xo9er2ef//9V5qnhBBCPDAkuXnAVa6cQr9+6YtmTpoUTEKC/fon3t7e3Lx5U5qnhBBCPDAkuXkIDBwYSZkyRm7c0PLFF/ajo25vnrpy5UoRRSiEEEIUHEluHgJ6vcL776cvP79ypS87d7rdsT+9eerEiRNZTvQkhBBClCSS3Dwk6tVLpGfP9IXOJkwoS3x85uaphIQETp06la/pyoUQQojiQpKbh8grr1yiTBkj165pmTIl2G6fSqXC39+fc+fOceHChSKKUAghhLh3ktw8RPR6hbFjz6FWK/z5p3em0VNarRY3Nzf+/fdfYmNjiyRGIUTxkJqaSnJy8n17pKam5ik+RVEYPHgwXl5eqFQqwsPDadGiBcOHDy+cF0SUKJq7FxEPklq1kujXL4oFCwKZOLEMtWsn4uVlse338PDg0qVLnDhxgrp169pWlhVCPDxSU1PZs2fPfe2D5+LiQsOGDXP9nrNmzRoWLFjApk2bKF++PD4+PqxYscJuTaSQkBCGDx8uCc9DSJKbh9DgwZFs2+bO6dNOfPxxGSZPPotK9d/+gIAALl26hIeHB1WqVEF1+04hxAPPYrGQmJiIVqtFp9Pd/YB7ZDKZSExMxGKx5Dq5OXPmDIGBgTRu3Ni2zcvLq7BCtJOampplnGazOdcLThbEcSJ70iz1ENJqFcaNO4eDg8LGjZ6sWmW/9pRGo8HX15dTp05x9erVIopSCFHUMtahK+xHXhOosLAwXnnlFS5cuIBKpSIkJATArlmqRYsWnD9/ntdffx2VSpXjl7TY2FheeOEFfH19cXNzo1WrVhw6dMi2f+zYsYSGhvLtt9/aLeaoUqmYPXs2Tz31FM7Oznz00UdA+mrdFSpUQKvVUqVKFRYtWmR3veyOEwVHkpuHVJUqKba1pyZPDubCBfs3F2dnZxwdHTl+/LgMDxdCFCvTp09n/PjxlC5dmsjISPbu3ZupzIoVKyhdujTjx48nMjIyx2VmunfvzrVr11i9ejX79++nbt26PPHEE8TExNjKnD59mp9//pkVK1YQHh5u2z527Fiefvpp/vnnH55//nlWrlzJa6+9xptvvsmRI0d48cUXGTBgABs3brS75p3HiYIlzVIPsX79oti1y439+115//1yzJt3EkfH/2Yp9vHx4dKlS5w8eZLatWuj0cjtIoQoeu7u7ri6uuLg4EBAQECWZby8vHBwcMDV1TXbMgDbtm1jz549XLt2zVaDNGXKFH755ReWL1/O4MGDgfSmqO+++w5fX1+74/v06cOAAQNsP/fu3ZuwsDCGDBkCwBtvvMGuXbuYMmUKLVu2zPY4UbCk5uYh5uAA48dH4O5u4fhxZ2bNKmW3X6VSERAQwIULFzh37lzRBCmEEIXo0KFDJCYm4u3tjYuLi+0RERHBmTNnbOXKli2bKbEBqF+/vt3Px48fp0mTJnbbmjRpwvHjx3M8ThQs+Sr+kPP3NzNq1DlGjKjIokUBPPpoPI89lmDb7+joiJeXFydPnsTV1RV/f/8ijFYIIQpWYmIigYGBbNq0KdM+Dw8P2/+dnZ2zPD677XeT3+NE7kjNjaBFizi6dbsOwJgx5YiJsc95XVxcUKlU0v9GCFGiaLXau864XrduXaKiotBoNFSsWNHu4ePjk+drVqtWje3bt9tt2759O9WrV8/zuUT+Sc2NAOD11y9y8KALZ88aGDs2hGnTTqO+LfX18/Pj4sWLHD9+nDp16kj/GyEeAiaTqURfJyQkhC1bttCrVy90Ol2WyUrr1q1p1KgRXbt2ZfLkyVSuXJkrV67wxx9/8PTTT+e5+eitt96iR48e1KlTh9atW/P777+zYsUK/v7774J6WiIX5BNKAOmzF0+ceJb+/auxY4c7CxYE8PzzUbb9KpWKUqVKcfHiRVxdXWX+GyEeYBqNBhcXFxITE/M8c3B+ubi4FPiXpvHjx/Piiy9SoUIFTCYTiqJkKqNSqfjzzz95//33GTBgANevXycgIIBmzZrlqxm+a9euTJ8+nSlTpvDaa69Rrlw55s+fT4sWLQrgGYncUilZ/bYfcPHx8bi7uxMXF4ebm9vdD8glk8nE5s2bMRgMODk5Fdh576dff/VmwoQQ1GqFGTNO0bBhgt3+pKQkYmNjqVevHkFBQUUUpRCioBiNRiIiIuzmb4H00UEWiyWHIwuWRqORGdEFkP09Cbn//JaaG2GnS5dowsNd+P13Hz74oByLFx/Hz89s2+/s7IzRaOTYsWM4OzvbdbgTQjw4tFqtJBuixJIOxSKTd965QKVKycTEOPLee+W488ubt7c3KSkpHD16FKPRWDRBCiGEENmQ5EZkotcrTJp0FmfnNMLDXZk5M3PzU2BgIFevXuX48eN3HY0ghBBC3E+S3IgslSljYsyYcwAsWhTAxo0edvvVajWBgYG2ia4ewq5bQgghiilJbkS2WrWKpW/f9IUzx44N4exZ+45dWq0Wb29vTpw4weXLl4siRCFEAZEvKKK4KIh7UZIbkaNXXrlE3boJJCU58MYbFYiLc7Db7+LigsFg4OjRo0RHRxdRlEKI/HJ0dAQgOTm5iCMRIl3GvZhxb+aHjJYSOdJoYNKks/TrV5VLl/S89155pk8/xe3TUXh5eREZGcmRI0eoV68eLi4uRRewECJPHBwc8PDw4Nq1awA4OTnJHFaiSCiKQnJyMteuXcPDwwMHB4e7H5QNSW7EXXl6WvjsszM8/3wVdu92Y8aMIIYPt2+GCggI4OLFixw9epTQ0FDb6rpCiOIvY9XsjARHiKLk4eGR40ruuSHJjciVypVTGDv2HO++W4HFiwOoWDGFTp1ibPszZjC+fPkyOp2ORx555J6ybiHE/aNSqQgMDMTPzw+z2Xz3A4QoJI6OjgXy2SHJjci11q1jGTgwkrlzA5k4sSwhIUZq1vyvnV6j0RAQEMDZs2cxGAxUrlxZqreFKEEcHBzkS4l4IEiHYpEnL754hWbNYklNVfPmmxWJjLSfwTRjcboTJ05w/vz5IopSCCHEw0ySG5EnajVMmBBBxYrJREc78tprFUlMtL+NnJ2dcXV15ejRo0RGRhZRpEIIIR5WktyIPHN2tjJt2ml8fFI5e9bA229XyLREg7u7OxqNhn/++UeGiAshhLivJLkR+RIQYGbatNMYDGns2ePGxx+X5c55l3x8fEhNTeXw4cPExcUVTaBCCCEeOpLciHyrWjWFiRMjUKsVfv3VhwULMg/dCwgIID4+nn/++YekpKQiiFIIIcTDRpIbcU+aNo3jzTcvAjBzZhB//eVptz9jiPiNGzf4559/ZBVxIYQQhU6SG3HPeva8Tu/e6WtQjRkTwu7drnb71Wo1pUqV4sqVKxw5coTU1NSiCFMIIcRDotglN1u2bKFz586UKlUKlUrFL7/8Yrc/LCwMlUpl92jXrl3RBCtshg+/ROvWMVgsakaMqMDRo052+x0cHAgKCuLChQscO3YMy509kIUQQogCUuySm6SkJGrXrs3MmTOzLdOuXTsiIyNtj++///4+Riiy4uAA48efo2HDeFJSHHjttYqcO2e/BINGoyEwMJCzZ89y/Phx0tLSiihaIYQQD7JiN0Nx+/btad++fY5ldDrdPa87IQqeVqvw6adnePnlyhw75sywYZWYO/ck/v7m28po8ff359SpUzg4OFC1alXU6mKXYwshhCjBSuSnyqZNm/Dz86NKlSq8/PLLd51HxWQyER8fb/cQhcPZ2cr06acpU8ZIVJSOV16pRFyc/XTuer0ePz8//v33X/7991+sVmsRRSuEEOJBVOKSm3bt2vHdd9+xfv16Jk2axObNm2nfvn2OTRwff/wx7u7utkdwcPB9jPjh4+lpYebMU/j6pk/yN3x4RZKT7W81g8GAt7c3J06c4NSpUyh3TpIjhBBC5JNKKcafKiqVipUrV9K1a9dsy5w9e5YKFSrw999/88QTT2RZxmQyYTKZbD/Hx8cTHBxMXFwcbm5uBRavyWRi8+bNGAwGnJyc7n7AA+7MGT2DBlUhPl5DvXoJTJ9+Cr3e/nZLSkoiJiaG6tWrU6lSJVloUwghRLbi4+Nxd3e/6+d3iau5uVP58uXx8fHh9OnT2ZbR6XS4ubnZPUThq1DByBdfnMLZOY39+10ZMaICJpN98uLs7IynpyfHjx/nzJkzUoMjhBDinuUpuUlJSbHrH7F+/Xo+++wz/vzzzwIPLLcuXbpEdHQ0gYGBRRaDyF7NmslMn34KgyGNXbvceeed8pjN9gmOi4sLHh4eHD16VBIcIYQQ9yxPyc1jjz1m64z78ccf89FHH6EoCnPmzGHEiBEFElBiYiLh4eGEh4cDEBERQXh4OBcuXCAxMZG33nqLXbt2ce7cOdavX0+XLl2oWLEibdu2LZDri4IXGprE1Kmn0emsbNvmwXvvlcu00KYkOEIIIQpKnvrc1KhRg6NHjwJQv359duzYgVarxWq1EhoayuHDh+85oE2bNtGyZctM2/v378/s2bPp2rUrBw8eJDY2llKlStGmTRsmTJiAv79/rq+R2za7vJI+NznbtcuV11+viNms5sknY/jwwwgc7AdSkZiYSGxsLNWqVaNixYoyTFwIIYRNbj+/8zTPjb+/Pzt27KBx48a29YJKlSpFQkLCPQecoUWLFjl+a//rr78K7Fri/nrssQQ+/fQMI0ZUYN06L9RqGDcuAs1td6GLiwsAx48fR1EUKlWqJAmOEEKIPMlTcjNv3jzCwsLQarU4OztTu3Zt6tevz7Vr1/j0008LK0bxAHn88Xg++eQs77xTgb/+8sJiUfHRR2czJTgqlcouwXG4s4pHCCGEyEa+hoIfO3aMU6dOYbFYCAoKokGDBiXqw0eapYre5s3uvPtuecxmNc2axfLJJ2fRau1vxeTkZG7cuEHlypWpWrVqibrHhBBCFLzcfn4X63luCoskN8XDjh1ujBhRgdRUNY0bxzF58plM8+AYjUauXbtGhQoVqFatGo6OjkUUrRBCiKJ23+e52b17d0GdSjwkGjeOZ9q09FFUO3a488YbFUlJsb8l9Xo9/v7+nD59miNHjthNxiiEEEJkpcCSm+7duxfUqcRDpGHDBL74In0enD173Hj11YokJtrfljqdjsDAQCIiIjh8+DApKSlFFK0QQoiSIE8dinv06JHldkVRiImJKZCAxMOnXr1EZsw4xauvVuLgQVcGD67Cl1+ewtv7v8lwtFotQUFBXLp0CYvFwiOPPGIbWSWEEELcLk/Jzd9//82iRYsyfagoisKWLVsKNDDxcKldO4mvvjrJq69W4t9/nRg4sAozZpyidOlUWxmNRkNQUBBXrlyxJTgeHh5FF7QQQohiKU/JTYsWLXB1daVZs2aZ9tWqVavAghIPp6pVU/j225MMG1aJS5f0DBxYlRkzTlGp0n/NUA4ODgQFBREZGcn+/fupVasWvr6+RRi1EEKI4kZGSxXgaKnIxER+2LmT+nq9jJa6B9evOzJsWCXOnDHg6mph6tTThIYm2ZVRFIWrV6+i0WioWbMmQUFBRRStEEKI++WhWRW8uDiRlES9Q4cYo9Fw4+HLFwuUr6+Zb745Se3aiSQkaBg6tDJbt7rblVGpVAQEBKBSqTh48CBnz56V9aiEEEIABZjc1K1bt6BOVSKVNxjw12pJUKmYZLXKB+09cnNLY+bMf3n88VhMJjVvvlmB5ct9MpXz9vbG2dmZw4cPc/z4cSx3rsgphBDioVNgyc2BAwcK6lQlklatZn7FijgqCruBn83mog6pxNPrFaZMOUPnzjewWlV88klZpk8Pwmq1L+fm5oa3tzcnTpzgn3/+wWg0Fk3AQgghioU8dSgGuHnzJmvXruXy5csAlCpVirZt2+Lp6VngwZU01ZyceD4tja80GqaZTDTUaCgjiz7eE40GRo8+T1CQiTlzgli0KIArV3SMGxdhN5uxk5OTbS4co9FIzZo1cXV1LcLIhRBCFJU8ffLOnTuXRo0asXv3bqxWK1arld27d9O4cWPmzp1bWDGWKF2tVuoCRmB0SgoWaZ66ZyoVvPBCFBMmRODoaGX9ek+GDKnMzZv2ublWq6V06dJcu3aN/fv3c/369SKKWAghRFHK02ipKlWqcODAAZydne22JyYmUrduXf79998CD7AwFPbaUvF6PQOsVhKBl7RaXtDpCuwaD7v9+114660KxMdrKF3ayLRppwkJsV+SIWMklYODAzVq1KB06dKoVKoiilgIIURBKZTRUiqVioSEhEzbExIS5MPjNv4qFW/r9QB8k5rKP2lpRRzRg6NevUTmzTtBUJCJS5f0DBhQlV277JufMkZSaTQaDh48yMmTJ6WjsRBCPETy1OdmypQpNG/e3G5ekUuXLnH06FE+++yzQgmwpGqv0bBVo2GdxcJ7KSkscXbGTRLAAhESYmL+/BOMGFGBw4ddePXVSrz66iX69r3G7S+xp6cnWq2WY8eOkZSURPXq1TEYDEUXuBBCiPsiz5P4paWlsWfPHq5cuQKkdyhu2LAhDg4OhRJgYSjsZimDwYCTkxOJisL/kpK4pCi00Gj4VK+XGq4ClJqqYtKkMvz6a/oQ8Y4do3nvvfPodPa3tNlsJjIyEh8fH2rUqIGXl1dRhCuEEOIe5fbzO98zFFssFjQaTbY/F2f3K7kBOJ6WxvPJyZiBETodvbTaArueAEWBZct8mTo1mLQ0FTVrJvLpp2fx9bUfim+1WomMjESn01GjRg2CgoIk0RRCiBKm0GcobtiwYY4/i3TVHBx47VaH4ukmE8el/02BUqmgV6/rfPnlKdzcLBw54kK/flU5csR++Qu1Wk1QUBBqtZoDBw5w/PhxzDIXkRBCPJDyndzcWeEjM/Jmr6ejIy00GszAuykpJMhrVeAaNkzgu++OU758Ctevaxk0qAorVvhw50vt5eWFp6cnJ06c4ODBg1l2kBdCCFGy5Tm5+e6771i4cCE3b97ku+++47vvvgOQKv4cqFQqRuv1BKpUXFYURqekYJUEp8CVLp3KvHknaN48FrNZzcSJZRk3rixGo/296eTkRFBQEFeuXGHv3r1ERUUVUcRCCCEKQ56Tm4waGkVR7GprpOYmZ24qFZMNBrTA1rQ0vklNLeqQHkguLlY+/fQMw4ZdQq1WWLXKhwEDqnLhgv1cQxqNhtKlS2Mymdi3bx///vuvDBcXQogHRL47FNetW9duPak7fy7O7meH4jutMpsZe2vto88MBpqXkE7YJdG+fS68/355oqMdcXZOY+zYc7RsGZupXGJiItHR0QQHB1OtWjVcXFzuf7BCCCHuqtA7FEufm/zp5OhIT0dHIH15hnN3rgIpCkz9+oksXnyc0NAEkpIceOutCkyfHsSdFTQuLi4EBQVx6dIldu/eTWRkpNzPQghRguU7udmzZ0+OP4vsva7TUcfBgSRgREoKifJBWmh8fc3MmfMv//tfer+aRYsCGDSoCpcv2w/J12g0BAcHYzab2bdvHydOnCBVmg6FEKJEylNyk5KSgvVWTYOjoyPr16/ns88+488//8TxVm3Ew0xRFEi+ezmNSsUnej1+KhXnrFZGygKbhUqjgeHDLzN58hlcXS38848LffpUZ+1a+5XsVSoVvr6+uLu7c+zYMfbv309sbGzRBC2EECLf8pTcPPbYY8THxwPw8ccf89FHH6EoCnPmzGHEiBGFEmBJYUm0cKrfKTTva1DMd09UvNVqPjMY0AM709KYYjJJU0gha9UqlqVLj1O7diJJSQ689155xo8vS0qK/Z+Bs7OzbXXx3bt3c+7cOVtSL4QQovjLU4fiGjVqcPToUQDq16/Pjh070Gq1WK1WQkNDOXz4cKEFWpAKo0NxypkU9tXbR1pcGqpuKlxG5q5T6iazmbeMRhTgDZ2OPjKDcaGzWODbbwOZOzcQRVFRtqyRiRPPUqVKSqaysbGxJCQkULZsWSpXroyzs3MRRCyEEAIKqUOxv78/O3bsANLXlLpx4waATIQGGCoYqDi3IgDKzwrmNbmb/baFo6NtBuOpJhNbZDhyodNo4KWXIpk9+198fVM5f15PWFhVli71484KGg8PD/z9/Tl37hy7d+/mypUrUsMmhBDFXJ5qbs6dO0dYWBharRZnZ2e2bdtG/fr1uXbtGhMnTqRt27aFGWuBKcyh4NsGbMPhewfQgdMCJxwq3X1BUUVRmGgysdJsxgB84+RE1RK0EGlJFhvrwPjxIWzZ4gFAw4bxjB59joAA++RUURSio6MxmUyUK1eOihUrygrjQghxnxXqwpnHjh3j1KlTWCwWgoKCaNCggawKzq15bjZsRjtGC3tBFazC+TtnVK53n73Zoii8lpLC7rQ0vFUq5jk5EaTO92A2kQeKAj/95Mv06aUxmdS4uFh4662LdOgQw50TbxuNRq5evYq3tzdVqlTB399fZucWQoj7pFDnualevTpdunShSpUq/Pvvv4SHh+c3zgePA6hHq1EFqlAuKqSMTkGx3j1/1KhUTDIYqKRWE60oDEtOJlo6sd4XKhX06HGdpUuP8cgjiSQmahgzphxvv12emzftJ1nU6/UEBweTnJzM3r17OXbsGMZbkzIKIYQoHvKU3DzxxBO2/y9dupRevXpx5MgRXnzxRWbMmFHgwZVUKncVhkkG0ELa1jRSZ+duvhQXlYovDQZKqVRcVBRelTlw7quyZU18881Jhgy5jEZjZeNGT3r2rM7mze525dRqNX5+fnh6enLy5El2795NVFSU9MURQohiIk/NUnXq1OHgwYMAPProo/z6668EBASQmJhI48aNH+rRUpB5+QXzKjPGsenf6vXj9Dh2zN1cQBesVl5ITiZGUajv4MB0gwGdNH3cVydPGhg9uhxnzqT3q+nU6Qavv34Jd/c0u3JWq5UbN25gNpspV64cFSpUyHbpDSGEEPemUJqlFEUhJSWFpKQkrFYrAQEBQPr09SWpz8394tjJEW1Y+tBu44dGLOG5GwlVRq3mC4MBZ2BfWhofGI0yyd99VqVKCosWHadfvyhUqvQFOHv0qMH69R525TJqcby8vDh16hS7d+/m8uXLMi+OEEIUoTwlN7GxsdSoUYOaNWsSHR1NZGQkkL7woFTJZ007RIumpQbMYHzLiPVK7j70qjo48JnBgCOw0WJhvNFImrzG95VWq/Dqq5eZO/ck5cqlEB3tyDvvVOCtt8pz44Z9XxyDwUCZMmVITU1l3759HDp0SKZIEEKIIpLvVcFvl5yczNWrVylXrlxBxFTo7veq4EqKQvILyVhPWlGXV+M0zwmVS+6amTaZzbxjNJIGPOXoyAc6HWpporrvUlNVzJsXwPz5gaSlqXB1tTB8+CWeeio604gqk8nE1atXcXFxoWLFigQHB6OR1d+FEOKeFfqq4LdzcnIqMYlNUVAZVBg+N6DyUWE9ayXlzRQUU+5yyhaOjnyo16MGfjOb+USWaSgSWq3CSy9FsnjxcapXTyIhQcOECSEMHVqJS5fsZ5XW6XSUKVMGtVrNwYMH2bdvn23CSyGEEIWvwCZSqVu3bkGd6oGk9ldjmGYAZ0jbn4ZxtBElLXdJypOOjozX61EBK8xmWYeqCFWqlMK8eScYPvwiOp2VPXvc6NmzBvPnB2A221fheHh4EBQUZFuj6tixY6SkZF7iQQghRMEqsOTmwIEDBXWqEmvBggXMmzcv2/0OVR0wTDGABizrLZg+y32S0s7RkTG3EpxlZjOfS4JTZDQa+N//rrFs2VEaNIjHZFIzc2YQvXtXY+9e1zvKaggKCsLV1ZUTJ06wa9cuLl26RFpaWjZnF0IIca8KpM9NSVMYfW4OHTpEaGgoAG+++Sa9e/fOtqx5rRnje+lDxLVDtegG6HJ9nV9SU/nQZAKgm6Mj70gfnCKlKLBmjRdTp5YmJiZ9qH/79tG89tolfHwsd5RNX8IhJSWFoKAgKlSogJeXV1GELYQQJVKhLb9w8+ZN1q5dy+XLl4H0BTTbtm2Lp6fnvUV8HxVWh+IxY8Ywfvx4HBwcmDp1Ko0bN862bOr3qZg+S09SdB/o0HbN/Wrgv5rNfHhrJfEOGg2j9Xo0kuAUqYQEB2bNKsXy5b4oigpn5zSGDLnMs89e585ZEsxmM9euXUOj0RASEkJISIjMjSOEELlQKB2K586dS6NGjdi9ezdWqxWr1cru3btp3Lgxc+fOveegS7qRI0fSunVr0tLSGDlyJKdOncq2rLa3Fm3/9ITG9JEp16uIA3RxdGSCXo8D8KfFwvtGI+aHrwKuWHF1TeOddy6ycOEJqldPIinJgU8/LUP//lU5dMjZrqyjoyNBQUG4uLhw4sQJdu7cyfnz57HIivBCCFEg8lRzU6VKFQ4cOICzs/2bdWJiInXr1uXff/8t8AALQ2EOBf/7778ZNWoUBw8exN/fnwULFuDr65tleUVRMH1swrzCDA6g/1iPY6vczWIM6cPERxqNmIHHHRyYJDMZFwtpabBypQ8zZgSRmJg+BLxt2xheeeVSlquN37x5k4SEBAICAqhQoQJ+fn6yGKcQQmShUGpuVCpVlhOTJSQkyJvxLY6Ojnz44YeULVuWq1ev8vrrr5OUlJRlWZVKhe5dHZpOGkgD43tGLNty/+29haMjnxsM6IBtaWmyFlUx4eAAzz57g59/PkrXrtdRqRT++suLbt1q8vXXgRiN//2tqFQqvLy8CAoK4ubNm+zevZvw8HBiY2OL7gkIIUQJl6eam1WrVvHmm29Ss2ZNgoKCALh06RJHjx7ls88+o1OnToUWaEG6H5P4xcTEMGDAAG7evEmDBg2YPn06Wm3W/WqUNAXjKCOWtRbQgmGqAc2juZ/0bb/FwuspKSQDFW8t3eCnLrCBcOIenThhYMqUYMLD00dS+fun8uqrl2jT5mamCQCNRiM3btxAq9VStmxZ6Y8jhBC3KbQOxWlpaezZs4crV64A6R2KGzZsWKLWlrpfMxQfPXqUl19+meTkZFq2bMknn3yS7eukWBSMI41YNlpAB4bP85bgnEhL47WUFKIVhYBbq4uXK0G/kwedosDff3syfXoQUVHpo+Nq105kxIiLVKuWnKl8YmIi0dHRuLm5Ub58eUqXLp1tciyEEA+LQpuh2MHBgUaNGnH8+HEMBgPly5cvUYnN/VSjRg2mTJmCo6MjGzduZOLEidnOTaPSqNB/pMfhcQcwQcrrKXlqoqrq4MA8JyfKqFREKQoDk5M5JHOpFBsqFTz55E2WLz/KSy9dRqezcuiQC889V4333y/H5cv2iYuLiwtlypRBpVIRHh7Ozp07uXTpknQ6FkKIXMj3PDdqtdrWzyYgIIC6detSr149278ZzVbF0f1eW2rDhg28++67WK1W+vXrx6uvvprtOZTUWzU4my2gudXJuGXuOxnHWq0MT0nhiNWKDvhIr6eFY+6PF/dHVJQjM2cGsXq1NwAajZXu3a8zcGAkHh72SanVaiUmJoaUlBT8/PwoX748fn5+qKXpUQjxkCm0ZqkMjz76KJGRkQwYMAAfHx8OHDjA/v37OXHiBGlpafj6+lK3bl3+/PPPfD+JwnK/kxuAX375hQ8//BCAwYMHM3jw4GzPo1hu9cFZZ0kfRTVOj2O73CcoKYrCeykpbE1LQwUM1Wrpr9VKp+9i6MQJA198UZo9e9LvQ2fnNPr3j6JPn6vo9fZ/mhaLhRs3bmCxWAgMDKRcuXL4+PjI71UI8dAo9OQG0pcbeO+992jQoAGff/45FSpUwGQyER4ezoEDBzh48CBff/11fk9faIoiuQFYvHgx06ZNA+Cll17ihRdeyPZcSpqCcYIRyyoLqED3ft4m+rMoCp+ZTPxkTh963FGj4X29Hq18EBZLu3a58sUXpfn33/T7xtc3lRdfvEKnTtHcuaB4amqqbSHOoKAgypYti5eXlyQ5QogH3n1JbiC94+P48eP56quvGDJkCKNGjSr2ozuKKrmB9IRwxowZAAwdOpQBAwZkez7FqmD65NY8OIB2iBbtgLzVwPyYmspnJhNpQG0HBz7V6/GS5oxiyWpNX8ph9uxSREamdzouVy6FF1+8QqtWsdz5a8sYWZWxflXZsmVL1EzhQgiRV/ctuclw6tQp3njjDfbv388nn3xCv379CuK0haIokxuA+fPnM3PmTACGDRtGWFhYtmUVRSF1RiqpC1MBcOzpiO5NHSp17hOcXRYL76akkAgEqlRMNRioKJ3Aiy2TScVPP/kyb14g8fHp1TaVKyfz4otXaNYsLtPw8ZSUFKKjo20zH5ctWxYPD4/7H7gQQhSy+5rcWCwWTpw4weHDh5k2bRr79+/n+vXrxXZRwKJObgC+/fZb5syZA9w9wQH7tag0T2rQj9Oj0uY+wTmXlsbrKSlcVBScgNF6Pa2lo3GxlpDgwNKlfixd6k9SUnoyWr16Ei+9dIVGjeIzJTnJyclER0ej1WoJDg4mODhYkhwhxAOl0JObTz75hH/++Yd//vmHEydOoNfrqVWrFqGhodSpU4ewsLBiO0S8OCQ3AF9//bWtT9KAAQMYMmRIjk1O5r/MGMcYwQIO9R0wTDGgcsl9ghOnKLyTksK+W0PEn3N0ZKhOJ4tuFnOxsQ4sXuzPDz/4YTSm/03VqpXIyy9foUGDzDOGZyQ5Op2OoKAggoODpblKCPFAKPTkRq1WExISQv/+/enduzeVK1fOd7D3W3FJbsC+D06PHj0YMWJEjkN8LbstpLyVAsmgrqDGMNWAulTu+9BYFIWZJhOLbnU0rufgwES9Hm/ph1PsxcRoWLgwgOXLfTGZ0n9f9eolMGjQFerVS8yxJuf2JEc6HgshSqpCT26aN29OeHg4CQkJODs7U6tWLerWrWt71KxZU2pucmn58uVMmjQJRVHo2LEjo0aNQnPnEJnbpJ1II+W1FJRoBZWXCsMUAw618vZa/202M95oJBnwVamYZDBQq5j+voS969cdmTcvgJUrfbBY0pOcWrUSef75SJo0ybq5KiYmBo1GQ6lSpQgODsbb21uSHCFEiXPf+tycOnWK/fv3c+DAAdsjNjYWnU7HI488wp49e+7l9IWiuCU3AKtXr2bs2LGkpaXRsmVLPvzwQ3Q6XbblrVFWUt5IwfqvFbSgH523uXAAItLSeMto5JzVigZ4Taejl6OjfOiVEFFRjixcGMCvv/qQmpqe5FSpkszzz0fSsmX2o6scHBwICAigTJky+Pj4yGSAQogS476PlrpdREQE+/bt4+DBg0ycOLGgT3/PimNyA7B582ZGjhxJamoqtWvX5rPPPsuxQ6iSfGuyv83pU/JrX9CiHazN00iqJEVhvNHI+lvT+jd1cGCMXo+HfOCVGDduaFiyxJ/ly31JSUmvfStfPoUBA6J48smYTPPkGI1GoqOjAfDz86Ns2bL4+vrmWFsohBDFQZEmN8VdcU1uAPbt28eIESNITEykbNmyfPHFFzkuZaFYbw0V/y59qLimpQb9GH2eOhorisJPZjPTTCZSSW+mmqDXU18+7EqU2FgHvv/en2XLfElMTP/dBQWZ6Ncvio4dozPNeGw2m4mOjsZiseDl5UVISAj+/v6yQKcQotiS5CYHxTm5ATh9+jSvvfYaV69excvLi2nTplG9evUcjzH/ZsY4MX0klTpEjf5TPQ7l8taH5t+0NEYajZy3WlEBz2u1DNJqZTRVCZOYqObHH/1YssSfuLj0JMfT00zPntd49tnrmdauslgs3Lx5k5SUFNzd3SlbtiyBgYHFfjJOIcTDR5KbHBT35Abg+vXrvPbaa/z777/o9Xo+/vhjmjZtmuMxaf+kkfJOCso1BZxAP0aP4xN564eToih8ajLx263RVLUdHJig11NKmqlKnJQUNStX+rB0qR9RUen9t3Q6K089dYO+fa9SunSqXXmr1UpsbCwJCQm4uLhQunRpSpUqhbu7u/TDEkIUC5Lc5KAkJDcASUlJvPvuu+zcuRO1Ws2rr75K3759c/ygsUZbMY40knYg/du5tp8W7RAtKk3ePpzWmM18bDSSBDgBb+h0dJHOxiWSxQJ//+3JokUBnDyZfl+q1QotW8by3HNR1KyZbFdeURQSEhJsAwMCAwMJCgqSzsdCiCInyU0OSkpyA+lNBp988gm//PILAB07duS9997LcSSVYlEwfWnCvCS99sWhgQP6CXrUPnn7YLpktTLGaOTQrUn/Hndw4AO9Hh/5gCuRFAX27XNl0SJ/duxwt22vUyeBvn2v0rRpHHfOBpCSkkJMTAwAPj4+lClTBl9f3xzvPyGEKCyS3OSgJCU3kP5NetmyZUydOpW0tDRq1qzJp59+iq+vb47HmdeaMU4wQgqovFTox+nRNMpbJ+E0RWGJ2cxskwkz4A68q9fzpCzdUKKdPq1nyRJ/Vq/2ss2VU6qUie7dr9Olyw3c3Oz75ZjNZlu/HA8PD8qUKYO/vz+urq5FEb4Q4iElyU0OSlpyk2HPnj28++67xMfH4+vry5QpU6hRo0aOx6RFpGF8z4j1lBUAx+cc0Q3RoXLMW/PS6bQ0xhiNnLSmn6eNRsPbOp0MGS/hrl1z5McffVm50tfW+Vins9KhQzQ9e16jYkWjXXmr1Up8fDzx8fEYDAYCAgIICgrCy8ur2E7aKYR4cOT287vYfTJt2bKFzp07U6pUKVQqla05JoOiKIwePZrAwEAMBgOtW7fm1KlTRRPsfdawYUO+++47ypcvz/Xr1xk0aBArVqwgp/zUoZwDTvOdcOyeXtNiXmQm+YVkrJesebp2RQcHFjg58YJWiwOw1mKhW3Iyf5rNOV5fFG9+fmaGDbvCH38c5oMPzlG5cjImk5qVK33p1asGL71UiU2b3LnVMolarbbV3Dg5OXH+/Hl27tzJ7t27uXDhAikpKUX7hIQQgmKY3CQlJVG7dm1mzpyZ5f7JkyfzxRdfMGfOHHbv3o2zszNt27bFaDRmWf5BU7p0aebNm0fz5s1JTU1l4sSJjB49muTk5GyPUelV6N/Ro/9UD65gPWolqW8S5tV5S0wcVSpe0umY5+RERbWaOEVhtNHIqykpXLHmLVkSxYter9C1azRLlhzn669P8sQTN3FwUNi3z40RIyrStWtNFi70Jzb2v9oZZ2dnSpcujZ+fH/Hx8ezfv5/t27dz7NgxYmJiJOkVQhSZYt0spVKpWLlyJV27dgXSa21KlSrFm2++yYgRIwCIi4vD39+fBQsW0KtXr1ydt6Q2S91OURQWLVrEzJkzSUtLo1y5ckyaNIny5cvneJw10krK+ylYD6cnI5pWGnQjdag985bnWhSF71JT+TY1lVRAD7x8a/kGBxlR9UCIinJk+XL7JitHRyutWsXyzDPXqVvXfrHO20dZOTo64uPjQ3BwMD4+PtIBWQhRIB6IPjd3Jjdnz56lQoUKHDx4kNDQUFu55s2bExoayvTp07M8j8lkwmQy2X6Oj48nODi4RCc3GQ4ePMh7773H9evX0ev1vPfee3To0CHHYxSLQurCVFK/ToW0W52N39ejaZ73GYnPW618ZDRy4Fa7RXW1mvf0eqpK/4sHhtGo4q+/vFi+3Jfjx51t20NCUnj66Rt06hSNu7t9B2STycTNmzdJTU3Fzc2NoKAg/P398fDwkOkEhBD5VmL73OQkKioKAH9/f7vt/v7+tn1Z+fjjj3F3d7c9goODCzXO+6lOnTosWbKEhg0bYjQaGT16NOPGjSMpKSnbY1QaFbqBOpwWOqEur0aJUUh5M4WUcSkoiXnLdcuq1cwxGHhfp8MFOGa10i85mUlGI/HFN28WeaDXK3TpEs2iRSdYtOg4Tz99HYMhjXPnDEydGkz79rUYPTqE8HBnMn7lOp2OgIAASpcuDcCJEyfYsWMHu3fv5tKlSw9NM7IQomiUqOQmv0aOHElcXJztcfHixaIOqUB5eXnx5ZdfMmjQIFQqFb///jt9+/blyJEjOR7nUNUBp0VOOD7nCCqw/G4hqVcSlp2WPF1frVLxtFbLcmdnntRosAI/mc08k5TEr2YzVklyHhjVqiXz/vsXWL36MO++e57KlZNJTVXz55/evPBCVXr2rM4PP/ja+uZkdEAODg7G09OTmJgY9u7dy7Zt2zh69Cg3btwgLS3tLlcVQoi8eSiape70IPS5yc7+/fsZPXo0V69excHBgUGDBjFgwIC7DtO1HLRgHGtEuZx+O2g6aNC9oUPtkff8d5/FwmSTibO3OhnXVKt5R6+nmjRVPXAUBY4edeLnn31Zu9YLkyn9fnF0tNKsWRydO9/gscfi7VYmz+ibEx8fj0qlwsvLi9KlS+Pt7S3z5gghcvRANkuVK1eOgIAA1q9fb9sWHx/P7t27adSoURFGVnzUq1eP77//nieffJK0tDTmzJnD4MGDuXLlSo7HaepocP7eGcfet2px/rSQ/GxynkdUAdTXaFjq5MRwnQ4n4MitpqqPjEaiZVTVA0Wlgpo1kxkz5jxr1hzmrbcuULlyMmazmvXrPRk+vBKdOz/Cl18Gce6c7tYxKtzc3GwjrZKSkjhw4ADbt2/nwIEDREZG2vWRE0KIvCp2NTeJiYmcPn0aSO9P8vnnn9OyZUu8vLwoU6YMkyZN4pNPPmHhwoWUK1eOUaNGcfjwYY4dO4Zer8/VNR7kmpsMiqLw559/MnnyZJKSknB2dubVV1/lmWeeuWuHzrQjaRg/NGI9nZ6IODR2QP+uHnWpvOfC161WpptMrLGkN3U5A/21WvpoteilY+kD6+RJA7//7s3q1d62kVYAtWol0rlzNE8+GYOLi32im5ycTFxcHGazGTc3NwIDA/Hz88PT01MmCBRCACV4tNSmTZto2bJlpu39+/dnwYIFKIrCmDFj+Prrr4mNjeXxxx9n1qxZVK5cOdfXeBiSmwyXL19m9OjRHDp0CIAGDRrwwQcfEBQUlONxikUh9btUUr9NJWOst/YFLdq+2jzPbgxw0GJhqsnEsVs1N/4qFUN1OtppNKglyXlgmc0qtmxxZ9Uqb3bscCctLf13rdNZadXqJh07RlO/foJds5XVaiUhIYGEhARUKhUeHh62hTvd3NxktJUQD7ESm9zcDw9TcgOQlpbGjz/+yIwZMzCZTBgMBl555RWeffbZu67ybD1nxTjxv1XGVWVU6N/Wo3ks78PGrYrCGouFmSYTV2/ddtXVal7X6aijyfv5RMly44aGP//05vffvYmIMNi2e3ubadMmhnbtYqhePdlu7hyLxUJcXByJiYnodDq8vb0pVaoUXl5euLi4FMGzEEIUJUlucvCwJTcZLl68yIQJEzhw4AAAdevWZdSoUXcdGq8oCpY/LZi+MKFE3+pw3FKD7k0d6oC8N1UZFYWlqaksSE0lY17lZhoNQ7RaKkrzwwMvoxPy77/78PffnnbNVmXKGGnfPob27aMpXTrV7jij0Uh8fDxGoxEnJyd8fHwICAjAy8sLg8Fw52WEEA8gSW5y8LAmN5Be5b98+XK+/PJLUlJS0Ol0DBgwgH79+qHVanM8VklUMH1lwvyjGdIAHWif16L9nxaVLu9NBdFWK3NSU9OHiwMqoJ1Gw2CdjmBZkPOhYDar2LnTjdWrvdiyxcM22gqgZs1E2rWLoU2bm3h52U9PkJSURHx8PBaLBScnJ/z8/PD398fLy0tmQxbiASbJTQ4e5uQmw+XLl5k4cSK7d+8GoGzZsrz77rs0aNDgrsemnU7DNNn0X1NVKRW6oTo0bTT56g8RkZbGV6mp/H2r07ED0MXRkRe0WvwkyXloJCWp2bjRgzVrvNizxw2rNf1ecnBQePTReNq0iaF58zhcXf+bF0dRFJKSkoiLi8NqteLi4oK/vz++vr54enpKoiPEA0aSmxxIcpNOURTWrl3L559/TnR0NADt27dn+PDheHt73/VYy18WTNNNKNfTbyF1TTW64To0ofnrP3MiLY1ZJhM7bk3qpgW6OzoSptXiKUnOQ+XGDQ3r1nmxerUXx479t+SDRmPlscfiad36ZqZEx2q1kpiYSHx8PECmROduNZNCiOJPkpscSHJjLyEhgVmzZrF8+XIURcHV1ZWXX36ZZ555Bs1dOvoqRoXUxamkLkyFlPRtmlYadK/qUJfOX0Jy0GJhZmoq4beSHAPwrKMj/9Nq8ZYk56Fz/ryOtWu9+PtvT86c+a9vzd0SnYwRV5Ce6Pj5+UmNjhAlnCQ3OZDkJmtHjx7l448/5sSJEwCUL1+eN954g8cee+yux1pvWEn9KhXzr2awAhpw7O6IdqA2X7McK4rCzrQ0ZptMHL81fFwHPOPoyHPSXPXQiojQ8/ffnqxb58nZs/8lOo6Otyc6sXZz6KSlpZGYmEhiYqKt6crX1xc/Pz88PDykM7IQJYgkNzmQ5CZ7aWlprFixgjlz5hAXFwdAs2bNGD58OGXKlLn78afTMH1hIm3HrW/RTqDtc6vTsUve++MoisL2tDS+NZk4civJcSS9T05/rZZASXIeWmfPpic6f/+dOdFp2DCBli1v0rRpHN7e/3VGzmi6SkhIwGq12joj+/r64uHhgbOzc1aXEkIUE5Lc5ECSm7uLj4/nm2++4ccffyQtLQ2NRkPv3r0ZOHBgruYXseyyYJphwnri1jdoN9D206LtqUVlyF+SszstjbmpqRy81VzlAHRydOQ5R0dCZAj5Q+3Mmf8Sndvn0FGpFGrXTqRFi1hatIi1G15utVpJTk4mISEBs9mMk5MTnp6eBAQE4OHhgaurq0wYKEQxI8lNDiS5yb1z587x+eefs2PHDgA8PDwYOHAg3bp1u/vQcUXBssFC6pxUrBHpSY7KW4V2gBbHZxxRafP3wbHfYuHb1FT23raadDONhn6OjoTKZIAPvbNn9Wzc6MHmzR52nZEBKlRIoWXLm7RoEUuVKim2CQMVRbElOiaTCb1ej4eHB/7+/nh6euLu7i5LQAhRDEhykwNJbvJu+/btTJ06lXPnzgFQqlQpXnzxRdq1a3fXN30lTcGyxoLpa5Nt1XGVvwptPy2OXRxR6fOX5BxKS+O71FQ2W/5rdqilVvOcVkszjQYH+db90IuKcmTz5vREZ/9+V9vyDwABASZbjU5oaKLdEhBGo5HExESSk5PRaDS4ubnZ5tFxd3eXDslCFBFJbnIgyU3+WCwWfvvtN77++mtu3LgBQKVKlRg6dChNmjS5axW+YlEw/2omdW4qyrVbSY63Cu1zt2pynPKXjJxLS2Ox2cwfZjPmW9vKqFT01Wrp6OgoC3QKAOLiHNi2zZ1NmzzYudMNo/G/pNzFxUKjRvE8/ngcTZrE4eHxX62g2Wy2dUhOL+uCj48PPj4+uLu74+LiIs1XQtwnktzkQJKbe2M0Gvnhhx9YsGCB7Q2/Tp06DB06lNDQ0Lser5gUzL+ZSV2YihJ1K8lxV+HY1xFtj/x1PAa4YbWyzGxmeWoqCbe2uatUPOPoSDdHRwKk87G4xWhUsWePGxs3erB1qzuxsY62fSqVwiOPJNGkSRyPPx5H5cr/NV9ZrVaSkpJITEzEbDaj1+txd3fH398fDw8P3N3d7zp9ghAi/yS5yYEkNwUjLi6OBQsWsGzZMlJT0ztqNmzYkMGDB/+/vTcPj6M687Z/tfSi7lZr323Jq4xsyyteIRgwYLMYJ4RA+JIAE0Imy0xmCQzhDRNgmAxvhjcwhCvLQFiGZMAkwUCCk4BtMBjjBbzgXbZsSbYsWfvW6rWqnu+P6ip1t7pbsnbJz31d56rqqurqqlJ19a3nPOec/klOKDxm1YsBUG34NnQB1i9bYbndAjFjYDLiJcJboRBeCQZRH769JQBXyjJut1iwUJL4P23GRFWBo0ed2L49DR99lIYTJ6K/u3l5Qaxc2YHPfa4DS5Z0ISWlp5m5z+eDx+OBz+eDJElmfzpG9ZXD4eB7jWGGEJabJLDcDC0NDQ349a9/jT/+8Y9Qw0m+FyQ5CkHZrCD4Qk/iMWyA5SYLrP+fFWLJwCRHIcJ2RcFroRA+jUg+LhVF3GaxYC1XWTFxaGiwYMcOXXT27EmNqr6yWjVcemkXVq7swPLlnSgpCZhRHUVRovrTcTgcZlTH7XbD7XbDYrEk+FSGYfoDy00SWG6Gh7q6Orz44ou9JOfee+/FwoUL+3w/aeHWVS8HoR0NS44AyKtkWL5qgTR/4BGXSlXFa6EQ/hwKIRBelgbgZosFt1itPFAnE5dAQMDevanYvj0NO3akoa4uOpG4oCCA5cs7sXx5J5Yu7TJ7SSYi+Hw+dHd3m1Edp9Np5uq43W7O1WGYAcBykwSWm+HFkJw//elPUMItmRYuXIi77rqrf4nHRFD3qwj+Jgh1e0/ERZwrwvpVK+SrZAjSwH4UOojwx1AIv4uosgKApZKEL1gsuFKWYeEfHCYORHoz848+SsPu3W7s3+9CKNQjxZJEmDOnGytWdGLFig6UlXlhNCRUFMXM1VEUBXa7HW632+wlOTU1lXtKZph+wHKTBJabkaG+vt6M5BiSM2PGDNx555247rrr+pV4qVarCP1vCKFNISDc/5pQKMB6qxWWmy0Q0gcmImq4ympjKISdqgrjS5AhCLhJlvEFqxXFHM1hkuDzidi714Vdu9zYuTMNNTX2qPVut4KlS/WozooVncjLC5nrjKbmPp8+IJvD4UB6ejpyc3ORmprKVVgMkwCWmySw3IwsjY2NePXVV/H666/D6/UCAPLz8/HVr34V69ev79d/rFqrhtDvQwj9LgTqCN+yNsCyxgLLbRZIlwy8g7V6TcOboRDeCoXQHPF1WBIRzbFyNIfpg/p6a1h03NizJxUeT7S8Fxf7sWRJF5Ys6cSll3aZzc2NnpK7u7sRCATMKqysrCxkZWUhNTUVqamp3Ikgw4DlJiksN6NDV1cX/vCHP+DVV19Fa2srACAtLQ233norbr31VuTk5PS5D/ITlHcVBF8LQqvoabUizhNhvc0KebUMwTIwEVGI8JGi4I1QCB9HRHPcANZYLLjRYsEcUeQ8CaZPFAU4csSJXbvc2LXLjSNHnNC06PumtNRrys7ChR44nVr4vXoVltfrRSgUgtVqhcPhMEc0T01NhcvlgsiRReYihOUmCSw3o4vf78fbb7+N3/72t6itrQUASJKEa6+9Fl/+8pcxd+7cPvdBRNAOaQj+LghliwKEOykWsgRYPm+BZb0FYuHAH/71moa3QiH8MRRCY8RXZKoo4kZZxg0WC49MzvSbri4J+/a58Omnqdizx41Tp6KjlUa+jiE75eXdsNn0+y4YDJqRHVVVYbVazZHNjXwdp9PJssNcFLDcJIHlZmygqiref/99vPrqq/jss8/M5eXl5fjyl7+M1atX9ysvR2vWEHozhNDrIVBT+HYWAGmZBMvnLZBXDTyaoxLhE1XF26EQ3lcUs6WVCGCZJOEmiwWrZJmblDMXREuLjE8/TcWnn6bik09SUVsbna9js2mYP9+DRYu6sHixB7Nn98hOIBAwZUfTNNhsNjidTpYd5qKA5SYJLDdjj2PHjuHVV1/Fu+++ayYf5+bm4tZbb8X69euRlZXV5z5IISjbFIQ2hqDu6WllJWQIkG+SYV1vhThl4A98DxG2hEJ4W1FwIKLfHBeAq2QZay0WXCpJPKYVc8HU11vxySepZmlujh6U1mrVMHduNxYt6sLChR7Mm9dtdibo9/vh9Xrh9XqjZCc7Oxvp6elwuVxwuVycs8NMCFhuksByM3Zpbm7Gxo0b8frrr6OlpQUAIMsyrrrqKnzxi1/E4sWL+5XzotVqCL0VQuhPIVBzzy0uLQxHc1bLAx6wEwBqNQ2bQiG8HQpFNSnPEgRcI8tYY7GgnPNzmAFABNTU2LBnj97cfN++VLS0RLeckiRCWVk3Fi3Sozvz53ebfez4/X6zjx0igsVigcPhQFZWFjIyMuByuZCamsrDRDDjEpabJLDcjH2CwSA2b96M3/3udzhy5Ii5vLi4GLfccgtuuukmpKen97kfUgjqDhXBN4NQd6iAkYPsBOSrZVhutEBaJEEQByYhGhEOqCreURRsURR0RHydCgUB11ksWCPLmMGiwwwQIuDMGZspOvv2uXD+fHRngoJAmDnTh0WLurBokQcLFniQmalHQAOBAHw+H7xeLxRFgcViQUpKCjIzM5GZmWlGdnikc2Y8wHKTBJab8UVFRQU2btyIv/zlL2ZTcqvVitWrV+OWW27BggUL+hfNadQQ+mM4mnOu57YX8gVYrrdAvlGGNGXgoXuFCLtVFX8NhfCBosAbsW6aKOI6WcbVsoxpXD3ADJL6eiv27XOZwnPmjL3XNpMm+TF/fjfmzfNg/nwPpk3zQxT1Uc69Xi98Ph+CwSBEUYTD4UBqaiqys7PN1lg8LhYzFmG5SQLLzfiku7sb77zzDjZu3Ijjx4+by4uLi7Fu3TrccMMNyMvL63M/RAT1MxXKJgWhzSHA07NOnC3CcoMF8hp5wAN3AoA/3Kz8HUXBDkUx+h8EAEwRRVwdFp1ZHNFhhoDmZhn79+tRnX37UnH6tB1E0feVy6WgvLwb8+frOTtz5nTD6dSgqip8Ph98Ph/8fj8AwG63w+FwRA0V4XQ6uWNBZtRhuUkCy8345+jRo3j99dfxzjvvmA9kQRCwbNky3HTTTbjyyitht/f+bzYWChCU7QpCm0JQP1YBI09YAqTlEizXWiBfKUNwDVxAPER4X1GwNRTCblVFKGJdkSDoohPuQ0dk0WGGgK4uCYcOOXHwoBMHD7pw6JATPl90xFAUCTNm+DB/vscUnoKCIAAy83a8Xi+ICLIsIyUlBenp6cjMzITT6YTL5UJKSgrLOTOisNwkgeVm4tDd3Y2tW7fi7bffxr59+8zlTqcT1113HdatW4fy8vL+VVu1alDe1UVHO9bTQSCsgLxChnytDPkKGYJjcKLzkaJgq6Lg44im5QCQKwi4SpZxlSxjgSRB5h8NZohQFKCyMgWffebCwYMuHDzoRH197xybnJwg5s7Vozpz53ajrMwLp1NDKBQyZceoyjKiO1lZWXC73XA6nXA6nbBarXGOgGGGBpabJLDcTExqa2uxadMmvP3226ivrzeXFxcXY82aNVizZg2mTJnSr32p1SqUdxUo7yrQqiNExwbIl4dF5/LBtbjyEeFjRcF7ioKPFAXdEetSAVwmy/icLGOlLCOVRYcZYhobLTh40InPPnPhs89cqKhwQFWj7zNRJEyd6o8SnmnTfBBFzexvx+fzQdM0M7qTmpqKrKwssyrL4XBwM3RmyGC5SQLLzcRG0zTs27cPb7/9NrZs2WJWWwHArFmzsGbNGlx33XXIz8/vc19EBK0yHNHZHALVRnxdUgD5ChnyVTLklYOL6ATCycjvhULYrqpRra4kAIskCZ+TZVwhy5jEnbMxw4DfL+DoUScOH3biyBF92tDQOwpjt6soK/OasjN3bjfy8kJQVcXM3QkE9Jik1Wo1q7MyMjJM2eFkZWagsNwkgeXm4qG7uxsffPAB3nnnHezatQtqROd7CxcuxJo1a7B69WpkZGT0uS8ignZcQ+jdEJQtCqg+4qtjDfeIfKUF0ioJYvrABUQlwiFVxYeqiu2KgipNi1o/TRTxOVnG5yQJc7n6ihlGmptlU3aM0t3dOwqTlRXCnDl6dGf2bC/KyrqRnq6azdD9fr9ZnWWz2ZCSkoKMjAykp6fD4XDA6XTCbrez8DB9wnKTBJabi5P29nZs2bIF7777blR+jiRJWLp0KVavXo1Vq1b1X3QOawi9F4LyvhId0REBaYGkR3SulCEWDC7SclbT8KGiYLuiYL+qQo1Y5wawTJaxQpaxQpKQw1EdZhjRNKCmxo4jRxym9Jw40bs6CwDy8wMoK/Pikkv0UlbmRUZGCH6/30xYVlUVgiCY+TsZGRlm/o7D4WDhYXrBcpMElhumoaEBmzdvxl//+teoZuWiKGLRokW4+uqrcdVVV/VvpHIiaKc0KO8rUN5XoJ2IjrSIl4iQr9RzdMRZg2v63RnO09keTkjuilk/UxSxQpaxUpIwX5Jg4R8GZpjx+wWcONEjO8eOOeL2uwMAeXnBsOh0RwhPsJfwRCYsG8JjVGdxC62LG5abJLDcMJFUV1dj69ateO+991BRUWEuFwQB5eXluPrqq7F69WoUFBT0a3/aOQ3KBwqUbQrUAxG9IgMQcgTIl8mQLpcgLx1cno5ChKOahp1h0TmqaYj8MjsAXBoWnRWyjCKO6jAjhMcjoqLCgWPHHDh+3IFjx5w4c8bWq+8dAMjNDZqiY0hPRkYgqkorUnjsdjsyMjKQlpZmyo7D4eCBQi8SWG6SwHLDJKK2thbvv/8+3nvvPRw6dChqXVlZGVatWoUrrrgCM2fO7H/z8g8VqNtVKHsUwBex0gJIiyW99dXlMsRJg3s4t2sadqkqdioKdqoqWmO+2pMEAUtkGUslCUskCen8Y8CMIN3dscLjQE1N784GASAzM4TSUi9mzvRh1iwvSkt9mDTJC0XRIzyBQACKokAQBFitVtjtdqSnp5vCY0gPdzo48WC5SQLLDdMfGhoaTNE5cOAAtIjE3vz8fHzuc5/DFVdcgcWLF/erbw8KENR9KpSPFCgfKVFDQACAOEXUIzorZEgLJAi2gUd1NCKc0DR8HBadgzG5OgBQKoq66MgyFkoSHBzqZ0aY7m4RJ07oomNIT02NHZrW+1602TRMn+7DzJk+lJbqwjNjhhcWi9es1gqF9C4yLRYL7HY7XC6XOTK68Vy22WxcrTWOYblJAssNc6G0trbigw8+wIcffog9e/aYTV0BwOFwYNmyZbjiiitw+eWX9z8huVqD+pEKZbsC9bOI3pEBwAZIiyTIy2RIyyWI0weXq+Mhwj5VxSeKgj2qilMxLbAkAOXhiM7ScCssztdhRgO/X0BlZQpOnHDg5MkUVFTo09gelg2KigKm7Myc6cWsWT5kZnoQCOgRnkAgACKKaqmVnp5u5vGkpKQgJSWFR0kfJ7DcJIHlhhkMfr8fn3zyCT788EN89NFHaGpqMtcZeTorV67EihUrUFZW1q9cAOoiKLsUKDsUqLtUUHP011LIFiAtlyAvlyEtlSBmDq5KqUXT8Imq6kVRUBfzGLADmCdJWBQucyQJNpYdZpTQNODcORsqKlJw8qQDJ07o8hOvHx4ASE1VMHOmD9On62XGDB9KSrphtXabwhMKhSCKIiwWC2w2mxnlcTqdpvDY7XbO5RljsNwkgeWGGSo0TUNFRQU+/PBDfPjhh1EJyQCQnp6OZcuWYcWKFVi+fDmys7P73KfR+krdrULZrUDdqyJqnAYAYqloio40X4KQMjjxqNU0M6rzqaqiLeaxYAEwNyw6CyUJ87gaixkDtLdLUbJz8mQKTp1Kids0HdCTl2fM6JGe6dN9KCrqBOAzpUfTtKjkZbfbjbS0tCjh4aqt0YPlJgksN8xw0dDQgI8++gi7du3Cnj170N3dHbW+tLQUK1aswIoVKzB//vx+JTxSQB/FXN2lQtnVu6k5ZECaI0G6NFzKpUENC6ER4bSmYb+qYl+4tMQ8JiQAl4iiHtkJj4XFQ0QwY4FQSMDp03acOqWLTmVlCk6dsuP8+d5jaQH6EBOTJgXMCM/06T5MndqN3NxOqGogKpdHlmWz1+W0tDSkpqaa0pOSksLjao0ALDdJYLlhRgJFUXDo0CHs3LkTO3fuxLFjx6LWOxwOLF68GMuWLcOll16K6dOn968FVosG9RNddNRPVFBDzFfYCkhzI2RnrgTBOnDxICKcJcK+cCeC+1QV9TGPDQHADFHEvHBUZ74koUgQ+L9bZszg8YgxwqNPOzri59pYLBqmTvWHZcePqVP9mDzZg+zsDmhaT9WWIAiwWCy9pMdut0dFepihgeUmCSw3zGjQ2tqK3bt3Y+fOndi1axdaW1uj1mdmZuLSSy/FkiVLsGTJEhQVFfUpB0QEOkdQPlWgfqpC/bR3vg5sgDRfgrRYgrRIgjR7cC2xAKA+MrKjKDgT5zGSKQim7MwTRZRx3g4zxiACWlpkU3oM4Tl92p4wgVmWNRQXB8LC48OUKX4UF3uQl9cBo3pLVVUQEaxWqyk9brfbjPQYVV5cvXXhsNwkgeWGGW00TcOJEyewa9cufPrpp9i/f39UCywAKCgowKWXXoqlS5fi0ksv7XdvyVRDUPaGZWevCmqN+YpbALFMhLxAb3IuzZMgpA/uAdusaTgYbnJ+UFVxTNMQitlGhl6VFRnd4eEimLGIpgH19VYzwlNVZUd1tV4SSY8gEAoLg5g2TReeqVN16SkoaIcsexEMBs1Ij1G9ZbPZzJweQ3iMwonM8WG5SQLLDTPWCAaDOHz4MD755BN8+umnOHToEBRFidpmypQpWLx4MRYuXIgFCxb0f1TzKs0UHfWACmrp/ZUXp4m66ISLUDC4KqUAEY7HCE9s3g4A5AsC5kgSZosi5kgSyiQJTv5PlhmjaBrQ0GBFVZU9oujy09mZuCl5Tk7QrNqaMsWPoqJuFBR0wu3uQigUMHN6jObqVqsVLpfLbK4eKT0Xe8eELDdJYLlhxjo+nw8HDhwwZefYsWOI/aoWFhZiwYIFWLRoERYsWICSkpJ+V2OpB1SzaNVar+2EXEGvypqvJyiLpSIEy+DyduqITNH5TFVRqWmI/WQBwFRRxJyw7MyWJMwURe5zhxnTEAGtrXKU7FRX23H6tB3NzYmTjG02DSUlfhQX+1FSEsCkSV4UFnYhL68DVqse7SEiM9pjs9nMFlxGXo+x7GKJ9rDcJIHlhhlvdHZ2Yt++fdi/fz/279+PiooKqGp0n8OZmZlYsGABFi5ciIULF2LmzJmQpPgh9Ei0Nk1vjWXIzjENvboztuoDgErleoKyVC5ByBtcdKebCMdUFUdUFUc0DUdVFefjPI4sAGaJImaH+9uZI0koFgSILDzMOKCrSzJFx6jaOnPGjtpaW8Im64A+BEVxsR/FxQGUlPhRWOhBQUEnsrI6AOjDTxARJEkyoz0Oh8McgsKQHpvNNqFye1huksByw4x3uru7cejQIVN2Dh8+jGAwGLWN0+lEeXk5ysvLMW/ePMydOxepqal97pv8BPVwWHYOqlCPqEBH7+2EbEGP6swVdeGZPfj+dpo1DUfDonMkXDrjbOcEMEuSMEsUcYkk4RJRRIkoQp4gD3Bm4qMoQF2dDTU1dtTU2HDmjB01NXacOWNDU1PiaI8oEgoLA6b0TJrkQ36+Bzk5HcjM9EBR/NA0rVduj1HNFZnMbEjReBIflpsksNwwE41gMIijR4+asvPZZ5/16mMHAKZNm4a5c+di3rx5KC8vx9SpU/sMZRMR6CxBPaTq0nNY1fvaiY3uSIA4XRcdcbYIabYEcZoIQR5cddY5IhwOi85RTcNxVY3t0xAAYIM+XtassOxcIkmYJoqwjqMHN8MA+phbZ8/azCiPIT01NXZ4vYmjsZJEKCoKYNKkACZPDqCw0Iv8/C7k5HQhM7MDQNCs3jaar1utVrjdbrhcrnEhPiw3SWC5YSY6qqri5MmTOHjwIA4dOoRDhw6htra213ZOpzNKdubOnduv7wT5CepxFdohTZeeI3H62wEAGyDOFCGVSZDKdOkRpwxOeBQiVGsajodF57im4YSqwhtnWxnA9IjozqxwDk/KGHtgM0x/MJquR0rP2bM21NbqJRhM/I+KKBLy84Nh8fGjoMCL/HwP8vK6kJnZDkmKLz4ulysqv8eo7rJaraOS48NykwSWG+ZipLW11RSdQ4cO4ciRI/D7/b22KykpwezZszF79myUlZXhkksugd1u73P/WoPWE9k5pkE9pgK9g0e68MwSIV2iV2WJlwxeeLRwR4PHVRXHVRUVYfGJV6UlAJgsCJgRFp2ZooiZkoQCzuNhxjGaBjQ2WlBba8PZs/bw1GZOEzVhN8jNjRafvLxu5OR0ITu7EzabF4CuCrIsm/LjcDiQmppq5vhEluEaiJTlJgksNwyj96BcWVkZJTxnz57ttZ0oipg2bZopPLNnz8aMGTP67GqeNALVEtSjqh7lOapBrUggPHZ9vCxplqSLT2m4SmsQw0gQEeqJUBGO7hhRnnhN0gE9j2d6WHRmiiJmiCJmSBJcLDzMOMeI+MQTnzNnbPB4kouI06miqCiAoqIACgr8pvjk5HQhI6MTkqR3WyGKIqxWKywWC9LS0rBgwYIhlxyWmySw3DBMfNra2nD06NGo0tLS0ms7WZZRWlqKsrIylJWVYc6cOZg6dWqfDzLSCHRGr9JSj6rQjmtQj6uIW6ckAWKJqEtPqd4cXSwVh2RE9EpNw0lNQ6Wq4qSm4XScTgcNCgUhWnhEEZM4eZmZIBABHR1SlPicOWNDXZ0N585ZkzZlB/TOC3NzQ6b45Of7kJ7eiqKiIL7xjXlITe076nshsNwkgeWGYfoHEaGpqSlKdo4dO4aOjt7Np6xWK6ZPn47S0lLMmjULpaWlKC0t7fO7QCpBO6vpkZ2TKrQKDdoJDdQe/9EkZAtRwiOVShAmCxCkweXxnNE0nDDEJ9wPT0OCx6MMoEQUMU0UMV0UMTU8ZelhJhp+v4D6el10amttOHeuR3zOnUte3dXc7EdWFsvNiMFywzADh4hQV1cXJTzHjx+P2zpLEARMnjzZlB1jmp2d3ednUBNBO6FBPaGaUzpLRtV/NHa9l2VxughpugRxhj4vZA+uL54OIjO6UxlOXK7SNPgSbG+BLj2G7EwLF5YeZiJCBLS3y73E58wZGR6PgIMHbf3K17sQWG6SwHLDMEOLpmmoq6tDRUUFKioqcOLECVRUVKCpqSnu9llZWZg1axZmzZqFmTNnYvr06SgpKem7WstL0CqjhUer1IDeedE6buiyM100izRdgpA2uOTlBiKcCldnnVZVnNa0fkmPITtTwmWyKPJgosyEw+v1wufz4YorrmC5GUmGW24sFsuQ7pdhxiutra2m6BjSU1NT02soCUBvfjplyhTMmDED06dPx4wZMzBjxgzk5eUljb6QGu6H55QK7ZTWU85o6DW+QxghR4iSHXG6CHGqCMExOOk5T6QLT4T0nNa0hO4lQM/pKQl3QlgSIT5ZwuCiTgwzWrDcjBLDJTeKomDv3r04f/48BEFARkYGR3AYJgafz4fKykpTeCorK3Hq1Cl4vfGyivW+eCJlx5hPS0tL+jkUIGg1PbKjntKjPFSf+JEn5AkQp+iiI04RzXkhc+CiEU96ajQN1ZqGriTvcwJRwlPC0R5mnMByM0oMl9wAeudpLS0tOHfuHM6fPw+/3w+32w23231RDGrGMANB0zTU19fj1KlTqKysNIWnurq61xhaBjk5OZgxYwamTp0aVfqUHk94pPTISE+lBmpN8ih0A+IUEdIUqUd8por66OkDTGQmIrQRmaITOT1HlCjoFBXtKQ7n8xSHpadAEDi3hxl1WG5GieGUm0g6OjrQ0NCA2tpadHZ2wmKxID09fcj/2AwzUQmFQqipqTFlxxCf+vr6hO/JzMzElClTeklPTk5O8uqtDoJWrUGt0kdK16o1aFUaqC5BEjOgDyhaHBHpKQmXySIE18AlI0iE2hjhqQ4XT5L3SdDFZ3JYdiJLIYsPM0Kw3IwSIyU3BsFgEM3NzTh37hyampoQCATMQcyGqxdHhpnIeDwenD59GpWVlaiqqjJLQ0NDwvc4nc640lNYWJh09HTyh5uqV4WLIT41GhBM+DYIWQLEySLEYhFCsaBLULEIcdLAOyckIrSGoz01moYzmobacDP2Wk2LO+aWgQSgQBDMaE+k+BSx+DBDCMvNKDHScmNAROjs7ERTUxNqa2vR0dEBQRDMQcs4eZBhBofX60V1dTWqqqpQXV2N06dPo6qqCufOnUtYvWW1WjFp0iSUlJSguLg4qmRmZib8XpJKoHqKivJoNRq0sxqoJfljVciLkJ3JEdGeIgGCZeC5PU1EOKtpeomc70N8RAD5goBCUURROMpTFJagQkFABic3MxcAy80oMVpyE0koFEJrayvOnz+PxsZGeDwec3RWTkJmmKElGAzi7NmzUdJTXV2NmpoaBAKJf/adTmcv6SkpKcHkyZPhcrkSvo884WjPmd4laRaxBAgFghnhEYvCkZ4iYdARn1jxMaI9Z5O05jJIAXTpCUd5isISVBQWIjuLDxMBy80oMRbkJhKfz4fW1lbU19ejubkZPp8PNpsNbrcbKSkpo314DDNhUVUV9fX1OHv2LGpqanDmzBmz1NfXx22ybpCVlWWKjiE+kyZNQlFRUcJ/UIgI1KEPQRFXfPqwDCFLiJKdSPkRsgYWXSEiNBPhXDiR+ZymoS48X6dpaCRKmHJkXgtBiJaecHJzgSgij6u8LjpYbkaJsSY3kXg8HrS2tqKurg5tbW3w+Xyw2+3myKsMw4wMgUAA586dw5kzZ3qJT7zxtiLJyspCUVGRKTuTJk0yS6KqLiICNVNP1dY5glarQTunQavtI+ID6L00x0R6xCK9CIUCBOvABCMQHoC0TtN0AYqQoHOaFncc1EhEADmCgPyw8OSLIvLD4mMIUArLz4SC5WaUGMtyY0BE8Hg8aGtrw/nz59Ha2gqfzwer1QqXywWn08l14AwzSng8HlN0DPE5e/Yszp07F3fcrUgcDkeU8ETO5+fnJ2xkQJ3RshMpP9RACTssNBCyBQiFAsQCEWKhCCFfgFgoQizQ5wdS5UVE6ATMaE+tpqEuLD71mobzRMlyrk3SBMEUnVjxyRdFpAH8vBtHsNyMEuNBbiIhInR3d6O9vR2NjY1obm6G1+uFIAhwuVxwuVzc6ophxghdXV2ora3tVc6dO4eGhoakVV2SJCE/Px9FRUUoLCxEQUFB1DQ7Oztuf1kUCic3J5CfhONCRCBkCXq+T0FYeMIiZCwTUi5cLrRw667zRDivaagnQn2E+NT30bTdwAGYEZ+8cFWXMc0NTzn6M3ZguRklxpvcxOLz+dDe3o6WlhY0NDTA4/FA0zQ4HA64XC7uR4dhxijBYBB1dXVRwhM5Hwwmj3NYLBYUFBT0kh5jmpWV1Ut+zDyfOoJWp/fQrNVr0Or1Pny0eg2I3zl0FEJGj/wIhQLEvHD0J0+EkCfo6wcgGB5DeMLTSAk6T4SWfv5EuQHkiSJyI4QnUoDyBYETn0cIlpsB8Mgjj+DRRx+NWjZr1iwcP3683/sY73ITSSgUQkdHh9lhYEdHB/x+PyRJMquvOKrDMGMfTdPQ3NyM2tpa1NXVoa6uDvX19ea0oaEhYXN2g0Tyk5+fj/z8fGRnZ/d6HhAR0AldeCLkxxAfrU5Dn4k1AGAFhFwBYr4uO4b0mBKUP7CODQPhyI8hPg1EaCRCQzjZuaEfeT8GkQJkTPNjhIgjQINnLMjNuPzVmzNnDrZs2WK+vph/vC0WC7Kzs5GdnY1p06bB4/Ggs7MTLS0taGpqMh+INpsNTqcTDoeDh4FgmDGIKIrIzc1Fbm4uFi1a1Gu9oihoamqKkp5ICWpoaEAoFDJzgeIhSRKys7ORl5eHvLw85Ofnm9P8/HzkL8pHWlparwgMdelRH60+LD91ep6Pdl6fUgsBQYBqCWptEgFzIlp68uJEgGJyf2yCgJLwcBOJ8MTITkN45PZGY17T4AXQCaBT03ASABKIohNATlh4sgUBOaKInPB8bng+SxBgZQka04xLK5BlGfn5+aN9GGMOQRCQmpqK1NRUFBUVIRQKoaury+w4sL29He3t7SAi2O12OBwOpKSksOwwzDhAlmUzKhMPRVHQ2NjYK+JjTBsbG6GqKhoaGpL25Gyz2XqJjzktyUPe0rxeLTcpRKBGgtYQlp4GDXQ++jU6AHQD2mkNOA2oiC8XQpoAIUfQo0A5IoRcAUK2ADFXNJcL6QIEsUcuXIIAlyRheoJzIiJ0AzgfIUCN4TygxrAINWgafPoholvTUJ3wCumkCwJyjBIhQIYY5YQ7P5RYgkaFcSk3J0+eRGFhIex2O1asWIHHH38cxcXFo31YYw6LxYLMzExzrB2/3x8lOx0dHWhrazNlJyUlBSkpKUm7omcYZmwiyzIKCwtRWFgYd72qqmhtbUVDQwPOnz+P8+fPm/OG8LS0tCAQCCSN/gCA2+1GXl6eGWnKycnpmc7IRc6KnF4RIPJRQvExBcirj/FFHQRUJhYgyOHWX7kCxOywAOX0CJApReEkaEEQ4AIwQ5IwI8E5GQLUrGloCld9NWkamsMdIEbOhwC0E6GdKGkUSITeB1CsAGUJArJEUZ+Gi4UlaEgZdzk3f/nLX+DxeDBr1izU19fj0Ucfxblz53D48GGkpqbGfU8gEIjqhbSzsxOTJ0+eEDk3g8Hn86GrqwtdXV1oampCZ2cnfD4fNE2D1WqFw+GAw+G4qKv9GOZiIhgMorGxsZf4RAqQx9Of9k16BCg7O7u3/ERMs7OzYbVaAYRzfzzQZacpHAlq0nqmTaSX1iQDmcbigi46kZGg7HAkKFvUW4hlX1gzeCJChyE8EeJjzBty1JJkZPd4pAG9hCfytSFFaYIAcYyL0FjIuRl3chNLe3s7SkpK8OSTT+Kee+6Ju028JGQAF73cxOL3++HxeODxeNDS0oL29nb4fD6EQiFIkmRGdux2O/c5wTAXKR6PxxSexsZGNDU1oampyZxvbGxEe3t7v/eXnp6eUICMfML09HQzokyK3tkhNRG0xh7piZpv6l8LMBMnomUnPBWzemRIyBYguKOrw5KhhpvBxwpQa1iAWsIC1EIE5QIOVQKQ2YcAGcscGJ3+gVhuhoglS5bgmmuuweOPPx53PUduBkYoFILH4zH72GlpaYHP50MgEAARwWq1mtVZxn9fDMMwwWAwSnoixSdyeSgU6tf+JElCRkYGsrOzkZWVZUpPvHmbzQYgPL5XU+8oEDUTtBZ9cFNqJiQdUbTXgaBHfrLC0Z94MpQpQLD1Tyq0cEeILTHC0xKuBotc1n6BP9c2ABmCgMxwyRAEZIpi72WCgPQhrBobC3Iz7usbPB4PTp06ha997WsJt7HZbOYNz/Qfi8WCjIwMZGRkYNKkSSAieL1edHd3o7u7G62trWhvb0dra6v5kLLb7WaxWCyjfAYMw4wGVqsVRUVFKCoqSrgNEaGjoyOu/BidlTY3N6OtrQ2qqpqv+yI1NdUUnSj5yctC9pweETJ/GLsBrVnTo0HNessvrblHfqglXNoJUKG3DmvQJSNhThAAuAAhU4CYKeqykxnuCyirZypm6NGiNCeQniQh2kAJR34M2YmNABlS1EIEL3RvOx9uSt8f3AAyRDFKemKnmYKADFFEKjCmq8fGXeTmvvvuw7p161BSUoK6ujo8/PDDOHDgAI4ePYqcnJx+7WMi9XMz2iiKgu7ubni9XnNcLI/HY1ZnCYIAm81mCg9HeBiGuRAURUFbWxuam5vR0tJiSk68+b46QYzEarUiKyvLbHSRrKSlpUFQBVBrYgGKfI3+BaR6sKCXAIkZEVIUWdIFCHLfUuELi1BbeNqqaeZ87LSdKJmmxUUCeolPenjeGQrBEQzi+5ddhtQhHhNxwkZuamtrcccdd6ClpQU5OTm4/PLLsWvXrn6LDTO0yLKMtLQ0pKWlmcuCwSC8Xq8Z5TGEx4jwRFZpGcLDzdEZhomHLMvIycnp8xlvjMeXTH6M+c7OTgSDQdTX16O+vr7PYxBFERkZGcjMzDSnZpkTLULp6emwBWzQ2jRdhuIUrVUDtYWTo7sBhKIjQn0hpMUIT0ZESdeLNV1AQbqAwnSxTxkyqsbaNC2u/JjzYUHqAqACaA6PKB8XiwX/3K+zGR7GXeRmKODIzcgTCoXg8/lM6eno6EB7e7uZD6VpGkRRhN1uN6sROcrDMMxwEAgE0NraaspOW1ubOW1tbY0qfQ2EGg+n04msrKxeImRU86enp5vTNHsapC5JF5+2cBSoLRwFaouQoja9XFATLINUmOIjpou6ABkiFCFExms4kicih+IIkDnVNLQoCryahp0rV3LODTOxsVgssFgsUTejpmnw+Xxm6erqMltoRebxSJJkCo/NZuNcHoZhBoXNZkvaIWIkiqKYDSoiJShWhoxlRlV9d3d30r6CInG5XKbsGCUjIwMZs2JEyJ2GNDENDr8DaEN0RKg9orSFpx3hZvNdei/TdIag9ceOLIgrPZHTzHQBWekChHRRjyRZe2TI6/XCdwFVhMMByw0zaoiiCKfTCafTGbXciPIYpbOz0+yDx+PxIBgMQhAESJIEq9VqRnmsVis3UWcYZkiRZdlMSu4Lo2osngAZ3WsYpa2tDR0dHdA0zeyC4+zZs/06JovFEiU9phCVxpEhOQ1uxQ25W+6RnrYEMtQWbj0Wgt6yrPECKnac4eqyNAFaqgbJKUFbqgGjNI4zyw0z5ogX5QH0ULLf74fP5zP75DGkp62tzcznEUXRlB2jcEeEDMMMN5FD4EyZMqXP7TVNQ2dnZ5TwxJtGzvv9foRCIbNJfX9xOBxmfmRaWhrcbrcuQEU9r9PS0pCWkgY33EjVUuEKuCB0CklliLrCVWXdAHXro88D+j+vkdGckYaf+My4waiWikxeBvRIj9/vN4vX60VnZyc8Hg+8Xi/a29uhqiqICLIsR0mPxWLh4SYYhhkVRFE0oy79xe/391uE2tra0NnZaXbj4fV6+5VAHXl8qampUVKUlpaGtIIeOXKnupFmTYNbcMNNbrhVN9AOqF1qvzs8HA44oZgTiicsmqaZ0R6/349AIGCGf7u7uxEKhRAMBqGGx4UxxMdisZhTjvgwDDOeUVUVHo8HHR0d/S6dnZ3wei+ki+dorFYrXC4XTp48iczMzCE8G04oZhiIomgOGRGLqqqm8BjFEB+jCXswGISiKBAEAYIgmNVlhvhYLBZuws4wzJhGkqRe3XX0h2AwaFaZdXZ2muIT+zq2KIpivjfes3ekYLlhLkokSYqbzAzo4hMMBqPExxhR3ZAeI/JjBD4FQYiSHpYfhmHGM1artd+J1AZG9ZcxwvxoNvBguWGYGCIHCY2FiMzqrEAgYE6Nllxerzeh/Miy3Et+uNqLYZiJgiAIcDqdyM/Pv+BI0VDDT1aGuQCMCI1RpxxLPPkJBoNmonN3dzcCgYApP4qimO+TJKmX+BiFYRiG6T/81GSYIaQv+QFg1kkbxZAhn89njtOlKIo5PpeR8AzoeURGBChSfiwWC/fxwzAME4blhmFGGENIHEkGlDOEJ3ZqRIB8Ph8CgYApQoqiILLhoxEFihQgo7AEMQwz0WG5YZgxiFE1lQwj8TkUCpnFeG307mzITyAQiCtBRiQoskiSxNVhDMOMa/jpxTDjlGSJz5EoihIlQJHF6PHZ5/OZeUKGBEVWhwmCYIqQIT+REiRJEkeEGIYZM7DcMMwExxCQviRI0zRTemKFyMgBMjpENPKFvF4vVFU1E6MNjNZhhvhECpFRWIYYhhkuWG6GkEDgHKzWfAgCd+fPjD9EUTSHuOgLQ4QMCTKiPcZ8ZP9Afr/flCMjIhQZFQJ6ZChSfmKFiPsMYhimv7DcDBFEhE8+mQ9N88LpnAOncy6cznJzqksP/6fKTAwuRIQAmPITWWKlKHKYjMgWZEZkSNO0qO9QpBCJohglQ8ZrjhAxzMUJy80QoSit0LRuaJofXV2foqvr06j1spwZITtz4XBcAodjFksPc1FwoQnKmqbFFaJYOTJkKDKx2u/3m9Gh2AgRgCjxMURIluVey/l7yTDjF5abIcJiycLnPueBz3cK3d2H0N19GB6PPvX5TkJRWtHR8QE6Oj6Iep8kueFwlCIlpRQOxyw4HLOQkjILDsdMSFLvoQEY5mJAFEWzv6D+ommaGeWJTIqOnY/sWNEYP8zoT0hVVXM/sWMKG0nVkVKUaJ6r0BhmdGG5GUIEQYLDUQqHoxQ5OV80l6uqH17vMXR3Hw6LzxF4vRXw+6ugqp1xIz0AYLNNQkpKKVJSpsNun4aUlGnmVJYz+D9LhonAkIq+mtDHEilFfU0je52+EDEyji9SfiKliOWIYYYWlpsRQJLsSE1diNTUhVHLNS0An+8UvN4KeL0V8PkqzHlFaUUgUItAoBbt7e/F2ac7SnZ6plNhsxVDkuwjdXoMM64ZqBQBvcUodj7ydSgUMvOJjJwiY3mkGGmaBk3Ten2WETmKJ0aRJXIdw1yssNyMIqJog9M5G07n7F7rQqGWsOicgN9fBb//NHy+0/D7qxAM1kNVO+HxHIDHcyDuvi2WHNhsxbDbJ8NmK4bNNhl2e8+UW3UxzOAZjBgBPblFkTKUqBhVarF9FcUKUqQkEVGvCG8iSRIEIaEscZSYGW+w3IxRLJYspKWtRFrayl7rVNULv7/alJ0e8TkNn68KmtaNUKgJoVATPJ69cfcvCDKs1qII+ZkEm60QVmsBrNZCc16SkveNwjDMwDFyiwZDrAQZcpNoeTxJiowuxQqSIUnxiBUlQ5Bip7HCxLLEDDcsN+MQSXIkjPgQERSlDYHAWfj9Z6KmgcAZ+P1nEQjUgkhBIFCDQKAm6WfJcnov4dGnkfMsQQwzWhi5OoMlVooiXyeaj2zSHylLsXIUW/ojS/FEKVaSYrdjGAOWmwmGIAiwWDJhsWTC5ZofdxsiFcHg+Sj5CQbPIRCoQzBYH57WQdN8UJR2KEo7vN5jST9XklJhseTCas2D1Zobns+FxRL5Wp/Xk6E5YZJhxhKDrWKLJDb6099poj6QIqUrGAyCiPotTADiilHssmTbsDiNP1huLkIEQYLNVgSbrQjAirjbEBFUtdMUnUCgPjzVBahnvg6a5oeqdkFVu+D3n+rHEUiwWnNixCcXFkt2uGRBlrNgsWSZr0VxcKF7hmFGDkMOhnLw1dho0IXMJ+svKV4VXKw09SVOkRKUTJCSLWOGFpYbJi56769pkOU0OJ1lCbfTq8E6EAo1IhhsjJg2RL0OBhsQCjVCUdoA6JGjYPA8urv7dzyS5ILFkh0hPVkxIpQdsVx/LYoO/o+LYSYIwyUBsRGgRNVpiZbH61cpsn+lRPIUKVHJ5AlILFCRy/ojUcZ2FwMsN8yg0KvB0mGxpMPhKO1ze00LIhRqNmWnR4AaEAq1hEszFKXFfA1oUFUPVNUDoPoCjs0CWU6HLGeYU4slI2JZRtR6fZ2xLI1bkzHMRcBwR04S5R1dSInXGWVk3lOiJPDYaV9RKKC3SCUSpMjrFitTsQPpjgYsN8yIIopW2Gx6cnJ/INLCkaFY6WlOIEP6cqIgiEJmq7GBIElpEdITKUR6REuS3BFTd69lkuS8aP5LYhgmPiNR7RQbBepLlvraJlm/TbHVfokkKjU1dVSr21humDGNIIiwWPSICzCjX+/R84W6oSht4YToNnM+FGrrc7mmeQEAqtoBVe3os0VZYkTIstuUH12WooUo2TJJSoUkucKSxHXyDMPEx2gxNlIdN8bLS4p9LQjCoLs5GAwsN8yEQ88XckGWXQAmX/D7NS0ARemAorSFpSdShNrC6zqhqp1QlI7wNHoeUAFoZmuzQGBw5ySKTkiSC7JsCI8rQn4i53uWJdtWFO0cVWIYZkCMtEwNBJYbholBFG2wWvUWXANB/y/GGyVAfcmQqnbEbN8RzjHSu+HXR5zvRijUMFRnGVeGdIlyQpIc4XkHJMkZMx89jZ53QBRTONLEMMyownLDMEOM/l+NMzyqe8GA96NLkj+cTN1lJlVHzitK/OWJ5z3hvWtQVV2mhgNRTBmAFEVum2IWSUqJ89oBURx8fywMw0xMWG4YZoyiS1JKuPfnnCHZJ5EGVfX2IUBeaFo3VLU7Yt4LVe2OmfeGt9HnNc1nfo6m+cKvm4fkuOMjJRCfZK8dF7Bt9PsEwcpVeQwzTmC5YZiLCEEQI/KR8od030QaNM0XI0UXJkg98z6zqKov6nUPakw0argRIIr2iGKLei0ItoTr+nrd3/cKgoUFi2H6AcsNwzBDgiCIEdVxw4NeVRdIKD+6SCUWo8SvvQnXGXlPAMURrJFGuGAxEgRreHnkvDX8Pmt4eeR87+2T74N/RpixB9+VDMOMG/SqOjskyQ4gY9g/T++zIxQhO35omh9EAXNeL8leR69L/t7e64gim9qRuW7sIMaRpQsVpHjCFbu9NWJqCc9bEi4TBIv5HkHggTUvNlhuGIZhEqD3xqr/eMpy2qgcg17dFxyQGOnvCYbnA+Z8z7JgeJ+R80FTqnrmI/cR26+BFpYtP1R1NK5Q/4gWnkjxiV0WLUwDkaneywbyeTJXQw4ClhuGYZgxjF7dZ0SrRh89mqUMWJDiyVb/9xEKR9KCZi/k+nzPVF/eu/t/fXkQmtbPAe3GDFJYliKL3GtZz2s5zrLReZ/NVjRqcsZywzAMw/QbPZplAWAZ1vyqwUCkgUiJEp54EtT/ZdHrBrIsUsoSLdM7/4xFhaapAMZSVWT/WLVKBcBywzAMwzCDRhBEs6pnPGFUQepipEREqkLmvLE8elkoLHPRy/TXSpxlQ72v3scKaKPamSfLDcMwDMOMAYwqSGBsVEGOZ7iPdIZhGIZhJhQsNwzDMAzDTChYbhiGYRiGmVCw3DAMwzAMM6FguWEYhmEYZkLBcsMwDMMwzISC5YZhGIZhmAkFyw3DMAzDMBMKlhuGYRiGYSYULDcMwzAMw0woWG4YhmEYhplQsNwwDMMwDDOhYLlhGIZhGGZCwXLDMAzDMMyEQh7tAxgNiAgA0NnZOcpHwjAMwzBMfzF+t43f8URclHLT1dUFAJg8efIoHwnDMAzDMBdKV1cX0tLSEq4XqC/9mYBomoa6ujqkpqZCEAQAug1OnjwZZ8+ehdvtHuUjHFvwtYkPX5fE8LWJD1+X+PB1SQxfm2iICF1dXSgsLIQoJs6suSgjN6IoYtKkSXHXud1uvoESwNcmPnxdEsPXJj58XeLD1yUxfG16SBaxMeCEYoZhGIZhJhQsNwzDMAzDTChYbsLYbDY8/PDDsNlso30oYw6+NvHh65IYvjbx4esSH74uieFrMzAuyoRihmEYhmEmLhy5YRiGYRhmQsFywzAMwzDMhILlhmEYhmGYCQXLDcMwDMMwE4oJLTc///nPMWXKFNjtdixbtgx79uxJuv3vf/97XHLJJbDb7SgvL8ef//znqPUbN27Eddddh6ysLAiCgAMHDgzj0Q8fQ3ldQqEQHnjgAZSXl8PpdKKwsBB33nkn6urqhvs0hoWhvmceeeQRXHLJJXA6ncjIyMA111yD3bt3D+cpDAtDfV0i+da3vgVBEPBf//VfQ3zUI8NQX5u7774bgiBElbVr1w7nKQwLw3HPHDt2DDfffDPS0tLgdDqxZMkSnDlzZrhOYVgY6usSe68Y5YknnhjO0xj70ARlw4YNZLVa6YUXXqAjR47QvffeS+np6dTQ0BB3+x07dpAkSfSf//mfdPToUXrooYfIYrHQoUOHzG1efvllevTRR+m5554jALR///4ROpuhY6ivS3t7O11zzTX02muv0fHjx2nnzp20dOlSWrx48Uie1pAwHPfM//7v/9LmzZvp1KlTdPjwYbrnnnvI7XZTY2PjSJ3WoBmO62KwceNGmj9/PhUWFtJTTz01zGcy9AzHtbnrrrto7dq1VF9fb5bW1taROqUhYTiuS2VlJWVmZtL9999P+/bto8rKSnrrrbcS7nMsMhzXJfI+qa+vpxdeeIEEQaBTp06N1GmNSSas3CxdupS++93vmq9VVaXCwkJ6/PHH425/22230Y033hi1bNmyZfS3f/u3vbatqqoat3IznNfFYM+ePQSAampqhuagR4iRuDYdHR0EgLZs2TI0Bz0CDNd1qa2tpaKiIjp8+DCVlJSMS7kZjmtz11130fr164fleEeK4bgut99+O331q18dngMeIUbiGbN+/Xq6+uqrh+aAxzETsloqGAxi7969uOaaa8xloijimmuuwc6dO+O+Z+fOnVHbA8CaNWsSbj8eGanr0tHRAUEQkJ6ePiTHPRKMxLUJBoN49tlnkZaWhvnz5w/dwQ8jw3VdNE3D1772Ndx///2YM2fO8Bz8MDOc98y2bduQm5uLWbNm4dvf/jZaWlqG/gSGieG4LpqmYdOmTSgtLcWaNWuQm5uLZcuW4c033xy28xhqRuIZ09DQgE2bNuGee+4ZugMfp0xIuWluboaqqsjLy4tanpeXh/Pnz8d9z/nz5y9o+/HISFwXv9+PBx54AHfccce4GuRtOK/N22+/DZfLBbvdjqeeegqbN29Gdnb20J7AMDFc1+UnP/kJZFnG9773vaE/6BFiuK7N2rVr8fLLL2Pr1q34yU9+gg8++ADXX389VFUd+pMYBobjujQ2NsLj8eD//t//i7Vr1+Ldd9/FF77wBdxyyy344IMPhudEhpiReP7+z//8D1JTU3HLLbcMzUGPYy7KUcGZ4SEUCuG2224DEeGXv/zlaB/OmOGqq67CgQMH0NzcjOeeew633XYbdu/ejdzc3NE+tFFh7969ePrpp7Fv3z4IgjDahzPm+PKXv2zOl5eXY968eZg+fTq2bduG1atXj+KRjR6apgEA1q9fj3/6p38CACxYsAAff/wxfvWrX2HVqlWjeXhjhhdeeAFf+cpXYLfbR/tQRp0JGbnJzs6GJEloaGiIWt7Q0ID8/Py478nPz7+g7ccjw3ldDLGpqanB5s2bx1XUBhjea+N0OjFjxgwsX74czz//PGRZxvPPPz+0JzBMDMd12b59OxobG1FcXAxZliHLMmpqavD9738fU6ZMGZbzGA5G6jkzbdo0ZGdno7KycvAHPQIMx3XJzs6GLMuYPXt21DZlZWXjprXUcN8v27dvR0VFBb7xjW8M3UGPYyak3FitVixevBhbt241l2mahq1bt2LFihVx37NixYqo7QFg8+bNCbcfjwzXdTHE5uTJk9iyZQuysrKG5wSGkZG8ZzRNQyAQGPxBjwDDcV2+9rWv4eDBgzhw4IBZCgsLcf/99+Odd94ZvpMZYkbqnqmtrUVLSwsKCgqG5sCHmeG4LlarFUuWLEFFRUXUNidOnEBJSckQn8HwMNz3y/PPP4/FixePm3y+YWe0M5qHiw0bNpDNZqOXXnqJjh49St/85jcpPT2dzp8/T0REX/va1+gHP/iBuf2OHTtIlmX6f//v/9GxY8fo4Ycf7tXkrqWlhfbv30+bNm0iALRhwwbav38/1dfXj/j5DZShvi7BYJBuvvlmmjRpEh04cCCqSWIgEBiVcxwoQ31tPB4PPfjgg7Rz506qrq6mTz/9lP7mb/6GbDYbHT58eFTOcSAMx3cplvHaWmqor01XVxfdd999tHPnTqqqqqItW7bQokWLaObMmeT3+0flHAfCcNwzGzduJIvFQs8++yydPHmSnnnmGZIkibZv3z7i5zdQhuu71NHRQQ6Hg375y1+O6PmMZSas3BARPfPMM1RcXExWq5WWLl1Ku3btMtetWrWK7rrrrqjtf/e731FpaSlZrVaaM2cObdq0KWr9iy++SAB6lYcffngEzmboGMrrYjSLj1fef//9ETqjoWMor43P56MvfOELVFhYSFarlQoKCujmm2+mPXv2jNTpDBlD/V2KZbzKDdHQXhuv10vXXXcd5eTkkMVioZKSErr33nvNH7/xxHDcM88//zzNmDGD7HY7zZ8/n958883hPo0hZziuy3//939TSkoKtbe3D/fhjxsEIqLRiRkxDMMwDMMMPRMy54ZhGIZhmIsXlhuGYRiGYSYULDcMwzAMw0woWG4YhmEYhplQsNwwDMMwDDOhYLlhGIZhGGZCwXLDMAzDMMyEguWGYS4Szp8/j2uvvRZOpxPp6emD3t+VV16Jf/zHfxz0NqNBS0sLcnNzUV1dPaT7FQQBb7755pDuc6KxfPlyvP7666N9GMwEh+WGYfrJ3XffDUEQ8K1vfavXuu9+97sQBAF33333yB9YP3nqqadQX1+PAwcO4MSJEwm3a21txT/+4z+ipKQEVqsVhYWF+PrXvz6gAQo3btyIxx57bDCHHcVQydKPf/xjrF+/PmqgzjfeeAPLly9HWloaUlNTMWfOnDEjZtu2bYMgCMjIyIDf749a98knn0AQhHEzwvpDDz2EH/zgB+ZI3wwzHLDcMMwFMHnyZGzYsAE+n89c5vf78corr6C4uHgUj6xvTp06hcWLF2PmzJnIzc2Nu01rayuWL1+OLVu24Fe/+hUqKyuxYcMGVFZWYsmSJTh9+vQFfWZmZiZSU1OH4vCHDK/Xi+effx733HOPuWzr1q24/fbb8cUvfhF79uzB3r178eMf/xihUGhEjy0YDCZdn5qaijfeeCNq2fPPPz/m771Irr/+enR1deEvf/nLaB8KM4FhuWGYC2DRokWYPHkyNm7caC7buHEjiouLsXDhwqht//rXv+Lyyy9Heno6srKycNNNN+HUqVPm+mAwiL/7u79DQUEB7HY7SkpK8PjjjwMAiAiPPPIIiouLYbPZUFhYiO9973tJj+2Xv/wlpk+fDqvVilmzZuE3v/mNuW7KlCl4/fXX8fLLLyeNMP3whz9EXV0dtmzZguuvvx7FxcW44oor8M4778BiseC73/1u1PaKouDv/u7vkJaWhuzsbPzrv/4rIkd0iY20BAIB3HfffSgqKoLT6cSyZcuwbdu2qH3u2LEDV155JRwOBzIyMrBmzRq0tbXh7rvvxgcffICnn37ajFRUV1ejra0NX/nKV5CTk4OUlBTMnDkTL774YsLr9Oc//xk2mw3Lly83l/3pT3/CZZddhvvvvx+zZs1CaWkpPv/5z+PnP/95v69xPB544AGUlpbC4XBg2rRp+Nd//dcoYXrkkUewYMEC/PrXv8bUqVNht9uT7u+uu+7CCy+8YL72+XzYsGED7rrrrqjtWlpacMcdd6CoqAgOhwPl5eV49dVXo7b5wx/+gPLycqSkpCArKwvXXHMNuru7AeiRoqVLl5pVmJdddhlqamrM97711ltYtGgR7HY7pk2bhkcffRSKogDo+96VJAk33HADNmzYkPRcGWZQjOrIVgwzjrjrrrto/fr19OSTT9Lq1avN5atXr6annnqK1q9fHzXo3R/+8Ad6/fXX6eTJk7R//35at24dlZeXk6qqRET0xBNP0OTJk+nDDz+k6upq2r59O73yyitERPT73/+e3G43/fnPf6aamhravXs3PfvsswmPzRgx+ec//zlVVFTQT3/6U5Ikid577z0iImpsbKS1a9fSbbfdRvX19XEH2FNVldLT0+mb3/xm3M/48Y9/TIIgUEtLCxHpg/y5XC76h3/4Bzp+/Dj99re/JYfDEXWcq1aton/4h38wX3/jG9+glStX0ocffkiVlZX0xBNPkM1moxMnThAR0f79+8lms9G3v/1tOnDgAB0+fJieeeYZampqovb2dlqxYgXde++95sjziqLQd7/7XVqwYAF98sknVFVVRZs3b6Y//vGPCa/V9773PVq7dm3Usscff5xycnKSjlze1zUmIgJAb7zxhvn6scceox07dlBVVRX98Y9/pLy8PPrJT35irn/44YfJ6XTS2rVrad++ffTZZ5/F/ez333+fAFBFRQXZbDaqqakhIqLf/OY3NH/+fHrjjTco8nFeW1tLTzzxBO3fv59OnTpFP/vZz0iSJNq9ezcREdXV1ZEsy/Tkk09SVVUVHTx4kH7+859TV1cXhUIhSktLo/vuu48qKyvp6NGj9NJLL5mf+eGHH5Lb7aaXXnqJTp06Re+++y5NmTKFHnnkESLq3737y1/+kkpKShJea4YZLCw3DNNPDLlpbGwkm81G1dXVVF1dTXa7nZqamnrJTSxNTU0EwPwB/fu//3u6+uqrSdO0Xtv+9Kc/pdLSUgoGg/06tpUrV9K9994btexLX/oS3XDDDebrvo7v/PnzBCDh6NwbN24kAOYP5KpVq6isrCzq+B944AEqKyszX0fKTU1NDUmSROfOnYva7+rVq+nBBx8kIqI77riDLrvssoTHGCtLRETr1q2jv/mbv0n4nljWr19PX//616OWeTweuuGGGwgAlZSU0O23307PP/88+f1+c5v+XONYuYnliSeeoMWLF5uvH374YbJYLNTY2Jj0mA25aWtro89//vP06KOPEhHRVVddRU8//XQvuYnHjTfeSN///veJiGjv3r0EgKqrq3tt19LSQgBo27ZtcfezevVq+o//+I+oZb/5zW+ooKCAiPp377711lskiqIp+gwz1HC1FMNcIDk5Objxxhvx0ksv4cUXX8SNN96I7OzsXtudPHkSd9xxB6ZNmwa3220mrxqJuXfffTcOHDiAWbNm4Xvf+x7effdd871f+tKX4PP5MG3aNNx777144403zLB/PI4dO4bLLrssatlll12GY8eOXfD5UUS1Ul8sX748KpF1xYoVOHnyJFRV7bXtoUOHoKoqSktL4XK5zPLBBx+Y1XUHDhzA6tWrL+h4v/3tb2PDhg1YsGAB/uVf/gUff/xx0u19Pl+v6h+n04lNmzahsrISDz30EFwuF77//e9j6dKl8Hq9AAZ2jV977TVcdtllyM/Ph8vlwkMPPdQrMbukpAQ5OTn9Pt+vf/3reOmll3D69Gns3LkTX/nKV3pto6oqHnvsMZSXlyMzMxMulwvvvPOO+dnz58/H6tWrUV5eji996Ut47rnn0NbWBkDPk7r77ruxZs0arFu3Dk8//TTq6+vNfX/22Wf4t3/7t6i/4b333ov6+np4vd5+3bspKSnQNA2BQKDf580wFwLLDcMMAOMH5n/+53/w9a9/Pe4269atQ2trK5577jns3r0bu3fvBtCTNLpo0SJUVVXhscceg8/nw2233YZbb70VgJ64XFFRgV/84hdISUnBd77zHVxxxRXDmuCak5OD9PT0hD/Wx44dgyAImDFjxoD27/F4IEkS9u7diwMHDpjl2LFjePrppwHoP3oXyvXXX4+amhr80z/9E+rq6rB69Wrcd999CbfPzs42f8hjmT59Or7xjW/g17/+Nfbt24ejR4/itddeu+BjAmCKxw033IC3334b+/fvxw9/+MNeScNOp/OC9nv99dfD5/Phnnvuwbp165CVldVrmyeeeAJPP/00HnjgAbz//vs4cOAA1qxZY362JEnYvHkz/vKXv2D27Nl45plnMGvWLFRVVQEAXnzxRezcuRMrV67Ea6+9htLSUuzatQuA/nd89NFHo/6Ghw4dwsmTJ2G32/t177a2tsLpdA7o780w/YHlhmEGwNq1axEMBhEKhbBmzZpe61taWlBRUYGHHnoIq1evRllZWdwfVLfbjdtvvx3PPfccXnvtNbz++utobW0FoP/Qr1u3Dj/72c+wbds27Ny5E4cOHYp7PGVlZdixY0fUsh07dmD27Nn9PidRFHHbbbfhlVdewfnz56PW+Xw+/OIXv8CaNWuQmZlpLjeEzWDXrl2YOXMmJEnqtf+FCxdCVVU0NjZixowZUSU/Px8AMG/ePGzdujXhMVqt1rhRoZycHNx111347W9/i//6r//Cs88+m3AfCxcuxNGjRxOuN5gyZQocDoeZZHuh1/jjjz9GSUkJfvjDH+LSSy/FzJkzo5JyB4osy7jzzjuxbdu2hGK9Y8cOrF+/Hl/96lcxf/58TJs2rVfzf0EQcNlll+HRRx/F/v37YbVao1piLVy4EA8++CA+/vhjzJ07F6+88goAXcorKip6/Q1nzJgBUdR/Uvq6dw8fPtwrAZ9hhhJ5tA+AYcYjkiSZEY54P+QZGRnIysrCs88+i4KCApw5cwY/+MEPorZ58sknUVBQgIULF0IURfz+979Hfn4+0tPT8dJLL0FVVSxbtgwOhwO//e1vkZKSgpKSkrjHc//99+O2227DwoULcc011+BPf/oTNm7ciC1btlzQef3Hf/wHtm7dimuvvRb/+Z//iblz56KqqgoPPfQQQqFQr9ZDZ86cwT//8z/jb//2b7Fv3z4888wz+OlPfxp336WlpfjKV76CO++8Ez/96U+xcOFCNDU1YevWrZg3bx5uvPFGPPjggygvL8d3vvMdfOtb34LVasX777+PL33pS8jOzsaUKVOwe/duVFdXw+VyITMzE4888ggWL16MOXPmIBAI4O2330ZZWVnCc1yzZg0efPBBtLW1ISMjA4Deasnr9eKGG25ASUkJ2tvb8bOf/QyhUAjXXnvtgK7xzJkzcebMGWzYsAFLlizBpk2bejXjHiiPPfYY7r///rhRG+Oz//CHP+Djjz9GRkYGnnzySTQ0NJgitnv3bmzduhXXXXcdcnNzsXv3bjQ1NaGsrAxVVVV49tlncfPNN6OwsBAVFRU4efIk7rzzTgDAj370I9x0000oLi7GrbfeClEU8dlnn+Hw4cP493//937du9u3b8d11103JNeCYeIy2kk/DDNeMBKKExGbsLt582YqKysjm81G8+bNo23btkUlnD777LO0YMECcjqd5Ha7afXq1bRv3z4iInrjjTdo2bJl5Ha7yel00vLly2nLli1Jj+8Xv/gFTZs2jSwWC5WWltLLL7+c9PgS0dTURH//939PkydPJovFQnl5eXT33XebrWUMVq1aRd/5znfoW9/6FrndbsrIyKD/83/+T1SCcWwCcDAYpB/96Ec0ZcoUslgsVFBQQF/4whfo4MGD5jbbtm2jlStXks1mo/T0dFqzZg21tbUREVFFRQUtX76cUlJSCABVVVXRY489RmVlZZSSkkKZmZm0fv16On36dNJzXLp0Kf3qV78yX7/33nv0xS9+kSZPnkxWq5Xy8vJo7dq1tH379gu6xohJKL7//vspKyuLXC4X3X777fTUU09RWlqauf7hhx+m+fPnJz1WouiE4njEJhS3tLTQ+vXryeVyUW5uLj300EN05513mvfv0aNHac2aNZSTk0M2m41KS0vpmWeeISI9sfzzn/88FRQUkNVqpZKSEvrRj34Ulfz717/+lVauXEkpKSnkdrtp6dKlZouovu7d2tpaslgsdPbs2T7Pm2EGikB0AdmDDMMwF8CKFSuwevVq/Pu///toH0oUmzZtwv3334/Dhw+bVSnMyPDAAw+gra0tadUhwwwW/lYzDDPkBAIBfPrppzhy5AjmzJkz2ofTixtvvBHf/OY3ce7cudE+lIuO3NzcIR2Sg2HiwZEbhmGGnDfffBN33nknbr75Zrz44ouwWCyjfUgMw1xEsNwwDMMwDDOh4GophmEYhmEmFCw3DMMwDMNMKFhuGIZhGIaZULDcMAzDMAwzoWC5YRiGYRhmQsFywzAMwzDMhILlhmEYhmGYCQXLDcMwDMMwEwqWG4ZhGIZhJhT/P+uX8JnZ2F1FAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#plotting different IMFs based on literature\n", + "plt.plot(BD_masses, power_law(BD_masses, M1_a), color = 'y', label = \"Mužić 2017\")\n", + "plt.plot(BD_masses, power_law(BD_masses, K_a), color = 'c', label = \"Kirkpatrick 2021\")\n", + "plt.plot(BD_masses, power_law(BD_masses, R_a), color = 'b', label = \"Ryan 2022\")\n", + "plt.plot(BD_masses, power_law(BD_masses, B_a), color = 'm', label = \"Best 2024\")\n", + "\n", + "#average our two fit parameters (one from power law, one from linear fit)\n", + "best_a = (avg_a + (-1*m)) / 2\n", + "\n", + "#finding upper and lower bounds using best_a\n", + "up_a = best_a + fit_err\n", + "down_a = best_a - fit_err\n", + "power_up = np.array(power_law(BD_masses, up_a))\n", + "power_down = power_law(BD_masses, down_a)\n", + "\n", + "#plotting our fit line and error margin\n", + "plt.plot(BD_masses, power_law(BD_masses, best_a), color = \"black\", label = \"fit for functions\")\n", + "plt.fill_between(BD_masses, power_up, power_down, color = \"black\", alpha = 0.2, label = \"fit error\")\n", + "\n", + "#organizing our graph\n", + "plt.title(\"Final Power-Law Curve Fit for Brown Dwarf Mass Objects\")\n", + "plt.xlabel(\"Mass of Objects (Solar Masses)\")\n", + "plt.ylabel(\"$M^{0.56 ± 0.16}$\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "id": "a0e7f65f-d511-4840-937f-4fd2c57a2bd7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.5643248]\n" + ] + } + ], + "source": [ + "print(best_a)" + ] + }, + { + "cell_type": "markdown", + "id": "706598df-cec8-495d-9fbc-cfd29c9193d3", + "metadata": {}, + "source": [ + "### Conclusions" + ] + }, + { + "cell_type": "markdown", + "id": "40494bed-857e-4527-b10b-d72856d034b2", + "metadata": {}, + "source": [ + "From this process, we have determined that the best IMF model for brown-dwarf mass objects is given by a power law, $M^{-\\alpha}$, where ${\\alpha} = 0.56 ± 0.16$. This fits within our expected output because, in average, brown dwarf mass objects have been represented with $\\alpha$ values between 0.5-1." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7df524b5-524e-49f3-a183-c547afd36419", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/changes/Exoplanet_IMF.ipynb b/changes/Exoplanet_IMF.ipynb new file mode 100644 index 00000000..0bd50ba4 --- /dev/null +++ b/changes/Exoplanet_IMF.ipynb @@ -0,0 +1,608 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "23642516", + "metadata": {}, + "source": [ + "## Plotting Studied Power-Law Functions For Exoplanets" + ] + }, + { + "cell_type": "markdown", + "id": "ad57fd40", + "metadata": {}, + "source": [ + "#### Importing Packages" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "id": "d6503a21", + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from scipy.optimize import curve_fit" + ] + }, + { + "cell_type": "markdown", + "id": "4f72f6f7", + "metadata": {}, + "source": [ + "#### Creating the general power-law function for small masses" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "d51b38dc", + "metadata": {}, + "outputs": [], + "source": [ + "#define function\n", + "def power_law(M, a):\n", + " return M**(-1*a)\n", + "\n", + "# M is a defined mass range according to a specified paper, and a is the associated alpha value" + ] + }, + { + "cell_type": "markdown", + "id": "3fe49d7b", + "metadata": {}, + "source": [ + "#### Defining different mass/alpha values based on published papers" + ] + }, + { + "cell_type": "markdown", + "id": "b7736fad", + "metadata": {}, + "source": [ + "***Masses are in solar masses!***" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "4145bc16", + "metadata": {}, + "outputs": [], + "source": [ + "#Moraux 2007 (0.03 - 0.6) a = 0.69 ± 0.15\n", + "M_mass = np.linspace(0.03, 0.6, 1000)\n", + "M_a = 0.69\n", + "M_aerr = 0.15\n", + "\n", + "#Suárez 2009 (0.02 - 0.50) a = 0.60 ± 0.13\n", + "S_mass = np.linspace(0.02, 0.5, 1000)\n", + "S_a = 0.60\n", + "S_aerr = 0.13\n", + "\n", + "#Lodieu 2009 (0.01 - 0.5) a = 0.5 ± 0.2\n", + "L_mass = np.linspace(0.01, 0.5, 1000)\n", + "L_a = 0.5\n", + "L_aerr = 0.2\n", + "\n", + "#Béjar 2011 (0.013 - 0.1) a = 0.7 ± 0.3\n", + "B_mass = np.linspace(0.013, 0.1, 1000)\n", + "B_a = 0.7\n", + "B_aerr = 0.3\n", + "\n", + "#Peña Ramírez 2012 (0.006 - 0.25) a = 0.6 ± 0.2\n", + "P_mass = np.linspace(0.006, 0.25, 1000)\n", + "P_a = 0.6\n", + "P_aerr = 0.2" + ] + }, + { + "cell_type": "markdown", + "id": "f2a24e63", + "metadata": {}, + "source": [ + "#### Plotting all of the curves together (w/o accounting for error)" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "60cab6f2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#plot all of the power law functions based on mass ranges\n", + "plt.plot(M_mass, power_law(M_mass, M_a), color='r', label='Moraux (a=0.69)')\n", + "plt.plot(S_mass, power_law(S_mass, S_a), color='b', label='Suárez (a=0.60)')\n", + "plt.plot(L_mass, power_law(L_mass, L_a), color='m', label='Lodieu (a=0.50)')\n", + "plt.plot(B_mass, power_law(B_mass, B_a), color='c', label='Béjar (a=0.70)')\n", + "plt.plot(P_mass, power_law(P_mass, P_a), color='y', label='Peña Ramírez (a=0.60)')\n", + "plt.title(\"Power Law Mass Functions for Planetary Masses According to Published Papers\")\n", + "plt.xlabel(\"Mass of Objects (Solar Masses)\")\n", + "plt.ylabel(\"M^(-a)\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "f5494d3d", + "metadata": {}, + "source": [ + "#### Accounting for error in a" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "id": "1e6c80f4", + "metadata": {}, + "outputs": [], + "source": [ + "#Moraux\n", + "M_aup = M_a + M_aerr\n", + "M_alow = M_a - M_aerr\n", + "M_outup = power_law(M_mass, M_aup)\n", + "M_outlow = power_law(M_mass, M_alow)\n", + "\n", + "#Suárez\n", + "S_aup = S_a + S_aerr\n", + "S_alow = S_a - S_aerr\n", + "S_outup = power_law(S_mass, S_aup)\n", + "S_outlow = power_law(S_mass, S_alow)\n", + "\n", + "#Lodieu\n", + "L_aup = L_a + L_aerr\n", + "L_alow = L_a - L_aerr\n", + "L_outup = power_law(L_mass, L_aup)\n", + "L_outlow = power_law(L_mass, L_alow)\n", + "\n", + "#Béjar\n", + "B_aup = B_a + B_aerr\n", + "B_alow = B_a - B_aerr\n", + "B_outup = power_law(B_mass, B_aup)\n", + "B_outlow = power_law(B_mass, B_alow)\n", + "\n", + "#Peña Ramírez\n", + "P_aup = P_a + P_aerr\n", + "P_alow = P_a - P_aerr\n", + "P_outup = power_law(P_mass, P_aup)\n", + "P_outlow = power_law(P_mass, P_alow)" + ] + }, + { + "cell_type": "markdown", + "id": "041954f2", + "metadata": {}, + "source": [ + "#### Graphing Individual Power-Law Functions (Accounting for Error in a)" + ] + }, + { + "cell_type": "code", + "execution_count": 128, + "id": "dc7a858e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Setting up subplots\n", + "fig, ax = plt.subplots(nrows=3, ncols=2, figsize=(10,10))\n", + "plt.subplots_adjust(hspace=0.75, wspace=1.25)\n", + "fig.delaxes(ax[2, 1])\n", + "\n", + "#Moraux\n", + "ax[0,0].plot(M_mass, power_law(M_mass, M_a), color='r')\n", + "ax[0,0].fill_between(M_mass, M_outup, M_outlow, color='r', alpha=0.2, label=\"error in a\")\n", + "ax[0,0].set_title(\"Moraux Mass Function for Planetary Masses in Blanco 1\")\n", + "ax[0,0].set_xlabel(\"Mass of Objects (Solar Masses)\")\n", + "ax[0,0].set_ylabel(\"M^(-0.69 ± 0.15)\")\n", + "ax[0,0].legend()\n", + "\n", + "#Suárez\n", + "ax[0,1].plot(S_mass, power_law(S_mass, S_a), color='b')\n", + "ax[0,1].fill_between(S_mass, S_outup, S_outlow, color='b', alpha=0.2, label=\"error in a\")\n", + "ax[0,1].set_title(\"Suárez Mass Function for Planetary Masses in 25 Ori Group\")\n", + "ax[0,1].set_xlabel(\"Mass of Objects (Solar Masses)\")\n", + "ax[0,1].set_ylabel(\"M^(-0.60 ± 0.13)\")\n", + "ax[0,1].legend()\n", + "\n", + "#Lodieu\n", + "ax[1,0].plot(L_mass, power_law(L_mass, L_a), color='m')\n", + "ax[1,0].fill_between(L_mass, L_outup, L_outlow, color='b', alpha=0.2, label=\"error in a\")\n", + "ax[1,0].set_title(\"Lodieu Mass Function for Planetary Masses in UKIDSS Galactic Clusters\")\n", + "ax[1,0].set_xlabel(\"Mass of Objects (Solar Masses)\")\n", + "ax[1,0].set_ylabel(\"M^(-0.5 ± 0.2)\")\n", + "ax[1,0].legend()\n", + "\n", + "#Béjar\n", + "ax[1,1].plot(B_mass, power_law(B_mass, B_a), color='c')\n", + "ax[1,1].fill_between(B_mass, B_outup, B_outlow, color='c', alpha=0.2, label=\"error in a\")\n", + "ax[1,1].set_title(\"Béjar Mass Function for Planetary Masses in σ Orionis\")\n", + "ax[1,1].set_xlabel(\"Mass of Objects (Solar Masses)\")\n", + "ax[1,1].set_ylabel(\"M^(-0.7 ± 0.3)\")\n", + "ax[1,1].legend()\n", + "\n", + "#Peña Ramírez\n", + "ax[2,0].plot(P_mass, power_law(P_mass, P_a), color='y')\n", + "ax[2,0].fill_between(P_mass, P_outup, P_outlow, color='y', alpha=0.2, label=\"error in a\")\n", + "ax[2,0].set_title(\"Peña Ramírez Mass Function for Planetary Masses in σ Orionis\")\n", + "ax[2,0].set_xlabel(\"Mass of Objects (Solar Masses)\")\n", + "ax[2,0].set_ylabel(\"M^(-0.6 ± 0.2)\")\n", + "ax[2,0].legend()\n", + "\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "f63bb9fc", + "metadata": {}, + "source": [ + "### Creating a General Power-Law Curve Fit" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "id": "ed848735", + "metadata": {}, + "outputs": [], + "source": [ + "#combine all mass data\n", + "all_masses = []\n", + "for a in M_mass:\n", + " all_masses.append(a)\n", + "for b in S_mass:\n", + " all_masses.append(b)\n", + "for c in L_mass:\n", + " all_masses.append(c)\n", + "for d in B_mass:\n", + " all_masses.append(d)\n", + "for e in P_mass:\n", + " all_masses.append(e)" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "id": "df52ba0f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5000\n" + ] + } + ], + "source": [ + "print(len(all_masses)) #to make sure the correct amount of entries were appended" + ] + }, + { + "cell_type": "code", + "execution_count": 96, + "id": "dfc306a1", + "metadata": {}, + "outputs": [], + "source": [ + "#combine all power_law output data\n", + "all_power = []\n", + "for f in M_mass:\n", + " all_power.append(power_law(f, M_a))\n", + "for g in S_mass:\n", + " all_power.append(power_law(g, S_a))\n", + "for h in L_mass:\n", + " all_power.append(power_law(h, L_a))\n", + "for k in B_mass:\n", + " all_power.append(power_law(k, B_a))\n", + "for l in P_mass:\n", + " all_power.append(power_law(l, P_a))" + ] + }, + { + "cell_type": "code", + "execution_count": 97, + "id": "15d0484d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5000\n" + ] + } + ], + "source": [ + "print(len(all_power))" + ] + }, + { + "cell_type": "code", + "execution_count": 109, + "id": "6a6629e9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#use scipy curve fit to create a general power law\n", + "popt, pcov = curve_fit(power_law, all_masses, all_power) #popt gives fit value for a\n", + "avg_a = popt\n", + "\n", + "#create an array with mass values using fitted a\n", + "avg_power = power_law(all_masses, avg_a)\n", + "\n", + "#plot combined mass and power law datasets\n", + "plt.figure()\n", + "plt.scatter(all_masses, all_power)\n", + "plt.plot(all_masses, avg_power, color='r')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 108, + "id": "3739e5d8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.64439915]\n" + ] + } + ], + "source": [ + "print(popt)" + ] + }, + { + "cell_type": "markdown", + "id": "109097ab", + "metadata": {}, + "source": [ + "#### Cleaning Up the Curve Fit" + ] + }, + { + "cell_type": "code", + "execution_count": 111, + "id": "7475e6d3", + "metadata": {}, + "outputs": [], + "source": [ + "#combining all mass and output data sets to fit\n", + "all_masses = np.array(all_masses)\n", + "all_power = np.array(all_power)\n", + "\n", + "#put combined mass data set into increasing order and reorder output array to match new indices \n", + "sorted_indices = np.argsort(all_masses)\n", + "sorted_masses = all_masses[sorted_indices]\n", + "sorted_powers = all_power[sorted_indices]" + ] + }, + { + "cell_type": "code", + "execution_count": 154, + "id": "acc33225", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#use scipy curve fit to create a general power law\n", + "popt, pcov = curve_fit(power_law, sorted_masses, sorted_powers,sigma=sorted_errors, absolute_sigma=True) #popt gives fit value for a\n", + "avg_a = popt\n", + "avg_aerr = np.sqrt(np.diag(pcov)) #gives the error in a\n", + "\n", + "#create an array with mass values using fitted a\n", + "avg_power = power_law(sorted_masses, avg_a)\n", + "\n", + "#plot combined mass and power law datasets\n", + "plt.figure()\n", + "plt.scatter(sorted_masses, sorted_powers, label='raw data')\n", + "plt.plot(sorted_masses, avg_power, color='r', label='curve fit')\n", + "plt.title(\"Power Law Curve Fit for 0.006 - 0.6 Solar Mass Objects\")\n", + "plt.xlabel(\"Mass of Objects (Solar Masses)\")\n", + "plt.ylabel(\"M^(-a)\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "bd3e02dd", + "metadata": {}, + "source": [ + "Based on the curve fit, our a value for the entire mass range is 0.60524093 ± 0.00211972" + ] + }, + { + "cell_type": "code", + "execution_count": 155, + "id": "0e0bc7ca", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.00211972]\n" + ] + } + ], + "source": [ + "print(avg_aerr)" + ] + }, + { + "cell_type": "code", + "execution_count": 156, + "id": "7037fa8c", + "metadata": {}, + "outputs": [], + "source": [ + "#calculate the low and high outputs based on error of a\n", + "avg_aup = avg_a + avg_aerr\n", + "avg_alow = avg_a - avg_aerr\n", + "avg_outup = power_law(sorted_masses, avg_aup)\n", + "avg_outlow = power_law(sorted_masses, avg_alow)" + ] + }, + { + "cell_type": "code", + "execution_count": 157, + "id": "1cb19a53", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#fit plot including error\n", + "plt.figure()\n", + "plt.scatter(sorted_masses, sorted_powers, color='k', label='data created from all papers')\n", + "plt.plot(sorted_masses, avg_power, color='c', label='calculated curve fit')\n", + "plt.fill_between(sorted_masses, avg_outup, avg_outlow, color='c', alpha=0.2, label=\"error in a\")\n", + "plt.title(\"Power Law Curve Fit for 0.006 - 0.6 Solar Mass Objects\")\n", + "plt.xlabel(\"Mass of Objects (Solar Masses)\")\n", + "plt.ylabel(\"M^(-0.605 ± 0.002)\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 144, + "id": "cf3ff96a", + "metadata": {}, + "outputs": [], + "source": [ + "#create an error array for all values in sorted_masses\n", + "power_errors = []\n", + "for m in M_mass:\n", + " power_errors.append(power_law(m, M_a) - power_law(m, M_alow))\n", + "for n in S_mass:\n", + " power_errors.append(power_law(n, S_a) - power_law(n, S_alow))\n", + "for o in L_mass:\n", + " power_errors.append(power_law(o, L_a) - power_law(o, L_alow))\n", + "for p in B_mass:\n", + " power_errors.append(power_law(p, B_a) - power_law(p, B_alow))\n", + "for q in P_mass:\n", + " power_errors.append(power_law(q, P_a) - power_law(q, P_alow))\n", + "\n", + "#sort errors based on sorted indices\n", + "\n", + "# convert sorted_indices to a NumPy array for indexing\n", + "sorted_indices = np.array(sorted_indices)\n", + "\n", + "# Sort errors based on sorted indices\n", + "sorted_errors = [power_errors[i] for i in sorted_indices]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "30d890fa", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c0206cbc", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/changes/Test_BD_Cluster.ipynb b/changes/Test_BD_Cluster.ipynb new file mode 100644 index 00000000..d5a5da69 --- /dev/null +++ b/changes/Test_BD_Cluster.ipynb @@ -0,0 +1,1326 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "4257f594-b092-40bc-85cf-2397fe17724c", + "metadata": {}, + "source": [ + "# SPISEA: Making a Cluster with BD Candidates" + ] + }, + { + "cell_type": "markdown", + "id": "08de775e-f1bb-464b-8148-48b51e6d8822", + "metadata": {}, + "source": [ + "This is a document to generate a synthetic cluster in SPISEA with the addition of brown dwarf candidates. It will follow the Quick Start Guide closely, but with changes due to a lower mass limit and ability to consider smaller objects." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "b7536665-00cf-49ad-9028-930f56cf3204", + "metadata": {}, + "outputs": [], + "source": [ + "# Import necessary packages. \n", + "from spisea import synthetic, evolution, atmospheres, reddening, ifmr\n", + "from spisea.imf import imf, multiplicity\n", + "import numpy as np\n", + "import pylab as py\n", + "import pdb\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "id": "60ee38e8-ba5c-4c23-b9a2-22773bd91a62", + "metadata": {}, + "source": [ + "### 1: Making an Isochrone Object for our Cluster" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "0cd4c0a3-39e8-4bbf-9eba-e1883b6dacec", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Changing to logg=4.00 for T= 32651 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logg=5.90\n", + "Changing to logg=5.00 for T= 42286 logg=5.90\n", + "Changing to logg=5.00 for T= 42345 logg=5.91\n", + "Changing to logg=5.00 for T= 42394 logg=5.92\n", + "Changing to logg=5.00 for T= 42462 logg=5.92\n", + "Changing to logg=5.00 for T= 42530 logg=5.92\n", + "Changing to logg=5.00 for T= 42619 logg=5.92\n", + "Changing to logg=5.00 for T= 42717 logg=5.93\n", + "Changing to logg=5.00 for T= 42825 logg=5.93\n", + "Changing to logg=5.00 for T= 42934 logg=5.94\n", + "Changing to logg=5.00 for T= 43053 logg=5.94\n", + "Changing to logg=5.00 for T= 43152 logg=5.94\n", + "Changing to logg=5.00 for T= 43271 logg=5.95\n", + "Changing to logg=5.00 for T= 43411 logg=5.95\n", + "Changing to logg=5.00 for T= 43561 logg=5.96\n", + "Changing to logg=5.00 for T= 43692 logg=5.96\n", + "Changing to logg=5.00 for T= 43833 logg=5.96\n", + "Changing to logg=5.00 for T= 43985 logg=5.97\n", + "Changing to logg=5.00 for T= 44147 logg=5.97\n", + "Changing to logg=5.00 for T= 44310 logg=5.97\n", + "Changing to logg=5.00 for T= 44484 logg=5.97\n", + "Changing to logg=5.00 for T= 44638 logg=5.97\n", + "Changing to logg=5.00 for T= 44802 logg=5.98\n", + "Changing to logg=5.00 for T= 44957 logg=5.98\n", + "Changing to logg=5.00 for T= 45144 logg=5.98\n", + "Changing to logg=5.00 for T= 45300 logg=5.99\n", + "Changing to logg=5.00 for T= 45478 logg=5.99\n", + "Changing to logg=5.00 for T= 45509 logg=5.99\n", + "Changing to logg=5.00 for T= 45646 logg=5.99\n", + "Changing to logg=5.00 for T= 45825 logg=5.99\n", + "Changing to logg=5.00 for T= 45983 logg=6.00\n", + "Changing to logg=5.00 for T= 46142 logg=6.00\n", + "Changing to logg=5.00 for T= 46313 logg=6.00\n", + "Changing to logg=5.00 for T= 46473 logg=6.00\n", + "Changing to logg=5.00 for T= 46623 logg=6.00\n", + "Changing to logg=5.00 for T= 46784 logg=6.00\n", + "Changing to logg=5.00 for T= 46946 logg=6.00\n", + "Changing to logg=5.00 for T= 47109 logg=6.00\n", + "Changing to logg=5.00 for T= 47261 logg=6.00\n", + "Changing to logg=5.00 for T= 47413 logg=6.01\n", + "Changing to logg=5.00 for T= 47566 logg=6.01\n", + "Changing to logg=5.00 for T= 47720 logg=6.01\n", + "Changing to logg=5.00 for T= 47863 logg=6.01\n", + "Changing to logg=5.00 for T= 48029 logg=6.01\n", + "Changing to logg=5.00 for T= 48173 logg=6.01\n", + "Changing to logg=5.00 for T= 48317 logg=6.02\n", + "Changing to logg=5.00 for T= 48473 logg=6.02\n", + "Changing to logg=5.00 for T= 48618 logg=6.02\n", + "Changing to logg=5.00 for T= 48753 logg=6.02\n", + "Changing to logg=5.00 for T= 48910 logg=6.02\n", + "Changing to logg=5.00 for T= 49057 logg=6.02\n", + "Changing to logg=5.00 for T= 49193 logg=6.02\n", + "Changing to logg=5.00 for T= 49329 logg=6.03\n", + "Changing to logg=5.00 for T= 49431 logg=6.03\n", + "Changing to logg=5.00 for T= 49465 logg=6.03\n", + "Changing to logg=5.00 for T= 49614 logg=6.03\n", + "Changing to logg=5.00 for T= 49751 logg=6.03\n", + "Changing to logg=5.00 for T= 49888 logg=6.03\n", + "Changing to T= 50000 for T= 50026 logg=6.03\n", + "Changing to logg=5.00 for T= 50026 logg=6.03\n", + "Changing to T= 50000 for T= 50176 logg=6.03\n", + "Changing to logg=5.00 for T= 50176 logg=6.03\n", + "Changing to T= 50000 for T= 50304 logg=6.03\n", + "Changing to logg=5.00 for T= 50304 logg=6.03\n", + "Changing to T= 50000 for T= 50431 logg=6.04\n", + "Changing to logg=5.00 for T= 50431 logg=6.04\n", + "Changing to T= 50000 for T= 50559 logg=6.04\n", + "Changing to logg=5.00 for T= 50559 logg=6.04\n", + "Changing to T= 50000 for T= 50699 logg=6.04\n", + "Changing to logg=5.00 for T= 50699 logg=6.04\n", + "Changing to T= 50000 for T= 50839 logg=6.04\n", + "Changing to logg=5.00 for T= 50839 logg=6.04\n", + "Changing to T= 50000 for T= 50957 logg=6.04\n", + "Changing to logg=5.00 for T= 50957 logg=6.04\n", + "Changing to T= 50000 for T= 51086 logg=6.04\n", + "Changing to logg=5.00 for T= 51086 logg=6.04\n", + "Changing to T= 50000 for T= 51215 logg=6.04\n", + "Changing to logg=5.00 for T= 51215 logg=6.04\n", + "Changing to T= 50000 for T= 51345 logg=6.04\n", + "Changing to logg=5.00 for T= 51345 logg=6.04\n", + "Changing to T= 50000 for T= 51475 logg=6.04\n", + "Changing to logg=5.00 for T= 51475 logg=6.04\n", + "Changing to T= 50000 for T= 51606 logg=6.04\n", + "Changing to logg=5.00 for T= 51606 logg=6.04\n", + "Changing to T= 50000 for T= 51737 logg=6.05\n", + "Changing to logg=5.00 for T= 51737 logg=6.05\n", + "Changing to T= 50000 for T= 51868 logg=6.05\n", + "Changing to logg=5.00 for T= 51868 logg=6.05\n", + "Changing to T= 50000 for T= 52000 logg=6.05\n", + "Changing to logg=5.00 for T= 52000 logg=6.05\n", + "Changing to T= 50000 for T= 52119 logg=6.05\n", + "Changing to logg=5.00 for T= 52119 logg=6.05\n", + "Changing to T= 50000 for T= 52240 logg=6.05\n", + "Changing to logg=5.00 for T= 52240 logg=6.05\n", + "Changing to T= 50000 for T= 52384 logg=6.05\n", + "Changing to logg=5.00 for T= 52384 logg=6.05\n", + "Changing to T= 50000 for T= 52505 logg=6.05\n", + "Changing to logg=5.00 for T= 52505 logg=6.05\n", + "Changing to T= 50000 for T= 52626 logg=6.05\n", + "Changing to logg=5.00 for T= 52626 logg=6.05\n", + "Changing to T= 50000 for T= 52747 logg=6.05\n", + "Changing to logg=5.00 for T= 52747 logg=6.05\n", + "Changing to T= 50000 for T= 52759 logg=6.05\n", + "Changing to logg=5.00 for T= 52759 logg=6.05\n", + "Changing to T= 50000 for T= 52857 logg=6.05\n", + "Changing to logg=5.00 for T= 52857 logg=6.05\n", + "Changing to T= 50000 for T= 52991 logg=6.05\n", + "Changing to logg=5.00 for T= 52991 logg=6.05\n", + "Changing to T= 50000 for T= 53125 logg=6.06\n", + "Changing to logg=5.00 for T= 53125 logg=6.06\n", + "Changing to T= 50000 for T= 53235 logg=6.06\n", + "Changing to logg=5.00 for T= 53235 logg=6.06\n", + "Changing to T= 50000 for T= 53358 logg=6.06\n", + "Changing to logg=5.00 for T= 53358 logg=6.06\n", + "Changing to T= 50000 for T= 53481 logg=6.06\n", + "Changing to logg=5.00 for T= 53481 logg=6.06\n", + "Changing to T= 50000 for T= 53592 logg=6.06\n", + "Changing to logg=5.00 for T= 53592 logg=6.06\n", + "Changing to T= 50000 for T= 53728 logg=6.06\n", + "Changing to logg=5.00 for T= 53728 logg=6.06\n", + "Changing to T= 50000 for T= 53864 logg=6.06\n", + "Changing to logg=5.00 for T= 53864 logg=6.06\n", + "Changing to T= 50000 for T= 53976 logg=6.07\n", + "Changing to logg=5.00 for T= 53976 logg=6.07\n", + "Changing to T= 50000 for T= 54100 logg=6.07\n", + "Changing to logg=5.00 for T= 54100 logg=6.07\n", + "Changing to T= 50000 for T= 54225 logg=6.07\n", + "Changing to logg=5.00 for T= 54225 logg=6.07\n", + "Changing to T= 50000 for T= 54363 logg=6.07\n", + "Changing to logg=5.00 for T= 54363 logg=6.07\n", + "Changing to T= 50000 for T= 54475 logg=6.07\n", + "Changing to logg=5.00 for T= 54475 logg=6.07\n", + "Changing to T= 50000 for T= 54588 logg=6.07\n", + "Changing to logg=5.00 for T= 54588 logg=6.07\n", + "Changing to T= 50000 for T= 54714 logg=6.08\n", + "Changing to logg=5.00 for T= 54714 logg=6.08\n", + "Changing to T= 50000 for T= 54853 logg=6.08\n", + "Changing to logg=5.00 for T= 54853 logg=6.08\n", + "Changing to T= 50000 for T= 54967 logg=6.08\n", + "Changing to logg=5.00 for T= 54967 logg=6.08\n", + "Changing to T= 50000 for T= 55093 logg=6.08\n", + "Changing to logg=5.00 for T= 55093 logg=6.08\n", + "Changing to T= 50000 for T= 55208 logg=6.08\n", + "Changing to logg=5.00 for T= 55208 logg=6.08\n", + "Changing to T= 50000 for T= 55322 logg=6.09\n", + "Changing to logg=5.00 for T= 55322 logg=6.09\n", + "Changing to T= 50000 for T= 55450 logg=6.09\n", + "Changing to logg=5.00 for T= 55450 logg=6.09\n", + "Changing to T= 50000 for T= 55590 logg=6.09\n", + "Changing to logg=5.00 for T= 55590 logg=6.09\n", + "Changing to T= 50000 for T= 55719 logg=6.09\n", + "Changing to logg=5.00 for T= 55719 logg=6.09\n", + "Changing to T= 50000 for T= 55834 logg=6.09\n", + "Changing to logg=5.00 for T= 55834 logg=6.09\n", + "Changing to T= 50000 for T= 55873 logg=6.09\n", + "Changing to logg=5.00 for T= 55873 logg=6.09\n", + "Changing to T= 50000 for T= 55963 logg=6.09\n", + "Changing to logg=5.00 for T= 55963 logg=6.09\n", + "Changing to T= 50000 for T= 56092 logg=6.10\n", + "Changing to logg=5.00 for T= 56092 logg=6.10\n", + "Changing to T= 50000 for T= 56234 logg=6.10\n", + "Changing to logg=5.00 for T= 56234 logg=6.10\n", + "Changing to T= 50000 for T= 56364 logg=6.10\n", + "Changing to logg=5.00 for T= 56364 logg=6.10\n", + "Changing to T= 50000 for T= 56507 logg=6.10\n", + "Changing to logg=5.00 for T= 56507 logg=6.10\n", + "Changing to T= 50000 for T= 56624 logg=6.11\n", + "Changing to logg=5.00 for T= 56624 logg=6.11\n", + "Changing to T= 50000 for T= 56754 logg=6.11\n", + "Changing to logg=5.00 for T= 56754 logg=6.11\n", + "Changing to T= 50000 for T= 56885 logg=6.11\n", + "Changing to logg=5.00 for T= 56885 logg=6.11\n", + "Changing to T= 50000 for T= 57030 logg=6.11\n", + "Changing to logg=5.00 for T= 57030 logg=6.11\n", + "Changing to T= 50000 for T= 57161 logg=6.11\n", + "Changing to logg=5.00 for T= 57161 logg=6.11\n", + "Changing to T= 50000 for T= 57293 logg=6.11\n", + "Changing to logg=5.00 for T= 57293 logg=6.11\n", + "Changing to T= 50000 for T= 57425 logg=6.11\n", + "Changing to logg=5.00 for T= 57425 logg=6.11\n", + "Changing to T= 50000 for T= 57570 logg=6.11\n", + "Changing to logg=5.00 for T= 57570 logg=6.11\n", + "Changing to T= 50000 for T= 57703 logg=6.11\n", + "Changing to logg=5.00 for T= 57703 logg=6.11\n", + "Changing to T= 50000 for T= 57850 logg=6.12\n", + "Changing to logg=5.00 for T= 57850 logg=6.12\n", + "Changing to T= 50000 for T= 57983 logg=6.12\n", + "Changing to logg=5.00 for T= 57983 logg=6.12\n", + "Changing to T= 50000 for T= 58117 logg=6.12\n", + "Changing to logg=5.00 for T= 58117 logg=6.12\n", + "Changing to T= 50000 for T= 58251 logg=6.13\n", + "Changing to logg=5.00 for T= 58251 logg=6.13\n", + "Changing to T= 50000 for T= 58398 logg=6.13\n", + "Changing to logg=5.00 for T= 58398 logg=6.13\n", + "Changing to T= 50000 for T= 58546 logg=6.13\n", + "Changing to logg=5.00 for T= 58546 logg=6.13\n", + "Changing to T= 50000 for T= 58695 logg=6.13\n", + "Changing to logg=5.00 for T= 58695 logg=6.13\n", + "Changing to T= 50000 for T= 58844 logg=6.14\n", + "Changing to logg=5.00 for T= 58844 logg=6.14\n", + "Changing to T= 50000 for T= 58993 logg=6.14\n", + "Changing to logg=5.00 for T= 58993 logg=6.14\n", + "Changing to T= 50000 for T= 59143 logg=6.14\n", + "Changing to logg=5.00 for T= 59143 logg=6.14\n", + "Changing to T= 50000 for T= 59293 logg=6.15\n", + "Changing to logg=5.00 for T= 59293 logg=6.15\n", + "Changing to T= 50000 for T= 59334 logg=6.15\n", + "Changing to logg=5.00 for T= 59334 logg=6.15\n", + "Changing to T= 50000 for T= 59457 logg=6.15\n", + "Changing to logg=5.00 for T= 59457 logg=6.15\n", + "Changing to T= 50000 for T= 59621 logg=6.16\n", + "Changing to logg=5.00 for T= 59621 logg=6.16\n", + "Changing to T= 50000 for T= 59800 logg=6.16\n", + "Changing to logg=5.00 for T= 59800 logg=6.16\n", + "Changing to T= 50000 for T= 59965 logg=6.16\n", + "Changing to logg=5.00 for T= 59965 logg=6.16\n", + "Changing to T= 50000 for T= 60159 logg=6.17\n", + "Changing to logg=5.00 for T= 60159 logg=6.17\n", + "Changing to T= 50000 for T= 60353 logg=6.17\n", + "Changing to logg=5.00 for T= 60353 logg=6.17\n", + "Changing to T= 50000 for T= 60534 logg=6.18\n", + "Changing to logg=5.00 for T= 60534 logg=6.18\n", + "Changing to T= 50000 for T= 60758 logg=6.18\n", + "Changing to logg=5.00 for T= 60758 logg=6.18\n", + "Changing to T= 50000 for T= 60968 logg=6.18\n", + "Changing to logg=5.00 for T= 60968 logg=6.18\n", + "Changing to T= 50000 for T= 61235 logg=6.19\n", + "Changing to logg=5.00 for T= 61235 logg=6.19\n", + "Changing to T= 50000 for T= 61504 logg=6.20\n", + "Changing to logg=5.00 for T= 61504 logg=6.20\n", + "Changing to T= 50000 for T= 61844 logg=6.21\n", + "Changing to logg=5.00 for T= 61844 logg=6.21\n", + "Changing to T= 50000 for T= 62287 logg=6.23\n", + "Changing to logg=5.00 for T= 62287 logg=6.23\n", + "Changing to T= 50000 for T= 63038 logg=6.27\n", + "Changing to logg=5.00 for T= 63038 logg=6.27\n", + "Changing to T= 50000 for T= 64239 logg=6.32\n", + "Changing to logg=5.00 for T= 64239 logg=6.32\n", + "Changing to T= 50000 for T= 65464 logg=6.37\n", + "Changing to logg=5.00 for T= 65464 logg=6.37\n", + "Changing to T= 50000 for T= 66696 logg=6.42\n", + "Changing to logg=5.00 for T= 66696 logg=6.42\n", + "Changing to T= 50000 for T= 67967 logg=6.47\n", + "Changing to logg=5.00 for T= 67967 logg=6.47\n", + "Changing to T= 50000 for T= 69263 logg=6.53\n", + "Changing to logg=5.00 for T= 69263 logg=6.53\n", + "Changing to T= 50000 for T= 71367 logg=6.63\n", + "Changing to logg=5.00 for T= 71367 logg=6.63\n", + "Isochrone generation took 112.722160 s.\n", + "Making photometry for isochrone: log(t) = 6.70 AKs = 0.80 dist = 4000\n", + " Starting at: 2024-08-02 09:54:23.120123 Usually takes ~5 minutes\n", + "Starting filter: wfc3,ir,f127m Elapsed time: 0.00 seconds\n", + "Starting synthetic photometry\n", + "M = 0.070 Msun T = 2928 K m_hst_f127m = 22.41\n", + "M = 1.175 Msun T = 4611 K m_hst_f127m = 18.72\n", + "M = 1.650 Msun T = 5355 K m_hst_f127m = 17.71\n", + "M = 1.973 Msun T = 6311 K m_hst_f127m = 16.34\n", + "M = 2.292 Msun T = 9669 K m_hst_f127m = 16.68\n", + "M = 2.648 Msun T = 11771 K m_hst_f127m = 16.64\n", + "M = 2.819 Msun T = 12291 K m_hst_f127m = 16.51\n", + "M = 3.075 Msun T = 13014 K m_hst_f127m = 16.33\n", + "M = 3.332 Msun T = 13709 K m_hst_f127m = 16.16\n", + "M = 3.482 Msun T = 14099 K m_hst_f127m = 16.07\n", + "M = 3.615 Msun T = 14438 K m_hst_f127m = 15.99\n", + "M = 8.977 Msun T = 23502 K m_hst_f127m = 14.07\n", + "M = 49.000 Msun T = 32344 K m_hst_f127m = 9.23\n", + "M = 50.757 Msun T = 31046 K m_hst_f127m = 9.25\n", + "M = 52.540 Msun T = 41937 K m_hst_f127m = 10.13\n", + "M = 54.406 Msun T = 48753 K m_hst_f127m = 10.85\n", + "M = 56.318 Msun T = 65464 K m_hst_f127m = 12.01\n", + "Starting filter: wfc3,ir,f139m Elapsed time: 25.91 seconds\n", + "Starting synthetic photometry\n", + "M = 0.070 Msun T = 2928 K m_hst_f139m = 22.11\n", + "M = 1.175 Msun T = 4611 K m_hst_f139m = 18.14\n", + "M = 1.650 Msun T = 5355 K m_hst_f139m = 17.18\n", + "M = 1.973 Msun T = 6311 K m_hst_f139m = 15.86\n", + "M = 2.292 Msun T = 9669 K m_hst_f139m = 16.28\n", + "M = 2.648 Msun T = 11771 K m_hst_f139m = 16.25\n", + "M = 2.819 Msun T = 12291 K m_hst_f139m = 16.12\n", + "M = 3.075 Msun T = 13014 K m_hst_f139m = 15.94\n", + "M = 3.332 Msun T = 13709 K m_hst_f139m = 15.77\n", + "M = 3.482 Msun T = 14099 K m_hst_f139m = 15.68\n", + "M = 3.615 Msun T = 14438 K m_hst_f139m = 15.60\n", + "M = 8.977 Msun T = 23502 K m_hst_f139m = 13.70\n", + "M = 49.000 Msun T = 32344 K m_hst_f139m = 8.87\n", + "M = 50.757 Msun T = 31046 K m_hst_f139m = 8.88\n", + "M = 52.540 Msun T = 41937 K m_hst_f139m = 9.77\n", + "M = 54.406 Msun T = 48753 K m_hst_f139m = 10.50\n", + "M = 56.318 Msun T = 65464 K m_hst_f139m = 11.66\n", + "Starting filter: wfc3,ir,f153m Elapsed time: 51.87 seconds\n", + "Starting synthetic photometry\n", + "M = 0.070 Msun T = 2928 K m_hst_f153m = 21.45\n", + "M = 1.175 Msun T = 4611 K m_hst_f153m = 17.51\n", + "M = 1.650 Msun T = 5355 K m_hst_f153m = 16.63\n", + "M = 1.973 Msun T = 6311 K m_hst_f153m = 15.37\n", + "M = 2.292 Msun T = 9669 K m_hst_f153m = 15.89\n", + "M = 2.648 Msun T = 11771 K m_hst_f153m = 15.87\n", + "M = 2.819 Msun T = 12291 K m_hst_f153m = 15.75\n", + "M = 3.075 Msun T = 13014 K m_hst_f153m = 15.57\n", + "M = 3.332 Msun T = 13709 K m_hst_f153m = 15.40\n", + "M = 3.482 Msun T = 14099 K m_hst_f153m = 15.31\n", + "M = 3.615 Msun T = 14438 K m_hst_f153m = 15.23\n", + "M = 8.977 Msun T = 23502 K m_hst_f153m = 13.34\n", + "M = 49.000 Msun T = 32344 K m_hst_f153m = 8.52\n", + "M = 50.757 Msun T = 31046 K m_hst_f153m = 8.53\n", + "M = 52.540 Msun T = 41937 K m_hst_f153m = 9.42\n", + "M = 54.406 Msun T = 48753 K m_hst_f153m = 10.15\n", + "M = 56.318 Msun T = 65464 K m_hst_f153m = 11.31\n", + " Time taken: 78.43 seconds\n" + ] + } + ], + "source": [ + "# Define isochrone parameters\n", + "logAge = np.log10(5*10**6.) # Age in log(years)\n", + "AKs = 0.8 # extinction in mags\n", + "dist = 4000 # distance in parsec\n", + "metallicity = 0 # Metallicity in [M/H]\n", + "\n", + "# Define evolution/atmosphere models and extinction law\n", + "evo_model = evolution.MergedBaraffePisaEkstromParsec() \n", + "atm_func = atmospheres.get_merged_atmosphere\n", + "red_law = reddening.RedLawHosek18b()\n", + "\n", + "# Also specify filters for synthetic photometry (optional). Here we use \n", + "# the HST WFC3-IR F127M, F139M, and F153M filters\n", + "filt_list = ['wfc3,ir,f127m', 'wfc3,ir,f139m', 'wfc3,ir,f153m']\n", + "\n", + "# Specify the directory we want the output isochrone\n", + "# table saved in. If the directory does not already exist,\n", + "# SPISEA will create it.\n", + "iso_dir = 'isochrones/'\n", + "\n", + "# Make IsochronePhot object. Note that this will take a minute or two, \n", + "# unless the isochrone has been generated previously.\n", + "#\n", + "# Note that this is not show all of the user options \n", + "# for IsochronePhot. See docs for complete list of options.\n", + "my_iso = synthetic.IsochronePhot(logAge, AKs, dist, metallicity=0,\n", + " evo_model=evo_model, atm_func=atm_func,\n", + " red_law=red_law, filters=filt_list,\n", + " iso_dir=iso_dir)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5a6e081f-84d3-4efb-a6d5-59d5f60d845f", + "metadata": {}, + "outputs": [], + "source": [ + "# The stars in the isochrone and associated properties \n", + "# are stored in an astropy table called \"points\" \n", + "# within the IsochronePhot object. \n", + "print(my_iso.points)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1205c450-d7f2-4ad7-86b0-006762426d5c", + "metadata": {}, + "outputs": [], + "source": [ + "# Example case:\n", + "# Identify a 1 M_sun star, print F127M, F139M, and F153M mags\n", + "idx = np.where( abs(my_iso.points['mass'] - 1.0) == min(abs(my_iso.points['mass'] - 1.0)) )[0]\n", + "f127m = np.round(my_iso.points[idx[0]]['m_hst_f127m'], decimals=3)\n", + "f139m = np.round(my_iso.points[idx[0]]['m_hst_f139m'], decimals=3)\n", + "f153m = np.round(my_iso.points[idx[0]]['m_hst_f153m'], decimals=3)\n", + "print('1 M_sun: F127M = {0} mag, F139M = {1} mag, F153M = {2} mag'.format(f127m, f139m, f153m))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a8169db9-486e-4d20-9a09-dfcd7ebbd3e1", + "metadata": {}, + "outputs": [], + "source": [ + "# Make a color-magnitude diagram from the isochrone\n", + "py.figure(1, figsize=(10,10))\n", + "py.clf()\n", + "py.plot(my_iso.points['m_hst_f127m'] - my_iso.points['m_hst_f153m'], \n", + " my_iso.points['m_hst_f153m'], 'r-', label='_nolegend_')\n", + "py.plot(my_iso.points['m_hst_f127m'][idx] - my_iso.points['m_hst_f153m'][idx], \n", + " my_iso.points['m_hst_f153m'][idx], 'b*', ms=15, label='1 $M_\\odot$')\n", + "py.xlabel('F127M - F153M')\n", + "py.ylabel('F153M')\n", + "py.gca().invert_yaxis()\n", + "py.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "7e9599c3-e7f7-4f1b-8eda-8148058b16c3", + "metadata": {}, + "source": [ + "### 2: Bringing in an IMF" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "493b8648-1c3b-4aab-858f-2f955195e634", + "metadata": {}, + "outputs": [], + "source": [ + "# Make multiplicity object Here, we use the MultiplicityUnresolved object, \n", + "# based on Lu+13. This means that star systems will be unresolved, i.e., \n", + "# that all components of a star system are combined into a single \"star\" in the cluster\n", + "imf_multi = multiplicity.MultiplicityUnresolved()\n", + "\n", + "# Make IMF object; we'll use a broken power law with the parameters from Kroupa+01\n", + "\n", + "# NOTE: when defining the power law slope for each segment of the IMF, we define\n", + "# the entire exponent, including the negative sign. For example, if dN/dm $\\propto$ m^-alpha,\n", + "# then you would use the value \"-2.3\" to specify an IMF with alpha = 2.3. \n", + "\n", + "my_imf = imf.Weidner_Kroupa_2004(multiplicity=imf_multi)" + ] + }, + { + "cell_type": "markdown", + "id": "0e42984d-bf09-4e71-a823-aa698672cfe6", + "metadata": {}, + "source": [ + "### 3: Generating Cluster" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0bf0fed8-2b70-41be-b950-83f1362af9f0", + "metadata": {}, + "outputs": [], + "source": [ + "# Define total cluster mass\n", + "mass = 10**5.\n", + "\n", + "# Make cluster object\n", + "cluster = synthetic.ResolvedCluster(my_iso, my_imf, mass)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c8de1a27-0b07-404c-a13d-8434e204017d", + "metadata": {}, + "outputs": [], + "source": [ + "# Look at star systems table\n", + "print(cluster.star_systems)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6b10a958-a0f8-443c-be6b-e07c5de2d4dc", + "metadata": {}, + "outputs": [], + "source": [ + "# The companions table is accessed in a similar way\n", + "print(cluster.companions)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "095a963e-c0de-4bbc-a03f-471f3cdb7b91", + "metadata": {}, + "outputs": [], + "source": [ + "# Look at the cluster CMD, compared to input isochrone. Note the impact of\n", + "# multiple systems on the photometry\n", + "clust = cluster.star_systems\n", + "iso = my_iso.points\n", + "\n", + "py.figure(2, figsize=(10,10))\n", + "py.clf()\n", + "py.plot(clust['m_hst_f127m'] - clust['m_hst_f153m'], clust['m_hst_f153m'],\n", + " 'k.', ms=5, alpha=0.1, label='__nolegend__')\n", + "py.plot(iso['m_hst_f127m'] - iso['m_hst_f153m'], iso['m_hst_f153m'],\n", + " 'r-', label='Isochrone')\n", + "py.xlabel('F127M - F153M')\n", + "py.ylabel('F153M')\n", + "py.gca().invert_yaxis()\n", + "py.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d694ed41-c732-4093-9f0a-ad021fe8397a", + "metadata": {}, + "outputs": [], + "source": [ + "print(\"minimum primary mass: \" + str(np.min(clust['mass'])))\n", + "print(\"minimum companion mass: \" + str(np.min(cluster.companions['mass'])))\n", + "print(\"maximum primary mass: \" + str(np.max(clust['mass'])))\n", + "print(\"maximum companion mass: \" + str(np.max(cluster.companions['mass'])))" + ] + }, + { + "cell_type": "markdown", + "id": "fa4c660d-ea4e-491a-95db-278617ee1757", + "metadata": {}, + "source": [ + "### Creating a histogram to compare Weidner Kroupa and Muzic" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c2540680-d69f-427f-b0d1-55130826ad8a", + "metadata": {}, + "outputs": [], + "source": [ + "#generate clusters for each class\n", + "w_imf = imf.Weidner_Kroupa_2004(multiplicity=imf_multi)\n", + "m_imf = imf.Muzic_2017(multiplicity=imf_multi)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4d1c647e-8e1a-4a24-8b20-26a8b14f4660", + "metadata": {}, + "outputs": [], + "source": [ + "# Define total cluster mass\n", + "mass = 10**5.\n", + "\n", + "# Make cluster objects for each\n", + "w_cluster = synthetic.ResolvedCluster(my_iso, w_imf, mass)\n", + "m_cluster = synthetic.ResolvedCluster(my_iso, m_imf, mass)" + ] + }, + { + "cell_type": "markdown", + "id": "f55b6d0a-ecc2-4bbb-aa5b-d8f23acfe441", + "metadata": {}, + "source": [ + "#### Comparing Weidner Kroupa and Muzic clusters data" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "eb3847e7-c184-4d49-a7ec-69d0a1e50fea", + "metadata": {}, + "outputs": [], + "source": [ + "#show total numbers for each cluster\n", + "print(\"primary masses in Weidner Kroupa cluster: \" + str(len(w_cluster.star_systems)))\n", + "print(\"companion masses in Weidner Kroupa cluster: \" + str(len(w_cluster.companions)))\n", + "print(\"primary masses in Muzic cluster: \" + str(len(m_cluster.star_systems)))\n", + "print(\"companion masses in Muzic cluster: \" + str(len(m_cluster.companions)))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9b2656bf-6a7e-4ca5-ad09-6ae59e8c6d0d", + "metadata": {}, + "outputs": [], + "source": [ + "#Comparing max/min primary/companion masses\n", + "#Weidner Kroupa\n", + "print('\\033[1m' + \"Weidner Kroupa\" + '\\033[0m')\n", + "print(\"minimum primary mass: \" + str(np.min(w_cluster.star_systems['mass'])))\n", + "print(\"minimum companion mass: \" + str(np.min(w_cluster.companions['mass'])))\n", + "print(\"maximum primary mass: \" + str(np.max(w_cluster.star_systems['mass'])))\n", + "print(\"maximum companion mass: \" + str(np.max(w_cluster.companions['mass'])))\n", + "print('\\n')\n", + "\n", + "#Muzic\n", + "print('\\033[1m' + \"Muzic\" + '\\033[0m')\n", + "print(\"minimum primary mass: \" + str(np.min(m_cluster.star_systems['mass'])))\n", + "print(\"minimum companion mass: \" + str(np.min(m_cluster.companions['mass'])))\n", + "print(\"maximum primary mass: \" + str(np.max(m_cluster.star_systems['mass'])))\n", + "print(\"maximum companion mass: \" + str(np.max(m_cluster.companions['mass'])))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "17d1685d-0f63-4f6e-ad62-4ba3a03f0780", + "metadata": {}, + "outputs": [], + "source": [ + "#compare total cluster masses\n", + "#create combined arrays of primary/companion masses\n", + "all_m_masses = np.concatenate((m_cluster.star_systems['mass'], m_cluster.companions['mass']))\n", + "all_w_masses = np.concatenate((w_cluster.star_systems['mass'], w_cluster.companions['mass']))\n", + "\n", + "#find total of added masses\n", + "print(\"total mass of WD cluster: \" + str(np.sum(all_w_masses)))\n", + "print(\"total mass of M cluster: \" + str(np.sum(all_m_masses)))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4e2fe19b-9da8-4388-92bd-c1390444e8c4", + "metadata": {}, + "outputs": [], + "source": [ + "#define mass range of histogram\n", + "bin_edges = [0.01, 0.08, 0.5, 1, 2]\n", + "\n", + "#setting up subplots\n", + "fig, ax = plt.subplots(nrows=2, ncols=1, figsize=(8,8))\n", + "plt.subplots_adjust(hspace=0.5, wspace=0.75)\n", + "\n", + "#create histograms to compare\n", + "counts_m, edges_m, _ = ax[0].hist(all_m_masses, bins=bin_edges, alpha=0.5, label='Muzic_2017', color='blue', edgecolor='black', histtype='bar')\n", + "counts_w, edges_w, _ = ax[1].hist(all_w_masses, bins=bin_edges, alpha=0.5, label='Weidner_Kroupa_2004', color='red', edgecolor='black', histtype='bar')\n", + "\n", + "#compute bin centers\n", + "bin_centers_m = (edges_m[:-1] + edges_m[1:]) / 2\n", + "bin_centers_w = (edges_w[:-1] + edges_w[1:]) / 2\n", + "\n", + "#generate x values for the broken power law curve\n", + "x_fit_m = np.linspace(bin_centers_m.min(), bin_centers_m.max(), 100)\n", + "x_fit_w = np.linspace(bin_centers_w.min(), bin_centers_w.max(), 100)\n", + "\n", + "\n", + "\n", + "#labels and legend\n", + "plt.xlabel('Stellar Mass (Solar Masses)')\n", + "plt.ylabel('Number of Stars')\n", + "plt.title('Comparison of Stellar Mass Distributions')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "04216fed-7f8b-4249-9c6c-29c82cc18bce", + "metadata": {}, + "source": [ + "## Generating a cluster with compound objects (using an IFMR)\n", + "This is before code is modified to allow for brown dwarves" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "25b1247a-0eb8-40bc-bf56-f89e788283cd", + "metadata": {}, + "outputs": [], + "source": [ + "# Create isochrone object \n", + "filt_list = ['wfc3,ir,f153m'] # We won't be doing much with synthetic photometry here, so only 1 filter\n", + "my_ifmr = ifmr.IFMR_Raithel18()\n", + "my_iso = synthetic.IsochronePhot(8, 0, 10,\n", + " evo_model = evolution.MergedBaraffePisaEkstromParsec(),\n", + " filters=filt_list)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "01f6f94c-1b23-4ae1-bfc2-96e2d4cacd27", + "metadata": {}, + "outputs": [], + "source": [ + "# Create IMF objects \n", + "imf_multi = multiplicity.MultiplicityUnresolved()\n", + "massLimits = np.array([0.01, 0.08, 0.5, 1, np.inf])\n", + "powers = np.array([-0.3, -1.3, -2.3, -2.35])\n", + "k_imf = imf.IMF_broken_powerlaw(massLimits, powers, multiplicity=imf_multi)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "1a914c4c-ac7e-4c61-9e40-1b0d5dd5568f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Found 580447 stars out of mass range\n", + "Found 113559 companions out of stellar mass range\n" + ] + } + ], + "source": [ + "# Make clusters\n", + "cluster_mass = 10**6\n", + "k_cluster = synthetic.ResolvedCluster(my_iso, k_imf, cluster_mass, ifmr=my_ifmr)\n", + "\n", + "# Get outputs\n", + "k_out = k_cluster.star_systems\n", + "k_comp = k_cluster.companions" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "62293dea-989b-4870-a77b-ba677010da81", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Locate BHs, NSs and WDs\n", + "p_bh = np.where(k_out['phase'] == 103)[0]\n", + "c_bh = np.where(k_comp['phase'] == 103)[0]\n", + "k_bh = np.concatenate([p_bh, c_bh])\n", + "p_ns = np.where(k_out['phase'] == 102)[0]\n", + "c_ns = np.where(k_comp['phase'] == 102)[0]\n", + "k_ns = np.concatenate([p_ns, c_ns])\n", + "p_wd = np.where(k_out['phase'] == 101)[0]\n", + "c_wd = np.where(k_comp['phase'] == 101)[0]\n", + "k_wd = np.concatenate([p_wd, c_wd])\n", + "\n", + "# Plot on histograms\n", + "bh_bins = np.linspace(0.01, 16, 20)\n", + "wd_bins = np.linspace(0.4, 1.4, 16)\n", + "\n", + "plt.figure(figsize=(14,6))\n", + "plt.subplot(1, 2, 1)\n", + "plt.hist(k_out[p_bh]['mass_current'], histtype = 'step',\n", + " bins = bh_bins, label = 'Generated Black Holes')\n", + "plt.title(\"Generated Black Holes by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "plt.subplot(1, 2, 2)\n", + "plt.hist(k_out[p_wd]['mass_current'], histtype = 'step',\n", + " bins = wd_bins, label = 'Generated White Dwarves')\n", + "plt.title(\"Generated White Dwarves by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "d36bba0d-3037-46c0-91f3-321e47241204", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "831012.4509070338\n", + "5.311329909891375\n" + ] + } + ], + "source": [ + "all_masses = np.concatenate([k_out['mass'], k_comp['mass']])\n", + "tot_mass = np.sum(all_masses)\n", + "print(tot_mass)\n", + "print(np.min(k_out[p_wd]['mass']))" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "1f999373-557e-42f1-9c0b-43d1cfab198e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0700003309744075\n", + "0.010000236016655941\n" + ] + } + ], + "source": [ + "print(np.min(k_out['mass']))\n", + "print(np.min(k_comp['mass']))" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "d7c2fa5e-49cd-4021-869a-6f9701677c68", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Current smallest mass of generated black holes: 0.07006468311672817\n", + "Current largest mass of generated black holes: 15.65838834836072\n" + ] + } + ], + "source": [ + "print(\"Current smallest mass of generated black holes: \" + str(np.min(k_out[k_bh]['mass_current'])))\n", + "print(\"Current largest mass of generated black holes: \" + str(np.max(k_out[k_bh]['mass_current'])))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7e056d1f-be87-43ee-9899-2a1859d5e2c5", + "metadata": {}, + "outputs": [], + "source": [ + "print('The cluster table contains these columns: {0}'.format(k_cluster.star_systems.keys()))" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "c02d7dbd-9690-49f4-931d-e7f66172ba12", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " mass isMultiple ... m_hst_f153m N_companions\n", + "------------------ ---------- ... ------------------- ------------\n", + "34.858558890643366 True ... nan 1\n", + " 24.21988253820487 True ... 0.19920518920036126 1\n", + " 53.76008089560359 True ... -0.2181337523917536 4\n", + "15.882675891462688 True ... -1.810589141056601 2\n", + " 57.37043948819449 True ... nan 3\n", + "31.414432201808793 True ... nan 1\n", + "22.819575828477465 True ... 1.0957723191576627 5\n", + " ... ... ... ... ...\n", + "23.712544384283426 True ... 1.6681099957862053 1\n", + " 52.89729960707116 True ... 1.3625884002383177 3\n", + " 82.84997226207857 True ... nan 2\n", + " 32.27796062878089 True ... 0.43046734619105526 3\n", + " 26.92983956402475 True ... nan 2\n", + " 27.13236574281697 True ... nan 2\n", + " 36.6006664768621 True ... 2.5063372504019394 3\n", + "Length = 1671 rows\n" + ] + } + ], + "source": [ + "print(k_out[p_bh])" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "ddc351e5-e465-4f2e-9703-cd5c819a75f2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " mass \n", + "------------------\n", + "34.858558890643366\n", + " 24.21988253820487\n", + " 53.76008089560359\n", + "15.882675891462688\n", + " 57.37043948819449\n", + "31.414432201808793\n", + "22.819575828477465\n", + " ...\n", + "23.712544384283426\n", + " 52.89729960707116\n", + " 82.84997226207857\n", + " 32.27796062878089\n", + " 26.92983956402475\n", + " 27.13236574281697\n", + " 36.6006664768621\n", + "Length = 1671 rows mass_current \n", + "------------------\n", + "12.446576185012097\n", + " 8.78166110167993\n", + " 8.806507411947209\n", + " 5.424709536731119\n", + " 7.981409529281804\n", + "11.216283709433917\n", + " 8.283995574428168\n", + " ...\n", + " 8.603336271797449\n", + " 9.056339719938071\n", + " 6.152701918097497\n", + "11.515219186451843\n", + " 9.707197419320156\n", + " 9.775168357448042\n", + "13.119673398892417\n", + "Length = 1671 rows\n" + ] + } + ], + "source": [ + "print(k_out[p_bh]['mass'], k_out[p_bh]['mass_current'])" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "f5ce39b9-2c6d-4e7c-a6f6-ffd7235ac9e8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial mass of smallest generated black hole: 15.000468103060483\n", + "Initial mass of largest generated black hole: 117.48601718195576\n" + ] + } + ], + "source": [ + "print(\"Initial mass of smallest generated black hole: \" + str(np.min(k_out[p_bh]['mass'])))\n", + "print(\"Initial mass of largest generated black hole: \" + str(np.max(k_out[p_bh]['mass'])))" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "1c41b219-7a85-4519-af99-77145daaa418", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial mass of smallest generated comp black hole: 15.037154672016358\n", + "Initial mass of largest generated comp black hole: 111.30489194158751\n" + ] + } + ], + "source": [ + "print(\"Initial mass of smallest generated comp black hole: \" + str(np.min(k_comp[c_bh]['mass'])))\n", + "print(\"Initial mass of largest generated comp black hole: \" + str(np.max(k_comp[c_bh]['mass'])))" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "3566ea45-31f6-4015-bf84-d34ff93ec18e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot on histograms\n", + "bh_bins = np.linspace(0.01, 16, 20)\n", + "wd_bins = np.linspace(0.4, 1.4, 16)\n", + "\n", + "plt.figure(figsize=(14,6))\n", + "plt.subplot(1, 2, 1)\n", + "plt.hist(k_comp[c_bh]['mass_current'], histtype = 'step',\n", + " bins = bh_bins, label = 'Generated Black Holes')\n", + "plt.title(\"Generated Black Holes by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "plt.subplot(1, 2, 2)\n", + "plt.hist(k_comp[c_wd]['mass_current'], histtype = 'step',\n", + " bins = wd_bins, label = 'Generated White Dwarves')\n", + "plt.title(\"Generated White Dwarves by Mass\")\n", + "plt.xlabel('Mass ($M_\\odot$)')\n", + "plt.ylabel('Number')\n", + "plt.legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "3b4167fc-fd67-4c11-9cb4-f46b1e8cb9a6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.9729527582037262\n" + ] + } + ], + "source": [ + "print(np.min(k_comp[c_wd]['mass_current']))" + ] + }, + { + "cell_type": "markdown", + "id": "c17cd2c5-164a-49be-b118-8023b6f3a3b4", + "metadata": {}, + "source": [ + "## New Cluster after addition of BD criterion" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "bd81a9c8-bc0c-46e3-a20d-bc2112a50f5c", + "metadata": {}, + "outputs": [], + "source": [ + "#locate brown dwarfs\n", + "p_bd = np.where(k_out['phase'] == 99)[0]\n", + "c_bd = np.where(k_comp['phase'] == 99)[0]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f49be47c-dc94-467e-bf4d-41b6f926ace5", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/changes/evolution_gaussian_fit.ipynb b/changes/evolution_gaussian_fit.ipynb new file mode 100644 index 00000000..957d09b3 --- /dev/null +++ b/changes/evolution_gaussian_fit.ipynb @@ -0,0 +1,1195 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9aaeb072-9ae6-4362-978f-4d9fd5802cd7", + "metadata": {}, + "source": [ + "## Generating Intermediary Data for Non-Overlapping Evolutionary Models" + ] + }, + { + "cell_type": "markdown", + "id": "5459271a-7e3f-4723-91eb-b8735a2a5ff1", + "metadata": {}, + "source": [ + "Oh no! Unfortunately our new evolutionary models for brown dwarf masses do not align with those previously implemented, leaving a mass gap. To address this, we have decided to use Gaussian processes to fit the two data regimes (Phillips and Pisa) and generate the associated data in this range. The parameters in question are mass, luminosity, effective temperature, and log gravity. This notebook shows an example case for solar metallicity and a log age of ~7.13." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "1cad6635-a51f-426b-a207-6e2be5710586", + "metadata": {}, + "outputs": [], + "source": [ + "# importing necessary packages\n", + "import matplotlib.pyplot as plt\n", + "from astropy.table import Table\n", + "import numpy as np\n", + "from sklearn.gaussian_process import GaussianProcessRegressor\n", + "from sklearn.gaussian_process.kernels import ConstantKernel as C, Matern\n", + "from sklearn.preprocessing import StandardScaler\n", + "from sklearn.model_selection import KFold" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "d22dab8a-4834-48ed-99b0-47295b685e38", + "metadata": {}, + "outputs": [], + "source": [ + "# importing compatible age fits files \n", + "phillips = '/System/Volumes/Data/mnt/g/lu/models/evolution/Phillips2020/iso/z00/iso_7.128205127364955.fits'\n", + "pisa = '/System/Volumes/Data/mnt/g/lu/models/evolution/Pisa2011/iso/z015/iso_7.13.fits'\n", + "\n", + "# loading tables and extracting data\n", + "phil_tbl = Table.read(phillips, format='fits')\n", + "pisa_tbl = Table.read(pisa, format='fits')\n", + "\n", + "phil_mass = phil_tbl['Mass']\n", + "pisa_mass = pisa_tbl['col3']\n", + "\n", + "phil_Teff = phil_tbl['Teff']\n", + "pisa_Teff = pisa_tbl['col2']\n", + "\n", + "phil_L = phil_tbl['Luminosity']\n", + "pisa_L = pisa_tbl['col1']\n", + "\n", + "phil_logg = phil_tbl['Gravity']\n", + "pisa_logg = pisa_tbl['col4']" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "fd004b17-6528-4633-a5a1-2ab841c41bb9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# creating graphs of mass vs. luminosity, Teff, and gravity\n", + "fig, axs = plt.subplots(3, 1, figsize=(6, 10))\n", + "\n", + "# create array for mass gap\n", + "mass_gap = np.linspace(np.max(phil_mass), np.min(pisa_mass), 1000)\n", + "\n", + "# mass vs. luminosity\n", + "axs[0].plot(phil_mass, phil_L, color='c', label='Phillips')\n", + "axs[0].plot(pisa_mass, pisa_L, color='pink', label='Pisa')\n", + "axs[0].set_title('Mass vs. Luminosity') # for logAge=7.13')\n", + "y_min0 = axs[0].get_ylim()[0]\n", + "y_max0 = axs[0].get_ylim()[1]\n", + "axs[0].fill_between(mass_gap, y_min0, y_max0, color='gray', label='mass gap', alpha=0.3)\n", + "axs[0].set_xlabel('Mass ($M_{\\odot}$)')\n", + "axs[0].set_ylabel('Luminosity (L/$L_{\\odot}$)')\n", + "axs[0].set_xlim(0,1)\n", + "axs[0].set_ylim(-4,0)\n", + "axs[0].legend()\n", + "\n", + "# mass vs. Teff\n", + "axs[1].plot(phil_mass, phil_Teff, color='c', label='Phillips')\n", + "axs[1].plot(pisa_mass, pisa_Teff, color='pink', label='Pisa')\n", + "y_min1 = axs[1].get_ylim()[0]\n", + "y_max1 = axs[1].get_ylim()[1]\n", + "axs[1].fill_between(mass_gap, y_min1, y_max1, color='gray', label='mass gap', alpha=0.3)\n", + "axs[1].set_title('Mass vs. Effective Temperature') # for logAge=7.13')\n", + "axs[1].set_xlabel('Mass ($M_{\\odot}$)')\n", + "axs[1].set_ylabel('log(Teff) (log(K))')\n", + "axs[1].set_xlim(0,1)\n", + "axs[1].set_ylim(3,4)\n", + "axs[1].legend()\n", + "\n", + "# mass vs. logg (problem child)\n", + "axs[2].plot(phil_mass, phil_logg, color='c', label='Phillips')\n", + "axs[2].plot(pisa_mass, pisa_logg, color='pink', label='Pisa')\n", + "y_min2 = axs[2].get_ylim()[0]\n", + "y_max2 = axs[2].get_ylim()[1]\n", + "axs[2].fill_between(mass_gap, y_min2, y_max2, color='gray', label='mass gap', alpha=0.3)\n", + "axs[2].set_title('Mass vs. Gravity') # for logAge=7.13'\n", + "axs[2].set_xlabel('Mass ($M_{\\odot}$)')\n", + "axs[2].set_ylabel('logg')\n", + "axs[2].set_xlim(0,1)\n", + "axs[2].set_ylim(4,4.5)\n", + "axs[2].legend()\n", + "\n", + "fig.tight_layout()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "35e9b3a9-8efe-4668-a359-c8332e34fbba", + "metadata": {}, + "source": [ + "From these zoomed in graphs it becomes clear that though a mass gap is present, luminosty and effective temperature still seem to line up if a model connects them. In contrast, the graph for log gravity is very clearly disconnected, which is worth refining as new models continue to be generated. To best address this problem, we decided to use GaussianProcessRegressor with the Matern kernel, as through trial and error this appeared to be the best fit. We then decided to generate a chi-squared heat map for luminosity to find the ideal parameters for length_scale and nu. This was done with and without the use of the kFold class from sklearn, with a determination that using it produces a much better fit." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "8df930e4-19df-4651-960b-91c7aa522482", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.075 0.2019\n" + ] + } + ], + "source": [ + "# creating arrays\n", + "## mass\n", + "phil_mass = phil_tbl['Mass']\n", + "pisa_mass = pisa_tbl['col3']\n", + "combined_masses = np.concatenate([phil_mass, pisa_mass])\n", + "\n", + "## Teff\n", + "phil_Teff = phil_tbl['Teff']\n", + "pisa_Teff = pisa_tbl['col2']\n", + "combined_Teff = np.concatenate([phil_Teff, pisa_Teff])\n", + "\n", + "## Luminosity\n", + "phil_L = phil_tbl['Luminosity']\n", + "pisa_L = pisa_tbl['col1']\n", + "combined_L = np.concatenate([phil_L, pisa_L])\n", + "\n", + "## logg\n", + "phil_logg = phil_tbl['Gravity']\n", + "pisa_logg = pisa_tbl['col4']\n", + "combined_logg = np.concatenate([phil_logg, pisa_logg])\n", + "print(np.max(phil_mass), np.min(pisa_mass))" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "38a5d619-8cb2-40d6-962b-6f1491366962", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "### USING SKLEARN\n", + "\n", + "# creating input array (mass) and output array (luminosity)\n", + "X = combined_masses.reshape(-1, 1)\n", + "y = combined_L #np.array([combined_Teff, combined_L, combined_logg])\n", + "x = np.linspace(np.min(phil_mass), np.max(pisa_mass), int(1e6)).reshape(-1, 1)\n", + "\n", + "# Define grid\n", + "length_scales = np.logspace(-1, 2, 20)\n", + "nus = [0.5, 1.5, 2.5] # available Matern values\n", + "\n", + "chi2_map = np.zeros((len(nus), len(length_scales)))\n", + "N_data = len(y)\n", + "N_params = 2\n", + "\n", + "kf = KFold(n_splits=5, shuffle=True, random_state=42)\n", + "chi2_map = np.zeros((len(nus), len(length_scales)))\n", + "\n", + "for i, nu in enumerate(nus):\n", + " for j, ls in enumerate(length_scales):\n", + " kernel = Matern(length_scale=ls, nu=nu)\n", + " gp = GaussianProcessRegressor(kernel=kernel, optimizer=None, normalize_y=True)\n", + "\n", + " residuals = []\n", + " try:\n", + " for train_idx, test_idx in kf.split(X):\n", + " gp.fit(X[train_idx], y[train_idx])\n", + " y_pred = gp.predict(X[test_idx])\n", + " residuals.append((y[test_idx] - y_pred)**2)\n", + "\n", + " residuals = np.concatenate(residuals)\n", + " chi2 = np.sum(residuals) # Assume unity residuals\n", + " chi2_red = chi2 / (len(y) - N_params) # Reduced chi^2\n", + " chi2_map[i, j] = np.log10(chi2_red)\n", + " except Exception as e:\n", + " chi2_map[i, j] = np.nan\n", + "\n", + "# Plotting\n", + "plt.figure(figsize=(10, 5))\n", + "im = plt.imshow(chi2_map, aspect='auto', origin='lower',\n", + " extent=[length_scales[0], length_scales[-1], 0, len(nus)-1],\n", + " cmap='viridis')\n", + "plt.colorbar(im, label=r'$\\chi^2$')\n", + "plt.xticks(length_scales, labels=[f'{s:.3f}' for s in length_scales], rotation=45)\n", + "plt.yticks(range(len(nus)), labels=[str(n) for n in nus])\n", + "plt.xlabel('Length Scale')\n", + "plt.ylabel(r'$\\nu$')\n", + "plt.xscale('log')\n", + "plt.title('Chi-Squared Heatmap for Luminosity Fit Parameters')\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "7a4edb19-1411-44f6-a50d-d1f1fc5b48e6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.5 1.2742749857031335\n" + ] + } + ], + "source": [ + "i_best, j_best = np.unravel_index(np.nanargmin(chi2_map), chi2_map.shape)\n", + "best_nu = nus[i_best]\n", + "best_length_scale = length_scales[j_best]\n", + "print(best_nu, best_length_scale)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "79f3a7d1-ecd9-4d77-8923-6f729f9f66e3", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Looking at physical interpretation of heatmap parameters\n", + "\n", + "# creating input array (mass) and output array (luminosity)\n", + "X = combined_masses.reshape(-1, 1)\n", + "y = combined_L #np.array([combined_Teff, combined_L, combined_logg])\n", + "x = np.linspace(np.min(phil_mass), np.max(pisa_mass), int(1e6)).reshape(-1, 1)\n", + "\n", + "# trying different kernel types\n", + "kernel = Matern(length_scale=best_length_scale, nu=best_nu)\n", + "gp = GaussianProcessRegressor(kernel=kernel, optimizer=None, normalize_y=True)\n", + "gp.fit(X, y)\n", + "y_pred_1, sigma_1 = gp.predict(x, return_std=True)\n", + "#chi2 = np.sum((y - y_pred_1)**2) #unit test for 2d function\n", + "#print(chi2)\n", + "\n", + "plt.figure()\n", + "plt.scatter(X, combined_L, color='blue', label='actual values')\n", + "plt.plot(x, y_pred_1, color='orange', label='predicted values')\n", + "plt.xlabel('Mass ($M_{\\odot}$)')\n", + "plt.ylabel('Luminosity')\n", + "plt.title(' Reduced $\\chi^2$ Determination of Luminosity Best Fit Using kFold')\n", + "plt.xlim(0, 1)\n", + "plt.ylim(-4,0)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "80feb1ea-eee1-489c-9fa1-05111ba6b86d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "### WITHOUT KFOLD\n", + "X = combined_masses.reshape(-1, 1)\n", + "y = combined_L #np.array([combined_Teff, combined_L, combined_logg])\n", + "x = np.linspace(np.min(phil_mass), np.max(pisa_mass), int(1e6)).reshape(-1, 1)\n", + "\n", + "# Define grid\n", + "length_scales = np.logspace(-2, 1, 20)\n", + "nus = [0.5, 1.5, 2.5] # available Matern values\n", + "\n", + "chi2_map = np.zeros((len(nus), len(length_scales)))\n", + "N_data = len(y)\n", + "N_params = 2\n", + "\n", + "chi2_map = np.zeros((len(nus), len(length_scales)))\n", + "\n", + "for i, nu in enumerate(nus):\n", + " for j, ls in enumerate(length_scales):\n", + " kernel = Matern(length_scale=ls, nu=nu)\n", + " gp = GaussianProcessRegressor(kernel=kernel, optimizer=None, normalize_y=True)\n", + "\n", + " try:\n", + " gp.fit(X, y)\n", + " y_pred = gp.predict(X)\n", + " residuals = (y - y_pred)**2\n", + "\n", + " chi2 = np.sum(residuals) # assume unity residuals\n", + " chi2_red = chi2 / (N_data - N_params) # reduced chi^2\n", + " chi2_map[i, j] = np.log10(chi2_red)\n", + "\n", + " except Exception as e:\n", + " print(f\"Error at nu={nu}, length_scale={ls}: {e}\")\n", + " chi2_map[i, j] = np.nan\n", + "\n", + "# Plotting\n", + "plt.figure(figsize=(10, 5))\n", + "im = plt.imshow(chi2_map, aspect='auto', origin='lower',\n", + " extent=[length_scales[0], length_scales[-1], 0, len(nus)-1],\n", + " cmap='viridis')\n", + "plt.colorbar(im, label=r'$\\chi^2$')\n", + "plt.xticks(length_scales, labels=[f'{s:.3f}' for s in length_scales], rotation=45)\n", + "plt.yticks(range(len(nus)), labels=[str(n) for n in nus])\n", + "plt.xlabel('Length Scale')\n", + "plt.ylabel(r'$\\nu$')\n", + "plt.xscale('log')\n", + "plt.title('Chi-Squared Heatmap for Luminosity Fit Parameters')\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "aab48c6d-6d83-4ed6-9b70-6cf8d2842cd6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.5 0.01\n" + ] + } + ], + "source": [ + "i_best, j_best = np.unravel_index(np.nanargmin(chi2_map), chi2_map.shape)\n", + "best_nu = nus[i_best]\n", + "best_length_scale = length_scales[j_best]\n", + "print(best_nu, best_length_scale)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "3fec5172-ea8b-4f28-810f-c5577edfceb3", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Looking at physical interpretation of heatmap parameters\n", + "\n", + "# creating input array (mass) and output array (everything else)\n", + "X = combined_masses.reshape(-1, 1)\n", + "y = combined_L #np.array([combined_Teff, combined_L, combined_logg])\n", + "x = np.linspace(np.min(phil_mass), np.max(pisa_mass), int(1e6)).reshape(-1, 1)\n", + "\n", + "# trying different kernel types\n", + "kernel = Matern(length_scale=best_length_scale, nu=best_nu)\n", + "gp = GaussianProcessRegressor(kernel=kernel, optimizer=None, normalize_y=True)\n", + "gp.fit(X, y)\n", + "y_pred_1, sigma_1 = gp.predict(x, return_std=True)\n", + "#chi2 = np.sum((y - y_pred_1)**2) #unit test for 2d function\n", + "#print(chi2)\n", + "\n", + "plt.figure()\n", + "plt.scatter(X, combined_L, color='blue', label='actual values')\n", + "plt.plot(x, y_pred_1, color='orange', label='predicted values')\n", + "plt.xlabel('Mass ($M_{\\odot}$)')\n", + "plt.ylabel('Luminosity')\n", + "plt.title('Reduced $\\chi^2$ Determination of Luminosity Best Fit Without kFold')\n", + "plt.xlim(0, 1)\n", + "plt.ylim(-4,0)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "99653c01-83e7-44c1-8a70-a04c185b0c3e", + "metadata": {}, + "source": [ + "Through the use of kFold we produced a pretty good fit! We can then repeat the process to find the best parameters for effective temperature and log gravity." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "53552603-6dce-4c96-9d22-0facf0c28767", + "metadata": {}, + "outputs": [], + "source": [ + "#assume unity uncertainties and focus on gap between model and data -- gives small value but scale by relative \n", + "#number of data points -- should give value close to 1" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "2b89c29a-9c7e-4f31-94a6-094df81e01c1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# creating input array (mass) and output array (teff)\n", + "X = combined_masses.reshape(-1, 1)\n", + "y_teff = combined_Teff #np.array([combined_Teff, combined_L, combined_logg])\n", + "x = np.linspace(np.min(phil_mass), np.max(pisa_mass), int(1e6)).reshape(-1, 1)\n", + "\n", + "# Scale X and y\n", + "#X_scaler = StandardScaler()\n", + "#y_scaler = StandardScaler()\n", + "\n", + "#X = X_scaler.fit_transform(combined_masses.reshape(-1, 1))\n", + "#y = y_scaler.fit_transform(combined_L.reshape(-1, 1)).ravel()\n", + "\n", + "# Define grid\n", + "length_scales = np.logspace(-1, 2, 20)\n", + "nus = [0.5, 1.5, 2.5] # available Matern values\n", + "\n", + "chi2_map_teff = np.zeros((len(nus), len(length_scales)))\n", + "N_data_teff = len(y_teff)\n", + "N_params = 2\n", + "\n", + "kf = KFold(n_splits=5, shuffle=True, random_state=42)\n", + "chi2_map_teff = np.zeros((len(nus), len(length_scales)))\n", + "\n", + "for i, nu in enumerate(nus):\n", + " for j, ls in enumerate(length_scales):\n", + " kernel = Matern(length_scale=ls, nu=nu)\n", + " gp = GaussianProcessRegressor(kernel=kernel, optimizer=None, normalize_y=True)\n", + " \n", + " residuals_teff = []\n", + " try:\n", + " for train_idx, test_idx in kf.split(X):\n", + " gp.fit(X[train_idx], y_teff[train_idx])\n", + " y_pred_teff = gp.predict(X[test_idx])\n", + " residuals_teff.append((y_teff[test_idx] - y_pred_teff)**2)\n", + "\n", + " residuals_teff = np.concatenate(residuals_teff) \n", + " chi2_teff = np.sum(residuals_teff)\n", + " chi2_red_teff = chi2_teff / (N_data_teff - N_params)\n", + " chi2_map_teff[i, j] = np.log10(chi2_red_teff)\n", + " except Exception as e:\n", + " chi2_map_teff[i, j] = np.nan\n", + "# Plotting\n", + "plt.figure(figsize=(10, 5))\n", + "im = plt.imshow(chi2_map_teff, aspect='auto', origin='lower',\n", + " extent=[length_scales[0], length_scales[-1], 0, len(nus)-1],\n", + " cmap='viridis')\n", + "plt.colorbar(im, label=r'$\\chi^2$')\n", + "plt.xticks(length_scales, labels=[f'{s:.3f}' for s in length_scales], rotation=45)\n", + "plt.yticks(range(len(nus)), labels=[str(n) for n in nus])\n", + "plt.xlabel('Length Scale')\n", + "plt.ylabel(r'$\\nu$')\n", + "plt.xscale('log')\n", + "plt.title('Chi-Squared Heatmap for Luminosity Fit Parameters')\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "b29c1755-4b8e-404b-a8f5-024a759179af", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.5 1.2742749857031335\n" + ] + } + ], + "source": [ + "i_best_Teff, j_best_Teff = np.unravel_index(np.nanargmin(chi2_map_teff), chi2_map_teff.shape)\n", + "best_nu_Teff = nus[i_best_Teff]\n", + "best_length_scale_Teff = length_scales[j_best_Teff]\n", + "print(best_nu_Teff, best_length_scale_Teff)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "926cbb27-cf76-4259-bff4-63cdad0fce02", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Looking at physical interpretation of heatmap parameters\n", + "\n", + "# creating input array (mass) and output array (everything else)\n", + "X = combined_masses.reshape(-1, 1)\n", + "y_teff = combined_Teff #np.array([combined_Teff, combined_L, combined_logg])\n", + "x = np.linspace(np.min(phil_mass), np.max(pisa_mass), int(1e6)).reshape(-1, 1)\n", + "\n", + "# trying different kernel types\n", + "kernel = Matern(length_scale=best_length_scale_Teff, nu=best_nu_Teff)\n", + "gp = GaussianProcessRegressor(kernel=kernel, optimizer=None, normalize_y=True)\n", + "gp.fit(X, y_teff)\n", + "y_pred_teff, sigma_teff = gp.predict(x, return_std=True)\n", + "\n", + "plt.figure()\n", + "plt.scatter(X, combined_Teff, color='blue', label='actual values')\n", + "plt.plot(x, y_pred_teff, color='orange', label='predicted values')\n", + "plt.xlabel('Mass ($M_{\\odot}$)')\n", + "plt.ylabel('Teff')\n", + "plt.title('Reduced $\\chi^2$ Determination of Effective Temperature Best Fit')\n", + "plt.xlim(0, 1)\n", + "plt.ylim(3.25,3.75)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "fb250ffb-e8f5-4b66-a9d0-ae79190d1d0d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# creating input array (mass) and output array (luminosity)\n", + "X = combined_masses.reshape(-1, 1)\n", + "y_logg = combined_logg #np.array([combined_Teff, combined_L, combined_logg])\n", + "x = np.linspace(np.min(phil_mass), np.max(pisa_mass), int(1e6)).reshape(-1, 1)\n", + "\n", + "# Define grid\n", + "length_scales = np.logspace(-1, 2, 20)\n", + "nus = [0.5, 1.5, 2.5] # available Matern values\n", + "\n", + "chi2_map_logg = np.zeros((len(nus), len(length_scales)))\n", + "N_data_logg = len(y_logg)\n", + "N_params = 2\n", + "\n", + "kf = KFold(n_splits=5, shuffle=True, random_state=42)\n", + "\n", + "for i, nu in enumerate(nus):\n", + " for j, ls in enumerate(length_scales):\n", + " kernel = Matern(length_scale=ls, nu=nu)\n", + " gp = GaussianProcessRegressor(kernel=kernel, optimizer=None, normalize_y=True)\n", + " \n", + " residuals_logg = []\n", + " try:\n", + " for train_idx, test_idx in kf.split(X):\n", + " gp.fit(X[train_idx], y_logg[train_idx])\n", + " y_pred_logg = gp.predict(X[test_idx])\n", + " residuals_logg.append((y_logg[test_idx] - y_pred_logg)**2)\n", + "\n", + " residuals_logg = np.concatenate(residuals_logg) \n", + " chi2_logg = np.sum(residuals_logg)\n", + " chi2_red_logg = chi2_logg / (N_data_logg - N_params)\n", + " chi2_map_logg[i, j] = np.log10(chi2_red_logg)\n", + " except Exception as e:\n", + " chi2_map_logg[i, j] = np.nan\n", + "\n", + "# Plotting\n", + "plt.figure(figsize=(10, 5))\n", + "im = plt.imshow(chi2_map_logg, aspect='auto', origin='lower',\n", + " extent=[length_scales[0], length_scales[-1], 0, len(nus)-1],\n", + " cmap='viridis')\n", + "plt.colorbar(im, label=r'$\\chi^2$')\n", + "plt.xticks(length_scales, labels=[f'{s:.3f}' for s in length_scales], rotation=45)\n", + "plt.yticks(range(len(nus)), labels=[str(n) for n in nus])\n", + "plt.xlabel('Length Scale')\n", + "plt.ylabel(r'$\\nu$')\n", + "plt.xscale('log')\n", + "plt.title('Chi-Squared Heatmap for log g Fit Parameters')\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "850e9dc3-5120-46ff-a15b-ccecc379e33d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.5 0.20691380811147897\n" + ] + } + ], + "source": [ + "i_best_logg, j_best_logg = np.unravel_index(np.nanargmin(chi2_map_logg), chi2_map_logg.shape)\n", + "best_nu_logg = nus[i_best_logg]\n", + "best_length_scale_logg = length_scales[j_best_logg]\n", + "print(best_nu_logg, best_length_scale_logg)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "ce7d8969-3bb4-4154-8d1a-baaa1975baa6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Looking at physical interpretation of heatmap parameters\n", + "\n", + "# creating input array (mass) and output array (everything else)\n", + "X = combined_masses.reshape(-1, 1)\n", + "y = combined_logg #np.array([combined_Teff, combined_L, combined_logg])\n", + "x = np.linspace(np.min(phil_mass), np.max(pisa_mass), int(1e6)).reshape(-1, 1)\n", + "\n", + "# trying different kernel types\n", + "kernel = Matern(length_scale=best_length_scale_logg, nu=best_nu_logg)\n", + "gp = GaussianProcessRegressor(kernel=kernel, optimizer=None, normalize_y=True)\n", + "gp.fit(X, y_logg)\n", + "y_pred_logg, sigma_logg = gp.predict(x, return_std=True)\n", + "\n", + "plt.figure()\n", + "plt.scatter(X, combined_logg, color='blue', label='actual values')\n", + "plt.plot(x, y_pred_logg, color='orange', label='predicted values')\n", + "plt.xlabel('Mass ($M_{\\odot}$)')\n", + "plt.ylabel('Log Gravity')\n", + "plt.title('Reduced $\\chi^2$ Determination of Gravity Best Fit')\n", + "plt.xlim(0, 1)\n", + "plt.ylim(4.0,4.5)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "147e614a-4e8f-485e-abc3-195630b144ae", + "metadata": {}, + "source": [ + "### Generating Data in the Interpolated Region" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "d78bbc34-8c01-46a2-83da-43ffde446c5d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# starting with luminosity\n", + "\n", + "best_kernel_L = Matern(length_scale=best_length_scale, nu=best_nu)\n", + "gp_best_L = GaussianProcessRegressor(kernel=best_kernel_L, optimizer=None, normalize_y=True)\n", + "gp_best_L.fit(X, y)\n", + "\n", + "mass_vals = np.linspace(np.max(phil_mass), np.min(pisa_mass), 20).reshape(-1, 1)\n", + "L_pred = gp_best_L.predict(mass_vals)\n", + "\n", + "plt.figure()\n", + "plt.scatter(X, combined_L, color='blue', label='actual values')\n", + "plt.scatter(mass_vals, L_pred, color='pink', alpha=0.5, label='generated mass gap values')\n", + "plt.title('Creating Points for Luminosity Mass Gap')\n", + "plt.xlabel('Mass ($M_{\\odot}$)')\n", + "plt.ylabel('Luminosity')\n", + "plt.xlim(0, 1)\n", + "plt.ylim(-4,0)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "5aee3424-7efa-4bed-8030-4e70eb1f47c2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# moving to effective temperature\n", + "\n", + "best_kernel_teff = Matern(length_scale=best_length_scale_Teff, nu=best_nu_Teff)\n", + "gp_best_teff = GaussianProcessRegressor(kernel=best_kernel_teff, optimizer=None, normalize_y=True)\n", + "gp_best_teff.fit(X, y_teff)\n", + "\n", + "mass_vals = np.linspace(np.max(phil_mass), np.min(pisa_mass), 20).reshape(-1, 1)\n", + "teff_pred = gp_best_teff.predict(mass_vals)\n", + "\n", + "plt.figure()\n", + "plt.scatter(X, combined_Teff, color='blue', label='actual values')\n", + "plt.scatter(mass_vals, teff_pred, color='pink', alpha=0.5, label='generated mass gap values')\n", + "plt.title('Creating Points for Teff Mass Gap')\n", + "plt.xlabel('Mass ($M_{\\odot}$)')\n", + "plt.ylabel('Teff')\n", + "plt.xlim(0, 1)\n", + "plt.ylim(3.25,3.75)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "53238900-30e4-4015-b033-d81dd763d773", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# moving to effective temperature\n", + "\n", + "best_kernel_logg = Matern(length_scale=best_length_scale_logg, nu=best_nu_logg)\n", + "gp_best_logg = GaussianProcessRegressor(kernel=best_kernel_logg, optimizer=None, normalize_y=True)\n", + "gp_best_logg.fit(X, y_logg)\n", + "\n", + "mass_vals = np.linspace(np.max(phil_mass), np.min(pisa_mass), 20).reshape(-1, 1)\n", + "logg_pred = gp_best_logg.predict(mass_vals)\n", + "\n", + "plt.figure()\n", + "plt.scatter(X, combined_logg, color='blue', label='actual values')\n", + "plt.scatter(mass_vals, logg_pred, color='pink', alpha=0.5, label='generated mass gap values')\n", + "plt.title('Creating Points for logg Mass Gap')\n", + "plt.xlabel('Mass ($M_{\\odot}$)')\n", + "plt.ylabel('logg')\n", + "plt.xlim(0, 1)\n", + "plt.ylim(4.0,4.5)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "3da35d6f-d88c-4582-be4f-7b65f069e784", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# creating graphs of mass vs. luminosity, Teff, and gravity\n", + "fig, axs = plt.subplots(3, 1, figsize=(6, 10))\n", + "\n", + "# plotting generated data for luminosity\n", + "axs[0].scatter(combined_masses, combined_L, color='blue', label='actual values')\n", + "axs[0].scatter(mass_vals, L_pred, color='pink', alpha=0.5, label='generated mass gap values')\n", + "axs[0].set_title('Creating Points for Luminosity Mass Gap')\n", + "axs[0].set_xlabel('Mass ($M_{\\odot}$)')\n", + "axs[0].set_ylabel('Luminosity')\n", + "axs[0].set_xlim(0, 1)\n", + "#axs[0].set_ylim(-4,0)\n", + "axs[0].legend()\n", + "\n", + "# mass vs. Teff\n", + "axs[1].scatter(combined_masses, combined_Teff, color='blue', label='actual values')\n", + "axs[1].scatter(mass_vals, teff_pred, color='pink', alpha=0.5, label='generated mass gap values')\n", + "axs[1].set_title('Creating Points for Teff Mass Gap')\n", + "axs[1].set_xlabel('Mass ($M_{\\odot}$)')\n", + "axs[1].set_ylabel('Teff')\n", + "axs[1].set_xlim(0, 1)\n", + "#axs[1].set_ylim(3.25,3.75)\n", + "axs[1].legend()\n", + "\n", + "# mass vs. logg (problem child)\n", + "axs[2].scatter(combined_masses, combined_logg, color='blue', label='actual values')\n", + "axs[2].scatter(mass_vals, logg_pred, color='pink', alpha=0.5, label='generated mass gap values')\n", + "axs[2].set_title('Creating Points for logg Mass Gap')\n", + "axs[2].set_xlabel('Mass ($M_{\\odot}$)')\n", + "axs[2].set_ylabel('logg')\n", + "axs[2].set_xlim(0, 1)\n", + "#axs[2].set_ylim(4.0,4.5)\n", + "axs[2].legend()\n", + "\n", + "fig.tight_layout()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "d3d88985-6d1f-4aa2-bd88-5f69b73897ea", + "metadata": {}, + "source": [ + "### Testing Fit Parameters for Another Cluster Age" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "c8631679-e803-4d74-a549-68f41ba1196c", + "metadata": {}, + "outputs": [], + "source": [ + "# importing compatible age fits files \n", + "phillips2 = '/System/Volumes/Data/mnt/g/lu/models/evolution/Phillips2020/iso/z00/iso_8.051282050278353.fits'\n", + "pisa2 = '/System/Volumes/Data/mnt/g/lu/models/evolution/Pisa2011/iso/z015/iso_8.00.fits'\n", + "\n", + "# loading tables and extracting data\n", + "phil2_tbl = Table.read(phillips2, format='fits')\n", + "pisa2_tbl = Table.read(pisa2, format='fits')\n", + "\n", + "phil2_mass = phil2_tbl['Mass']\n", + "pisa2_mass = pisa2_tbl['col3']\n", + "combined_masses2 = np.concatenate([phil2_mass, pisa2_mass])\n", + "\n", + "phil2_teff = phil2_tbl['Teff']\n", + "pisa2_teff = pisa2_tbl['col2']\n", + "combined_teff2 = np.concatenate([phil2_teff, pisa2_teff])\n", + "\n", + "phil2_L = phil2_tbl['Luminosity']\n", + "pisa2_L = pisa2_tbl['col1']\n", + "combined_L2 = np.concatenate([phil2_L, pisa2_L])\n", + "\n", + "phil2_logg = phil2_tbl['Gravity']\n", + "pisa2_logg = pisa2_tbl['col4']\n", + "combined_logg2 = np.concatenate([phil2_logg, pisa2_logg])" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "a95f9710-bc1b-40ae-9b4b-73dec1e9e6a6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# creating graphs of mass vs. luminosity, Teff, and gravity\n", + "fig, axs = plt.subplots(3, 1, figsize=(6, 10))\n", + "\n", + "\n", + "# generated data for mass vs. luminosity\n", + "best_kernel_L2 = Matern(length_scale=best_length_scale, nu=best_nu)\n", + "gp_best_L2 = GaussianProcessRegressor(kernel=best_kernel_L2, optimizer=None, normalize_y=True)\n", + "gp_best_L2.fit(combined_masses2.reshape(-1, 1), combined_L2)\n", + "\n", + "mass_vals2 = np.linspace(np.max(phil2_mass), np.min(pisa2_mass), 20).reshape(-1, 1)\n", + "L_pred2 = gp_best_L2.predict(mass_vals2)\n", + "\n", + "# plotting generated data for luminosity\n", + "axs[0].scatter(combined_masses2, combined_L2, color='blue', label='actual values')\n", + "axs[0].scatter(mass_vals2, L_pred2, color='pink', alpha=0.5, label='generated mass gap values')\n", + "axs[0].set_title('Creating Points for Luminosity Mass Gap')\n", + "axs[0].set_xlabel('Mass ($M_{\\odot}$)')\n", + "axs[0].set_ylabel('Luminosity')\n", + "axs[0].set_xlim(0, 1)\n", + "#axs[0].set_ylim(-4,0)\n", + "axs[0].legend()\n", + "\n", + "# generated data for mass vs. teff\n", + "best_kernel_teff2 = Matern(length_scale=best_length_scale_Teff, nu=best_nu_Teff)\n", + "gp_best_teff2 = GaussianProcessRegressor(kernel=best_kernel_teff2, optimizer=None, normalize_y=True)\n", + "gp_best_teff2.fit(combined_masses2.reshape(-1, 1), combined_teff2)\n", + "\n", + "teff_pred2 = gp_best_teff2.predict(mass_vals2)\n", + "\n", + "# mass vs. Teff\n", + "axs[1].scatter(combined_masses2, combined_teff2, color='blue', label='actual values')\n", + "axs[1].scatter(mass_vals2, teff_pred2, color='pink', alpha=0.5, label='generated mass gap values')\n", + "axs[1].set_title('Creating Points for Teff Mass Gap')\n", + "axs[1].set_xlabel('Mass ($M_{\\odot}$)')\n", + "axs[1].set_ylabel('Teff')\n", + "axs[1].set_xlim(0, 1)\n", + "#axs[1].set_ylim(3.25,3.75)\n", + "axs[1].legend()\n", + "\n", + "# generated data for mass vs. logg\n", + "best_kernel_logg2 = Matern(length_scale=best_length_scale_logg, nu=best_nu_logg)\n", + "gp_best_logg2 = GaussianProcessRegressor(kernel=best_kernel_logg2, optimizer=None, normalize_y=True)\n", + "gp_best_logg2.fit(combined_masses2.reshape(-1, 1), combined_logg2)\n", + "\n", + "logg_pred2 = gp_best_logg2.predict(mass_vals2)\n", + "\n", + "# mass vs. logg (problem child)\n", + "axs[2].scatter(combined_masses2, combined_logg2, color='blue', label='actual values')\n", + "axs[2].scatter(mass_vals2, logg_pred2, color='pink', alpha=0.5, label='generated mass gap values')\n", + "axs[2].set_title('Creating Points for logg Mass Gap')\n", + "axs[2].set_xlabel('Mass ($M_{\\odot}$)')\n", + "axs[2].set_ylabel('logg')\n", + "axs[2].set_xlim(0, 1)\n", + "#axs[2].set_ylim(4.0,4.5)\n", + "axs[2].legend()\n", + "\n", + "fig.tight_layout()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "95d0dfdc-6f4d-49be-89c7-cc8337b466c3", + "metadata": {}, + "source": [ + "### Now for logAge = 6.00!" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "2a136d24-1b35-4164-882f-a78d70c3583a", + "metadata": {}, + "outputs": [], + "source": [ + "# importing compatible age fits files \n", + "phillips3 = '/System/Volumes/Data/mnt/g/lu/models/evolution/Phillips2020/iso/z00/iso_6.0.fits'\n", + "pisa3 = '/System/Volumes/Data/mnt/g/lu/models/evolution/Pisa2011/iso/z015/iso_6.00.fits'\n", + "\n", + "# loading tables and extracting data\n", + "phil3_tbl = Table.read(phillips3, format='fits')\n", + "pisa3_tbl = Table.read(pisa3, format='fits')\n", + "\n", + "phil3_mass = phil3_tbl['Mass']\n", + "pisa3_mass = pisa3_tbl['col3']\n", + "combined_masses3 = np.concatenate([phil3_mass, pisa3_mass])\n", + "\n", + "phil3_teff = phil3_tbl['Teff']\n", + "pisa3_teff = pisa3_tbl['col2']\n", + "combined_teff3 = np.concatenate([phil3_teff, pisa3_teff])\n", + "\n", + "phil3_L = phil3_tbl['Luminosity']\n", + "pisa3_L = pisa3_tbl['col1']\n", + "combined_L3 = np.concatenate([phil3_L, pisa3_L])\n", + "\n", + "phil3_logg = phil3_tbl['Gravity']\n", + "pisa3_logg = pisa3_tbl['col4']\n", + "combined_logg3 = np.concatenate([phil3_logg, pisa3_logg])" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "e6040f03-c6e6-4b09-90d5-8d89f593822d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# creating graphs of mass vs. luminosity, Teff, and gravity\n", + "fig, axs = plt.subplots(3, 1, figsize=(6, 10))\n", + "\n", + "\n", + "# generated data for mass vs. luminosity\n", + "best_kernel_L3 = Matern(length_scale=best_length_scale, nu=best_nu)\n", + "gp_best_L3 = GaussianProcessRegressor(kernel=best_kernel_L3, optimizer=None, normalize_y=True)\n", + "gp_best_L3.fit(combined_masses3.reshape(-1, 1), combined_L3)\n", + "\n", + "mass_vals3 = np.linspace(np.max(phil3_mass), np.min(pisa3_mass), 20).reshape(-1, 1)\n", + "L_pred3 = gp_best_L3.predict(mass_vals3)\n", + "\n", + "# plotting generated data for luminosity\n", + "axs[0].scatter(combined_masses3, combined_L3, color='blue', label='actual values')\n", + "axs[0].scatter(mass_vals3, L_pred3, color='pink', alpha=0.5, label='generated mass gap values')\n", + "axs[0].set_title('Creating Points for Luminosity Mass Gap')\n", + "axs[0].set_xlabel('Mass ($M_{\\odot}$)')\n", + "axs[0].set_ylabel('Luminosity')\n", + "axs[0].set_xlim(0, 1)\n", + "#axs[0].set_ylim(-4,0)\n", + "axs[0].legend()\n", + "\n", + "# generated data for mass vs. teff\n", + "best_kernel_teff3 = Matern(length_scale=best_length_scale_Teff, nu=best_nu_Teff)\n", + "gp_best_teff3 = GaussianProcessRegressor(kernel=best_kernel_teff3, optimizer=None, normalize_y=True)\n", + "gp_best_teff3.fit(combined_masses3.reshape(-1, 1), combined_teff3)\n", + "\n", + "teff_pred3 = gp_best_teff3.predict(mass_vals3)\n", + "\n", + "# mass vs. Teff\n", + "axs[1].scatter(combined_masses3, combined_teff3, color='blue', label='actual values')\n", + "axs[1].scatter(mass_vals3, teff_pred3, color='pink', alpha=0.5, label='generated mass gap values')\n", + "axs[1].set_title('Creating Points for Teff Mass Gap')\n", + "axs[1].set_xlabel('Mass ($M_{\\odot}$)')\n", + "axs[1].set_ylabel('Teff')\n", + "axs[1].set_xlim(0, 1)\n", + "#axs[1].set_ylim(3.25,3.75)\n", + "axs[1].legend()\n", + "\n", + "# generated data for mass vs. logg\n", + "best_kernel_logg3 = Matern(length_scale=best_length_scale_logg, nu=best_nu_logg)\n", + "gp_best_logg3 = GaussianProcessRegressor(kernel=best_kernel_logg3, optimizer=None, normalize_y=True)\n", + "gp_best_logg3.fit(combined_masses3.reshape(-1, 1), combined_logg3)\n", + "\n", + "logg_pred3 = gp_best_logg3.predict(mass_vals3)\n", + "\n", + "# mass vs. logg (problem child)\n", + "axs[2].scatter(combined_masses3, combined_logg3, color='blue', label='actual values')\n", + "axs[2].scatter(mass_vals3, logg_pred3, color='pink', alpha=0.5, label='generated mass gap values')\n", + "axs[2].set_title('Creating Points for logg Mass Gap')\n", + "axs[2].set_xlabel('Mass ($M_{\\odot}$)')\n", + "axs[2].set_ylabel('logg')\n", + "axs[2].set_xlim(0, 1)\n", + "#axs[2].set_ylim(4.0,4.5)\n", + "axs[2].legend()\n", + "\n", + "fig.tight_layout()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "01fbb0b7-0d7c-4e04-b458-5635d4c0fcb5", + "metadata": {}, + "source": [ + "### Creating a Function to Apply Model to All Pisa/Phillips Files" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "accb8141-1888-49cf-84be-161bc3dbc197", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/changes/mass_to_age.py b/changes/mass_to_age.py new file mode 100644 index 00000000..0ac86c9c --- /dev/null +++ b/changes/mass_to_age.py @@ -0,0 +1,2518 @@ +import math +import logging +from numpy import genfromtxt +import numpy as np +import os +import glob +import pandas as pd +import pdb +import warnings +from astropy.table import Table, vstack, Column +from scipy import interpolate +import pylab as py +from spisea.utils import objects +from scipy.interpolate import RegularGridInterpolator +from spisea import exceptions +import re +import matplotlib +import matplotlib.pyplot as plt +from spisea import atmospheres + +logger = logging.getLogger('evolution') + +# Fetch root directory of evolution models. +try: + models_dir = os.environ['SPISEA_MODELS'] + models_dir += '/evolution/' +except KeyError: + warnings.warn("SPISEA_MODELS is undefined; functionality " + "will be SEVERELY crippled.") + models_dir = '' + +# Code to deconstruct current Phillips2020 evolution files and reconstruct iso files based on age + +# Define input and output directories +input_dir = '/System/Volumes/Data/mnt/g/lu/models/evolution/Phillips2020/z00_mass' +output_dir = '/System/Volumes/Data/mnt/g/lu/models/evolution/Phillips2020/z00_age' +os.makedirs(output_dir, exist_ok=True) + +# Combine data from all files +combined_data = [] + +for filename in os.listdir(input_dir): + if filename.endswith('.txt'): + file_path = os.path.join(input_dir, filename) + table = Table.read(file_path, format='ascii') + combined_data.append(table) + +# Concatenate all data into a single table +all_data = combined_data[0] + +# Add the remaining tables to the main table +for table in combined_data[1:]: + all_data = vstack([all_data, table]) # Use vstack to stack tables + +# Group data by age +ages = np.unique(all_data['Age']) + +# Iterate over each unique age and filter data +for age in ages: + age_group = all_data[all_data['Age'] == age] + output_path = os.path.join(output_dir, f"ATMO_{age}.txt") + + # Save each age group as a .txt file + age_group.write(output_path, format='ascii', overwrite=True) + +print(f"New files created in: {output_dir}") + +# Code to eradicate duplicate lines seen in above code +"""new_input_dir = output_dir + +for filename2 in os.listdir(new_input_dir): + if filename2.endswith('.txt'): + file_path2 = os.path.join(new_input_dir, filename2) + + # Remove duplicates before loading as a table + with open(file_path2, 'r') as f: + lines = f.readlines() + + header = lines[0] + data_lines = [line for line in lines[1:] if not line.startswith(header.split()[0])] + + with open(file_path2, 'w') as f: + f.write(header) + f.writelines(data_lines) + + # Now process with Astropy Table + table2 = Table.read(file_path2, format='ascii') + unique_table2 = unique(table2) + unique_table2.write(file_path2, format='ascii', overwrite=True) + +print('files overwritten successfully!') + + +# Reformatting files to match Parsec +def reformat(): + for file in os.listdir(output_dir): + if file.endswith('.txt'): + new_fp = os.path.join(output_dir, file) + + # Add metallicity column of all 0.0 + r_table = Table.read(new_fp, format='ascii') + r_table.add_column(0.0, name='Z', index=0) + + # Duplicate mass to include current mass column + r_table.add_column(r_table['Mass'], name='Mass_current') + + # Update age column to make it log scale + r_table['Age'] = np.log10(r_table['Age'] * 1e9) #originally in Gyr + + # Update Teff column to make it log scale + r_table['Teff'] = np.log10(r_table['Teff']) + + # Reorder columns to match Parsec + new_order = ['Z', 'Age', 'Mass', 'Mass_current', 'Luminosity', 'Teff', 'Gravity', 'Gaia_Gbp', 'Gaia_G', 'Gaia_Grp'] + t_new = r_table[new_order] + t_new.write(new_fp, format='ascii', overwrite=True) + + print(f"{file} reformatted successfully!") + + return + +# Transform reformatted .txt files to iso fits files +def ATMO_to_iso(): + i_dir = output_dir + o_dir = '/System/Volumes/Data/mnt/g/lu/models/evolution/Phillips2020/iso' #output directory SPISEA will pull from + + for file in os.listdir(i_dir): + if file.endswith('.txt'): + fp = os.path.join(i_dir, file) + + try: + age_str = file.split('_')[1].split('.txt')[0] + age = float(age_str) + log_age = np.log10(age * 1e9) + except (IndexError, ValueError): + print(f"{file} cannot be processed.") + continue + + try: + # load in .txt file as ascii table + table = Table.read(fp, format='ascii') + except Exception as e: + print(f"{fp} could not be read: {e}") + continue + + #create output file name + o_file = os.path.join(o_dir, f'iso_{log_age}.fits') + + try: + # write to output directory as fits file + table.write(o_file, format='fits', overwrite=True) + print(f"{o_file} created successfully!") + except Exception as e: + print(f"{o_file} could not be generated: {e}") + continue + + return + + +""" +### CODE TO UNPACK MARLEY FILES ### +def Marley_deconstruct(): + """ + Code to deconstruct big Marley files into individual age files + """ + in_dir = '/System/Volumes/Data/mnt/g/lu/models/evolution/Marley2021/Marley_age' + out_dir = '/System/Volumes/Data/mnt/g/lu/models/evolution/Marley2021/iso' + + # Set path to each file + for filename in os.listdir(in_dir): + file_path = os.path.join(in_dir, filename) + + # Extract metallicity from filename + match = re.search(r'nc([+-]\d+\.\d+)_co', filename) + metallicity = match.group(1) if match else "unknown" + + # Deconstruct initial format of single column table + with open(file_path, 'r') as f: + lines = f.readlines() + header = ['Age', 'Mass', 'log_L', 'Teff', 'logg', 'Radius'] + data = [line.strip().split() for line in lines[1:]] + data = [row for row in data if len(row) > 1] + table = Table(rows=data, names=header) + + # Find unique ages to create iso age_based files + ages = np.unique(table['Age']) + + for age in ages: + age_group = table[table['Age'] == age] + out_path = os.path.join(out_dir, f"Marley_{metallicity}_{age}.txt") + + # Save each age group as a .txt file + age_group.write(out_path, format='ascii', overwrite=True) + + print(f"New files created in: {out_dir}") + + return + +# Reformatting files to match Parsec +def reformat_Marley(): + age_dir = '/System/Volumes/Data/mnt/g/lu/models/evolution/Marley2021/age_txt' + for file in os.listdir(age_dir): + if file.endswith('.txt'): + new_fp = os.path.join(age_dir, file) + + # Add metallicity column + table = Table.read(new_fp, format='ascii') + + # Extract metallicity from filename + match = re.search(r'Marley_([+-]?\d+\.\d+)_\d+\.\d+.txt', file) + metallicity = float(match.group(1)) if match else np.nan + + # Replace or add metallicity column + if 'Z' in table.colnames: + table.replace_column('Z', [metallicity] * len(table)) + else: + table.add_column([metallicity] * len(table), name='Z', index=0) + + # Duplicate mass to include current mass column + #table.add_column(table['Mass'], name='Mass_current') + + # Update age column to make it log scale + #table['Age'] = np.log10(table['Age'] * 1e9) #originally in Gyr + + # Update Teff column to make it log scale + #table['Teff'] = np.log10(table['Teff']) + + # Reorder columns to match Parsec + new_order = ['Z', 'Age', 'Mass', 'Mass_current', 'log_L', 'Teff', 'logg', 'Radius'] + t_new = table[new_order] + t_new.write(new_fp, format='ascii', overwrite=True) + + print(f"{file} reformatted successfully!") + + return + +def Marley_to_iso(): + in_dir = '/System/Volumes/Data/mnt/g/lu/models/evolution/Marley2021/age_txt' + out_dir_1 = '/System/Volumes/Data/mnt/g/lu/models/evolution/Marley2021/iso/zm05' + out_dir_2 = '/System/Volumes/Data/mnt/g/lu/models/evolution/Marley2021/iso/zp00' + out_dir_3 = '/System/Volumes/Data/mnt/g/lu/models/evolution/Marley2021/iso/zp05' + + for file in os.listdir(in_dir): + if file.endswith('.txt'): + fp = os.path.join(in_dir, file) + + try: + parts = file.split('_') + metal_str = parts[1] # Second part is metallicity + age_str = parts[2].split('.txt')[0] + + age = float(age_str) + metallicity = float(metal_str) + log_age = np.log10(age * 1e9) + except (IndexError, ValueError): + print(f"{file} cannot be processed.") + continue + + try: + # load in .txt file as ascii table + table = Table.read(fp, format='ascii') + except Exception as e: + print(f"{fp} could not be read: {e}") + continue + + # Determine output directory based on metallicity + if metallicity == -0.5: + out_dir = out_dir_1 + elif metallicity == 0.0: + out_dir = out_dir_2 + elif metallicity == 0.5: + out_dir = out_dir_3 + else: + print(f"Skipping {file}: Unexpected metallicity value ({metallicity}).") + continue + + # Create output filename + out_file = os.path.join(out_dir, f'iso_{log_age}.fits') + + try: + # Write to output directory as FITS file + table.write(out_file, format='fits', overwrite=True) + print(f"{out_file} created successfully!") + except Exception as e: + print(f"Error writing {out_file}: {e}") + continue + + return + +### CREATING MERGED EVO MODEL WITH PHILLIPS ### +def get_phillips_isochrone(logAge, metallicity='solar'): + """ + Load mass, effective temperature, log gravity, and log luminosity + for the Phillips isochrones at given logAge. Code will quit if that + logAge value doesn't exist (can make some sort of interpolation thing + later). + + Note: mass is currently initial mass, not instantaneous mass + + Inputs: + logAge - Logarithmic Age + metallicity - in Z (def = solar of 0.014) + """ + rootDir = models_dir + 'Phillips2020/iso/' + metSuffix = 'z00/' + if metallicity != 'solar': + print( 'Non-solar Phillips 2020 metallicities not supported yet') + return + rootDir += metSuffix + + # List available isochrone files + available_ages = [] + for filename in os.listdir(rootDir): + if filename.startswith('iso_') and filename.endswith('.fits'): + age_str = filename.split('_')[1].split('.fits')[0] # Extract the age part from filename + available_ages.append(float(age_str)) + + # Find the closest available age from Phillips + closest_age = min(available_ages, key=lambda x: abs(x - logAge)) + print(closest_age) + + # Load the corresponding isochrone + isoFile = rootDir + f'iso_{closest_age}.fits' + print(f"Loading isochrone for logAge = {closest_age}") + + # Check to see if isochrone exists + if not os.path.exists(isoFile): + print( f'Phillips isochrone for logAge = {closest_age} does\'t exist') + print( 'Quitting') + return + + data = Table.read(isoFile, format='fits') + print("Available Columns:", data.keys()) + cols = data.keys() + mass = data[cols[2]] #Note: this is initial mass, in M_sun + logT = data[cols[5]] # K + logL = data[cols[4]] # L_sun + logg = data[cols[6]] + mass_current = data[cols[3]] # Matches initial mass -- BD masses assumed to not change w current models + phase = np.ones(len(mass), dtype=int) + + obj = objects.DataHolder() + obj.mass = mass + obj.logT = logT + obj.logg = logg + obj.logL = logL + obj.mass_current = mass_current + obj.phase = phase + + return obj + +def get_Baraffe15_isochrone(logAge, metallicity='solar'): + """ + Load mass, effective temperature, log gravity, and log luminosity + for the Baraffe+15 isochrones at given logAge. Code will quit if that + logAge value doesn't exist (can make some sort of interpolation thing + later). + + ALSO interpolates isochrone to a finer mass grid. + + Inputs: + logAge - Logarithmic Age + metallicity - in Z (def = solar of 0.014) + """ + rootDir = models_dir + 'Baraffe15/iso/' + if metallicity != 'solar': + print( 'Non-solar Baraffe+15 metallicities not supported yet') + return + + # Check to see if isochrone exists + isoFile = rootDir + 'iso_%.2f.fits' % logAge + if not os.path.exists(isoFile): + print( 'Baraffe+15 isochrone for logAge = {0:3.2f} does\'t exist'.format(logAge)) + print( 'Quitting') + return + + data = Table.read(isoFile, format='fits') + mass = data['Mass'] #Note: this is initial mass, in M_sun + logT = np.log10(data['Teff']) # K + logL = data['logL'] # L_sun + logg = data['logG'] + + # Interpolate isochrone to finer mass grid. Spacing + # is one model every 0.02 M_sun down to 0.2 M_sun, then + # one model every 0.005 M_sun down to 0.07 M_sun + new_masses0 = np.arange(min(mass), 0.1, 0.005) + new_masses2 = np.arange(0.1, max(mass), 0.02) + + #new_masses = np.concatenate((new_masses0, new_masses1, new_masses2)) + new_masses = np.concatenate((new_masses0, new_masses2)) + + # Build interpolators in linear space + f_logT = interpolate.interp1d(mass, 10**logT, kind='linear') + f_logL = interpolate.interp1d(mass, 10**logL, kind='linear') + f_logg = interpolate.interp1d(mass, 10**logg, kind='linear') + + # Do interpolation, convert back to logspace + logT_interp = np.log10(f_logT(new_masses)) + logL_interp = np.log10(f_logL(new_masses)) + logg_interp = np.log10(f_logg(new_masses)) + + # Hack, add new mass_current and phase columns. + mass_current = np.array(new_masses) + phase = np.ones(len(new_masses), dtype=int) + + # Test the interpolation, if desired + test = False + if test: + py.figure(1, figsize=(10,10)) + py.clf() + py.plot(mass, logT, 'k.', ms = 10, label='Orig') + py.plot(new_masses, logT_interp, 'r.', ms=7, label='Interp') + py.xlabel('Mass') + py.ylabel('logT') + py.legend() + + py.figure(2, figsize=(10,10)) + py.clf() + py.plot(mass, logL, 'k.', ms = 10, label='Orig') + py.plot(new_masses, logL_interp, 'r.', ms=7, label='Interp') + py.xlabel('Mass') + py.ylabel('logL') + py.legend() + + py.figure(3, figsize=(10,10)) + py.clf() + py.plot(mass, logg, 'k.', ms = 10, label='Orig') + py.plot(new_masses, logg_interp, 'r.', ms=7, label='Interp') + py.xlabel('Mass') + py.ylabel('logg') + py.legend() + + pdb.set_trace() + + # Make isochrone + obj = objects.DataHolder() + obj.mass = new_masses + obj.logT = logT_interp + obj.logg = logg_interp + obj.logL = logL_interp + obj.mass_current = mass_current + obj.phase = phase + + return obj + +def merge_isochrone_baraffe_phillips(logAge, metallicity='solar'): + """ + Function to merge Baraffe+15 and Phillips 2020 models. Will take + 100% Phillips2020 between 0.01 - 0.07 M_sun, transition between + 0.07 - 0.075 M_sun, and take 100% Baraffe from 0.075 M_sun and up. + + Can only handle ages at which models already exist: + logAge = 6.0 - 8.0, delta logAge = 0.01 + """ + if metallicity != 'solar': + print( 'Non-solar metallicity not supported yet') + return + + # Get individual Baraffe and Phillips isochrones at desired age. Note + # that this will also give the Baraffe models a finer mass sampling + isoBaraffe = get_Baraffe15_isochrone(logAge, metallicity=metallicity) + isoPhillips = get_phillips_isochrone(logAge, metallicity=metallicity) + + # Identify M >= 0.075 M_sun in Baraffe and M <= 0.07 M_sun in Phillips + good_b = np.where(isoBaraffe.mass >= 0.075) + good_p = np.where(isoPhillips.mass <= 0.07) + + # Sample between 0.4 M_sun and 0.5 M_sun in steps of 0.02 M_sun. + # Will do linear combo of Baraffe and Phillips over this range + mid_mass = np.arange(0.07, 0.075, 0.002) + mid_logT = [] + mid_logL = [] + mid_logG = [] + mid_Mcurr = [] + mid_phase = [] + for mass in mid_mass: + # Find the appropriate masses in Baraffe + Phillips to build from. + # Baraffe has identical sampling over this range, and Phillips sampling + # is very close. As a result, we will just take the closest mass model + # to each mid_mass + idx_b = np.where( abs(isoBaraffe.mass - mass) == min(abs(isoBaraffe.mass - mass)) ) + idx_p = np.where( abs(isoPhillips.mass - mass) == min(abs(isoPhillips.mass - mass)) ) + + # Quality control check: we won't let the difference between model mass and + # chosen mass to be >= 0.01 M_sun + if ((isoPhillips.mass[idx_p] - mass) >= 0.002) | ((isoBaraffe.mass[idx_b] - mass) >= 0.002): + print( 'WARNING: Baraffe or Phillips model interpolation between 0.01 - 0.08 M_sun may \ + be inaccurate. Check this!') + pdb.set_trace() + + # Now, do the linear combo of models at this mass, weighted by distance from + # 0.07 or 0.075 (whichever is appropriate) + diff = 0.075 - 0.07 + weight_p = (0.075 - mass) / diff + weight_b = 1.0 - weight_p + print( 'Baraffe {0} and Phillips {1} at mass {2}'.format(weight_p, weight_b, mass)) + + # Now, do the merge IN LINEAR SPACE! + Teff = (10**isoPhillips.logT[idx_p] * weight_p) + \ + (10**isoBaraffe.logT[idx_b] * weight_b) + L = (10**isoPhillips.logL[idx_p] * weight_p) + \ + (10**isoBaraffe.logL[idx_b] * weight_b) + g = (10**isoPhillips.logg[idx_p] * weight_p) + \ + (10**isoBaraffe.logg[idx_b] * weight_b) + mcurr = (isoPhillips.mass_current[idx_p] * weight_p) + \ + (isoBaraffe.mass_current[idx_b] * weight_b) + phase = np.round((isoPhillips.mass_current[idx_p] * weight_p) + \ + (isoBaraffe.mass_current[idx_b] * weight_b)) + + mid_logT = np.concatenate((mid_logT, np.log10(Teff))) + mid_logL = np.concatenate((mid_logL, np.log10(L))) + mid_logG = np.concatenate((mid_logG, np.log10(g))) + mid_Mcurr = np.concatenate((mid_Mcurr, mcurr)) + mid_phase = np.concatenate((mid_phase, phase)) + + # Now, final isochrone will be combination of Baraffe at M>=0.075, + # Phillips at M<=0.075, and the combination inbetween + mass = np.concatenate((isoPhillips.mass[good_p], mid_mass, isoBaraffe.mass[good_b])) + logT = np.concatenate((isoPhillips.logT[good_p], mid_logT, isoBaraffe.logT[good_b])) + logL = np.concatenate((isoPhillips.logL[good_p], mid_logL, isoBaraffe.logL[good_b])) + logG = np.concatenate((isoPhillips.logg[good_p], mid_logG, isoBaraffe.logg[good_b])) + mcurr = np.concatenate((isoPhillips.mass_current[good_p], mid_Mcurr, isoBaraffe.mass_current[good_b])) + phase = np.concatenate((isoPhillips.phase[good_p], mid_phase, isoBaraffe.phase[good_b])) + + # Also add a source flag + source = np.concatenate( (['Phillips']*len(good_p[0]), + ['Baraffe+Phillips']*len(mid_mass), + ['Baraffe']*len(good_b[0])) ) + + iso = objects.DataHolder() + iso.mass = mass + iso.logL = logL + iso.logg = logG + iso.logT = logT + iso.mass_current = mcurr + iso.phase = phase + iso.source = source + + return iso + +def merge_isochrone_baraffe_pisa(logAge, metallicity='solar'): + """ + Function to merge Baraffe+15 and Pisa 2011 models. Will take + 100% Baraffe+15 between 0.07 - 0.4 M_sun, transition between + 0.4 - 0.5 M_sun, and take 100% Pisa from 0.5 M_sun and up. + + Can only handle ages at which models already exist: + logAge = 6.0 - 8.0, delta logAge = 0.01 + """ + if metallicity != 'solar': + print( 'Non-solar metallicity not supported yet') + return + + # Get individual Baraffe and Pisa isochrones at desired age. Note + # that this will also give the Baraffe models a finer mass sampling + isoBaraffe = get_Baraffe15_isochrone(logAge, metallicity=metallicity) + isoPisa = get_pisa_isochrone(logAge, metallicity=metallicity) + + # Identify M <= 0.4 M_sun in Baraffe and M >= 0.5 M_sun in Pisa + good_b = np.where(isoBaraffe.mass <= 0.4) + good_p = np.where(isoPisa.mass >= 0.5) + + # Sample between 0.4 M_sun and 0.5 M_sun in steps of 0.02 M_sun. + # Will do linear combo of Baraffe and Pisa over this range + mid_mass = np.arange(0.4, 0.5+0.01, 0.02) + mid_logT = [] + mid_logL = [] + mid_logG = [] + mid_Mcurr = [] + mid_phase = [] + for mass in mid_mass: + # Find the appropriate masses in Baraffe + Pisa to build from. + # Baraffe has identical sampling over this range, and Pisa sampling + # is very close. As a result, we will just take the closest mass model + # to each mid_mass + idx_b = np.where( abs(isoBaraffe.mass - mass) == min(abs(isoBaraffe.mass - mass)) ) + idx_p = np.where( abs(isoPisa.mass - mass) == min(abs(isoPisa.mass - mass)) ) + + # Quality control check: we won't let the difference between model mass and + # chosen mass to be >= 0.01 M_sun + if ((isoPisa.mass[idx_p] - mass) >= 0.02) | ((isoBaraffe.mass[idx_b] - mass) >= 0.02): + print( 'WARNING: Baraffe or Pisa model interpolation between 0.4 - 0.5 M_sun may \ + be inaccurate. Check this!') + pdb.set_trace() + + # Now, do the linear combo of models at this mass, weighted by distance from + # 0.4 or 0.5 (whichever is appropriate) + diff = 0.5 - 0.4 + weight_b = (0.5 - mass) / diff + weight_p = 1.0 - weight_b + print( 'Baraffe {0} and Pisa {1} at mass {2}'.format(weight_b, weight_p, mass)) + + # Now, do the merge IN LINEAR SPACE! + Teff = (10**isoBaraffe.logT[idx_b] * weight_b) + \ + (10**isoPisa.logT[idx_p] * weight_p) + L = (10**isoBaraffe.logL[idx_b] * weight_b) + \ + (10**isoPisa.logL[idx_p] * weight_p) + g = (10**isoBaraffe.logg[idx_b] * weight_b) + \ + (10**isoPisa.logg[idx_p] * weight_p) + mcurr = (isoBaraffe.mass_current[idx_b] * weight_b) + \ + (isoPisa.mass_current[idx_p] * weight_p) + phase = np.round((isoBaraffe.mass_current[idx_b] * weight_b) + \ + (isoPisa.mass_current[idx_p] * weight_p)) + + mid_logT = np.concatenate((mid_logT, np.log10(Teff))) + mid_logL = np.concatenate((mid_logL, np.log10(L))) + mid_logG = np.concatenate((mid_logG, np.log10(g))) + mid_Mcurr = np.concatenate((mid_Mcurr, mcurr)) + mid_phase = np.concatenate((mid_phase, phase)) + + # Now, final isochrone will be combination of Baraffe at M<=0.4, + # Pisa at M>=0.5, and the combination inbetween + mass = np.concatenate((isoBaraffe.mass[good_b], mid_mass, isoPisa.mass[good_p])) + logT = np.concatenate((isoBaraffe.logT[good_b], mid_logT, isoPisa.logT[good_p])) + logL = np.concatenate((isoBaraffe.logL[good_b], mid_logL, isoPisa.logL[good_p])) + logG = np.concatenate((isoBaraffe.logg[good_b], mid_logG, isoPisa.logg[good_p])) + mcurr = np.concatenate((isoBaraffe.mass_current[good_b], mid_Mcurr, isoPisa.mass_current[good_p])) + phase = np.concatenate((isoBaraffe.phase[good_b], mid_phase, isoPisa.phase[good_p])) + + # Also add a source flag + source = np.concatenate( (['Baraffe']*len(good_b[0]), ['Baraffe+Pisa']*len(mid_mass), + ['Pisa']*len(good_p[0])) ) + + iso = objects.DataHolder() + iso.mass = mass + iso.logL = logL + iso.logg = logG + iso.logT = logT + iso.mass_current = mcurr + iso.phase = phase + iso.source = source + + return iso + + +import matplotlib.pyplot as plt +import numpy as np + +"""def plot_merged_isochrone(iso): + "" + Function to plot the merged isochrone model to visualize the transition + between Phillips 2020 and Baraffe+15 models. + + Parameters: + ----------- + iso : DataHolder object + Merged isochrone returned by merge_isochrone_baraffe_phillips(). + "" + + # Define colors for different sources + color_map = {'Phillips': 'blue', 'Baraffe': 'red', 'Baraffe+Phillips': 'pink'} + + # Create figure and subplots + fig, axes = plt.subplots(1, 3, figsize=(18, 5)) + + # Mass vs. logT (Effective Temperature) + for source in np.unique(iso.source): + mask = iso.source == source + axes[0].scatter(iso.mass[mask], iso.logT[mask], label=source, color=color_map[source], alpha=0.7) + axes[0].plot(iso.mass[mask], iso.logT[mask], label='linear representation') + axes[0].set_xlabel("Mass ($M_{\odot}$)") + axes[0].set_ylabel("$\log T_{\mathrm{eff}}$ (K)") + axes[0].set_title("Mass vs. Effective Temperature") + axes[0].axvline(0.07, linestyle="--", color="gray", alpha=0.5) # Transition marker + axes[0].axvline(0.08, linestyle="--", color="gray", alpha=0.5) # Transition marker + axes[0].set_xlim(0.0, 0.1) + axes[0].legend() + + # Mass vs. logL (Luminosity) + for source in np.unique(iso.source): + mask = iso.source == source + axes[1].scatter(iso.mass[mask], iso.logL[mask], label=source, color=color_map[source], alpha=0.7) + axes[1].plot(iso.mass[mask], iso.logL[mask], label='linear representation') + axes[1].set_xlabel("Mass ($M_{\odot}$)") + axes[1].set_ylabel("$\log L$ ($L_{\odot}$)") + axes[1].set_title("Mass vs. Luminosity") + axes[1].axvline(0.07, linestyle="--", color="gray", alpha=0.5) + axes[1].axvline(0.08, linestyle="--", color="gray", alpha=0.5) + axes[1].set_xlim(0.0, 0.1) + axes[1].legend() + + # Mass vs. logg (Surface Gravity) + for source in np.unique(iso.source): + mask = iso.source == source + axes[2].scatter(iso.mass[mask], iso.logg[mask], label=source, color=color_map[source], alpha=0.7) + axes[2].plot(iso.mass[mask], iso.logg[mask], label='linear representation') + axes[2].set_xlabel("Mass ($M_{\odot}$)") + axes[2].set_ylabel("$\log g$ (cm/s²)") + axes[2].set_title("Mass vs. Surface Gravity") + axes[2].axvline(0.07, linestyle="--", color="gray", alpha=0.5) + axes[2].axvline(0.08, linestyle="--", color="gray", alpha=0.5) + axes[2].set_xlim(0.0, 0.1) + axes[2].legend() + + # Adjust layout and show plot + plt.tight_layout() + plt.show() +""" + +import numpy as np +import matplotlib.pyplot as plt + +def plot_merged_isochrone(iso): + """ + Function to plot the merged isochrone model to visualize the transition + between Phillips 2020 and Baraffe+15 models. + + Parameters: + ----------- + iso : DataHolder object + Merged isochrone returned by merge_isochrone_baraffe_phillips(). + """ + + # Define colors for different sources + color_map = {'Phillips': 'blue', 'Baraffe': 'red', 'Baraffe+Phillips': 'pink'} + + # Create figure and subplots + fig, axes = plt.subplots(1, 3, figsize=(18, 5)) + + # Mass vs. logT (Effective Temperature) + for source in np.unique(iso.source): + mask = iso.source == source + axes[0].scatter(iso.mass[mask], iso.logT[mask], label=source, color=color_map[source], alpha=0.7) + axes[0].plot(iso.mass[mask], iso.logT[mask], color=color_map[source]) # Fixed plot function + axes[0].set_xlabel("Mass ($M_{\odot}$)") + axes[0].set_ylabel("$\log T_{\mathrm{eff}}$ (K)") + axes[0].set_title("Mass vs. Effective Temperature") + axes[0].axvline(0.07, linestyle="--", color="gray", alpha=0.5) # Transition marker + axes[0].axvline(0.08, linestyle="--", color="gray", alpha=0.5) # Transition marker + axes[0].set_xlim(0.0, 0.1) + axes[0].legend() + + # Mass vs. logL (Luminosity) + for source in np.unique(iso.source): + mask = iso.source == source + axes[1].scatter(iso.mass[mask], iso.logL[mask], label=source, color=color_map[source], alpha=0.7) + axes[1].plot(iso.mass[mask], iso.logL[mask], color=color_map[source]) # Fixed plot function + axes[1].set_xlabel("Mass ($M_{\odot}$)") + axes[1].set_ylabel("$\log L$ ($L_{\odot}$)") + axes[1].set_title("Mass vs. Luminosity") + axes[1].axvline(0.07, linestyle="--", color="gray", alpha=0.5) + axes[1].axvline(0.08, linestyle="--", color="gray", alpha=0.5) + axes[1].set_xlim(0.0, 0.1) + axes[1].legend() + + # Mass vs. logg (Surface Gravity) + for source in np.unique(iso.source): + mask = iso.source == source + axes[2].scatter(iso.mass[mask], iso.logg[mask], label=source, color=color_map[source], alpha=0.7) + axes[2].plot(iso.mass[mask], iso.logg[mask], color=color_map[source]) # Fixed plot function + axes[2].set_xlabel("Mass ($M_{\odot}$)") + axes[2].set_ylabel("$\log g$ (cm/s²)") + axes[2].set_title("Mass vs. Surface Gravity") + axes[2].axvline(0.07, linestyle="--", color="gray", alpha=0.5) + axes[2].axvline(0.08, linestyle="--", color="gray", alpha=0.5) + axes[2].set_xlim(0.0, 0.1) + axes[2].legend() + + # Adjust layout and show plot + plt.tight_layout() + plt.show() + +def plot_merged_bpp_isochrone(iso): + """ + Function to plot the merged isochrone model to visualize the transition + between Phillips 2020, Baraffe+15, and Pisa models. + + Parameters: + ----------- + iso : DataHolder object + Merged isochrone returned by merge_isochrone_baraffe_phillips(). + """ + + # Define colors for different sources + color_map = {'Phillips': 'blue', + 'Baraffe': 'red', + 'Pisa':'green', + 'Baraffe+Phillips': 'pink', + 'Baraffe+Pisa': 'cyan' + } + + # Create figure and subplots + fig, axes = plt.subplots(1, 3, figsize=(18, 5)) + + # Mass vs. logT (Effective Temperature) + for source in np.unique(iso.source): + mask = iso.source == source + axes[0].scatter(iso.mass[mask], iso.logT[mask], label=source, color=color_map[source], alpha=0.7) + axes[0].plot(iso.mass[mask], iso.logT[mask], color=color_map[source]) # Fixed plot function + axes[0].set_xlabel("Mass ($M_{\odot}$)") + axes[0].set_ylabel("$\log T_{\mathrm{eff}}$ (K)") + axes[0].set_title("Mass vs. Effective Temperature") + axes[0].axvline(0.07, linestyle="--", color="gray", alpha=0.5) # Transition marker + axes[0].axvline(0.08, linestyle="--", color="gray", alpha=0.5) # Transition marker + axes[0].legend() + + # Mass vs. logL (Luminosity) + for source in np.unique(iso.source): + mask = iso.source == source + axes[1].scatter(iso.mass[mask], iso.logL[mask], label=source, color=color_map[source], alpha=0.7) + axes[1].plot(iso.mass[mask], iso.logL[mask], color=color_map[source]) # Fixed plot function + axes[1].set_xlabel("Mass ($M_{\odot}$)") + axes[1].set_ylabel("$\log L$ ($L_{\odot}$)") + axes[1].set_title("Mass vs. Luminosity") + axes[1].axvline(0.07, linestyle="--", color="gray", alpha=0.5) + axes[1].axvline(0.08, linestyle="--", color="gray", alpha=0.5) + axes[1].legend() + + # Mass vs. logg (Surface Gravity) + for source in np.unique(iso.source): + mask = iso.source == source + axes[2].scatter(iso.mass[mask], iso.logg[mask], label=source, color=color_map[source], alpha=0.7) + axes[2].plot(iso.mass[mask], iso.logg[mask], color=color_map[source]) # Fixed plot function + axes[2].set_xlabel("Mass ($M_{\odot}$)") + axes[2].set_ylabel("$\log g$ (cm/s²)") + axes[2].set_title("Mass vs. Surface Gravity") + axes[2].axvline(0.07, linestyle="--", color="gray", alpha=0.5) + axes[2].axvline(0.08, linestyle="--", color="gray", alpha=0.5) + axes[2].legend() + + # Adjust layout and show plot + plt.tight_layout() + plt.show() + +"""def merge_isochrone_pisa_baraffe_phillips(logAge, metallicity='solar', rotation=True, iso_in=None): #????? + "" + Function to merge Pisa 2011, Baraffe, and Phillips 2020 models. Solar metallicity is + Z = 0.015 for Pisa 2011 and Z = 0.015 for Phillips 2020. + + If iso_in = None, will take Pisa models to smallest available mass, + then switch to Baraffe/Phillips. If iso_in is defined, then will take this + isochrone to highest mass and switch to Ekstrom + + Can only handle ages at which models already exist: + logAge = 6.0 - 8.0, delta logAge = 0.01 + "" + # Get individual Ekstrom and Pisa isochrones at desired age + isoBaraffePhillips = merge_Ekstrom_isochrone(logAge, metallicity=metallicity, + rotation=rotation) + + if iso_in == None: + isoPisa = get_pisa_isochrone(logAge, metallicity=metallicity) + # Create array specifying source for Pisa isochrone + isoPisa.source = np.array(['Pisa']*len(isoPisa.mass)) + else: + # iso_in isn't really a Pisa isochrone (it could be Baraffe-Pisa merge), + # but name it isoPisa for simplicity anyway. + isoPisa = iso_in + + # Take Pisa isochrone as high up in mass as it goes, then switch to Ekstrom. + # Will trim Ekstrom isochrone here + max_Pisa = max(isoPisa.mass) + good = np.where(isoEkstrom.mass > max_Pisa) + isoEkstrom.mass = isoEkstrom.mass[good] + isoEkstrom.logT = isoEkstrom.logT[good] + isoEkstrom.logg = isoEkstrom.logg[good] + isoEkstrom.logL = isoEkstrom.logL[good] + isoEkstrom.mass_current = isoEkstrom.mass_current[good] + isoEkstrom.phase = isoEkstrom.phase[good] + isoEkstrom.logT_WR = isoEkstrom.logT_WR[good] + + # Make array containing Ekstrom source ID + isoEkstrom.source = np.array(['Ekstrom']*len(isoEkstrom.mass)) + + # Combine the arrays + M = np.append(isoPisa.mass, isoEkstrom.mass) + logT = np.append(isoPisa.logT, isoEkstrom.logT) + logg = np.append(isoPisa.logg, isoEkstrom.logg) + logL = np.append(isoPisa.logL, isoEkstrom.logL) + mcurr = np.append(isoPisa.mass_current, isoEkstrom.mass_current) + phase = np.append(isoPisa.phase, isoEkstrom.phase) + logT_WR = np.append(isoPisa.logT, isoEkstrom.logT_WR) + source = np.append(isoPisa.source, isoEkstrom.source) + + iso = objects.DataHolder() + iso.mass = M + iso.logL = logL + iso.logg = logg + iso.logT = logT + iso.mass_current = mcurr + iso.phase = phase + iso.logT_WR = logT_WR + iso.source = source + + return iso +""" + +def merge_isochrone_baraffe_pisa(logAge, metallicity='solar'): + """ + Function to merge Baraffe+15 and Pisa 2011 models. Will take + 100% Baraffe+15 between 0.07 - 0.4 M_sun, transition between + 0.4 - 0.5 M_sun, and take 100% Pisa from 0.5 M_sun and up. + + Can only handle ages at which models already exist: + logAge = 6.0 - 8.0, delta logAge = 0.01 + """ + if metallicity != 'solar': + print( 'Non-solar metallicity not supported yet') + return + + # Get individual Baraffe and Pisa isochrones at desired age. Note + # that this will also give the Baraffe models a finer mass sampling + isoBaraffe = get_Baraffe15_isochrone(logAge, metallicity=metallicity) + isoPisa = get_pisa_isochrone(logAge, metallicity=metallicity) + + # Identify M <= 0.4 M_sun in Baraffe and M >= 0.5 M_sun in Pisa + good_b = np.where(isoBaraffe.mass <= 0.4) + good_p = np.where(isoPisa.mass >= 0.5) + + # Sample between 0.4 M_sun and 0.5 M_sun in steps of 0.02 M_sun. + # Will do linear combo of Baraffe and Pisa over this range + mid_mass = np.arange(0.4, 0.5+0.01, 0.02) + mid_logT = [] + mid_logL = [] + mid_logG = [] + mid_Mcurr = [] + mid_phase = [] + for mass in mid_mass: + # Find the appropriate masses in Baraffe + Pisa to build from. + # Baraffe has identical sampling over this range, and Pisa sampling + # is very close. As a result, we will just take the closest mass model + # to each mid_mass + idx_b = np.where( abs(isoBaraffe.mass - mass) == min(abs(isoBaraffe.mass - mass)) ) + idx_p = np.where( abs(isoPisa.mass - mass) == min(abs(isoPisa.mass - mass)) ) + + # Quality control check: we won't let the difference between model mass and + # chosen mass to be >= 0.01 M_sun + if ((isoPisa.mass[idx_p] - mass) >= 0.02) | ((isoBaraffe.mass[idx_b] - mass) >= 0.02): + print( 'WARNING: Baraffe or Pisa model interpolation between 0.4 - 0.5 M_sun may \ + be inaccurate. Check this!') + pdb.set_trace() + + # Now, do the linear combo of models at this mass, weighted by distance from + # 0.4 or 0.5 (whichever is appropriate) + diff = 0.5 - 0.4 + weight_b = (0.5 - mass) / diff + weight_p = 1.0 - weight_b + print( 'Baraffe {0} and Pisa {1} at mass {2}'.format(weight_b, weight_p, mass)) + + # Now, do the merge IN LINEAR SPACE! + Teff = (10**isoBaraffe.logT[idx_b] * weight_b) + \ + (10**isoPisa.logT[idx_p] * weight_p) + L = (10**isoBaraffe.logL[idx_b] * weight_b) + \ + (10**isoPisa.logL[idx_p] * weight_p) + g = (10**isoBaraffe.logg[idx_b] * weight_b) + \ + (10**isoPisa.logg[idx_p] * weight_p) + mcurr = (isoBaraffe.mass_current[idx_b] * weight_b) + \ + (isoPisa.mass_current[idx_p] * weight_p) + phase = np.round((isoBaraffe.mass_current[idx_b] * weight_b) + \ + (isoPisa.mass_current[idx_p] * weight_p)) + + mid_logT = np.concatenate((mid_logT, np.log10(Teff))) + mid_logL = np.concatenate((mid_logL, np.log10(L))) + mid_logG = np.concatenate((mid_logG, np.log10(g))) + mid_Mcurr = np.concatenate((mid_Mcurr, mcurr)) + mid_phase = np.concatenate((mid_phase, phase)) + + # Now, final isochrone will be combination of Baraffe at M<=0.4, + # Pisa at M>=0.5, and the combination inbetween + mass = np.concatenate((isoBaraffe.mass[good_b], mid_mass, isoPisa.mass[good_p])) + logT = np.concatenate((isoBaraffe.logT[good_b], mid_logT, isoPisa.logT[good_p])) + logL = np.concatenate((isoBaraffe.logL[good_b], mid_logL, isoPisa.logL[good_p])) + logG = np.concatenate((isoBaraffe.logg[good_b], mid_logG, isoPisa.logg[good_p])) + mcurr = np.concatenate((isoBaraffe.mass_current[good_b], mid_Mcurr, isoPisa.mass_current[good_p])) + phase = np.concatenate((isoBaraffe.phase[good_b], mid_phase, isoPisa.phase[good_p])) + + # Also add a source flag + source = np.concatenate( (['Baraffe']*len(good_b[0]), ['Baraffe+Pisa']*len(mid_mass), + ['Pisa']*len(good_p[0])) ) + + iso = objects.DataHolder() + iso.mass = mass + iso.logL = logL + iso.logg = logG + iso.logT = logT + iso.mass_current = mcurr + iso.phase = phase + iso.source = source + + return iso + +def merge_isochrone_baraffe_pisa_phillips(logAge, metallicity='solar', rotation=True, iso_in=None): + """ + Merges Phillips, Baraffe, and Pisa isochrones to create a complete evolutionary track. + + Inputs: + logAge - Logarithmic Age + metallicity - Metallicity (default is 'solar') + rotation - Boolean indicating whether to include rotation in the models (default is True) + + Outputs: + iso - An object containing the merged isochrone data. + """ + # Merge Phillips with Baraffe + print(f"Merging Phillips with Baraffe for logAge = {logAge}") + isoBaraffePhillips = merge_isochrone_baraffe_phillips(logAge, metallicity=metallicity) + + # Merge Baraffe+Phillips with Pisa (depending on the logAge) + if logAge <= 7.4: + print(f"Merging Baraffe+Phillips with Pisa for logAge = {logAge}") + iso = merge_isochrone_baraffe_pisa(logAge, metallicity=metallicity, iso_in=isoBaraffePhillips) + else: + # If logAge > 7.4, you may want to merge with different models (Parsec/Ekstrom) + print(f"Merging Baraffe+Phillips with higher mass models for logAge = {logAge}") + iso = merge_isochrone_baraffe_pisa(logAge, metallicity=metallicity, iso_in=isoBaraffePhillips) + + return iso + + +def merge_all_isochrones_phillips_baraffe_pisa_ekstrom_parsec(metallicity='solar', rotation=True, plot=False): + """ + Make evolutionary isochrones containing a continuous distribution of + masses from the PMS to the MS. The models used are the following: + + PMS + Phillips from 0.01 - 0.07 M_sun + Baraffe+15 from 0.07 - 0.4 M_sun + Pisa 2011 from 0.5 - top of grid (~7 M_sun) + + MS (M > Pisa 2011) + Ekstrom+12 for logAge < 7.4 + Parsec V1.2s for logAge > 7.4 + + BD stars + Phillips for 6.0 <= logAge <= 10.0 + + metallicity = 'solar' --> Ekstrom+12 z014, Pisa2011 z015, Parsec z015, Phillips z00 + + if plot = True, will make plots of merged isochrones in 'plots' directory, + which must already exist + + Code is expected to be run in merged model working directory. + """ + # Root data directory for Ekstrom+12 isochrones + rootDirE = models_dir + 'Ekstrom2012/iso/' + metalPart = 'z014/' + if metallicity != 'solar': + print( 'Non-solar metallicities not supported yet') + return + rotPart = 'rot/' + if not rotation: + rotPart = 'norot/' + rootDirE += metalPart+rotPart + + # Root data directory for the Baraffe isochrones + rootDirBaraffe = models_dir + 'Baraffe15/iso/' + + # Root data directory for Pisa isochrones + rootDirPisa = models_dir + 'Pisa2011/iso/' + metSuffix = 'z015/' + if metallicity != 'solar': + print( 'Non-solar metallicities not supported yet') + return + rootDirPisa += metSuffix + + # Root data directory for Parsec isochrones + rootDirParsec = models_dir + 'ParsecV1.2s/iso/' + metalSuffix = 'z015/' + if metallicity != 'solar': + print( 'Non-solar metallicities not supported yet') + return + rootDirParsec += metalSuffix + + # Root data directory for Phillips isochrones + rootDirPhillips = models_dir + 'Phillips2020/iso/' + mSuffix = 'z00/' + if metallicity != 'solar': + print( 'Non-solar metallicities not supported yet') + return + rootDirPhillips +=mSuffix + + # Search both directories for iso_*.dat files + isoFilesE = glob.glob(rootDirE + 'iso_*.dat') + isoFilesB = glob.glob(rootDirBaraffe + 'iso_*.fits') + isoFilesPi = glob.glob(rootDirPisa + 'iso_*.dat') + isoFilesPa = glob.glob(rootDirParsec + 'iso_*') + isoFilesPh = glob.glob(rootDirPhillips + 'iso_*.fits') + + # Output of merged isochrones + if rotation == True: + outDir = models_dir + 'merged/phillips_baraffe_pisa_ekstrom_parsec/{0}_rot_test/'.format(metSuffix[:-1]) + # Raise error if wanting Phillips data? + else: + outDir = models_dir + 'merged/phillips_baraffe_pisa_ekstrom_parsec/{0}_norot/'.format(metSuffix[:-1]) + if not os.path.exists(outDir): + os.mkdir(outDir) + + # Isolate the iso*.dat file names + for ii in range(len(isoFilesE)): + isoFilesE[ii] = isoFilesE[ii].split('/')[-1] + + for ii in range(len(isoFilesB)): + isoFilesB[ii] = isoFilesB[ii].split('/')[-1] + + for ii in range(len(isoFilesPi)): + isoFilesPi[ii] = isoFilesPi[ii].split('/')[-1] + + for ii in range(len(isoFilesPa)): + isoFilesPa[ii] = isoFilesPa[ii].split('/')[-1] + + for ii in range(len(isoFilesPh)): + isoFilesPh[ii] = isoFilesPh[ii].split('/')[-1] + + # Loop through the Pisa isochrones, adding the MS and Baraffe models + # as appropriate + for ii in range(len(isoFilesPi)): + isoFilePi = isoFilesPi[ii] + + logAgeStr = isoFilePi.replace('iso_', '').replace('.dat', '') + logAge = float(logAgeStr) + + #-----PRE-MAIN SEQUENCE----# + # Merge with the Baraffe+15 models from 0.07 - 0.4 M_sun. Includes + # transition region between 0.4 - 0.5 M_sun in which we shift + # from 100% Baraffe to 100% Pisa + + print( 'Merging isochrones Pisa + Baraffe + Phillips from ', isoFilePi) + isoPMS = merge_isochrone_phillips_baraffe_pisa(logAge, metallicity=metallicity) + + #--------MAIN SEQUENCE-------# + # Case where logAge <= 7.4, we merge with Ekstrom. Otherwise, merge + # which parsec + if logAge <= 7.4: + if isoFilePi not in isoFilesE: + print( 'Skipping isochrones from ', isoFilePi) + print( 'PROBLEM WITH PISA OR EKSTROM') + pdb.set_trace() + + print( 'Merging isochrones Phillips+Pisa+Ekstrom from ', isoFilePi) + iso = merge_isochrone_phillips_pisa_Ekstrom(logAge, metallicity=metallicity, + rotation=rotation, iso_in=isoPMS) + else: + if isoFilePi not in isoFilesPa: + print( 'Skipping isochrones from ', isoFilePi) + print( 'PROBLEM WITH PISA OR PARSEC') + pdb.set_trace() + + print( 'Merging isochrones Phillips+Pisa+Parsec from ', isoFilePi) + iso = merge_isochrone_phillips_pisa_parsec(logAge, metallicity=metallicity, + iso_in=isoPMS) + + # Make test plot, if desired. These are put in plots directory + if plot: + # Make different models different colors + phillips_ind = np.where(iso.source == 'Phillips') + merge_pb = np.where(iso.source == 'Phillips+Baraffe') + baraffe_ind = np.where(iso.source == 'Baraffe') + merge_ind = np.where(iso.source == 'Baraffe+Pisa') + pisa_ind = np.where(iso.source == 'Pisa') + MS_ind = np.where( (iso.source == 'Ekstrom') | (iso.source == 'Parsec')) + #Extract age + logAge = isoFilePi.split('_')[1][:-4] + + # Temporarily turn off interactive plot. Turn back on at end + py.ioff() + + py.figure(1) + py.clf() + py.plot(iso.logT[phillips_ind], iso.logL[phillips_ind], 'c-', label = 'Phillips', + linewidth=2) + py.plot(iso.logT[merge_pb], iso.logL[merge_pb], 'y-', label = 'Phillips+Baraffe', + linewidth=2) + py.plot(iso.logT[baraffe_ind], iso.logL[baraffe_ind], 'k-', label = 'Baraffe', + linewidth=2) + py.plot(iso.logT[merge_ind], iso.logL[merge_ind], 'r-', label = 'Baraffe+Pisa', + linewidth=2) + py.plot(iso.logT[pisa_ind], iso.logL[pisa_ind], 'g-', label = 'Pisa', + linewidth=2) + py.plot(iso.logT[MS_ind], iso.logL[MS_ind], 'b-', + label = 'Ekstrom/Parsec', linewidth=2) + py.xlabel('log Teff') + py.ylabel('log L') + py.title('Log Age = {0:s}'.format(logAge)) + py.legend(loc=3) + py.axis([4.9, 3.2, -3.0, 8]) + py.savefig(outDir+'plots/iso_'+logAge+'.png') + + py.ion() + + + _out = open(outDir + isoFilePi, 'w') + + hdr_fmt = '%12s %10s %10s %10s %10s %12s %5s %-10s\n' + _out.write(hdr_fmt % + ('# M_init', 'log T', 'log L', 'log g', 'logT_WR', 'M_curr', 'phase', 'Source')) + _out.write(hdr_fmt % + ('# (Msun)', '(Kelvin)', '(Lsun)', '(cgs)', '(Kelvin)', '(Msun)', '()', '()')) + + for kk in range(len(iso.mass)): + _out.write('%12.6f %10.4f %10.4f %10.4f %10.4f %12.6f %5d %-10s\n' % + (iso.mass[kk], iso.logT[kk], iso.logL[kk], + iso.logg[kk], iso.logT_WR[kk], + iso.mass_current[kk], iso.phase[kk], iso.source[kk])) + + _out.close() + return + +def get_pisa_isochrone(logAge, metallicity='solar'): + """ + Load mass, effective temperature, log gravity, and log luminosity + for the Pisa isochrones at given logAge. Code will quit if that + logAge value doesn't exist (can make some sort of interpolation thing + later). + + Note: mass is currently initial mass, not instantaneous mass + + Inputs: + logAge - Logarithmic Age + metallicity - in Z (def = solar of 0.014) + """ + rootDir = models_dir + 'Pisa2011/iso/' + metSuffix = 'z015/' + if metallicity != 'solar': + print( 'Non-solar Pisa 2011 metallicities not supported yet') + return + rootDir += metSuffix + + # Check to see if isochrone exists + isoFile = rootDir + 'iso_%.2f.dat' % logAge + if not os.path.exists(isoFile): + print( 'Pisa isochrone for logAge = {0:3.2f} does\'t exist'.format(logAge)) + print( 'Quitting') + return + + data = Table.read(isoFile, format='ascii') + cols = data.keys() + mass = data[cols[2]] #Note: this is initial mass, in M_sun + logT = data[cols[1]] # K + logL = data[cols[0]] # L_sun + logg = data[cols[3]] + + # Hack: Make mass_current and phase + mass_current = np.array(mass) + phase = np.ones(len(mass), dtype=int) + + obj = objects.DataHolder() + obj.mass = mass + obj.logT = logT + obj.logg = logg + obj.logL = logL + obj.mass_current = mass_current + obj.phase = phase + + return obj + +def get_phillips_pisa_isochrone(logAge, metallicity='solar'): + """ + Load mass, effective temperature, log gravity, and log luminosity + for the Phillips/Pisa isochrones at given logAge. Code will quit if that + logAge value doesn't exist (can make some sort of interpolation thing + later). + + Note: mass is currently initial mass, not instantaneous mass + + Inputs: + logAge - Logarithmic Age + metallicity - in Z (def = solar of 0.014) + """ + rootDir = models_dir + 'merged/phillips_pisa' + metSuffix = 'z015/' + if metallicity != 'solar': + print( 'Non-solar Phillips 2020 & Pisa 2011 metallicities not supported yet') + return + rootDir += metSuffix + + # Check to see if isochrone exists + isoFile = rootDir + 'iso_%.2f.fits' % logAge + if not os.path.exists(isoFile): + print( 'Phillips/Pisa isochrone for logAge = {0:3.2f} does\'t exist'.format(logAge)) + print( 'Quitting') + return + + data = Table.read(isoFile, format='fits') + cols = data.keys() + mass = data[cols[0]] #Note: this is initial mass, in M_sun + logT = data[cols[2]] # K + logL = data[cols[1]] # L_sun + logg = data[cols[3]] + interpolated = data['interpolated'] + + # warning if data point is coming from interpolated region + if warn_interpolated and np.any(interpolated): + print( f"Warning: {np.sum(interpolated)} of {len(interpolated)} data points are interpolated.") + + # Hack: Make mass_current and phase + mass_current = np.array(mass) + phase = np.ones(len(mass), dtype=int) + + obj = objects.DataHolder() + obj.mass = mass + obj.logT = logT + obj.logg = logg + obj.logL = logL + obj.mass_current = mass_current + obj.phase = phase + obj.interpolated = interpolated + + return obj + +def merge_isochrone_baraffe_pisa(logAge, metallicity='solar'): + """ + Function to merge Baraffe+15 and Pisa 2011 models. Will take + 100% Baraffe+15 between 0.07 - 0.4 M_sun, transition between + 0.4 - 0.5 M_sun, and take 100% Pisa from 0.5 M_sun and up. + + Can only handle ages at which models already exist: + logAge = 6.0 - 8.0, delta logAge = 0.01 + """ + if metallicity != 'solar': + print( 'Non-solar metallicity not supported yet') + return + + # Get individual Baraffe and Pisa isochrones at desired age. Note + # that this will also give the Baraffe models a finer mass sampling + isoBaraffe = get_Baraffe15_isochrone(logAge, metallicity=metallicity) + isoPisa = get_pisa_isochrone(logAge, metallicity=metallicity) + + # Identify M <= 0.4 M_sun in Baraffe and M >= 0.5 M_sun in Pisa + good_b = np.where(isoBaraffe.mass <= 0.4) + good_p = np.where(isoPisa.mass >= 0.5) + + # Sample between 0.4 M_sun and 0.5 M_sun in steps of 0.02 M_sun. + # Will do linear combo of Baraffe and Pisa over this range + mid_mass = np.arange(0.4, 0.5+0.01, 0.02) + mid_logT = [] + mid_logL = [] + mid_logG = [] + mid_Mcurr = [] + mid_phase = [] + for mass in mid_mass: + # Find the appropriate masses in Baraffe + Pisa to build from. + # Baraffe has identical sampling over this range, and Pisa sampling + # is very close. As a result, we will just take the closest mass model + # to each mid_mass + idx_b = np.where( abs(isoBaraffe.mass - mass) == min(abs(isoBaraffe.mass - mass)) ) + idx_p = np.where( abs(isoPisa.mass - mass) == min(abs(isoPisa.mass - mass)) ) + + # Quality control check: we won't let the difference between model mass and + # chosen mass to be >= 0.01 M_sun + if ((isoPisa.mass[idx_p] - mass) >= 0.02) | ((isoBaraffe.mass[idx_b] - mass) >= 0.02): + print( 'WARNING: Baraffe or Pisa model interpolation between 0.4 - 0.5 M_sun may \ + be inaccurate. Check this!') + pdb.set_trace() + + # Now, do the linear combo of models at this mass, weighted by distance from + # 0.4 or 0.5 (whichever is appropriate) + diff = 0.5 - 0.4 + weight_b = (0.5 - mass) / diff + weight_p = 1.0 - weight_b + print( 'Baraffe {0} and Pisa {1} at mass {2}'.format(weight_b, weight_p, mass)) + + # Now, do the merge IN LINEAR SPACE! + Teff = (10**isoBaraffe.logT[idx_b] * weight_b) + \ + (10**isoPisa.logT[idx_p] * weight_p) + L = (10**isoBaraffe.logL[idx_b] * weight_b) + \ + (10**isoPisa.logL[idx_p] * weight_p) + g = (10**isoBaraffe.logg[idx_b] * weight_b) + \ + (10**isoPisa.logg[idx_p] * weight_p) + mcurr = (isoBaraffe.mass_current[idx_b] * weight_b) + \ + (isoPisa.mass_current[idx_p] * weight_p) + phase = np.round((isoBaraffe.mass_current[idx_b] * weight_b) + \ + (isoPisa.mass_current[idx_p] * weight_p)) + + mid_logT = np.concatenate((mid_logT, np.log10(Teff))) + mid_logL = np.concatenate((mid_logL, np.log10(L))) + mid_logG = np.concatenate((mid_logG, np.log10(g))) + mid_Mcurr = np.concatenate((mid_Mcurr, mcurr)) + mid_phase = np.concatenate((mid_phase, phase)) + + # Now, final isochrone will be combination of Baraffe at M<=0.4, + # Pisa at M>=0.5, and the combination inbetween + mass = np.concatenate((isoBaraffe.mass[good_b], mid_mass, isoPisa.mass[good_p])) + logT = np.concatenate((isoBaraffe.logT[good_b], mid_logT, isoPisa.logT[good_p])) + logL = np.concatenate((isoBaraffe.logL[good_b], mid_logL, isoPisa.logL[good_p])) + logG = np.concatenate((isoBaraffe.logg[good_b], mid_logG, isoPisa.logg[good_p])) + mcurr = np.concatenate((isoBaraffe.mass_current[good_b], mid_Mcurr, isoPisa.mass_current[good_p])) + phase = np.concatenate((isoBaraffe.phase[good_b], mid_phase, isoPisa.phase[good_p])) + + # Also add a source flag + source = np.concatenate( (['Baraffe']*len(good_b[0]), ['Baraffe+Pisa']*len(mid_mass), + ['Pisa']*len(good_p[0])) ) + + iso = objects.DataHolder() + iso.mass = mass + iso.logL = logL + iso.logg = logG + iso.logT = logT + iso.mass_current = mcurr + iso.phase = phase + iso.source = source + + return iso + +def merge_isochrone_phillips_baraffe_pisa(logAge, metallicity='solar'): + """ + Function to merge Phillips 2020, Baraffe+15, and Pisa 2011 models. + + - Uses Phillips for M <= 0.07 M_sun + - Transitions from Phillips to Baraffe between 0.07 - 0.075 M_sun + - Uses Baraffe for 0.075 - 0.4 M_sun + - Transitions from Baraffe to Pisa between 0.4 - 0.5 M_sun + - Uses Pisa for M >= 0.5 M_sun + + Can only handle ages where models exist: + logAge = 6.0 - 8.0, delta logAge = 0.01 + """ + if metallicity != 'solar': + print('Non-solar metallicity not supported yet') + return + + # Load individual isochrones + isoPhillips = get_phillips_isochrone(logAge, metallicity=metallicity) + isoBaraffe = get_Baraffe15_isochrone(logAge, metallicity=metallicity) + isoPisa = get_pisa_isochrone(logAge, metallicity=metallicity) + + # Identify mass ranges + good_p = np.where(isoPhillips.mass <= 0.07) + good_b = np.where((isoBaraffe.mass >= 0.075) & (isoBaraffe.mass <= 0.4)) + good_pisa = np.where(isoPisa.mass >= 0.5) + + # Transition Phillips → Baraffe (0.07 - 0.075 M_sun) + mid_mass_phillips_baraffe = np.arange(0.07, 0.075, 0.002) + mid_logT_phillips_baraffe, mid_logL_phillips_baraffe, mid_logG_phillips_baraffe = [], [], [] + mid_Mcurr_phillips_baraffe, mid_phase_phillips_baraffe = [], [] + + for mass in mid_mass_phillips_baraffe: + idx_p = np.argmin(np.abs(isoPhillips.mass - mass)) + idx_b = np.argmin(np.abs(isoBaraffe.mass - mass)) + + weight_p = (0.075 - mass) / 0.005 + weight_b = 1.0 - weight_p + + Teff = (10**isoPhillips.logT[idx_p] * weight_p) + (10**isoBaraffe.logT[idx_b] * weight_b) + L = (10**isoPhillips.logL[idx_p] * weight_p) + (10**isoBaraffe.logL[idx_b] * weight_b) + g = (10**isoPhillips.logg[idx_p] * weight_p) + (10**isoBaraffe.logg[idx_b] * weight_b) + mcurr = (isoPhillips.mass_current[idx_p] * weight_p) + (isoBaraffe.mass_current[idx_b] * weight_b) + phase = np.round((isoPhillips.phase[idx_p] * weight_p) + (isoBaraffe.phase[idx_b] * weight_b)) + + mid_logT_phillips_baraffe.append(np.log10(Teff)) + mid_logL_phillips_baraffe.append(np.log10(L)) + mid_logG_phillips_baraffe.append(np.log10(g)) + mid_Mcurr_phillips_baraffe.append(mcurr) + mid_phase_phillips_baraffe.append(phase) + + # Transition Baraffe → Pisa (0.4 - 0.5 M_sun) + mid_mass_baraffe_pisa = np.arange(0.4, 0.5 + 0.01, 0.02) + mid_logT_baraffe_pisa, mid_logL_baraffe_pisa, mid_logG_baraffe_pisa = [], [], [] + mid_Mcurr_baraffe_pisa, mid_phase_baraffe_pisa = [], [] + + for mass in mid_mass_baraffe_pisa: + idx_b = np.argmin(np.abs(isoBaraffe.mass - mass)) + idx_p = np.argmin(np.abs(isoPisa.mass - mass)) + + weight_b = (0.5 - mass) / 0.1 + weight_p = 1.0 - weight_b + + Teff = (10**isoBaraffe.logT[idx_b] * weight_b) + (10**isoPisa.logT[idx_p] * weight_p) + L = (10**isoBaraffe.logL[idx_b] * weight_b) + (10**isoPisa.logL[idx_p] * weight_p) + g = (10**isoBaraffe.logg[idx_b] * weight_b) + (10**isoPisa.logg[idx_p] * weight_p) + mcurr = (isoBaraffe.mass_current[idx_b] * weight_b) + (isoPisa.mass_current[idx_p] * weight_p) + phase = np.round((isoBaraffe.phase[idx_b] * weight_b) + (isoPisa.phase[idx_p] * weight_p)) + + mid_logT_baraffe_pisa.append(np.log10(Teff)) + mid_logL_baraffe_pisa.append(np.log10(L)) + mid_logG_baraffe_pisa.append(np.log10(g)) + mid_Mcurr_baraffe_pisa.append(mcurr) + mid_phase_baraffe_pisa.append(phase) + + # Merge all mass regimes + mass = np.concatenate((isoPhillips.mass[good_p], mid_mass_phillips_baraffe, isoBaraffe.mass[good_b], + mid_mass_baraffe_pisa, isoPisa.mass[good_pisa])) + + logT = np.concatenate((isoPhillips.logT[good_p], mid_logT_phillips_baraffe, isoBaraffe.logT[good_b], + mid_logT_baraffe_pisa, isoPisa.logT[good_pisa])) + + logL = np.concatenate((isoPhillips.logL[good_p], mid_logL_phillips_baraffe, isoBaraffe.logL[good_b], + mid_logL_baraffe_pisa, isoPisa.logL[good_pisa])) + + logG = np.concatenate((isoPhillips.logg[good_p], mid_logG_phillips_baraffe, isoBaraffe.logg[good_b], + mid_logG_baraffe_pisa, isoPisa.logg[good_pisa])) + + mcurr = np.concatenate((isoPhillips.mass_current[good_p], + mid_Mcurr_phillips_baraffe, + isoBaraffe.mass_current[good_b], + mid_Mcurr_baraffe_pisa, + isoPisa.mass_current[good_pisa])) + + phase = np.concatenate((isoPhillips.phase[good_p], mid_phase_phillips_baraffe, isoBaraffe.phase[good_b], + mid_phase_baraffe_pisa, isoPisa.phase[good_pisa])) + + # Source flag + source = np.concatenate((['Phillips']*len(good_p[0]), ['Phillips+Baraffe']*len(mid_mass_phillips_baraffe), + ['Baraffe']*len(good_b[0]), ['Baraffe+Pisa']*len(mid_mass_baraffe_pisa), + ['Pisa']*len(good_pisa[0]))) + + # Create final merged isochrone object + iso = objects.DataHolder() + iso.mass = mass + iso.logL = logL + iso.logg = logG + iso.logT = logT + iso.mass_current = mcurr + iso.phase = phase + iso.source = source + + return iso + +def merge_isochrone_pisa_Ekstrom(logAge, metallicity='solar', rotation=True, iso_in=None): + """ + Function to merge Pisa 2011 and Ekstrom 2012 models. Solar metallicity is + Z = 0.015 for Pisa 2011 and Z = 0.014 for Ekstrom+12. + + If iso_in = None, will take Pisa models to highest available mass, + then switch to Ekstrom. If iso_in is defined, then will take this + isochrone to highest mass and switch to Ekstrom + + Can only handle ages at which models already exist: + logAge = 6.0 - 8.0, delta logAge = 0.01 + """ + # Get individual Ekstrom and Pisa isochrones at desired age + isoEkstrom = get_Ekstrom_isochrone(logAge, metallicity=metallicity, + rotation=rotation) + + if iso_in == None: + isoPisa = get_pisa_isochrone(logAge, metallicity=metallicity) + # Create array specifying source for Pisa isochrone + isoPisa.source = np.array(['Pisa']*len(isoPisa.mass)) + else: + # iso_in isn't really a Pisa isochrone (it could be Baraffe-Pisa merge), + # but name it isoPisa for simplicity anyway. + isoPisa = iso_in + + # Take Pisa isochrone as high up in mass as it goes, then switch to Ekstrom. + # Will trim Ekstrom isochrone here + max_Pisa = max(isoPisa.mass) + good = np.where(isoEkstrom.mass > max_Pisa) + isoEkstrom.mass = isoEkstrom.mass[good] + isoEkstrom.logT = isoEkstrom.logT[good] + isoEkstrom.logg = isoEkstrom.logg[good] + isoEkstrom.logL = isoEkstrom.logL[good] + isoEkstrom.mass_current = isoEkstrom.mass_current[good] + isoEkstrom.phase = isoEkstrom.phase[good] + isoEkstrom.logT_WR = isoEkstrom.logT_WR[good] + + # Make array containing Ekstrom source ID + isoEkstrom.source = np.array(['Ekstrom']*len(isoEkstrom.mass)) + + # Combine the arrays + M = np.append(isoPisa.mass, isoEkstrom.mass) + logT = np.append(isoPisa.logT, isoEkstrom.logT) + logg = np.append(isoPisa.logg, isoEkstrom.logg) + logL = np.append(isoPisa.logL, isoEkstrom.logL) + mcurr = np.append(isoPisa.mass_current, isoEkstrom.mass_current) + phase = np.append(isoPisa.phase, isoEkstrom.phase) + logT_WR = np.append(isoPisa.logT, isoEkstrom.logT_WR) + source = np.append(isoPisa.source, isoEkstrom.source) + + iso = objects.DataHolder() + iso.mass = M + iso.logL = logL + iso.logg = logg + iso.logT = logT + iso.mass_current = mcurr + iso.phase = phase + iso.logT_WR = logT_WR + iso.source = source + + return iso + +def merge_isochrone_phillips_pisa_Ekstrom(logAge, metallicity='solar', rotation=True, iso_in=None): + """ + Function to merge Phillips 2020, Pisa 2011, and Ekstrom 2012 models. Solar metallicity is + Z = 0.015 for Pisa 2011 and Phillips 2020 and Z = 0.014 for Ekstrom+12. + + If iso_in = None, will take Pisa/Phillips models to highest available mass, + then switch to Ekstrom. If iso_in is defined, then will take this + isochrone to highest mass and switch to Ekstrom + + Can only handle ages at which models already exist: + logAge = 6.0 - 8.0, delta logAge = 0.01 + """ + # Get individual Ekstrom and Pisa isochrones at desired age + isoEkstrom = get_Ekstrom_isochrone(logAge, metallicity=metallicity, + rotation=rotation) + + if iso_in == None: + isoPhPisa = get_phillips_pisa_isochrone(logAge, metallicity=metallicity) + # Create array specifying source for Pisa isochrone + isoPhPisa.source = np.array(['Phillips/Pisa']*len(isoPhPisa.mass)) + else: + # iso_in isn't really a Pisa isochrone (it could be Baraffe-Pisa merge), + # but name it isoPisa for simplicity anyway. + isoPhPisa = iso_in + + # Take Pisa isochrone as high up in mass as it goes, then switch to Ekstrom. + # Will trim Ekstrom isochrone here + max_PhPisa = max(isoPhPisa.mass) + good = np.where(isoEkstrom.mass > max_PhPisa) + isoEkstrom.mass = isoEkstrom.mass[good] + isoEkstrom.logT = isoEkstrom.logT[good] + isoEkstrom.logg = isoEkstrom.logg[good] + isoEkstrom.logL = isoEkstrom.logL[good] + isoEkstrom.mass_current = isoEkstrom.mass_current[good] + isoEkstrom.phase = isoEkstrom.phase[good] + isoEkstrom.logT_WR = isoEkstrom.logT_WR[good] + + # Make array containing Ekstrom source ID + isoEkstrom.source = np.array(['Ekstrom']*len(isoEkstrom.mass)) + + # Combine the arrays + M = np.append(isoPhPisa.mass, isoEkstrom.mass) + logT = np.append(isoPhPisa.logT, isoEkstrom.logT) + logg = np.append(isoPhPisa.logg, isoEkstrom.logg) + logL = np.append(isoPhPisa.logL, isoEkstrom.logL) + mcurr = np.append(isoPhPisa.mass_current, isoEkstrom.mass_current) + phase = np.append(isoPhPisa.phase, isoEkstrom.phase) + logT_WR = np.append(isoPhPisa.logT, isoEkstrom.logT_WR) + source = np.append(isoPhPisa.source, isoEkstrom.source) + + iso = objects.DataHolder() + iso.mass = M + iso.logL = logL + iso.logg = logg + iso.logT = logT + iso.mass_current = mcurr + iso.phase = phase + iso.logT_WR = logT_WR + iso.source = source + + # add interpolation flag + if hasattr(isoPhPisa, 'interpolated'): + interpolated = np.append(isoPhPisa.interpolated, np.full(len(isoEkstrom.mass), False)) + iso.interpolated = interpolated + + # fix phase values in interpolated region (assign same as min-mass Parsec object) + min_ekstrom_mass_idx = np.argmin(isoEkstrom.mass) + min_ekstrom_phase = isoEkstrom.phase[min_ekstrom_mass_idx] + interp_mask = iso.interpolated == True + iso.phase[interp_mask] = min_ekstrom_phase + + return iso + +def get_Ekstrom_isochrone(logAge, metallicity='solar', rotation=True): + """ + Load mass, effective temperature, log gravity, and log luminosity + for the Ekstrom isochrones at given logAge. Code will quit if that + logAge value doesn't exist (can make some sort of interpolation thing + later). Also interpolate model to finer mass grid + + Note: mass is currently initial mass, not instantaneous mass + + Inputs: + logAge - Logarithmic Age + metallicity - in Z (def = solar of 0.014) + """ + rootDir = models_dir + 'Ekstrom2012/iso/' + metSuffix = 'z014/' + if metallicity != 'solar': + print( 'Non-solar Ekstrom+12 metallicities not supported yet') + return + rotSuffix = 'rot/' + if not rotation: + rotSuffix = 'norot/' + + rootDir += metSuffix + rotSuffix + + # Check to see if isochrone exists + isoFile = rootDir + 'iso_%.2f.dat' % logAge + if not os.path.exists(isoFile): + print( 'Ekstrom isochrone for logAge = {0:3.2f} does\'t exist'.format(logAge)) + print( 'Quitting') + return + + data = Table.read(isoFile, format='ascii') + cols = data.keys() + mass = data[cols[2]] #Note: this is initial mass, in M_sun + logT = data[cols[7]] # K + logL = data[cols[6]] # L_sun + logT_WR = data[cols[8]] # K; if this doesn't equal logT, we have a WR star + mass_curr = data[cols[3]] + phase = np.ones(len(data), dtype=int) + + # Need to calculate log g from mass and R + R_sun = 7.*10**10 #cm + M_sun = 2.*10**33 #g + G_const = 6.67*10**-8 #cgs + + radius = data[cols[19]] #R_sun + logg = np.log10( (G_const * np.array(mass).astype(float) * M_sun) / + (np.array(radius).astype(float) * R_sun)**2 ) + + # Interpolate isochrone to finer mass grid on main-ish sequence + # (1-60 M_sun, or the highest mass in the model); don't want to + # completely redo all sampling, just this region + if max(mass) > 60: + new_masses = np.arange(1, 60+0.1, 0.5) + else: + new_masses = np.arange(1, max(mass), 0.5) + mass_grid = np.append(new_masses, mass) + mass_grid.sort() # Make sure grid is in proper order + + # Build interpolators in linear space + f_logT = interpolate.interp1d(mass, 10**logT, kind='linear') + f_logL = interpolate.interp1d(mass, 10**logL, kind='linear') + f_logT_WR = interpolate.interp1d(mass, 10**logT_WR, kind='linear') + f_logg = interpolate.interp1d(mass, 10**logg, kind='linear') + f_Mcurr = interpolate.interp1d(mass, mass_curr, kind='linear') + f_phase = interpolate.interp1d(mass, phase, kind='linear') + + # Do interpolation, convert back to logspace + logT_interp = np.log10(f_logT(mass_grid)) + logL_interp = np.log10(f_logL(mass_grid)) + logT_WR_interp = np.log10(f_logT_WR(mass_grid)) + logg_interp = np.log10(f_logg(mass_grid)) + Mcurr_interp = f_Mcurr(mass_grid) + phase_interp = f_phase(mass_grid) + + # Make isochrone + obj = objects.DataHolder() + obj.mass = mass_grid + obj.logT = logT_interp + obj.logg = logg_interp + obj.logL = logL_interp + obj.logT_WR = logT_WR_interp + obj.mass_current = Mcurr_interp + obj.phase = phase_interp + + return obj + +def merge_isochrone_pisa_parsec(logAge, metallicity='solar', iso_in=None): + """ + Function to merge Pisa 2011 and ParsecV1.2s models. Solar metallicity is + Z = 0.015. + + If iso_in = None, will take Pisa models to highest available mass, + then switch to Parsec. If iso_in is defined, then will take this + isochrone to highest mass and switch to Parsec + + Can only handle ages at which both sets of models already exist: + logAge = 6.6 - 8.0, delta logAge = 0.01 + """ + isoParsec = get_parsec_isochrone(logAge, metallicity=metallicity) + # Make Parsec source array + isoParsec.source = np.array(['Parsec']*len(isoParsec.mass)) + + # Define isoPisa based on iso_in input + if iso_in != None: + isoPisa = iso_in + else: + isoPisa = get_pisa_isochrone(logAge, metallicity=metallicity) + isoPisa.source = np.array(['Pisa']*len(isoPisa.mass)) + + # Use Pisa model as high up as it goes, then switch to Parsec + max_Pisa = max(isoPisa.mass) + good = np.where(isoParsec.mass > max_Pisa) + isoParsec.mass = isoParsec.mass[good] + isoParsec.logT = isoParsec.logT[good] + isoParsec.logg = isoParsec.logg[good] + isoParsec.logL = isoParsec.logL[good] + isoParsec.mass_current = isoParsec.mass_current[good] + isoParsec.phase = isoParsec.phase[good] + isoParsec.source = isoParsec.source[good] + + # Combine the arrays + M = np.append(isoPisa.mass, isoParsec.mass) + logT = np.append(isoPisa.logT, isoParsec.logT) + logg = np.append(isoPisa.logg, isoParsec.logg) + logL = np.append(isoPisa.logL, isoParsec.logL) + mcurr = np.append(isoPisa.mass_current, isoParsec.mass_current) + phase = np.append(isoPisa.phase, isoParsec.phase) + logT_WR = np.append(isoPisa.logT, isoParsec.logT) + source = np.append(isoPisa.source, isoParsec.source) + + iso = objects.DataHolder() + iso.mass = M + iso.logL = logL + iso.logg = logg + iso.logT = logT + iso.mass_current = mcurr + iso.phase = phase + iso.logT_WR = logT_WR + iso.source = source + + return iso + +def merge_isochrone_phillips_pisa_parsec(logAge, metallicity='solar', iso_in=None): + """ + Function to merge Phillips 2020, Pisa 2011, and ParsecV1.2s models. + Solar metallicity is Z = 0.015. + + If iso_in = None, will take Phillips/Pisa models to highest available mass, + then switch to Parsec. If iso_in is defined, then will take this + isochrone to highest mass and switch to Parsec + + Can only handle ages at which both sets of models already exist: + logAge = 6.6 - 8.0, delta logAge = 0.01 + """ + isoParsec = get_parsec_isochrone(logAge, metallicity=metallicity) + # Make Parsec source array + isoParsec.source = np.array(['Parsec']*len(isoParsec.mass)) + + # Define isoPhPisa based on iso_in input + if iso_in != None: + isoPhPisa = iso_in + else: + isoPhPisa = get_phillips_pisa_isochrone(logAge, metallicity=metallicity) + isoPhPisa.source = np.array(['Phillips/Pisa']*len(isoPhPisa.mass)) + + # Use Phillips/Pisa model as high up as it goes, then switch to Parsec + max_PhPisa = max(isoPhPisa.mass) + good = np.where(isoParsec.mass > max_PhPisa) + isoParsec.mass = isoParsec.mass[good] + isoParsec.logT = isoParsec.logT[good] + isoParsec.logg = isoParsec.logg[good] + isoParsec.logL = isoParsec.logL[good] + isoParsec.mass_current = isoParsec.mass_current[good] + isoParsec.phase = isoParsec.phase[good] + isoParsec.source = isoParsec.source[good] + + + # Combine the arrays + M = np.append(isoPhPisa.mass, isoParsec.mass) + logT = np.append(isoPhPisa.logT, isoParsec.logT) + logg = np.append(isoPhPisa.logg, isoParsec.logg) + logL = np.append(isoPhPisa.logL, isoParsec.logL) + mcurr = np.append(isoPhPisa.mass_current, isoParsec.mass_current) + phase = np.append(isoPhPisa.phase, isoParsec.phase) + logT_WR = np.append(isoPhPisa.logT, isoParsec.logT) + source = np.append(isoPhPisa.source, isoParsec.source) + + iso = objects.DataHolder() + iso.mass = M + iso.logL = logL + iso.logg = logg + iso.logT = logT + iso.mass_current = mcurr + iso.phase = phase + iso.logT_WR = logT_WR + iso.source = source + + # add interpolation flag + if hasattr(isoPhPisa, 'interpolated'): + interpolated = np.append(isoPhPisa.interpolated, np.full(len(isoEkstrom.mass), False)) + iso.interpolated = interpolated + + # fix phase values in interpolated region (assign same as min-mass Parsec object) + min_parsec_mass_idx = np.argmin(isoParsec.mass) + min_parsec_phase = isoParsec.phase[min_parsec_mass_idx] + interp_mask = iso.interpolated == True + iso.phase[interp_mask] = min_parsec_phase + + return iso + +def make_parsec_iso(logAge, metallicity='solar'): + """ + Make parsec isochrone in Popstar iso object + """ + isoParsec = get_parsec_isochrone(logAge, metallicity=metallicity) + isoParsec.source = np.array(['Parsec']*len(isoParsec.mass)) + + iso = objects.DataHolder() + iso.mass = isoParsec.mass + iso.logL = isoParsec.logL + iso.logg = isoParsec.logg + iso.logT = isoParsec.logT + iso.mass_current = isoParsec.mass_current + iso.phase = isoParsec.phase + iso.logT_WR = isoParsec.logT + iso.source = isoParsec.source + + return iso +def get_phillips_parsec_isochrone(logAge, metallicity='solar'): + """ + Load mass, effective temperature, log gravity, and log luminosity + for the Phillips/Parsec isochrones at given logAge. Code will quit if that + logAge value doesn't exist (can make some sort of interpolation thing + later). + + Note: mass is currently initial mass, not instantaneous mass + + Inputs: + logAge - Logarithmic Age + metallicity - in Z (def = solar of 0.014) + """ + rootDir = models_dir + 'merged/phillips_parsec/' + print(rootDir) + metSuffix = 'z015/' + if metallicity != 'solar': + print( 'Non-solar Phillips 2020/Parsec 2011 metallicities not supported yet') + return + rootDir += metSuffix + print(rootDir) + + # Check to see if isochrone exists + #isoFile = rootDir + 'iso_%.2f.fits' % logAge + isoFile = os.path.join(rootDir, f'iso_{logAge:.2f}.fits') # not a valid path! + print(isoFile) + print(os.path.exists(isoFile)) + if not os.path.exists(isoFile): + print( 'Phillips/Parsec isochrone for logAge = {0:3.2f} does\'t exist'.format(logAge)) # formatting in this is mismatched! + print( 'Quitting') #raise IO Error instead and merge with top print statement + return + + data = Table.read(isoFile, format='fits') + cols = data.keys() + mass = data[cols[0]] #Note: this is initial mass, in M_sun + logT = data[cols[2]] # K + logL = data[cols[1]] # L_sun + logg = data[cols[3]] + # current mass + Mcurr = data[cols[3]] #issue! + phase = np.ones(len(data), dtype=int) + + obj = objects.DataHolder() + obj.mass = mass + obj.logT = logT + obj.logg = logg + obj.logL = logL + obj.mass_current = Mcurr + obj.phase = phase + + return obj + +def make_phillips_parsec_iso(logAge, metallicity='solar'): + """ + Make Phillips/Parsec isochrone in Popstar iso object + """ + isoPhParsec = get_phillips_parsec_isochrone(logAge, metallicity=metallicity) + isoPhParsec.source = np.array(['Phillips+Parsec']*len(isoPhParsec.mass)) + + iso = objects.DataHolder() + iso.mass = isoPhParsec.mass + iso.logL = isoPhParsec.logL + iso.logg = isoPhParsec.logg + iso.logT = isoPhParsec.logT + iso.mass_current = isoPhParsec.mass_current + iso.phase = isoPhParsec.phase + iso.logT_WR = isoPhParsec.logT + iso.source = isoPhParsec.source + + return iso + +def get_parsec_isochrone(logAge, metallicity='solar'): + """ + Load mass, effective temperature, log gravity, and log luminosity + for the Parsec isochrones at given logAge. Code will quit if that + logAge value doesn't exist (can make some sort of interpolation thing + later). + + Note: mass is currently initial mass, not instantaneous mass + + Inputs: + logAge - Logarithmic Age + metallicity - in Z (def = solar of 0.014) + """ + rootDir = models_dir + 'ParsecV1.2s/iso/' + metSuffix = 'z015/' + if metallicity != 'solar': + print( 'Non-solar Parsec 2011 metallicities not supported yet') + return + rootDir += metSuffix + + # Check to see if isochrone exists + isoFile = rootDir + 'iso_%.2f.dat' % logAge + if not os.path.exists(isoFile): + print( 'Parsec isochrone for logAge = {0:3.2f} does\'t exist'.format(logAge)) + print( 'Quitting') + return + + data = Table.read(isoFile, format='ascii') + cols = data.keys() + mass = data[cols[2]] #Note: this is initial mass, in M_sun + logT = data[cols[5]] # K + logL = data[cols[4]] # L_sun + logg = data[cols[6]] + Mcurr = data[cols[3]] + phase = np.ones(len(data), dtype=int) + + obj = objects.DataHolder() + obj.mass = mass + obj.logT = logT + obj.logg = logg + obj.logL = logL + obj.mass_current = Mcurr + obj.phase = phase + + return obj + +#### CREATING FINAL ISOCHRONES #### + +def merge_all_isochrones_phillips_baraffe_pisa_ekstrom_parsec2(logAge_arr=np.arange(6.0, 10.1, 0.01), + metallicity='solar', + rotation=True, plot=False): + """ + Make evolutionary isochrones containing a continuous distribution of + masses from the PMS to the MS. The models used are the following: + + PMS (logAge < 8) + Phillips 2020 from 0.01 to 0.07 M_sun + Baraffe+15 from 0.075 - 0.4 M_sun + Pisa 2011 from 0.5 - top of grid (~7 M_sun) + + MS (M > Pisa 2011) + Ekstrom+12 for logAge < 7.4 + Parsec V1.2s for logAge > 7.4 + + metallicity = 'solar' --> Ekstrom+12 z014, Pisa2011 z015, Parsec z015 + + if plot = True, will make plots of merged isochrones in 'plots' directory, + which must already exist + + Code is expected to be run in merged model working directory. + """ + # Root data directory for Ekstrom+12 isochrones + rootDirE = models_dir + 'Ekstrom2012/iso/' + metalPart = 'z014/' + if metallicity != 'solar': + print( 'Non-solar metallicities not supported yet') + return + rotPart = 'rot/' + if not rotation: + rotPart = 'norot/' + rootDirE += metalPart+rotPart + + # Root data directory for the Baraffe isochrones + rootDirBaraffe = models_dir + 'Baraffe15/iso/' + + # Root data directory for Pisa isochrones + rootDirPisa = models_dir + 'Pisa2011/iso/' + metSuffix = 'z015/' + if metallicity != 'solar': + print( 'Non-solar metallicities not supported yet') + return + rootDirPisa += metSuffix + + # Root data directory for Parsec isochrones + rootDirParsec = models_dir + 'ParsecV1.2s/iso/' + metalSuffix = 'z015/' + if metallicity != 'solar': + print( 'Non-solar metallicities not supported yet') + return + rootDirParsec += metalSuffix + + # Root data directory for Phillips isochrones + rootDirPhillips = models_dir + 'Phillips2020/iso/' + metalSuffix = 'z00/' + if metallicity != 'solar': + print( 'Non-solar metallicities not supported yet') + return + rootDirPhillips += metalSuffix + + # Search both directories for iso_*.dat files + isoFilesE = glob.glob(rootDirE + 'iso_*.dat') + isoFilesB = glob.glob(rootDirBaraffe + 'iso_*.fits') + isoFilesPi = glob.glob(rootDirPisa + 'iso_*.dat') + isoFilesPa = glob.glob(rootDirParsec + 'iso_*') + isoFilesPh = glob.glob(rootDirPhillips + 'iso_*.fits') + + # Output of merged isochrones + if rotation == True: + outDir = models_dir + 'merged/phillips_baraffe_pisa_ekstrom_parsec/{0}_rot/'.format(metSuffix[:-1]) + #outDir = models_dir + 'merged/test/{0}_rot/'.format(metSuffix[:-1]) + else: + outDir = models_dir + 'merged/phillips_baraffe_pisa_ekstrom_parsec/{0}_norot/'.format(metSuffix[:-1]) + #outDir = models_dir + 'merged/test/{0}_norot/'.format(metSuffix[:-1]) + if not os.path.exists(outDir): + os.mkdir(outDir) + + # Isolate the iso*.dat file names + for ii in range(len(isoFilesE)): + isoFilesE[ii] = isoFilesE[ii].split('/')[-1] + + for ii in range(len(isoFilesB)): + isoFilesB[ii] = isoFilesB[ii].split('/')[-1] + + for ii in range(len(isoFilesPi)): + isoFilesPi[ii] = isoFilesPi[ii].split('/')[-1] + + for ii in range(len(isoFilesPa)): + isoFilesPa[ii] = isoFilesPa[ii].split('/')[-1] + + for ii in range(len(isoFilesPh)): + isoFilesPh[ii] = isoFilesPh[ii].split('/')[-1] + + # Loop through the Pisa isochrones, adding the MS and Baraffe/Phillips models + # as appropriate + for ii in range(len(logAge_arr)): + logAge = logAge_arr[ii] + iso_name = 'iso_{0:.2f}.dat'.format(logAge) + + #-----PRE-MAIN SEQUENCE (only for logAge < 8)----# + if logAge <= 8.0: + # Merge with the Phillips 2020 models from 0.01 - 0.07 M_sun and + # Baraffe+15 models from 0.075 - 0.4 M_sun. Includes + # transition region between 0.4 - 0.5 M_sun in which we shift + # from 100% Baraffe to 100% Pisa and 0.07 - 0.075 M_sun in which we + #shift from 100% Phillips to 100% Baraffe + + print( 'Merging isochrones Pisa + Phillips + Baraffe from ', iso_name) + isoPMS = merge_isochrone_phillips_baraffe_pisa(logAge, metallicity=metallicity) + + #--------MAIN SEQUENCE-------# + # Case where logAge <= 7.4, we merge with Ekstrom. Otherwise, merge + # which parsec + if logAge <= 7.4: + if iso_name not in isoFilesE: + print( 'Skipping isochrones from ', iso_name) + print( 'PROBLEM WITH PISA OR EKSTROM') + pdb.set_trace() + + print( 'Merging isochrones Phillips+Pisa+Ekstrom from ', iso_name) + iso = merge_isochrone_phillips_pisa_Ekstrom(logAge, metallicity=metallicity, + rotation=rotation, iso_in=isoPMS) + else: + if iso_name not in isoFilesPa: + print( 'Skipping isochrones from ', iso_name) + print( 'PROBLEM WITH PISA OR PARSEC') + pdb.set_trace() + + print( 'Merging isochrones Phillips+Pisa+Parsec from ', iso_name) + iso = merge_isochrone_phillips_pisa_parsec(logAge, metallicity=metallicity, + iso_in=isoPMS) + else: + # If logAge > 8.0, just take the Phillips/Parsec model for the entire isochrone + print( 'Making Phillips/Parsec from ', iso_name) + # change to fits format + iso = make_phillips_parsec_iso(logAge, metallicity=metallicity) + + # Make test plot, if desired. These are put in plots directory + if plot: + # Make different models different colors + phillips_ind = np.where(iso.source == 'Phillips') + merge_pb = np.where(iso.source == 'Phillips+Baraffe') + baraffe_ind = np.where(iso.source == 'Baraffe') + merge_ind = np.where(iso.source == 'Baraffe+Pisa') + pisa_ind = np.where(iso.source == 'Pisa') + MS_ind = np.where( (iso.source == 'Ekstrom') | (iso.source == 'Parsec')) + + # Temporarily turn off interactive plot. Turn back on at end + py.ioff() + + py.figure(1) + py.clf() + py.plot(iso.logT[phillips_ind], iso.logL[phillips_ind], 'c-', label = 'Phillips', + linewidth=2) + py.plot(iso.logT[merge_pb], iso.logL[merge_pb], 'y-', label = 'Phillips+Baraffe', + linewidth=2) + py.plot(iso.logT[baraffe_ind], iso.logL[baraffe_ind], 'k-', label = 'Baraffe', + linewidth=2) + py.plot(iso.logT[merge_ind], iso.logL[merge_ind], 'r-', label = 'Baraffe+Pisa', + linewidth=2) + py.plot(iso.logT[pisa_ind], iso.logL[pisa_ind], 'g-', label = 'Pisa', + linewidth=2) + py.plot(iso.logT[MS_ind], iso.logL[MS_ind], 'b-', + label = 'Ekstrom/Parsec', linewidth=2) + py.xlabel('log Teff') + py.ylabel('log L') + py.title('Log Age = {0}'.format(logAge)) + py.legend(loc=3) + py.axis([4.9, 3.2, -3.0, 8]) + py.savefig(outDir+'plots/iso_{0:.2f}.png'.format(logAge)) + + py.ion() + + + _out = open(outDir + iso_name, 'w') + + hdr_fmt = '%12s %10s %10s %10s %10s %12s %5s %-10s\n' + _out.write(hdr_fmt % + ('# M_init', 'log T', 'log L', 'log g', 'logT_WR', 'M_curr', 'phase', 'Source')) + _out.write(hdr_fmt % + ('# (Msun)', '(Kelvin)', '(Lsun)', '(cgs)', '(Kelvin)', '(Msun)', '()', '()')) + + for kk in range(len(iso.mass)): + _out.write('%12.6f %10.4f %10.4f %10.4f %10.4f %12.6f %5d %-10s\n' % + (iso.mass[kk], iso.logT[kk], iso.logL[kk], + iso.logg[kk], iso.logT_WR[kk], + iso.mass_current[kk], iso.phase[kk], iso.source[kk])) + + _out.close() + return + + +##### CREATING MERGED ATMOSPHERE MODEL ##### +def create_merged_models(cdbs_path, plot=False): + """ + for 1200 - 1000 K, merge Meisner and BTSettl! + + From 1000 K - 1200 K, merge the Meisner and BTSettl atmospheres. + More like BTSettl near 1200 K, more like Meisner near 1000 K + + cdbs_path is path to cdbs directory (including cdbs). Will make new directory + in cdbs/grid named "merged_meisner_BTsettl" with with merged models. If plot = True, will plot + the normalized merged model plus the original Meisner and BTSettl models + + Temp 1000 - 1200, steps of 20; logg 2.5 - 5.5, steps of 0.5, metallicity covering + Meisner range (2.5 -- 5.5, in steps of 0.5). (So, this is one model at 5250)? + + Note: metallicity directories created by hand + + Creates new directory "merged_meisner_BTSettl" in cdbs/grid with new spectrum + catalog file. + Also includes the atlas 5500K model and phoenix 5000K model, for interpolation purposes + """ + #Setting logg sampling + logg_arr = np.arange(2.5, 5.5+0.1, 0.5) + + # Setting metallicity sub-directories + atlas_dir = ['ckm25', 'ckm20', 'ckm15', 'ckm10', 'ckm05', 'ckp00', 'ckp02', 'ckp05'] + phoenix_dir = ['phoenixm30', 'phoenixm20', 'phoenixm15', 'phoenixm10', 'phoenixm05', 'phoenixm00', 'phoenixp05', 'phoenixp05'] + output_dir = ['mergedm25', 'mergedm20', 'mergedm15', 'mergedm10', 'mergedm05', 'mergedp00', 'mergedp02', 'mergedp05'] + metal_arr = [-2.5, -2.0, -1.5, -1.0, -0.5, 0, 0.2, 0.5] + + assert len(atlas_dir) == len(phoenix_dir) == len(output_dir) + + # Make new cdbs merged directory, if it doesn't already exist + newPath = '{0}/grid/merged_atlas_phoenix'.format(cdbs_path) + if not os.path.exists(newPath): + os.mkdir(newPath) + + # For each metallicity, create merged model + for ii in range(len(output_dir)): + # Make metallicity dir for merged model + final_dir = '{0}/{1}'.format(newPath, output_dir[ii]) + if not os.path.exists(final_dir): + os.mkdir(final_dir) + + # Extract the relevant ATLAS and PHEONIX models near 5250 K + atlas_path = '{0}/grid/ck04models/{1}/'.format(cdbs_path, atlas_dir[ii]) + atlas_hdu = fits.open('{0}/{1}_5250.fits'.format(atlas_path, atlas_dir[ii])) + atlas_5250 = atlas_hdu[1].data + phoenix_path = '{0}/grid/phoenix_v16_rebin/{1}'.format(cdbs_path, phoenix_dir[ii]) + phoenix_hdu1 = fits.open('{0}/{1}_05200.fits'.format(phoenix_path, phoenix_dir[ii])) + phoenix_hdu2 = fits.open('{0}/{1}_05300.fits'.format(phoenix_path, phoenix_dir[ii])) + phoenix_5200 = phoenix_hdu1[1].data + phoenix_5300 = phoenix_hdu2[1].data + print('Done reading input models') + + # Trim both models to the wavelength region we want: VRIJHKL (0.25 - 4.2 mircons) + good = np.where( (atlas_5250['Wavelength'] > 2500) & + (atlas_5250['Wavelength'] < 52000) ) + atlas_5250 = atlas_5250[good] + good = np.where( (phoenix_5200['Wavelength'] > 2500) & + (phoenix_5200['Wavelength'] < 52000) ) + phoenix_5200 = phoenix_5200[good] + phoenix_5300 = phoenix_5300[good] + + #----------------------------# + # For each logg val, create phoenix spectrum for 5250 K, + # degrade resolution to match atlas, then average with + # 5250 K atlas model to get merged model at 5250 K + #----------------------------# + new_model = [] + phoenix_5250_f = [] + atlas_5250_f = [] + for logg in logg_arr: + # Create phoenix models at 5250 K + low = phoenix_5200['g{0:2.1f}'.format(logg)] + high = phoenix_5300['g{0:2.1f}'.format(logg)] + + arr = np.transpose([low, high]) + phoenix_5250 = np.mean(arr, axis=1) + + phoenix_5250_rebin = rebin_spec(phoenix_5200['Wavelength'], phoenix_5250, + atlas_5250['Wavelength']) + + # Store phoenix rebinned average spectrum + phoenix_5250_f.append(phoenix_5250_rebin) + + # Store atlas spectrum for later + grav = str(logg).split('.') + atlas_5250_f.append(atlas_5250['g'+grav[0]+grav[1]]) + + # Now, final 5250 K model will be average of atlas and phoenix + # models (since exactly inbetween 5000 K and 5500 K) + arr = np.transpose([phoenix_5250_rebin, atlas_5250['g'+grav[0]+grav[1]]]) + final = np.mean(arr, axis=1) + + new_model.append(final) + print('Done with logg {0:2.1f}'.format(logg)) + + # Create fits table with new model. First column is wavelength, followed by + # fluxes for different logg + wave = atlas_5250['Wavelength'] # Still same wavelength array as before + c0 = fits.Column(name='Wavelength', format='D', array=wave) + c1 = fits.Column(name='g0.0', format='E', array=new_model[0]) + c2 = fits.Column(name='g0.5', format='E', array=new_model[1]) + c3 = fits.Column(name='g1.0', format='E', array=new_model[2]) + c4 = fits.Column(name='g1.5', format='E', array=new_model[3]) + c5 = fits.Column(name='g2.0', format='E', array=new_model[4]) + c6 = fits.Column(name='g2.5', format='E', array=new_model[5]) + c7 = fits.Column(name='g3.0', format='E', array=new_model[6]) + c8 = fits.Column(name='g3.5', format='E', array=new_model[7]) + c9 = fits.Column(name='g4.0', format='E', array=new_model[8]) + c10 = fits.Column(name='g4.5', format='E', array=new_model[9]) + c11 = fits.Column(name='g5.0', format='E', array=new_model[10]) + + cols = fits.ColDefs([c0,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11]) + tbhdr = phoenix_hdu1[1].header + prihdr = phoenix_hdu1[0].header + prihdu = fits.PrimaryHDU(header=prihdr) + tbhdu = fits.BinTableHDU.from_columns(cols, header=tbhdr) + # Add TUNIT keysto tbhdu + tbhdu = make_merged_header(tbhdu) + + # Make final hdu table, save it + finalhdu = fits.HDUList([prihdu, tbhdu]) + finalhdu.writeto('{0}/{1}_05250.fits'.format(final_dir, output_dir[ii]), clobber=True) + + # Test plot, if desired + if plot == True: + py.figure(1, figsize=(10,10)) + py.clf() + # Plot merged model + py.semilogy(wave, wave * new_model[8], 'r-', label='Merged') + # Plot atlas 5250 K model + py.semilogy(wave, wave * atlas_5250_f[8], 'b-', label = 'Atlas') + # Plot phoenix 5250 K model + py.semilogy(wave, wave * phoenix_5250_f[8], 'g-', label = 'Phoenix') + py.legend() + py.xlabel('Wavelength (Angstrom)') + py.ylabel(r'log ($\lambda$ F$_{\lambda}$)') + py.axis([5000, 40000, 2*10**9, 4*10**10]) + py.title('Merged 5250 K Spectrum') + py.savefig('Merged_atlas_phoenix_{0}.png'.format(output_dir[ii])) + + pdb.set_trace() + py.close('all') + + # Copy the atlas 5500 K and phoenix 5000 K models into the + # merged directory to accompany the merged model. This is for + # interpolation purposes for pysynphot + cmd = 'cp {0}/{1}_5500.fits {2}'.format(atlas_path, atlas_dir[ii], final_dir) + cmd2 = 'cp {0}/{1}_05000.fits {2}'.format(phoenix_path, phoenix_dir[ii], final_dir) + os.system(cmd) + os.system(cmd2) + + cmd = 'mv {0}/{1}_5500.fits {0}/{2}_05500.fits'.format(final_dir, atlas_dir[ii], output_dir[ii]) + cmd2 = 'mv {0}/{1}_05000.fits {0}/{2}_05000.fits'.format(final_dir, phoenix_dir[ii], output_dir[ii]) + os.system(cmd) + os.system(cmd2) + + # Close all open hdu + atlas_hdu.close() + phoenix_hdu1.close() + phoenix_hdu2.close() + + print('Done {0}'.format(output_dir[ii])) + + # Make catalog.fits table for new merged model, plus the atlas and + # phoenix models at the high and low extremes of the temp range. Note temp + # of merged model goes first, for filename purposes + catalog, filenames = make_merged_catalog(output_dir, [5250, 5000, 5500], logg_arr, metal_arr) + catalog.write(cdbs_path+'/grid/merged_atlas_phoenix/catalog.fits', overwrite=True) + + return + + + +def create_merged_meisner_btsettl(cdbs_path, plot=False): + """ + From 1000 K - 1200 K, merge the BTSettl_CIFITS2011_2015 and Meisner 2023 atmospheres. + BTSettl at 1200 K, Meisner near 1000 K + + cdbs_path is path to cdbs directory (including cdbs). Will make new directory + in cdbs/grid named "merged_meisner_btsettl" with with merged models. If plot = True, will plot + the normalized merged model plus the original models + + + (Only 1 truely merged model at 3500 K, with log g from 2.5 - 5.5)? + + Creates new directory "merged_meisner_btsettl" in cdbs/grid with new spectrum + catalog file. + (Also includes the atlas 5500K model and phoenix 5000K model, for interpolation purposes)? + """ + # Set log g sampling + logg_solar_arr = np.arange(3.5, 5.5+0.1, 0.5) + logg_nonsolar_arr = np.array([3.5, 5.0]) + + # Setting metallicity sub-directories + meisner_dir = ['mm05', 'mp00'] + output_dir = ['mergedm05', 'mergedp00'] + metal_arr = [-0.5, 0] + + assert len(meisner_dir) == len(output_dir) + + # Make new cdbs merged directory, if it doesn't already exist + newPath = '{0}/grid/merged_meisner_BTSettl'.format(cdbs_path) + if not os.path.exists(newPath): + os.mkdir(newPath) + + # For each metallicity, create merged model + for ii in range(len(output_dir)): + # Make metallicity dir for merged model + final_dir = '{0}/{1}'.format(newPath, output_dir[ii]) + if not os.path.exists(final_dir): + os.mkdir(final_dir) + + # For each gravity, extract BTSettl and Meisner models at 1100 K and + # average them to get the merged model. Also write BTSettl models at + # 1200 K and Meisner models at 1000 K + if metal_arr[ii] == 0: + logg_tmp = logg_solar_arr + BT_func = atmospheres.get_BTSettl_atmosphere + else: + BT_func = atmospheres.get_BTSettl_atmosphere + logg_tmp = logg_nonsolar_arr + + for jj in logg_tmp: + BT_atmo = BT_func(temperature=1100, gravity=jj, rebin=True) + meisner_atmo = atmospheres.get_Meisner2023_atmosphere(temperature=1100, gravity=jj, rebin=True) + + # Check to make sure wavelengths are the same between atmospheres + print("BT_func assigned to:", BT_func) + print(f"BT_func({1100}, {jj}, rebin=True) -> {BT_atmo}") + diff = BT_atmo.wave - meisner_atmo.wave + if np.sum(diff > 0): + print('Wavelength mismatch problem!') + pdb.set_trace() + + merged_flux = np.mean(np.array([meisner_atmo.flux, BT_atmo.flux]), axis=0) + + # Create fits file with new atmosphere + c0 = fits.Column(name='Wavelength', format='D', array=BT_atmo.wave) + c1 = fits.Column(name='Flux', format='E', array=merged_flux) + + cols = fits.ColDefs([c0, c1]) + tbhdu = fits.BinTableHDU.from_columns(cols) + + prihdu = fits.PrimaryHDU() + tbhdu.header['TUNIT1'] = 'ANGSTROM' + tbhdu.header['TUNIT2'] = 'FLAM' + hdu_new = fits.HDUList([prihdu, tbhdu]) + + # Save fits file to merged Meisner-BTSettl direcotry + hdu_new.writeto('{0}/{1}_03500_{2}.fits'.format(final_dir, output_dir[ii], jj), overwrite=True) + + # Make test plot, if desired + if plot: + py.figure(1, figsize=(10,10)) + py.clf() + py.semilogy(BT_atmo.wave, BT_atmo.wave * merged_flux, 'r-', label='Merged') + py.semilogy(BT_atmo.wave, BT_atmo.wave * BT_atmo.flux, 'b-', label = 'BTSettl') + py.semilogy(meisner_atmo.wave, meisner_atmo.wave * meisner_atmo.flux, 'g-', label = 'Meisner') + py.legend() + py.xlabel('Wavelength (Angstrom)') + py.ylabel(r'log ($\lambda$ F$_{\lambda}$)') + py.xlim(5000, 40000) + py.ylim(10**8, 10**10) + py.title('Merged 1100 K Spectrum, Z = {1}, logg = {0}'.format(jj, metal_arr[ii])) + py.savefig('Merged_Meisner_BTSettl_{1}_{0}.png'.format(jj, metal_arr[ii])) + + # Now to bring over the 1000 K Meisner and 1200 K BTSettl models + BT_atmo = BT_func(temperature=1200, gravity=jj, rebin=True) + meisner_atmo = atmospheres.get_Meisner2023_atmosphere(temperature=1000, gravity=jj, rebin=True) + + # Create new fits files for these as well + c0_b = fits.Column(name='Wavelength', format='D', array=BT_atmo.wave) + c1_b = fits.Column(name='Flux', format='E', array=BT_atmo.flux) + c0_m = fits.Column(name='Wavelength', format='D', array=meisner_atmo.wave) + c1_m = fits.Column(name='Flux', format='E', array=meisner_atmo.flux) + + cols_b = fits.ColDefs([c0_b, c1_b]) + tbhdu_b = fits.BinTableHDU.from_columns(cols_b) + cols_m = fits.ColDefs([c0_m, c1_m]) + tbhdu_m = fits.BinTableHDU.from_columns(cols_m) + + prihdu = fits.PrimaryHDU() + tbhdu_b.header['TUNIT1'] = 'ANGSTROM' + tbhdu_b.header['TUNIT2'] = 'FLAM' + tbhdu_m.header['TUNIT1'] = 'ANGSTROM' + tbhdu_m.header['TUNIT2'] = 'FLAM' + + hdu_newb = fits.HDUList([prihdu, tbhdu_b]) + hdu_newm = fits.HDUList([prihdu, tbhdu_m]) + + # Save fits file to merged Meisner-BTSettl direcotry + hdu_newb.writeto('{0}/{1}_03200_{2}.fits'.format(final_dir, output_dir[ii], jj), clobber=True) + hdu_newp.writeto('{0}/{1}_03800_{2}.fits'.format(final_dir, output_dir[ii], jj), clobber=True) + hdu_new.close() + hdu_newb.close() + hdu_newp.close() + + print('Done {0}'.format(output_dir[ii])) + + return + +def make_catalog_merged_models2(path='/g/lu/models/cdbs/grid/merged_BTSettl_phoenix/'): + """ + Make cdbs catalog.fits file for merged BTSettl/phoenix direcotry. path should + point to this directory. + + Writes catalog.fits file in the cdbs directory + """ + output_dir = ['mergedm25', 'mergedm20', 'mergedm15', 'mergedm10', 'mergedm05', 'mergedp00', 'mergedp02', 'mergedp05'] + metal_arr = [-2.5, -2.0, -1.5, -1.0, -0.5, 0, 0.2, 0.5] + + index_str = [] + name_str = [] + for ii in range(len(output_dir)): + files = glob.glob('{0}/{1}/*.fits'.format(path, output_dir[ii])) + + # Extract parameters for each atmosphere from the filename, + # construct columns for catalog file + for name in files: + final = name.split('/')[-1] + tmp = final.split('_') + temp = float(tmp[1]) # In kelvin + logg = float(tmp[2][:-5]) + + index_str.append('{0},{1},{2:3.2f}'.format(int(temp), metal_arr[ii], logg)) + name_str.append('{0}/{1}[Flux]'.format(output_dir[ii], final)) + + # Make catalog + catalog = Table([index_str, name_str], names = ('INDEX', 'FILENAME')) + + # Create catalog.fits file in directory with the models + catalog.write(path+'catalog.fits', format = 'fits', overwrite=True) + + return \ No newline at end of file diff --git a/spisea/atmospheres.py b/spisea/atmospheres.py index 8df2fbe1..0f4c90e5 100755 --- a/spisea/atmospheres.py +++ b/spisea/atmospheres.py @@ -523,6 +523,7 @@ def get_BTSettl_2015_atmosphere(metallicity=0, temperature=2500, gravity=4, rebi gravity=gravity) sp = pysynphot.Icat(atm_name, temperature, metallicity, gravity) + #print(dir(obj)) # Do some error checking @@ -607,6 +608,10 @@ def get_BTSettl_atmosphere(metallicity=0, temperature=2500, gravity=4.5, rebin=T If true, rebins the atmospheres so that they are the same resolution as the Castelli+04 atmospheres. Default is False, which is often sufficient synthetic photometry in most cases. + + **PRINT STATEMENTS TO DEBUG + **check get_atmosphere_bounds + **comment out try/except clause and check break """ if rebin == True: atm_name = 'BTSettl_rebin' @@ -624,17 +629,83 @@ def get_BTSettl_atmosphere(metallicity=0, temperature=2500, gravity=4.5, rebin=T sp = pysynphot.Icat(atm_name, temperature, metallicity, gravity) +def get_Meisner2023_atmosphere(metallicity=0, temperature=1000, gravity=4.5, rebin=True): + """ + Return atmosphere from Meisner2023 grid + (`Meisner et al. 2023 `_) + + Grid originally downloaded `here `_ + + Grid range: + * Teff = 250 - 1200 K + * gravity: 2.5 - 5.5 cgs (in steps of 0.5) + * [M/H] = -1.0, -0.5, 0, +0, +0.3 + + """ + if rebin == True: + atm_name = 'Meisner2023_rebin' + else: + atm_name = 'Meisner2023' + + try: + sp = pysynphot.Icat(atm_name, temperature, metallicity, gravity) + except: + # Check atmosphere catalog bounds + (temperature, gravity) = get_atmosphere_bounds(atm_name, + metallicity=metallicity, + temperature=temperature, + gravity=gravity) + sp = pysynphot.Icat(atm_name, temperature, metallicity, gravity) + # Do some error checking idx = np.where(sp.flux != 0)[0] if len(idx) == 0: - print( 'Could not find BTSettl_2015 atmosphere model for') + print( 'Could not find Meisner2023 atmosphere model for') print( ' temperature = %d' % temperature) print( ' metallicity = %.1f' % metallicity) print( ' log gravity = %.1f' % gravity) return sp +def get_Phillips2020_atmosphere(metallicity=0, temperature=1000, gravity=4.5, rebin=True): + """ + Return atmosphere from Phillips et al., 2020 using ATMO model + (`Phillips et al. 2020 `_) + + Grid originally downloaded `here `_ + + Grid Range: + * Teff: 200 - 3000 K + * gravity: 2.5 - 5.5 cgs + * [M/H] = 0 + """ + if rebin == True: + atm_name = 'Phillips2020_rebin' + else: + atm_name = 'Phillips2020' + + try: + sp = pysynphot.Icat(atm_name, temperature, metallicity, gravity) + except: + # Check atmosphere catalog bounds + (temperature, gravity) = get_atmosphere_bounds(atm_name, + metallicity=metallicity, + temperature=temperature, + gravity=gravity) + + sp = pysynphot.Icat(atm_name, temperature, metallicity, gravity) + + # Do some error checking + idx = np.where(sp.flux != 0)[0] + if len(idx) == 0: + print( 'Could not find Phillips2020 atmosphere model for') + print( ' temperature = %d' % temperature) + print( ' metallicity = %.1f' % metallicity) + print( ' log gravity = %.1f' % gravity) + + return sp + def get_wdKoester_atmosphere(metallicity=0, temperature=20000, gravity=7): """ Return white dwarf atmospheres from @@ -723,6 +794,34 @@ def get_BTSettl_phoenix_atmosphere(metallicity=0, temperature=5250, gravity=4): return sp +def get_BTSettl_meisner_atmosphere(metallicity=0, temperature=5250, gravity=4): + """ + Return atmosphere that is a linear merge of BTSettl_CITFITS2011_2015 model + and Meisner2023. + + Only valid for temps between 1000 - 1200K, gravity from 3.5 - 5.5 + """ + try: + sp = pysynphot.Icat('merged_BTSettl_meisner', temperature, metallicity, gravity) + except: + # Check atmosphere catalog bounds + (temperature, gravity) = get_atmosphere_bounds('merged_BTSettl_meisner', + metallicity=metallicity, + temperature=temperature, + gravity=gravity) + + sp = pysynphot.Icat('merged_BTSettl_meisner', temperature, metallicity, gravity) + + # Do some error checking + idx = np.where(sp.flux != 0)[0] + if len(idx) == 0: + print( 'Could not find BTSettl-Meisner merge atmosphere model for') + print( ' temperature = %d' % temperature) + print( ' metallicity = %.1f' % metallicity) + print( ' log gravity = %.1f' % gravity) + + return sp + #---------------------------------------------------------------------# def get_merged_atmosphere(metallicity=0, temperature=20000, gravity=4.5, verbose=False, rebin=True): @@ -767,6 +866,8 @@ def get_merged_atmosphere(metallicity=0, temperature=20000, gravity=4.5, verbose * T < 3800, logg < 2.5: PHOENIX v16 * 3200 <= T < 3800, logg > 2.5: BTSettl_CIFITS2011_2015/PHOENIXV16 merge * 3200 < T <= 1200, logg > 2.5: BTSettl_CIFITS2011_2015 + * 1200 < T <= 1000, logg >= 3.5: BTSettl_CIFITS2011_2015/Meisner2023 merge + * 1000 < T <= 250, logg > 2.5: Meisner2023 Otherwise, if T < 3800 and [M/H] != 0: @@ -777,6 +878,7 @@ def get_merged_atmosphere(metallicity=0, temperature=20000, gravity=4.5, verbose * ATLAS: ATLAS9 models (`Castelli & Kurucz 2004 `_) * PHOENIXv16 (`Husser et al. 2013 `_) * BTSettl_CIFITS2011_2015: Baraffee+15, Allard+ (https://phoenix.ens-lyon.fr/Grids/BT-Settl/CIFIST2011_2015/SPECTRA/) + * Meisner2023: ATMO 1D models (`Meisner et al. 2023 `_) LTE WARNING: @@ -799,6 +901,30 @@ def get_merged_atmosphere(metallicity=0, temperature=20000, gravity=4.5, verbose # If solar metallicity, use BTSettl 2015 grid. Only solar metallicity is # currently available here, so if non-solar metallicity, just stick with # the Phoenix grid + if (temperature < 1000): + if verbose: + print( 'Meisner2023 atmosphere') + return get_Meisner2023_atmosphere(metallicity=metallicity, + temperature=temperature, + gravity=gravity, + rebin=rebin) + + if (temperature <= 1200) & (temperature >= 1000): + if (gravity >= 3.5): + if verbose: + print( 'BTSettl/Meisner2023 merged atmosphere') + return get_Meisner2023_atmosphere(metallicity=metallicity, + temperature=temperature, + gravity=gravity, + rebin=rebin) + if (gravity < 3.5) & (gravity >=2.5): + if verbose: + print( 'Meisner2023 atmosphere') + return get_Meisner2023_atmosphere(metallicity=metallicity, + temperature=temperature, + gravity=gravity, + rebin=rebin) + if (temperature <= 3800) & (metallicity == 0): # High gravity are in BTSettl regime if (temperature <= 3200) & (gravity > 2.5): @@ -910,6 +1036,46 @@ def get_wd_atmosphere(metallicity=0, temperature=20000, gravity=4, verbose=False bbspec = get_bb_atmosphere(temperature=temperature, verbose=verbose) return bbspec + +def get_bd_atmosphere(metallicity=0, temperature=1000, gravity=4, verbose=False): + """ + Return the brown dwarf atmosphere from + `Meisner et al. 2023 `_. + If desired parameters are + outside of grid, return a blackbody spectrum instead + + Parameters + ---------- + metallicity: float + The stellar metallicity, in terms of [Z] + + temperature: float + The stellar temperature, in units of K + + gravity: float + The stellar gravity, in cgs units + + rebin: boolean + If true, rebins the atmospheres so that they are the same + resolution as the Castelli+04 atmospheres. Default is False, + which is often sufficient synthetic photometry in most cases. + + verbose: boolean + True for verbose output + """ + try: + if verbose: + print('Meisner2023 atmosphere') + + return get_Meisner2023_atmosphere(metallicity=metallicity, + temperature=temperature, + gravity=gravity) + + except pysynphot.exceptions.ParameterOutOfBounds: + # Use a black-body atmosphere + bbspec = get_bb_atmosphere(temperature=temperature, verbose=verbose) + return bbspec + def get_bb_atmosphere(metallicity=None, temperature=20_000, gravity=None, verbose=False, rebin=None, wave_min=500, wave_max=50_000, wave_num=20_000): @@ -2020,6 +2186,183 @@ def rebin_BTSettl(make_unique=False): return +def organize_all_Meisner2023_atmospheres(): + """ + Construct cdbs-ready atmospheres for the Meisner2023 grid. + The code expects tp be run in cdbs/grid/Meisner2023, and expects that the + individual model files have been downloaded from online + and processed into python-readable ascii files. + """ + orig_dir = os.getcwd() + dirs = ['mm10', 'mm05', 'mp00', 'mp03'] + + # Go through each directory, turning each spectrum into a cdbs-ready file. + # Save as a fits file, for faster access later + for ii in dirs: + print('Starting {0}'.format(ii)) + os.chdir(ii) + + files = glob.glob('*.fits') + count=0 + for jj in files: + # Open each .fits file and read the data + with fits.open(jj) as hdul: + data = hdul[1].data + wavelength = data['Wavelength'] + flux = data['Flux'] + + # Make flux independent of R&D + flux_new = flux / 5e-20 + + # Create new columns with desired format + c0 = fits.Column(name='Wavelength', format='D', array=wavelength) + c1 = fits.Column(name='Flux', format='E', array=flux_new) + + cols = fits.ColDefs([c0, c1]) + tbhdu = fits.BinTableHDU.from_columns(cols) + + # Add unit keywords + prihdu = fits.PrimaryHDU() + tbhdu.header['TUNIT1'] = 'ANGSTROM' + tbhdu.header['TUNIT2'] = 'FLAM' + hdu_new = fits.HDUList([prihdu, tbhdu]) + + # Write the new fits table in the cdbs directory + output_filename = '{0}.fits'.format(jj[:-5]) # Removing the original .fits extension + hdu_new.writeto(output_filename, overwrite=True) + hdu_new.close() + count += 1 + print('Done {0} of {1}'.format(count, len(files))) + + # Go back to original directory, move to next metallicity directory + os.chdir(orig_dir) + + return + +def make_Meisner2023_catalog(): + """ + Create cdbs catalog.fits of Meisner2023 grid. + THIS IS STEP 2, after organize_Meisner2023_atmospheres has + been run. + + Code expects to be run in cdbs/grid/Meisner2023 + Will create catalog.fits file in atmosphere directory with + description of each model + """ + # Record current working directory for later + start_dir = os.getcwd() + dirs = ['mm10', 'mm05', 'mp00', 'mp03'] + + # Construct the catalog.fits file input. The input consists of + # and index string that specifies the stellar paramters, and a + # name string that points to the file + # Loop over all the metallicity directories to construct these inputs + index_str = [] + name_str = [] + for ii in dirs: + os.chdir(ii) + files = glob.glob('spec_jwst_*.fits') + + for jj in files: + # Parse temperature, log(g), and metallicity from filename + temp_str = jj.split('_')[2] + logg_str = jj.split('_')[3] + metal_str = jj.split('_')[4] + + # Extract temperature, surface gravity, and metallicity + temp = float(temp_str[1:]) # Temperature in Kelvin + logg = float(logg_str[1:]) # Surface gravity log(g) + + # Build metallicity value + if metal_str.startswith('m'): + metallicity = -1 * float(metal_str[1:]) + else: + metallicity = float(metal_str[1:]) + + # Construct index and filename strings + index_str.append('{0},{1},{2:3.2f}'.format(int(temp), metallicity, logg)) + name_str.append('{0}/{1}[Flux]'.format(ii, jj)) + + print('Processed directory:', ii) + os.chdir(start_dir) + + + # Make catalog + catalog = Table([index_str, name_str], names = ('INDEX', 'FILENAME')) + + # Create catalog.fits file in directory with the models + catalog.write('catalog.fits', format = 'fits', overwrite=True) + + # Move back to original directory, create the catalog.fits file + os.chdir(start_dir) + + return + +def rebin_Meisner2023(make_unique=False): + """ + Rebin Meisner2023 models to atlas ck04 resolution; this makes + spectrophotometry MUCH faster + + makes new directory: Meisner2023_rebin + + Code expects to be run in cdbs/grid directory + """ + # Get an atlas ck04 model, we will use this to set wavelength grid + sp_atlas = get_castelli_atmosphere() + + # Create a directory for rebinned Meisner2023 models + rebin_path = 'Meisner2023_rebin/' + if not os.path.exists(rebin_path): + os.mkdir(rebin_path) + + # Load the catalog.fits file and extract all spectra file paths + cat = Table.read('Meisner2023/catalog.fits') + files_all = [cat[ii]['FILENAME'].split('[')[0] for ii in range(len(cat))] + + print('Rebinning Meisner2023 spectra') + if make_unique: + print('Making unique') + make_wavelength_unique(files_all, 'Meisner2023') + print('Done') + + for ff, file in enumerate(files_all): + vals = cat[ff]['INDEX'].split(',') + temp = float(vals[0]) + metal = float(vals[1]) + logg = float(vals[2]) + + # Fetch the Meisner2023 spectrum and rebin its flux + try: + sp = pysynphot.Icat('Meisner2023', temp, metal, logg) + flux_rebin = rebin_spec(sp.wave, sp.flux, sp_atlas.wave) + + # Create the output FITS file + c0 = fits.Column(name='Wavelength', format='D', array=sp_atlas.wave) + c1 = fits.Column(name='Flux', format='E', array=flux_rebin) + + cols = fits.ColDefs([c0, c1]) + tbhdu = fits.BinTableHDU.from_columns(cols) + prihdu = fits.PrimaryHDU() + tbhdu.header['TUNIT1'] = 'ANGSTROM' + tbhdu.header['TUNIT2'] = 'FLAM' + + # Write the new rebinned file in the Meisner2023_rebin directory + outfile = os.path.join(rebin_path, os.path.basename(file)) + finalhdu = fits.HDUList([prihdu, tbhdu]) + finalhdu.writeto(outfile, overwrite=True) + + except Exception as e: + print(f"Error processing {file}: {e}") + orig_file = os.path.join('Meisner2023', file) + outfile = os.path.join(rebin_path, os.path.basename(file)) + os.system(f'cp {orig_file} {outfile}') + + print('Done {0} of {1}'.format(ff + 1, len(files_all))) + + return + + + def organize_WDKoester_atmospheres(path_to_dir): """ Construct cdbs-ready wdKoester WD atmospheres for each model. (from Koester 2010) diff --git a/spisea/evolution.py b/spisea/evolution.py index 6cf765d5..a12014ad 100755 --- a/spisea/evolution.py +++ b/spisea/evolution.py @@ -4,12 +4,14 @@ import numpy as np import os import glob +import pandas as pd import pdb import warnings from astropy.table import Table, vstack, Column from scipy import interpolate import pylab as py from spisea.utils import objects +from scipy.interpolate import RegularGridInterpolator from spisea import exceptions logger = logging.getLogger('evolution') @@ -526,6 +528,298 @@ def format_isochrones(input_iso_dir, metallicity_list): os.chdir(start_dir) return +class Phillips2020(StellarEvolution): + """ + Evolution models from + `Phillips et al. 2020 `_. + + Downloaded from `here _` + + Notes + ----- + Evolution model parameters used in download: + + * Assume chemical equilibrium + * Solar metallicity + * For young BDs + CHANGE!!! + """ + + def __init__(self): + r""" + Define intrinsic properties for the Phillips brown dwarf stellar models + """ + # specify location of model files + self.model_dir = models_dir + 'Phillips2020/' + + # specifying metallicity + self.z_list = [0.015] + self.z_file_map = {0.015: 'z00'} + self.z_solar = 0.015 + + # populate list of isochrone ages (log scale) + self.age_list = np.arange(6.0, 10.0, 0.001) + + # define required evo_grid number + self.evo_grid_min = 1.0 + + def isochrone(self, age= 1.e8, metallicity=0.0): + r""" + Extract an individual isochrone from the Phillips2020 collection. + """ + # Error check to see if installed evolution model + # grid is compatible with code version. Also return + # current grid num + self.evo_grid_num = check_evo_grid_number(self.evo_grid_min, models_dir) + + # convert metallicity to mass fraction + z_defined = self.z_solar*10.**metallicity + + log_age = math.log10(age) + + # check age and metallicity are within bounds + if ((log_age < np.min(self.age_list)) or (log_age > np.max(self.age_list))): + logger.error('Requested age {0} is out of bounds.'.format(log_age)) + + if ((z_defined < np.min(self.z_list)) or + (z_defined > np.max(self.z_list))): + logger.error('Requested metallicity {0} is out of bounds.'.format(z_defined)) + + # find closest metallicity value + z_idx = np.where(abs(np.array(self.z_list) - z_defined) == min(abs(np.array(self.z_list) - z_defined)) )[0][0] + z_dir = self.z_file_map[self.z_list[z_idx]] + + # Specify subdirectory for metallicity + iso_path = os.path.join(self.model_dir, 'iso', z_dir) + + # Find nearest age in grid to input grid by parsing through available files + p_files = glob.glob(os.path.join(iso_path, 'iso_*.fits')) + p_ages = np.array([float(f.split('_')[1].replace('.fits', '')) for f in p_files]) + close_age = np.argmin(abs(p_ages - log_age)) + close_file = p_files[close_age] + print(f"Found nearest age file as {close_file} for requested age of {log_age}") + + # Make sure the closest file exists + if not os.path.exists(close_file): + raise FileNotFoundError(f"Isochrone file not found: {close_file}.") + + # return isochrone data + iso = Table.read(close_file, format='fits') + iso.rename_column('Z', 'Z') + iso.rename_column('Age', 'logAge') + iso.rename_column('Mass', 'mass') + iso.rename_column('Mass_current', 'mass_current') + iso.rename_column('Luminosity', 'logL') + iso.rename_column('Teff', 'logT') + iso.rename_column('Gravity', 'logg') + iso['logT_WR'] = iso['logT'] + + # Phillips doesn't identify WR stars, so identify all as "False" + isWR = Column([False] * len(iso), name='isWR') + iso.add_column(isWR) + + iso.meta['log_age'] = log_age + iso.meta['metallicity_in'] = metallicity + iso.meta['metallicity_act'] = metallicity + + return iso + + def format_isochrones(input_iso_dir, metallicity_list): + r""" + Change + """ + # Store current directory for later + start_dir = os.getcwd() + + # Move into isochrone directory + os.chdir(input_iso_dir) + + # Work on each metallicity isochrones individually + for metal in metallicity_list: + # More into metallicity directory, read isochrone file + os.chdir(metal) + + isoFile = glob.glob('output*') + print( 'Read Input: this is slow') + iso = Table.read(isoFile[0], format='fits') + print( 'Done') + + ages_all = iso['col2'] + + # Extract the unique ages + age_arr = np.unique(ages_all) + + # For each unique age, extract the proper rows and make corresponding + # table + print( 'Making individual isochrone files') + for age in age_arr: + good = np.where(ages_all == age) + tmp = iso[good] + + #Write table + tmp.write('iso_{0:4.2f}.fits'.format(age)) + + # Move back into iso directory + os.chdir('..') + + # Return to starting directory + os.chdir(start_dir) + return + + +class Marley2021(StellarEvolution): + """ + Evolution models from + `Marley et al. 2021 `_. + + Downloaded from `here _` + + Notes + ----- + Evolution model parameters used in download: + + * + CHANGE!!! + """ + def __init__(self): + r""" + Define intrinsic properties for the Marley brown dwarf stellar models. + """ + # populate list of model masses (in solar masses) + #mass_list = [(0.1 + i*0.005) for i in range(181)] + + # define metallicity parameters for Parsec models + self.z_solar = 0.0142 + self.z_list = [self.z_solar * (10.**m) for m in [-0.5, 0.0, 0.5]] + + # populate list of isochrone ages (log scale) + self.age_list = [10.0, 7.0, 8.0, 9.0, 6.0, 7.176091259055681, 8.176091259055681, 9.176091259055681, 6.301029995663981, + 7.301029995663981, 8.301029995663981, 9.301029995663981, 6.477121254719663, 7.477121254719663, + 8.477121254719663, 9.477121254719663, 6.6020599913279625, 7.6020599913279625, 8.602059991327963, + 9.602059991327963, 6.778151250383644, 7.778151250383644, 8.778151250383644, 9.778151250383644, + 6.903089986991944, 7.903089986991944, 8.903089986991944, 9.903089986991944] + + # Specify location of model files + self.model_dir = models_dir+'Marley2021/' + + # Specifying metallicity + self.z_file_map = { + self.z_list[0]: 'zm05/', + self.z_list[1]: 'zp00/', + self.z_list[2]: 'zp05/' + } + + # Define required evo_grid number + self.evo_grid_min = 1.0 + + def isochrone(self, age=1.e8, metallicity=0.0): + r""" + Extract an individual isochrone from the Marley2021 collection. + """ + # Error check to see if installed evolution model + # grid is compatible with code version. Also return + # current grid num + self.evo_grid_num = check_evo_grid_number(self.evo_grid_min, models_dir) + + # convert metallicity to mass fraction + z_defined = self.z_solar*10.**metallicity + + log_age = math.log10(age) + + # check age and metallicity are within bounds + if ((log_age < np.min(self.age_list)) or (log_age > np.max(self.age_list))): + logger.error('Requested age {0} is out of bounds.'.format(log_age)) + + if ((z_defined < np.min(self.z_list)) or + (z_defined > np.max(self.z_list))): + logger.error('Requested metallicity {0} is out of bounds.'.format(z_defined)) + + z_idx = np.where(abs(np.array(self.z_list) - z_defined) == min(abs(np.array(self.z_list) - z_defined)) )[0][0] + z_dir = self.z_file_map[self.z_list[z_idx]] + + # Find closest age in grid + age_idx = np.where(abs(np.array(self.age_list) - log_age) == min(abs(np.array(self.age_list) - log_age)) )[0][0] + iso_file = f'iso_{self.age_list[age_idx]}.fits' + + # Create path to iso file + full_iso_file = os.path.join(self.model_dir, 'iso', z_dir, iso_file) + + print(f"Found nearest age file as {full_iso_file} for requested age of {log_age}") + + # Make sure the closest file exists + #if not os.path.exists(close_file): + #raise FileNotFoundError(f"Isochrone file not found: {close_file}.") + + # return isochrone data + iso = Table.read(full_iso_file, format='fits') + iso.rename_column('Z', 'Z') + iso.rename_column('Age', 'logAge') + iso.rename_column('Mass', 'mass') + iso.rename_column('Mass_current', 'mass_current') + iso.rename_column('log_L', 'logL') + iso.rename_column('Teff', 'logT') + iso.rename_column('logg', 'logg') + iso.rename_column('Radius', 'radius') + iso['logT_WR'] = iso['logT'] + + # Marley doesn't identify WR stars, so identify all as "False" + isWR = Column([False] * len(iso), name='isWR') + iso.add_column(isWR) + + iso.meta['log_age'] = log_age + iso.meta['metallicity_in'] = metallicity + iso.meta['metallicity_act'] = np.log10(z_defined / self.z_solar) + + return iso + + def format_isochrones(input_iso_dir, metallicity_list): + r""" + Parse isochrone files downloaded from Marley 2021 for different + metallicities, create individual isochrone files for the different ages. + + input_iso_dir: points to Marley2021/iso directory. Assumes metallicity + subdirectories already exist with isochrone files downloaded in them + (isochrones files expected to start with "output*") + + """ + # Store current directory for later + start_dir = os.getcwd() + + # Move into isochrone directory + os.chdir(input_iso_dir) + + # Work on each metallicity isochrones individually + for metal in metallicity_list: + # More into metallicity directory, read isochrone file + os.chdir(metal) + + isoFile = glob.glob('output*') + print( 'Read Input: this is slow') + iso = Table.read(isoFile[0], format='fits') + print( 'Done') + + ages_all = iso['Age'] + + # Extract the unique ages + age_arr = np.unique(ages_all) + + # For each unique age, extract the proper rows and make corresponding + # table + print( 'Making individual isochrone files') + for age in age_arr: + good = np.where(ages_all == age) + tmp = iso[good] + + #Write table + tmp.write('iso_{0:4.2f}.fits'.format(age)) + + # Move back into iso directory + os.chdir('..') + + # Return to starting directory + os.chdir(start_dir) + return + #---------------------------------------# # Now for the Pisa (Tognelli+11) models #---------------------------------------# @@ -1201,6 +1495,132 @@ def format_isochrones(self): #==============================# # Merged model classes #==============================# +class MergedPhillipsBaraffePisaEkstromParsec(StellarEvolution): + """ + This is a combination of several different evolution models: + + * Phillips (`Phillips et al. 2020 `_) + * Baraffe (`Baraffe et al. 2015 `_) + * Pisa (`Tognelli et al. 2011 `_) + * Geneva (`Ekstrom et al. 2012 `_) + * Parsec (version 1.2s, `Bressan+12 `_) + + The model used depends on the age of the population and what stellar masses + are being modeled: + + + For logAge < 7.4: + + * Phillips: 0.01 - 0.07 M_sun + * Phillips/Baraffe transition: 0.070 - 0.075 M_sun + * Baraffe: 0.075 - 0.4 M_sun + * Baraffe/Pisa transition: 0.4 - 0.5 M_sun + * Pisa: 0.5 M_sun to the highest mass in Pisa isochrone (typically 5 - 7 Msun) + * Geneva: Highest mass of Pisa models to 120 M_sun + + For logAge > 7.4: + + * Phillips: 0.01 - 0.075 M_sun + * Phillips/Parsec v1.2s transition: 0.075 - 0.2 M_sun + * Parsec v1.2s: full mass range above 0.2 M_sun + + Parameters + ---------- + rot: boolean, optional + If true, then use rotating Ekstrom models. Default is true. + """ + def __init__(self, rot=True): + # populate list of model masses (in solar masses) + mass_list = [(0.01 + i*0.005) for i in range(181)] # generates masses from 0.01 - 1 M_sun + + # define metallicity parameters for Geneva models + z_list = [0.015] + + # populate list of isochrone ages (log scale) + age_list = np.arange(6.0, 10.0, 0.01).tolist() + + # specify location of model files + model_dir = models_dir + 'merged/phillips_baraffe_pisa_ekstrom_parsec/' + StellarEvolution.__init__(self, model_dir, age_list, mass_list, z_list) + self.z_solar = 0.015 + + # Switch to specify rotating/non-rotating models + if rot: + self.z_file_map = {0.015: 'z015_rot/'} + else: + self.z_file_map = {0.015: 'z015_norot/'} + + # Define required evo_grid number + self.evo_grid_min = 1.0 + + + def isochrone(self, age=1.e8, metallicity=0.0): + r""" + Extract an individual isochrone from the Baraffe-Pisa-Ekstrom-Parsec + collection + """ + # Error check to see if installed evolution model + # grid is compatible with code version. Also return + # current grid num + self.evo_grid_num = check_evo_grid_number(self.evo_grid_min, models_dir) + + # convert metallicity to mass fraction + z_defined = self.z_solar*10.**metallicity + + log_age = math.log10(age) + + # check age and metallicity are within bounds + if ((log_age < np.min(self.age_list)) or (log_age > np.max(self.age_list))): + logger.error('Requested age {0} is out of bounds.'.format(log_age)) + + if ((z_defined < np.min(self.z_list)) or + (z_defined > np.max(self.z_list))): + logger.error('Requested metallicity {0} is out of bounds.'.format(z_defined)) + + # Find nearest age in grid to input grid + age_idx = np.where(abs(np.array(self.age_list) - log_age) == min(abs(np.array(self.age_list) - log_age)) )[0][0] + iso_file = 'iso_{0:.2f}.dat'.format(self.age_list[age_idx]) + + # find closest metallicity value + z_idx = np.where(abs(np.array(self.z_list) - z_defined) == min(abs(np.array(self.z_list) - z_defined)) )[0][0] + z_dir = self.z_file_map[self.z_list[z_idx]] + + # generate isochrone file string + full_iso_file = self.model_dir + z_dir + iso_file + + # return isochrone data + iso = Table.read(full_iso_file, format='ascii') + iso.rename_column('col1', 'mass') + iso.rename_column('col2', 'logT') + iso.rename_column('col3', 'logL') + iso.rename_column('col4', 'logg') + iso.rename_column('col5', 'logT_WR') + iso.rename_column('col6', 'mass_current') + iso.rename_column('col7', 'phase') + iso.rename_column('col8', 'model_ref') + + # Define "isWR" column based on phase info + isWR = Column([False] * len(iso), name='isWR') + idx_WR = np.where(iso['logT'] != iso['logT_WR']) + isWR[idx_WR] = True + iso.add_column(isWR) + + iso.meta['log_age'] = log_age + iso.meta['metallicity_in'] = metallicity + iso.meta['metallicity_act'] = np.log10(self.z_list[z_idx] / self.z_solar) + + # Assume mass of brown dwarfs does not change over their lifetime + #bd_idx = iso['mass'] < 0.08 + #iso['mass_current'][bd_idx] = iso['mass'][bd_idx] + + # Handling NaN effective temperatures + #nan_teff_idx = np.isnan(iso['logT']) + #if np.any(nan_teff_idx): + # iso['logT'][nan_teff_idx] = self.estimate_teff(iso['mass'][nan_teff_idx]) + + return iso + + class MergedBaraffePisaEkstromParsec(StellarEvolution): """ This is a combination of several different evolution models: diff --git a/spisea/ifmr.py b/spisea/ifmr.py index f88afdbe..a413f240 100755 --- a/spisea/ifmr.py +++ b/spisea/ifmr.py @@ -36,24 +36,25 @@ def get_Z(self, Fe_H): """ return 10**(Fe_H - 1.85387) - def Kalirai_mass(self, MZAMS): + def Kalirai_mass(self, MZAMS): # for white dwarfs """ From Kalirai+08 https://ui.adsabs.harvard.edu/abs/2008ApJ...676..594K/abstract 1.16 < MZAMS < 6.5 But we use this function for anything between 0.5 and 9 depending on the IFMR. FIXME: need to extend these ranges... explain extension somewhere? Paper maybe? """ - + result = 0.109*MZAMS + 0.394 final = np.zeros(len(MZAMS)) - bad_idx = np.where(MZAMS < 0.5) + bad_idx = np.where((MZAMS < 0.5) | (MZAMS >= 9)) final[bad_idx] = -99 - good_idx = np.where(MZAMS >= 0.5) + good_idx = np.where((MZAMS >= 0.5) & (MZAMS < 9)) final[good_idx] = result[good_idx] + return final @@ -552,11 +553,12 @@ def generate_death_mass(self, mass_array, metallicity_array): * WD: typecode = 101 * NS: typecode = 102 * BH: typecode = 103 + * BD: typecode = 90 A typecode of value -1 means you're outside the range of validity for applying the ifmr formula. A remnant mass of -99 means you're outside the range of validity for applying the ifmr formula. - Range of validity: MZAMS > 0.5 + Range of validity: MZAMS > 0.5 and 0.01 < MZAMS < 0.08 Returns ------- @@ -569,7 +571,7 @@ def generate_death_mass(self, mass_array, metallicity_array): #output_array[1] holds the remnant type output_array = np.zeros((2, len(mass_array))) - codes = {'WD': 101, 'NS': 102, 'BH': 103} + codes = {'WD': 101, 'NS': 102, 'BH': 103, 'BD': 90} #create array to store the remnant masses generated by Spera equations rem_mass_array = np.zeros(len(mass_array)) @@ -647,6 +649,12 @@ def generate_death_mass(self, mass_array, metallicity_array): #remnant masses of stars with Z > 4.0e-3 and MZAMS > 10.0 high_metal_high_mass_idx = np.where((Z_array > 4.0e-3) & (core_mass > 10.0)) rem_mass_array[high_metal_high_mass_idx] = self.M_rem_high_metal_high_mass(Z_array[high_metal_high_mass_idx], core_mass[high_metal_high_mass_idx]) + + #classify brown dwarfs before checking for bad indices (in case they are looped into them) + BD_idx = np.where((mass_array >= 0.01) & (mass_array < 0.08)) + rem_mass_array[BD_idx] = mass_array[BD_idx] + output_array[0][BD_idx] = rem_mass_array[BD_idx] + output_array[1][BD_idx] = codes['BD'] #assign object types based on remnant mass bad_idx = np.where(rem_mass_array < 0) #outside the range of validity for the ifmr @@ -721,7 +729,7 @@ def NS_mass(self, MZAMS): """ Drawing the NS mass from a Gaussian distrobuton based on observational data. - Gaussian fit by Emily Ramey and Sergiy Vasylyev of University of Caifornia, Berkeley using a + Gaussian fit by Emily Ramey and Sergiy Vasylyev of University of California, Berkeley using a sample of NSs from Ozel & Freire (2016) — J1811+2405 Ng et al. (2020), J2302+4442 Kirichenko et al. (2018), J2215+5135 Linares et al. (2018), J1913+1102 Ferdman & Collaboration (2017), J1411+2551 Martinez et al. (2017), @@ -751,6 +759,7 @@ def generate_death_mass(self, mass_array): * WD: typecode = 101 * NS: typecode = 102 * BH: typecode = 103 + * BD: typecode = 90 A typecode of value -1 means you're outside the range of validity for applying the ifmr formula. @@ -758,7 +767,7 @@ def generate_death_mass(self, mass_array): A remnant mass of -99 means you're outside the range of validity for applying the ifmr formula. - Range of validity: 0.5 < MZAMS < 120 + Range of validity: 0.01 < MZAMS < 0.08 and 0.5 < MZAMS < 120 Returns ------- @@ -774,23 +783,33 @@ def generate_death_mass(self, mass_array): #Random array to get probabilities for what type of object will form random_array = np.random.randint(1, 1001, size = len(mass_array)) - codes = {'WD': 101, 'NS': 102, 'BH': 103} + codes = {'WD': 101, 'NS': 102, 'BH': 103, 'BD': 90} """ The id_arrays are to separate all the different formation regimes """ - id_array0 = np.where((mass_array < 0.5) | (mass_array >= 120)) - output_array[0][id_array0] = -99 * np.ones(len(id_array0)) - output_array[1][id_array0] = -1 * np.ones(len(id_array0)) + #classifying brown dwarfs + id_array_BD = np.where((mass_array >= 0.01) & (mass_array < 0.08)) + output_array[0][id_array_BD] = mass_array[id_array_BD] + output_array[1][id_array_BD] = codes['BD'] + + #classifying invalid mass ranges + id_array0 = np.where((mass_array < 0.01) | ((mass_array >= 0.08) & (mass_array < 0.5)) | (mass_array >= 120)) + output_array[0][id_array0] = -99 + output_array[1][id_array0] = -1 + + #classifying white dwarfs id_array1 = np.where((mass_array >= 0.5) & (mass_array < 9)) output_array[0][id_array1] = self.Kalirai_mass(mass_array[id_array1]) output_array[1][id_array1]= codes['WD'] + #classifying neutron stars id_array2 = np.where((mass_array >= 9) & (mass_array < 15)) output_array[0][id_array2] = self.NS_mass(mass_array[id_array2]) output_array[1][id_array2] = codes['NS'] + #classifying black holes id_array3_BH = np.where((mass_array >= 15) & (mass_array < 17.8) & (random_array > 679)) output_array[0][id_array3_BH] = self.BH_mass_low(mass_array[id_array3_BH], 0.9) output_array[1][id_array3_BH] = codes['BH'] @@ -843,6 +862,7 @@ def generate_death_mass(self, mass_array): output_array[0][id_array10_NS] = self.NS_mass(mass_array[id_array10_NS]) output_array[1][id_array10_NS] = codes['NS'] + return(output_array) class IFMR_N20_Sukhbold(IFMR): diff --git a/spisea/imf/imf.py b/spisea/imf/imf.py index 758eda00..adf0c3b0 100755 --- a/spisea/imf/imf.py +++ b/spisea/imf/imf.py @@ -47,7 +47,7 @@ class IMF(object): If None, no multiplicity is assumed. Otherwise, use multiplicity object to create multiple star systems. """ - def __init__(self, massLimits=np.array([0.1,150]), multiplicity=None): + def __init__(self, massLimits=np.array([0.01,150]), multiplicity=None): self._multi_props = multiplicity self._mass_limits = massLimits @@ -199,7 +199,10 @@ def generate_cluster(self, totalMass, seed=None): def calc_multi(self, newMasses, compMasses, newSystemMasses, newIsMultiple, CSF, MF): """ Helper function to calculate multiples more efficiently. - We will use array operations as much as possible + We will use array operations as much as possible. + Uses Fontanive+18 parameters for brown dwarf masses + (M <= 0.08 M_sun) while keeping default parameters for + all other stellar primaries. """ # Identify multiple systems, calculate number of companions for # each @@ -210,18 +213,37 @@ def calc_multi(self, newMasses, compMasses, newSystemMasses, newIsMultiple, CSF, n_comp_arr[too_many] = self._multi_props.CSF_max primary = newMasses[idx] + # limiting BD companions to 1 (mass-based) + bd_mask = primary <= 0.08 + n_comp_arr[bd_mask & (n_comp_arr > 1)] = 1 + # We will deal with each number of multiple system independently. This is # so we can put in uniform arrays in _multi_props.random_q. num = np.unique(n_comp_arr) for ii in num: tmp = np.where(n_comp_arr == ii)[0] + prim_subset = primary[tmp] + + # define masks based on stellar or substellar range + bd_mask = prim_subset <= 0.08 + star_mask = ~bd_mask if ii == 1: # Single companion case - q_values = self._multi_props.random_q(np.random.rand(len(tmp))) + q_values = np.empty(len(tmp)) + + if np.any(star_mask): + rand_vals = np.random.rand(star_mask.sum()) + q_values[star_mask] = self._multi_props.random_q(rand_vals) + + if np.any(bd_mask): + rand_vals = np.random.rand(bd_mask.sum()) + b = 1.0 + 6.1 #gamma from Fontanive+18 + q_values[bd_mask] = (rand_vals * (1.0 - self._multi_props.q_min ** b) + + self._multi_props.q_min ** b) ** (1.0 / b) # Calculate mass of companion - m_comp = q_values * primary[tmp] + m_comp = q_values * prim_subset # Only keep companions that are more than the minimum mass. Update # compMasses, newSystemMasses, and newIsMultiple appropriately @@ -233,22 +255,30 @@ def calc_multi(self, newMasses, compMasses, newSystemMasses, newIsMultiple, CSF, bad = np.where(m_comp < self._mass_limits[0])[0] newIsMultiple[idx[tmp[bad]]] = False else: - # Multple companion case - q_values = self._multi_props.random_q(np.random.rand(len(tmp), ii)) - - # Calculate masses of companions - m_comp = np.multiply(q_values, np.transpose([primary[tmp]])) - - # Update compMasses, newSystemMasses, and newIsMultiple appropriately + # Multi-companion case for jj in range(len(tmp)): - m_comp_tmp = m_comp[jj] + prim = prim_subset[jj] + + # Finding q values of stellar and substellar primaries + if prim <= 0.08: + # BD case (Fontanive+18) + b = 1.0 + 6.1 + rand_vals = np.random.rand(ii) + q_values = (rand_vals * (1.0 - self._multi_props.q_min ** b) + + self._multi_props.q_min ** b) ** (1.0 / b) + else: + # Stellar case (Duchene & Kraus) + q_values = self._multi_props.random_q(np.random.rand(ii)) + + # Calculate masses of companions & update compMasses, newSystemMasses, and newIsMultiple appropriately + m_comp_tmp = q_values * prim compMasses[idx[tmp[jj]]] = m_comp_tmp[m_comp_tmp >= self._mass_limits[0]] newSystemMasses[idx[tmp[jj]]] += compMasses[idx[tmp[jj]]].sum() - - # Double check for the case when we drop all companions. - # This happens a lot near the minimum allowed mass. + + # Drop system if no valid companions remain if len(compMasses[idx[tmp[jj]]]) == 0: newIsMultiple[idx[tmp[jj]]] = False + return compMasses, newSystemMasses, newIsMultiple @@ -684,12 +714,29 @@ class Weidner_Kroupa_2004(IMF_broken_powerlaw): Mass range is 0.01 M_sun - inf M_sun. """ def __init__(self, multiplicity=None): - massLimits = np.array([0.01, 0.08, 0.5, 1, np.inf]) + massLimits = np.array([0.01, 0.08, 0.5, 1, 120]) powers = np.array([-0.3, -1.3, -2.3, -2.35]) IMF_broken_powerlaw.__init__(self, massLimits, powers, multiplicity=multiplicity) - + +class Salpeter_Kirkpatrick_2024(IMF_broken_powerlaw): + """ + Define combined IMF from Kirkpatrick (2024) and Salpeter (1955) to allow + inclusion of the brown dwarf mass range. + Mass range: + * 0.01 M_sun - 8 M_sun: Kirkpatrick 2024 + `_. + * 8 M_sun - 120 M_sun: Salpeter 1955 + `_. + """ + def __init__(self, multiplicity=None): + massLimits = np.array([0.01, 0.05, 0.22, 0.55, 8, 120]) + powers = np.array([-0.6, -0.25, -1.3, -2.3, -2.35]) + + IMF_broken_powerlaw.__init__(self, massLimits, powers, + multiplicity=multiplicity) + ################################################## # # Generic functions -- see if we can move these up. diff --git a/spisea/imf/multiplicity.py b/spisea/imf/multiplicity.py index 0d28ced6..82a8c765 100755 --- a/spisea/imf/multiplicity.py +++ b/spisea/imf/multiplicity.py @@ -41,6 +41,11 @@ class MultiplicityUnresolved(object): MF(mass) = MF_amp * (mass ** MF_power) + However, in the brown dwarf mass regime, it is currently recognized + that only binaries are possible, and the MF decreases dissimilarly + to higher masses (> 0.08 solar masses). The values for this range + are given by Aberasturi et al. (2014) and Fontanive et al. (2023). + **Companion Star Fraction** -- the expected number of companions in a multiple system. The companion star fraction (CSF) also changes with mass and this dependency can be described as @@ -52,6 +57,9 @@ class MultiplicityUnresolved(object): value, CSF_max. The actual number of companions is drawn from a Poisson distribution with an expectation value of CSF. + In the brown dwarf regime we impose an assumption that only + binary systems are possible due to current literature trends. + **Mass Ratio (Q)** -- The ratio between the companion star mass and primary star mass, Q = (m_comp / m_prim ) has a probability density function described by a powerlaw:: @@ -116,6 +124,9 @@ def multiplicity_fraction(self, mass): Given a star's mass, determine the probability that the star is in a multiple system (multiplicity fraction = MF). + Modified to allow binary fraction to decrease in brown dwarf regime. + Supported by Aberasturi et al. (2014) and Fontanive et al. (2018). + Parameters ---------- mass : float or numpy array @@ -133,6 +144,13 @@ def multiplicity_fraction(self, mass): if np.isscalar(mf): if mf > 1: mf = 1 + # physically override mf for brown dwarfs + if (mass <= 0.08) & (mass > 0.06): + mf = 0.16 + if (mass <= 0.06) & (mass > 0.02): + mf = 0.08 + if (mass < 0.02): + mf = 0 else: mf[mf > 1] = 1 @@ -141,7 +159,8 @@ def multiplicity_fraction(self, mass): def companion_star_fraction(self, mass): """ Given a star's mass, determine the average number of - companion stars (companion star fraction = CSF). + companion stars (companion star fraction = CSF). For + brown dwarfs we impose a hard limit of one companion. Parameters ---------- @@ -160,8 +179,12 @@ def companion_star_fraction(self, mass): if np.isscalar(csf): if csf > self.CSF_max: csf = self.CSF_max + if (mass <= 0.08): + csf = self.multiplicity_fraction(mass) else: csf[csf > self.CSF_max] = self.CSF_max + bd = mass <= 0.08 + csf[bd] = self.multiplicity_fraction(mass[bd]) return csf @@ -198,6 +221,10 @@ def random_companion_count(self, x, CSF, MF): """ Helper function: calculate number of companions. """ + # bd stipulation since mf=0 + if MF <= 0: + return 0 + n_comp = 1 + np.random.poisson((CSF / MF) - 1) if self.companion_max == True: @@ -210,6 +237,8 @@ class MultiplicityResolvedDK(MultiplicityUnresolved): """ Sub-class of MultiplicityUnresolved that adds semimajor axis and eccentricity information for multiple objects from distributions described in Duchene and Kraus 2013 + + For brown dwarf regime, mean separation and std are given by Fontanive et al. (2018). Parameters -------------- @@ -246,6 +275,8 @@ def log_semimajoraxis(self, mass): Generate the semimajor axis for a given mass. The mean and standard deviation of a given mass are determined by fitting the data from fitting the semimajor axis data as a function of mass in table 1 of Duchene and Kraus 2013. Then a random semimajor axis is drawn from a log normal distribution with that mean and standard deviation. + + The brown dwarf range is described by mean seperation and std values given in Fontanive et al. (2018). Parameters ---------- @@ -265,6 +296,9 @@ def log_semimajoraxis(self, mass): log_a_std = log_a_std_func(np.log10(2.9)) #sigma_log(a) if log_a_std < 0.1: log_a_std = 0.1 + if mass <= 0.08: + log_a_mean = np.log10(2.9) + log_a_std = 0.21 log_semimajoraxis = np.random.normal(log_a_mean, log_a_std) while 10**log_semimajoraxis > 2000 or log_semimajoraxis < -2: #AU diff --git a/spisea/imf/tests/test_imf.py b/spisea/imf/tests/test_imf.py index 571f6edc..373cf8f4 100755 --- a/spisea/imf/tests/test_imf.py +++ b/spisea/imf/tests/test_imf.py @@ -9,9 +9,9 @@ def test_generate_cluster(): # Make multiplicity object imf_multi = multiplicity.MultiplicityUnresolved() - # Make IMF object; we'll use a broken power law with the parameters from Kroupa+01 - massLimits = np.array([0.08, 0.5, 1, 120]) # Define boundaries of each mass segement - powers = np.array([-1.3, -2.3, -2.3]) # Power law slope associated with each mass segment + # Make IMF object; we'll use a broken power law with the parameters from Salpeter_Kirkpatrick+24 (updated with brown dwarf addition + massLimits = np.array([0.01, 0.05, 0.22, 0.55, 8, 120]) # Define boundaries of each mass segement + powers = np.array([-0.6, -0.25, -1.3, -2.3, -2.35]) # Power law slope associated with each mass segment my_imf = imf.IMF_broken_powerlaw(massLimits, powers, imf_multi) # Define total cluster mass @@ -169,7 +169,6 @@ def test_xi2(): plt.clf() plt.loglog(masses[sdx], pdf_sorted, 'k.') plt.axis('equal') - # pdb.set_trace() return diff --git a/spisea/imf/tests/test_multiplicity.py b/spisea/imf/tests/test_multiplicity.py index 3a9dc9b7..8412dc2b 100755 --- a/spisea/imf/tests/test_multiplicity.py +++ b/spisea/imf/tests/test_multiplicity.py @@ -33,6 +33,7 @@ def test_create_MultiplicityUnresolved(): assert mu2.q_pow == 0.4 assert mu2.q_min == 0.04 + def test_multiplicity_fraction(): """ Test creating a MultiplicityUnresolved object and getting @@ -66,6 +67,14 @@ def test_multiplicity_fraction(): mf2_3 = mu1.multiplicity_fraction(0.1) np.testing.assert_almost_equal(mf2_3, 0.136, decimal=2) + # Test brown dwarf mass fractions + mf_bd1 = mu1.multiplicity_fraction(0.07) # near upper BD limit + mf_bd2 = mu1.multiplicity_fraction(0.04) # mid BD + mf_bd3 = mu1.multiplicity_fraction(0.01) # lower BD limit + assert np.isclose(mf_bd1, 0.16, atol=0.01) + assert np.isclose(mf_bd2, 0.08, atol=0.01) + assert np.isclose(mf_bd3, 0.0, atol=1e-6) + def test_multiplicity_fraction_array(): """ @@ -77,12 +86,23 @@ def test_multiplicity_fraction_array(): # First set of multiplicity parameters mu1 = multiplicity.MultiplicityUnresolved() - mass_array = np.array([1.0, 10.0, 0.1]) + mass_array = np.array([1.0, 10.0, 0.1, 0.07, 0.04, 0.01]) mf_array = mu1.multiplicity_fraction(mass_array) + # Stellar regime checks np.testing.assert_almost_equal(mf_array[0], 0.44, decimal=2) np.testing.assert_almost_equal(mf_array[1], 1.0, decimal=2) np.testing.assert_almost_equal(mf_array[2], 0.136, decimal=2) + + # BD regime checks + # interpolation between values implies lower masses --> lower mf + assert mf_array[3] < mf_array[2] + assert mf_array[4] <= mf_array[3] + assert mf_array[5] <= mf_array[4] + + # Ensure mf stars within reasonable bound (upper limit is 0.2) + assert np.all(mf_array[3:] >= 0.0) + assert np.all(mf_array[3:] <= 0.2) def test_companion_star_fraction(): @@ -117,11 +137,20 @@ def test_companion_star_fraction(): # csf2_3 = mu1.companion_star_fraction(0.1) # np.testing.assert_almost_equal(csf2_3, 0.159, decimal=2) + # Test brown dwarf csf + csf_bd1 = mu1.companion_star_fraction(0.07) + csf_bd2 = mu1.companion_star_fraction(0.04) + csf_bd3 = mu1.companion_star_fraction(0.01) + assert np.isclose(csf_bd1, 0.16, atol=0.01) + assert np.isclose(csf_bd2, 0.08, atol=0.01) + assert np.isclose(csf_bd3, 0.0, atol=1e-6) + def test_resolvedmult(): """ Test creating a MultiplicityResolvedDK object and that the parameters it's populated with are correct. + Updated to test for specific brown dwarf characteristics. """ from spisea import synthetic, evolution, atmospheres, reddening, ifmr from spisea.imf import imf, multiplicity @@ -132,7 +161,7 @@ def test_resolvedmult(): dist = 4000 # distance in parsecs metallicity = 0 # metallicity in [M/H] atm_func = atmospheres.get_merged_atmosphere - evo_merged = evolution.MISTv1() + evo_merged = evolution.MergedPhillipsBaraffePisaEkstromParsec() redlaw = reddening.RedLawCardelli(3.1) # Rv = 3.1 filt_list = ['nirc2,J', 'nirc2,Kp'] @@ -149,7 +178,7 @@ def test_resolvedmult(): clust_multiplicity = multiplicity.MultiplicityResolvedDK() # Multiplicity is defined in the IMF object - clust_imf_Mult = imf.Kroupa_2001(multiplicity=clust_multiplicity) + clust_imf_Mult = imf.Salpeter_Kirkpatrick_2024(multiplicity=clust_multiplicity) # Make clusters clust_Mult = synthetic.ResolvedCluster(iso_merged, clust_imf_Mult, clust_mtot) @@ -184,7 +213,31 @@ def test_resolvedmult(): n, bins = np.histogram(clust_Mult.companions['i']) bin_centers = 0.5*(bins[1:] + bins[:-1]) assert all(np.abs(i) < 0.15 for i in n/max(n) - np.sin(np.pi*bin_centers/180)) - - return + #checks for brown dwarf specific features + bd_idx = np.where(clust_Mult.star_systems['mass'] < 0.08)[0] + + #check there is only one possible companion per BD + assert all(clust_Mult.star_systems['N_companions'][bd_idx] <= 1), \ + "Brown dwarf primaries have >1 companion." + + comp_rows = [] + start = 0 + for ii, N in enumerate(clust_Mult.star_systems['N_companions']): + if ii in bd_idx and N > 0: + comp_rows.extend(range(start, start+N)) + start += N + + bd_companions = clust_Mult.companions[comp_rows] + if len(bd_companions) > 30: # only test if enough BD binaries + mean_log_a = np.mean(bd_companions['log_a']) + std_log_a = np.std(bd_companions['log_a']) + + #expect lognormal centered near log10(2.9 AU), width ~0.21 + assert abs(mean_log_a - np.log10(2.9)) < 0.25, \ + f"BD mean log(a) off: {mean_log_a:.2f}" + assert abs(std_log_a - 0.21) < 0.15, \ + f"BD sigma log(a) off: {std_log_a:.2f}" + + return diff --git a/spisea/synthetic.py b/spisea/synthetic.py index 4e9cbcad..94247205 100755 --- a/spisea/synthetic.py +++ b/spisea/synthetic.py @@ -13,7 +13,7 @@ from pysynphot import observation as obs import pysynphot from astropy import constants, units -from astropy.table import Table, Column, MaskedColumn +from astropy.table import Table, Column, MaskedColumn, vstack import pickle import time, datetime import math @@ -154,8 +154,9 @@ def __init__(self, iso, imf, cluster_mass, ifmr=None, verbose=True, self.iso_interps = {} for ikey in interp_keys: self.iso_interps[ikey] = interpolate.interp1d(self.iso.points['mass'], self.iso.points[ikey], - kind='linear', bounds_error=False, fill_value=np.nan) - + kind='linear', bounds_error=False, fill_value=np.nan, + assume_sorted=False) #BDs out of bounds + #____ ##### # Make a table to contain all the information about each stellar system. ##### @@ -192,6 +193,7 @@ def set_filter_names(self): filt_names.append(col_name) return filt_names + def _make_star_systems_table(self, mass, isMulti, sysMass): """ @@ -231,14 +233,32 @@ def _make_star_systems_table(self, mass, isMulti, sysMass): # Note: this only becomes relevant when the cluster is > 10**6 M-sun, this # effect is so small # Convert nan_to_num to avoid errors on greater than, less than comparisons + + # Define brown dwarf mass range + bd_mask = (star_systems['mass'] >= 0.01) & (star_systems['mass'] <= 0.08) + #hard code BDs as 90 and invariant masses + star_systems['phase'][bd_mask] = 90 + star_systems['mass_current'][bd_mask] = star_systems['mass'][bd_mask] + + # Identify bad phases (non-brown-dwarfs only) star_systems_phase_non_nan = np.nan_to_num(star_systems['phase'], nan=-99) - bad = np.where( (star_systems_phase_non_nan > 5) & (star_systems_phase_non_nan < 101) & (star_systems_phase_non_nan != 9) & (star_systems_phase_non_nan != -99)) - # Print warning, if desired - verbose=False + bad = np.where( + (star_systems_phase_non_nan > 5) + & (star_systems_phase_non_nan < 90) + & (star_systems_phase_non_nan != 9) + & (star_systems_phase_non_nan != -99) + & (~bd_mask) + ) + + # Verbose warnings (optional) + verbose = False if verbose: for ii in range(len(bad[0])): - print('WARNING: changing phase {0} to 5'.format(star_systems['phase'][bad[0][ii]])) - star_systems['phase'][bad] = 5 + print(f"WARNING: changing phase {star_systems['phase'][bad[0][ii]]} to 5") + + # Only modify non-90, non-BD entries + mask = (np.floor(star_systems['phase'][bad]) != 90) + star_systems['phase'][bad][mask] = 5 for filt in self.filt_names: star_systems[filt] = self.iso_interps[filt](star_systems['mass']) @@ -251,9 +271,11 @@ def _make_star_systems_table(self, mass, isMulti, sysMass): # Remnants have flux = 0 in all bands if they are generated here. ##### if self.ifmr != None: - # Identify compact objects as those with Teff = 0 or with phase > 100. + # Identify compact objects as those with Teff = 0 or with phase > 100 or BDs highest_mass_iso = self.iso.points['mass'].max() - idx_rem = np.where((np.isnan(star_systems['Teff'])) & (star_systems['mass'] > highest_mass_iso))[0] + idx_rem = np.where((np.isnan(star_systems['Teff']) & (star_systems['mass'] > highest_mass_iso)))[0] + + # Calculate remnant mass and ID for compact objects; update remnant_id and # remnant_mass arrays accordingly @@ -353,18 +375,27 @@ def _make_companions_table(self, star_systems, compMass): companions['isWR'][cdx] = np.round(self.iso_interps['isWR'](comp_mass)) companions['mass_current'] = self.iso_interps['mass_current'](companions['mass']) companions['phase'] = np.round(self.iso_interps['phase'](companions['mass'])) - companions['metallicity'] = np.ones(N_comp_tot)*self.iso.metallicity + companions['metallicity'] = np.ones(N_comp_tot)*self.iso.metallicity #**** # For a very small fraction of stars, the star phase falls on integers in-between # the ones we have definition for, as a result of the interpolation. For these # stars, round phase down to nearest defined phase (e.g., if phase is 71, # then round it down to 5, rather than up to 101). # Convert nan_to_num to avoid errors on greater than, less than comparisons + + # reinforce BD phase of 90 and invariant masses + bd_mask = (companions['mass'] >= 0.01) & (companions['mass'] < 0.08) + companions['phase'][bd_mask] = 90 + companions['mass_current'][bd_mask] = companions['mass'][bd_mask] + companions_phase_non_nan = np.nan_to_num(companions['phase'], nan=-99) - bad = np.where( (companions_phase_non_nan > 5) & - (companions_phase_non_nan < 101) & - (companions_phase_non_nan != 9) & - (companions_phase_non_nan != -99)) + bad = np.where( + (companions_phase_non_nan > 5) & + (companions_phase_non_nan < 90) & + (companions_phase_non_nan != 9) & + (companions_phase_non_nan != -99) & + (~bd_mask)) + # Print warning, if desired verbose=False if verbose: @@ -395,14 +426,17 @@ def _make_companions_table(self, star_systems, compMass): star_systems[filt][idx[good]] = -2.5 * np.log10(f1[good] + f2[good]) star_systems[filt][idx[bad]] = np.nan + ##### # Make Remnants with flux = 0 in all bands. ##### if self.ifmr != None: # Identify compact objects as those with Teff = 0 or with masses above the max iso mass + # Exclude BDs from designation highest_mass_iso = self.iso.points['mass'].max() - cdx_rem = np.where(np.isnan(companions['Teff']) & - (companions['mass'] > highest_mass_iso))[0] + cdx_rem = np.where((np.isnan(companions['Teff'])) & + (companions['mass'] > highest_mass_iso) & + (companions['mass'] >= 0.08))[0] # Calculate remnant mass and ID for compact objects; update remnant_id and # remnant_mass arrays accordingly @@ -410,12 +444,11 @@ def _make_companions_table(self, star_systems, compMass): r_mass_tmp, r_id_tmp = self.ifmr.generate_death_mass(mass_array=companions['mass'][cdx_rem], metallicity_array=companions['metallicity'][cdx_rem]) else: - r_mass_tmp, r_id_tmp = self.ifmr.generate_death_mass(mass_array=companions['mass'][cdx_rem]) - + r_mass_tmp, r_id_tmp = self.ifmr.generate_death_mass(mass_array=companions['mass'][cdx_rem]) # Drop remnants where it is not relevant (e.g. not a compact object or # outside mass range IFMR is defined for) - good = np.where(r_id_tmp > 0) + good = np.where(r_id_tmp > 0) #**** cdx_rem_good = cdx_rem[good] companions['mass_current'][cdx_rem_good] = r_mass_tmp[good] @@ -425,7 +458,19 @@ def _make_companions_table(self, star_systems, compMass): for filt in self.filt_names: companions[filt][cdx_rem_good] = np.full(len(cdx_rem_good), np.nan) + # For brown dwarfs, we have Teff and logg from the isochrone. + # We want to use the atmosphere model to get their magnitudes + idx_bd = np.where(companions['mass'] < 0.08)[0] + for i in idx_bd: + T = companions['Teff'][i] + g = companions['logg'][i] + + # Check if we have valid Teff and logg + if np.isnan(T) or np.isnan(g): + print('T/logg assigned nan for BD object!') + continue + # Notify if we have a lot of bad ones. # Convert nan_to_num to avoid errors on greater than, less than comparisons companions_teff_non_nan = np.nan_to_num(companions['Teff'], nan=-99) @@ -433,6 +478,10 @@ def _make_companions_table(self, star_systems, compMass): if len(idx) != N_comp_tot and self.verbose: print( 'Found {0:d} companions out of stellar mass range'.format(N_comp_tot - len(idx))) + # Final check for brown dwarf phase + bd_idx_final = np.where((companions['mass'] >= 0.01) & (companions['mass'] < 0.08))[0] + + # Double check that everything behaved properly. assert companions['mass'][idx].min() > 0 @@ -448,6 +497,7 @@ def _remove_bad_systems(self, star_systems, compMass): removed. If self.ifmr != None, then we will save the high mass systems since they will be plugged into an ifmr later. """ + N_systems = len(star_systems) # Get rid of the bad ones @@ -459,7 +509,8 @@ def _remove_bad_systems(self, star_systems, compMass): idx = np.where(star_systems_teff_non_nan > 0)[0] else: # Keep stars (with Teff) and any other compact objects (with phase info). - idx = np.where( (star_systems_teff_non_nan > 0) | (star_systems_phase_non_nan >= 0) )[0] + idx = np.where((star_systems_teff_non_nan > 0) | (star_systems_phase_non_nan >= 0) | + (star_systems_phase_non_nan == 90))[0] if len(idx) != N_systems and self.verbose: print( 'Found {0:d} stars out of mass range'.format(N_systems - len(idx))) @@ -689,7 +740,7 @@ class Isochrone(object): wd_atm_func: white dwarf model atmosphere function, optional Set the stellar atmosphere models for the white dwafs. - Default is get_wd_atmosphere + Default is get_wd_atmosphere mass_sampling : int, optional Sample the raw isochrone every `mass_sampling` steps. The default @@ -737,7 +788,7 @@ def __init__(self, logAge, AKs, distance, metallicity=0.0, # Get solar metallicity models for a population at a specific age. # Takes about 0.1 seconds. evol = evo_model.isochrone(age=10**logAge, - metallicity=metallicity) + metallicity=metallicity) # Eliminate cases where log g is less than 0 idx = np.where(evol['logg'] > 0) @@ -756,7 +807,7 @@ def __init__(self, logAge, AKs, distance, metallicity=0.0, evol = evol[::mass_sampling] # Give luminosity, temperature, mass, radius units (astropy units). - L_all = 10**evol['logL'] * c.L_sun # luminsoity in W + L_all = 10**evol['logL'] * c.L_sun # luminosity in W T_all = 10**evol['logT'] * units.K R_all = np.sqrt(L_all / (4.0 * math.pi * c.sigma_sb * T_all**4)) mass_all = evol['mass'] * units.Msun # masses in solar masses @@ -785,6 +836,7 @@ def __init__(self, logAge, AKs, distance, metallicity=0.0, # This is the time-intensive call... everything else is negligable. # If source is a star, pull from star atmospheres. If it is a WD, # pull from WD atmospheres + if phase == 101: star = wd_atm_func(temperature=T, gravity=gravity, metallicity=metallicity, verbose=False) @@ -904,9 +956,13 @@ class IsochronePhot(Isochrone): Default is atmospheres.get_merged_atmosphere. wd_atm_func: white dwarf model atmosphere function, optional - Set the stellar atmosphere models for the white dwafs. + Set the stellar atmosphere models for the white dwarfs. Default is atmospheres.get_wd_atmosphere + bd_atm_func: brown dwarf model atmosphere function, optimal + Set the stellar atmosphere models for the brown dwarfs. + Default is atmospheres.get_bd_atmosphere + red_law : reddening law object, optional Define the reddening law for the synthetic photometry. Default is reddening.RedLawNishiyama09(). @@ -953,7 +1009,7 @@ class IsochronePhot(Isochrone): def __init__(self, logAge, AKs, distance, metallicity=0.0, evo_model=default_evo_model, atm_func=default_atm_func, - wd_atm_func = default_wd_atm_func, + wd_atm_func = default_wd_atm_func, #bd_atm_func = default_bd_atm_func, wave_range=[3000, 52000], red_law=default_red_law, mass_sampling=1, iso_dir='./', min_mass=None, max_mass=None, rebin=True, recomp=False, @@ -1000,6 +1056,8 @@ def __init__(self, logAge, AKs, distance, metallicity=metallicity, evo_model=evo_model, atm_func=atm_func, wd_atm_func=wd_atm_func, + #bd_atm_func=bd_atm_func, + wave_range=wave_range, red_law=red_law, mass_sampling=mass_sampling, min_mass=min_mass, max_mass=max_mass, rebin=rebin) diff --git a/spisea/tests/test_models.py b/spisea/tests/test_models.py index e80684be..9046ea06 100644 --- a/spisea/tests/test_models.py +++ b/spisea/tests/test_models.py @@ -1,4 +1,3 @@ -# Test functions for the different stellar evolution and atmosphere models import numpy as np import pdb @@ -27,21 +26,25 @@ def test_evolution_models(): age_young_arr = [6.7, 7.9] age_all_arr = [6.7, 8.0, 9.7] age_all_MIST_arr = [5.2, 6.7, 9.7, 10.13] + bd_test = [6.0, 6.5, 7.4, 8.4, 10.0] # Metallicity ranges to test (if applicable) metal_range = [-2.5, -1.5, 0, 0.25, 0.4] metal_solar = [0] + metal_Marley = [-0.5, 0.0, 0.5] # Array of evolution models to test evo_models = [evolution.MISTv1(version=1.2), evolution.MergedBaraffePisaEkstromParsec(), - evolution.Parsec(), evolution.Baraffe15(), evolution.Ekstrom12(), evolution.Pisa()] + evolution.Parsec(), evolution.Baraffe15(), evolution.Ekstrom12(), evolution.Pisa(), + evolution.Phillips2020(), evolution.Marley2021(), + evolution.MergedPhillipsBaraffePisaEkstromParsec()] # Array of age_ranges for the specific evolution models to test - age_vals = [age_all_MIST_arr, age_all_arr, age_all_arr, age_young_arr, age_young_arr, age_young_arr] + age_vals = [age_all_MIST_arr, age_all_arr, age_all_arr, age_young_arr, age_young_arr, age_young_arr, age_all_arr, age_all_arr, bd_test] # Array of metallicities for the specific evolution models to test - metal_vals = [metal_range, metal_solar, metal_solar, metal_solar, metal_solar, metal_solar] + metal_vals = [metal_range, metal_solar, metal_solar, metal_solar, metal_solar, metal_solar, metal_solar, metal_Marley, metal_solar] assert len(evo_models) == len(age_vals) == len(metal_vals) @@ -79,13 +82,17 @@ def test_atmosphere_models(): from spisea import atmospheres as atm # Array of atmospheres - atm_arr = [atm.get_merged_atmosphere, atm.get_castelli_atmosphere, atm.get_phoenixv16_atmosphere, atm.get_BTSettl_2015_atmosphere, - atm.get_BTSettl_atmosphere, atm.get_kurucz_atmosphere, atm.get_phoenix_atmosphere, atm.get_wdKoester_atmosphere] + atm_arr = [atm.get_merged_atmosphere, atm.get_castelli_atmosphere, atm.get_phoenixv16_atmosphere, + atm.get_BTSettl_2015_atmosphere, atm.get_BTSettl_atmosphere, atm.get_kurucz_atmosphere, + atm.get_phoenix_atmosphere, atm.get_wdKoester_atmosphere, atm.get_Phillips2020_atmosphere, + atm.get_Meisner2023_atmosphere] # Array of metallicities metals_range = [-2.0, 0, 0.15] + bd_metals_range = [-1.0, -0.5, 0, 0.3] metals_solar = [0] - metals_arr = [metals_solar, metals_range, metals_range, metals_solar, metals_range, metals_range, metals_range, metals_solar] + metals_arr = [metals_solar, metals_range, metals_range, metals_solar, metals_range, metals_range, metals_range, + metals_solar, metals_solar, bd_metals_range] assert len(atm_arr) == len(metals_arr) @@ -103,9 +110,9 @@ def test_atmosphere_models(): print('Done {0}'.format(atm_func)) # Test get_merged_atmospheres at different temps - temp_range = [2000, 3500, 4000, 5250, 6000, 12000] + temp_range = [200, 1000, 2000, 3500, 4000, 5250, 6000, 12000] atm_func = atm.get_merged_atmosphere - for ii in metals_range: + for ii in bd_metals_range: for jj in temp_range: try: test = atm_func(metallicity=ii, temperature=jj, verbose=True) @@ -117,7 +124,7 @@ def test_atmosphere_models(): # Test get_bb_atmosphere at different temps # This func only requests temp - temp_range = [2000, 3500, 4000, 5250, 6000, 12000] + temp_range = [1000, 2000, 3500, 4000, 5250, 6000, 12000] atm_func = atm.get_bb_atmosphere for jj in temp_range: try: @@ -126,6 +133,18 @@ def test_atmosphere_models(): raise Exception('ATM TEST FAILED: {0}, temp = {2}'.format(atm_func, jj)) print('get_bb_atmosphere: all temps passed') + + # Test get_bd_atmosphere at different temps + # This func only requests temp + temp_range = [250, 400, 500, 750, 950, 1200] + atm_func = atm.get_bd_atmosphere + for jj in temp_range: + try: + test = atm_func(temperature=jj, verbose=True) + except: + raise Exception('ATM TEST FAILED: {0}, temp = {1}'.format(atm_func, jj)) + + print('get_bd_atmosphere: all temps passed') return diff --git a/spisea/tests/test_synthetic.py b/spisea/tests/test_synthetic.py index bdd9064d..f319e337 100755 --- a/spisea/tests/test_synthetic.py +++ b/spisea/tests/test_synthetic.py @@ -211,8 +211,8 @@ def test_ResolvedCluster(): print('Constructed isochrone: %d seconds' % (time.time() - startTime)) # Now to create the cluster. - imf_mass_limits = np.array([0.07, 0.5, 1, np.inf]) - imf_powers = np.array([-1.3, -2.3, -2.3]) + imf_mass_limits = np.array([0.01, 0.05, 0.22, 0.55, 8, 120]) + imf_powers = np.array([-0.6, -0.25, -1.3, -2.3, -2.35]) ########## # Start without multiplicity @@ -390,7 +390,7 @@ def test_UnresolvedCluster(): startTime = time.time() multi = multiplicity.MultiplicityUnresolved() - imf_in = imf.Kroupa_2001(multiplicity=multi) + imf_in = imf.Salpeter_Kirkpatrick_2024(multiplicity=multi) evo = evolution.MergedBaraffePisaEkstromParsec() atm_func = atmospheres.get_merged_atmosphere iso = syn.Isochrone(log_age, AKs, distance, metallicity=metallicity, @@ -421,7 +421,7 @@ def test_ifmr_multiplicity(): startTime = time.time() - evo = evolution.MISTv1() + evo = evolution.MergedBaraffePisaEkstromParsec() atm_func = atmospheres.get_merged_atmosphere ifmr_obj = ifmr.IFMR_Raithel18() @@ -430,19 +430,18 @@ def test_ifmr_multiplicity(): iso = syn.IsochronePhot(logAge, AKs, distance, evo_model=evo, atm_func=atm_func, red_law=red_law, filters=filt_list, - mass_sampling=mass_sampling) + mass_sampling=mass_sampling, recomp=True) print('Constructed isochrone: %d seconds' % (time.time() - startTime)) # Now to create the cluster. - imf_mass_limits = np.array([0.07, 0.5, 1, np.inf]) - imf_powers = np.array([-1.3, -2.3, -2.3]) + imf_mass_limits = np.array([0.01, 0.07, 0.5, 1, np.inf]) + imf_powers = np.array([-0.3, -1.3, -2.3, -2.3]) ########## # Start without multiplicity and IFMR ########## - my_imf1 = imf.IMF_broken_powerlaw(imf_mass_limits, imf_powers, - multiplicity=None) + my_imf1 = imf.Salpeter_Kirkpatrick_2024(multiplicity=None) print('Constructed IMF: %d seconds' % (time.time() - startTime)) cluster1 = syn.ResolvedCluster(iso, my_imf1, cluster_mass, ifmr=ifmr_obj) @@ -454,8 +453,7 @@ def test_ifmr_multiplicity(): # Test with multiplicity and IFMR ########## multi = multiplicity.MultiplicityUnresolved() - my_imf2 = imf.IMF_broken_powerlaw(imf_mass_limits, imf_powers, - multiplicity=multi) + my_imf2 = imf.Salpeter_Kirkpatrick_2024(multiplicity=multi) print('Constructed IMF with multiples: %d seconds' % (time.time() - startTime)) cluster2 = syn.ResolvedCluster(iso, my_imf2, cluster_mass, ifmr=ifmr_obj) @@ -474,17 +472,73 @@ def test_ifmr_multiplicity(): assert len(np.where(clust2['phase'] == 102)) > 0 assert len(np.where(clust1['phase'] == 103)) > 0 # BH assert len(np.where(clust2['phase'] == 103)) > 0 + assert len(np.where(clust1['phase'] == 90)) > 0 # BD + assert len(np.where(clust2['phase'] == 90)) > 0 - # Now check that we have companions that are WDs, NSs, and BHs + # Now check that we have companions that are WDs, NSs, BHs, and BDs assert len(np.where(comps2['phase'] == 101)) > 0 assert len(np.where(comps2['phase'] == 102)) > 0 assert len(np.where(comps2['phase'] == 103)) > 0 + assert len(np.where(comps2['phase'] == 90)) > 0 # Make sure no funky phase designations (due to interpolation effects) # slipped through - idx = np.where( (clust1['phase'] > 5) & (clust1['phase'] < 101) & (clust1['phase'] != 9) ) - idx2 = np.where( (comps2['phase'] > 5) & (comps2['phase'] < 101) & (comps2['phase'] != 9) ) + + bd_masses = np.where((clust1['mass'] >= 0.01) & (clust1['mass'] <= 0.08)) + bd_mask = (clust1['mass'] >= 0.01) & (clust1['mass'] <= 0.08) + print(clust1[['mass', 'phase']][bd_masses]) + idx = np.where( (clust1['phase'] > 5) & (clust1['phase'] < 90) & (clust1['phase'] != 9) ) assert len(idx[0]) == 0 + + """ + 07/2024: Added more testing criteria for brown dwarf stars to ensure they are labeled appropriately for masses from 0.01 - 0.08 M_sun. + """ + # For cluster objects + MIN_MASS = 0.1 + BD_MIN_MASS = 0.01 + BD_MAX_MASS = 0.08 + + wd_idx = np.where(clust1['phase'] == 101) + ns_idx = np.where(clust1['phase'] == 102) + bh_idx = np.where(clust1['phase'] == 103) + bd_idx = np.where(clust1['phase'] == 90) + + print(clust1[bd_idx]) + assert np.all(clust1['mass'][wd_idx] > MIN_MASS) + assert np.all(clust1['mass'][ns_idx] > MIN_MASS) + assert np.all(clust1['mass'][bh_idx] > MIN_MASS) + assert np.all(clust1['mass'][bd_idx] < MIN_MASS) + + # For companion objects + comp_wd_idx = np.where(comps2['phase'] == 101) + comp_ns_idx = np.where(comps2['phase'] == 102) + comp_bh_idx = np.where(comps2['phase'] == 103) + comp_bd_idx = np.where(comps2['phase'] == 90) + assert np.all(comps2['mass'][comp_wd_idx] > MIN_MASS) + assert np.all(comps2['mass'][comp_ns_idx] > MIN_MASS) + assert np.all(comps2['mass'][comp_bh_idx] > MIN_MASS) + assert np.all(comps2['mass'][comp_bd_idx] < MIN_MASS) + + # Ensure brown dwarfs are within 0.01 and 0.08 solar masses + assert np.all((clust1['mass'][bd_idx] >= BD_MIN_MASS) & + (clust1['mass'][bd_idx] <= BD_MAX_MASS)) + assert np.all((comps2['mass'][comp_bd_idx] >= BD_MIN_MASS) & + (comps2['mass'][comp_bd_idx] <= BD_MAX_MASS)) + + # Ensure no other objects are in the brown dwarf mass range + non_bd_idx = np.where((clust1['phase'] != 90) & + (clust1['mass'] >= BD_MIN_MASS) & + (clust1['mass'] <= BD_MAX_MASS)) + assert len(non_bd_idx[0]) == 0 # asserting no non-brown dwarf objects in BD mass range + + comp_non_bd_idx = np.where((comps2['phase'] != 90) & + (comps2['mass'] >= BD_MIN_MASS) & + (comps2['mass'] <= BD_MAX_MASS)) + assert len(comp_non_bd_idx[0]) == 0 # asserting no non-brown dwarf companions in BD mass range + + # Ensure BD temperature assignment is working correctly + assert np.all(clust1['Teff'][bd_idx] != np.nan) + assert np.all(comps2['Teff'][comp_bd_idx] != np.nan) return @@ -964,4 +1018,4 @@ def test_Raithel18_IFMR_5(): assert len(WD_idx) == 2 , "There are not the right number of WDs for the Raithel18 IFMR" - return + return \ No newline at end of file