Add unpolarized unbinned source injector capability [Yong2Sheng's]

[israelmcmc]

I'm bringing @Yong2Sheng from my fork to develop, now that the interfaces branch is merged.

Summary

This PR introduces an initial implementation for unpolarized unbinned continuum point source injector in the spacecraft frame. It follows the existing line injector workflow, but with additional steps to (1) compute the integrated detected rate across an energy band and (2) sample detected photon energies across that band.

Compute incident photons and simulate events

1) Define a continuum spectrum (differential photon flux)

A power-law spectrum is used as the working example in the tutorial:

$$S(E)=K\left(\frac{E}{\mathrm{piv}}\right)^{\mathrm{index}}, \qquad [S(E)] = \frac{\mathrm{ph}}{\mathrm{cm^2}\times\mathrm{s}\times\mathrm{keV}} $$

where $K$ is the normalization (differential flux at the pivot energy $\mathrm{piv}$).

2) Convolve the spectrum with effective area

The detected count-rate density is

$$ w(E) \equiv S(E)\times A_{\text{eff}}(E), \qquad [w(E)] = \frac{\mathrm{ph}}{\mathrm{s}\times\mathrm{keV}}. $$

3) Integrate $w(E)$ to get the total detected rate and total counts

The integrated detected photon rate is

$$ I_0 = \int_{E_\mathrm{min}}^{E_\mathrm{max}} w(E) dE, \qquad [I_0] = \frac{\mathrm{ph}}{\mathrm{s}}. $$

In practice, the spectrum might not be analytical. And the effective area is also usually not analytical as well. So we do not perform the integral directly. Instead, we will use a very fine energy grid to obtain the integral by trapezoids.

The expected detected counts is

$$ \mu = T\times I_0, $$

and the realized detected counts are sampled as

$$ N \sim \mathrm{Poisson}(\mu). $$

4) Build an inverse-CDF sampler to draw detected photon energies

• Construct a discrete CDF from $w(E)$ on the energy grid via cumulative trapezoidal integration, and normalized it by $I_0$ to $[0,1]$.
• Draw a uniform distribution from [0,1): $u \sim \mathrm{Unif}(0,1)$.
• Apply inverse transform sampling: $E_i = CDF^{-1}(u)$, where $CDF^{-1}$ is implemented using scipy.interpolate.interp1d with linear interpolation.

5) Simulate each sampled energy

Feed the sampled photon energies (and their multiplicities, although they should show up only once) into UnpolarizedIdealComptonIRF.random_events(...) to produce the event list.

Implementation notes

1. A new class RandomEventDataFromContinuumInSCFrame is responsible for continuum injection.
2. For performance and clarity, I cache the following intermediates with @cached_property:
   • energy_grid
   • unpolarized_aeff
   • unpol_counts
   • incident_photons
3. A structured return container for detected-count (unpol_counts) bookkeeping:
   • UnpolCountsSummary(rate_density, rate, total_expected_counts)

What is not included yet

• Polarization handling for the continuum branch (this PR is unpolarized only).

[codecov]

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✅ Project coverage is 70.17%. Comparing base (6765236) to head (b41310a).

Files with missing lines	Patch %	Lines
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Files with missing lines	Coverage Δ
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[Yong2Sheng]

I will add the unit tests after the changes have been reviewed and approved. I’d like to avoid adding them too early, since they may need to be updated if the code changes during review.

[israelmcmc]

See my comment in #528

This is also related to #499: if the user passes a UnbinnedThreeMLModelFoldingInterface, we can inject event data right from the same class.

It's fine for now, but eventually this capability should be moved to the SourceInjector class.