Mapping First Stars’ Mass via 21-cm Signal

Certainly! Here is a concise and clear synthesis of the methodology described in your passage about modeling Pop III stellar spectra, X-ray binaries (XRBs), and simulating the 21-cm cosmological signal using 21CMSPACE, including the use of emulators for efficient Bayesian analysis:

Modelling Pop III Stellar Spectra

• Stellar Evolution Tracks: Pop III stars are modeled using MESA (version 12115) assuming isolated, non-rotating, metal-free (Z=0), and negligible mass loss stars evolving from zero-age main sequence to core hydrogen depletion for (M \lesssim 310\, M_{\odot}).
• Stellar Atmospheres: TLUSTY (version 205) computes a grid of stellar atmospheres/spectra across effective temperature and surface gravity, using non-LTE modeling with H and He only (Big Bang proportions), motivated by zero surface metallicity predictions.
• Population Spectra: Integrated spectra along evolutionary tracks are combined and weighted by the Pop III initial mass function (IMF) to compute population-averaged Lyman-band and Lyman-Werner band emissivities in 21CMSPACE.
• Binary Effects: Neglecting binaries in Pop III stellar spectra causes, at most, a 25% underestimation of Lyman–Werner emissivities, a relatively small impact compared to other uncertainties.

Modelling Pop III X-ray Binaries (XRBs)

• Cataloguing Metal-free Binaries: Using 21CMSPACE Pop III star formation rates, stars are sampled per IMF, with 28% assumed in binaries—a conservative fraction. Binaries are paired randomly without mass-dependence; binary fraction uncertainty scales X-ray emissivities by at most a factor of 3.
• Binary Population Synthesis: The catalog is input into BINARY_C with consistent Z=0 stellar evolution tracks. XRBs are defined as binaries with primary compact object (BH or NS) accreting mass via wind or Roche-lobe overflow.
• XRB Spectral Modeling: Thin accretion disks plus Comptonization are used to model SEDs based on accretion rate, compact object mass, and orbital parameters; X-ray escape fractions consider halo-mass-dependent absorption by primordial gas.
• X-ray Emissivities: Pop III XRB emissivity peaks mostly between 0.9 – 3.8 keV, crucial for IGM heating. The integrated specific X-ray emissivities (f_{X,III}) vary by a factor ~257 across IMFs due to competing effects: number of binaries, fraction forming XRBs, XRB lifetimes, and individual XRB luminosities.
• Uncertainties: Effects such as supernova kicks, common-envelope evolution, and mass transfer are tested and found likely subdominant compared to IMF variation; these introduce mostly IMF-independent scalings.

Simulations of the 21-cm Signal with 21CMSPACE

• Code Overview: 21CMSPACE simulates large-scale structure and astrophysics impacting 21-cm signals with a grid of (128^3) cells (3 cMpc sides), modeling sub-grid physics analytically or via fits.
• Implemented Physics: Includes Pop III and Pop II star formation, radiative processes, WF coupling, feedback mechanisms, X-ray heating and ionization, reionization, redshift-space distortions, etc.
• X-ray Emissivity Implementation: Separate specific X-ray emissivities and SEDs are assigned to Pop II and Pop III halos:

  [
  \frac{LX^{\text{halo}}}{\text{SFR}^{\text{halo}}} = 3 \times 10^{40} f{X,j} \; \mathrm{erg\,s^{-1} M_{\odot}^{-1} yr}
  ]

  where (j \in {\mathrm{II}, \mathrm{III}}), with (f{X,III}) IMF-dependent and (f{X,II}) free parameter.

• Correlation of Parameters: Because both (f_{X,II}) and Pop III IMF impact X-ray heating similarly, their parameters are fit simultaneously, preventing biased or over-confident IMF constraints.

Emulation of the 21-cm Signal for Bayesian Analysis

• Motivation: Direct 21CMSPACE runs (~hours each) are computationally unfeasible for nested sampling requiring millions of likelihood evaluations.
• Neural Network Emulators: Created separate emulators for global signal and power spectrum for each of six IMFs (12 networks total), trained on 10,000 simulations per IMF covering redshift (7 \leq z \leq 39) and (0.085 \leq k \leq 1) cMpc(^{-1}):
  • Global signal emulators: 5 hidden layers, 16 nodes/layer
  • Power spectrum emulators: 4 hidden layers, 100 nodes/layer
• Training and Validation: Use 90% of simulations for training, 10% for testing; error metrics are root-mean-square error for the global signal and a modified fractional error for the power spectrum.
• Performance: Emulator errors comparable to or better than previous studies, enabling fast, accurate, and reliable Bayesian inference on the Pop III IMF and astrophysical parameters.

Summary:

This methodology builds a self-consistent framework linking Pop III stellar evolution and XRB modeling to 21-cm cosmological signals, leveraging sophisticated population synthesis and large-scale simulation codes, and accelerates inference via neural network emulators, enabling robust predictions and parameter estimation of the Pop III IMF and related astrophysics from upcoming 21-cm observations.

If you want, I can also help summarize specific parts, outline pros/cons, or assist with any clarifications or computations related to this methodology.