Robust Ly$\alpha$ forest constraints on reionization from semi-analytic galaxy formation models

Technical Summary: Robust Ly$\alpha$ Forest Constraints on Reionization from Semi-Analytic Galaxy Formation Models

Problem Statement
The Epoch of Reionization (EoR) represents the final major phase transition of baryonic matter in the Universe. While previous work (specifically Qin et al. 2025, hereafter Q25) demonstrated that the high-redshift Ly$\alpha$ forest provides tight constraints on the timing and morphology of reionization, a critical question remains regarding the robustness of these inferences. Existing EoR inference frameworks often rely on simplified scaling relations between galaxy properties and halo mass, compressing the complexity of galaxy formation into deterministic mappings. High-redshift galaxies are expected to exhibit substantial stochasticity in stellar masses, star-formation histories, and escape fractions. This paper investigates whether the tight late-time reionization history inferred from Ly$\alpha$ forest data remains valid when tested against more physically flexible semi-analytic models that incorporate stochasticity, active galactic nuclei (AGN), and circumgalactic medium (CGM) attenuation.

Methodology
The authors utilize Meraxes, a semi-analytic model of galaxy formation and reionization, applied to a cosmological $N$-body simulation volume of $(210 h^{-1} \text{cMpc})^3$. Meraxes tracks the assembly histories of galaxies, including gas accretion, cooling, star formation, supernova feedback, and blackhole growth. To resolve the low-mass galaxy population expected to dominate the ionizing budget, merger trees are augmented down to the atomic-cooling threshold using a Monte-Carlo algorithm.

The study constructs a suite of source models where the galaxy ionizing escape fraction ($f_{\text{esc}}^{\text{gal}}$) is parameterized differently:

1. Fiducial Model: $f_{\text{esc}}^{\text{gal}}$ scales as a power law of halo mass ($M_{\text{vir}}$).
2. AGN-Assisted Model: Adds ionizing photons from accreting blackholes, calibrated to observed faint AGN populations.
3. CGM-Attenuated Model: Introduces an additional suppression of escaping photons based on the local clumping factor ($C$) and CGM column density, phenomenologically modeling dense gas structures absorbing photons before they reach the intergalactic medium (IGM).
4. Galaxy-Property-Dependent Models: $f_{\text{esc}}^{\text{gal}}$ is parameterized as a function of stellar mass ($M_*$), star formation rate (SFR), specific star formation rate (sSFR), and star-forming disc surface density ($\Sigma_{\text{SF}}$).

All models are calibrated to the observed cumulative distribution of Ly$\alpha$ effective optical depths ($\tau_{\text{eff}}$) from the XQR-30+ dataset (Bosman et al. 2022). The ionization fields are calculated using a customized version of 21cmFAST, incorporating sub-grid density distributions to account for unresolved recombinations and self-shielding. Ly$\alpha$ forest transmission is forward-modeled using the fluctuating Gunn-Peterson approximation, corrected via stochastic mapping calibrated against high-resolution hydrodynamical simulations.

Key Results
Despite significant variations in how ionizing photons are allocated among halo masses, galaxy luminosities, and source types (stars vs. AGN), all viable calibrated models converge on a similar late-time reionization history:

• Reionization Timing: The midpoint of reionization ($z|_{x_{\text{HI}}=0.5}$) occurs between $z \sim 6.2$ and $6.9$. The final stages ($z|_{x_{\text{HI}}=0.05}$) occur between $z \sim 5.36$ and $5.57$.
• Source Redistribution:
  • The Fiducial and AGN-Assisted models shift the escaping photon budget toward lower-mass halos. In the AGN model, AGN contribute up to $\sim 15\%$ of the ionizing emissivity at $z \sim 5$, compensating for a steeper stellar escape fraction that otherwise would under-ionize the IGM at late times.
  • The CGM-Attenuated model allows for a larger intrinsic contribution from massive halos but requires strong late-time suppression (scaling as $C^3$) to match the observed opacity, effectively reducing the escaping stellar emissivity by $\sim 15\%$ near the end of reionization.
  • Galaxy-Property Models: Models tied to $M_*$ and SFR behave similarly to the fiducial case due to strong correlations with halo mass. The sSFR model introduces significant scatter but maintains a similar qualitative hierarchy. The SF-disc model, which is the most massive-halo-weighted scenario, still converges to the same late-time history after calibration, though it requires additional CGM suppression.
• Clumping Factor: The fiducial model predicts a clumping factor ($C$) that rises to $\sim 10$ by the end of reionization, balancing high ionizing emissivity without over-ionizing the IGM.
• CMB Optical Depth: The resulting Thomson scattering optical depths ($\tau_e$) for the calibrated models range from 0.0535 to 0.0652, consistent with Planck constraints.

Significance and Claims
The paper claims that the late and extended reionization history inferred from Ly$\alpha$ forest data is robust to physically motivated variations in the galaxy-halo connection, modest AGN contributions, and phenomenological CGM attenuation.

The authors conclude that while the Ly$\alpha$ forest strongly restricts the timing and progression of the final stages of reionization, it does not uniquely determine the physical origin of the ionizing photon budget (i.e., the specific balance between low-mass galaxies, massive galaxies, AGN, and absorption). The spread among the calibrated Meraxes models provides an estimate of the systematic uncertainty on EoR inference arising from source modeling. The study reinforces that the tight constraints on the late EoR derived in previous work (Q25) hold even when moving from simple halo-based prescriptions to a more detailed, stochastic semi-analytic framework.