Influence of the Spectral Energy Distribution of Reionization-Era Sources on the Lyman-$α$ Forest

TL;DR

This study quantifies how the spectral energy distribution of reionization-era ionizing sources shapes the ionization and thermal state of the IGM and imprints on the Ly$\alpha$ forest. By post-processing Sherwood-type hydrodynamic simulations with the 3D multi-frequency radiative transfer code CRASH, the authors compare six SED scenarios, including X-ray binaries, ISM Bremsstrahlung, binary stars, a blackbody, and two power-law forms. They find that harder SEDs create extended partially ionized zones and hotter IGM, with only modest changes to the overall reionization history, but notable differences in proximity-zone behavior and intermediate-scale Ly$\alpha$ flux power, which could help disentangle source populations with future surveys like ELT and DESI. The work emphasizes that incorporating physically motivated SEDs is essential to robustly interpret Ly$\alpha$ forest data and connect it to the end of reionization and the properties of contributing sources.

Abstract

Interpreting Lyman-$α$ forest properties during the epoch of reionization requires assumptions about the spectral energy distribution (SED) of ionizing sources. These are often simplified to blackbody or power-law spectra, potentially overlooking contributions from high-energy processes. In this work, we investigate how different SED models of reionization-era sources shape the thermal and ionization state of the intergalactic medium (IGM) and imprint on the Ly$α$ forest during the late stages of reionization. We perform $3D$ radiative transfer simulations with CRASH, post-processed on Sherwood-type hydrodynamical outputs, exploring both physically motivated SEDs including X-ray binaries, Bremsstrahlung from shock-heated interstellar medium, and binary stars and idealized blackbody and power-law spectra. While the large-scale morphology of ionized regions is broadly similar across all models, harder spectral components extend partially ionized zones, produce larger He III regions, and heat the surrounding IGM. By adopting simplified spectra there is the risk of underestimating the contribution of high-energy sources, which for most models we consider are found to alter the effective optical depth, the flux power, and the local transmissivity within the current $\sim 1 σ$ measurement uncertainties. The differences across models are most pronounced in the behavior of the proximity zone and in the power at intermediate scales, offering the most promising diagnostics to disentangle source populations. With upcoming high precision measurements from ELT and DESI, realistic SED modelling will be essential for robustly connecting Ly$α$ forest observations to the sources driving the end of reionization.

Figures (11)

• Figure 1: Redshift evolution of the total ionizing photon production rate adopted in the study (black solid line) with a compilation of observational constraints becker2021gaikwad2023davies2024.
• Figure 2: Averaged spectral energy distribution $\bar{S}(\nu,z)$ for: single stars (SS, solid orange curve); a combination of single stars, ISM and XRBs (SS+ISM+XRBs, dashed sky blue); a combination of binary stars, ISM and XRBs (BS+ISM+XRBs, dash-dotted green); a black-body spectrum with 50,000 K (BB, short-dashed yellow); a power-law spectrum with a slope of -3 (SOFT-PL, long-dashed blue), and a power-law spectrum with a slope of -1.8 (AGN-PL, dotted vermilion). The vertical gray lines indicate the ionization thresholds for neutral hydrogen (13.6 eV), neutral helium (24.6 eV) and singly ionized helium (54.4 eV).
• Figure 3: From top to bottom, slice maps of the H ii, He ii, He iii fractions and IGM temperature at $z = 6$ for different combinations of SED models: single stars ( SS, first column); single stars, ISM and XRBs ( SS+ISM+XRBs, second); binary stars, ISM and XRBs ( BS+ISM+XRBs, third); blackbody ( BB, fourth); galaxy power-law ( SOFT-PL, fifth) and AGN power-law ( AGN-PL, sixth). The lower sets of rows show the difference with respect to the simulations with single stars only. The maps are $20 h^{-1} \rm{cMpc}$ wide and $78 h^{-1} \rm{ckpc}$ thick.
• Figure 4: Volume averaged H i photoionization rate for model SS (solid orange curve), SS+ISM+XRBs (dashed sky blue), BS+ISM+XRBs (dash-dotted green), BB (short-dashed yellow), SOFT-PL (long-dashed blue) and AGN-PL (dotted vermilion). The symbols denote a compilation of observational constraints from the literature Calverley2011wyithe2011daloisio2018Davies2018davies2024.
• Figure 5: Top panel: Redshift evolution of the volume averaged $\mathit{x}\rm{_{HI}}$ for all SED models: SS (solid orange curve), SS+ISM+XRBs (dashed sky blue), BS+ISM+XRBs (dash-dotted green), BB (short-dashed yellow), SOFT-PL (long-dashed blue) and AGN-PL (dotted vermilion). The symbols denote a compilation of observational constraints from the literature McGreer2015Davies2018greig2019hoag2019Whitler2020Bosman2022Jin2023Greig2024durovcicova2024nakane2024umeda2024spina2024zhu2024Mason2025. Bottom panel: Fractional difference with respect to the SS simulation.