Effect of ionizing photon escape fraction in faint galaxies on modeling reionization history of the universe

TL;DR

Problem: determining how the escape fraction and faint galaxies shape the hydrogen reionization history. Approach: combine a GRUMPY-based high-z galaxy formation model with three $f_{ m esc}$ prescriptions and a range of IGM clumping factors to compute $Q_{HII}(z)$ down to $M_{1500}=-5$. Key results: including faint galaxies with $f_{ m esc}=0.1$ can reproduce constraints; a luminosity-dependent $f_{ m esc}$ yields too-early reionization, while a redshift-independent, SPHINX-inspired $f_{ m esc}$ matches observations despite significant tail in $Q_{HII}$ at $z=8-12$. Significance: the relative contribution of faint dwarfs is highly sensitive to $f_{ m esc}$, making escape physics the dominant uncertainty in reionization modeling and guiding future observations and simulations.

Abstract

We present model calculations of the reionization history of hydrogen using star formation histories, computed with a galaxy formation model which reproduces properties of local dwarf galaxies and UV luminosity functions of galaxies at $z=5-16$. We use the ionizing photon density functions predicted by the model along with different models for the escape fraction of ionizing photons, $f_{\rm esc}$, to study the effects of ionizing photons from faint galaxies and different assumptions about $f_{\rm esc}$ on the evolution of hydrogen ionized fraction with redshift, $Q_{\rm HII}(z)$. We show that accounting for the contribution of faint galaxies with UV luminosities $M_{1500}>-13$, and with a constant ionizing photon escape fraction of $f_{\rm esc}=0.1$ results in the hydrogen reionization history consistent with all current observational constraints. Comparing results of the $f_{\rm esc}=0.1$ model and two alternative models shows that the model with a strong luminosity dependence of $f_{\rm esc}$, which assigns high $f_{\rm esc}$ to faint galaxies, results in early reionization inconsistent with observational constraints. However, the model in which $f_{\rm esc}$ follows a universal redshift-independent correlation with the recent maximum specific star formation rate, motivated by the results of the SPHINX galaxy formation simulation, results in the reionization history in good agreement with existing observational constraints, even though this model produces a sizeable ionized hydrogen fraction of $Q_{\rm HII}\approx 0.15-0.2$ at redshifts $z=8-12$. Our results show that the relative contribution of faint dwarf galaxies to reionization depends sensitively on assumptions about the escape fraction for galaxies of different luminosities, and that this is the main source of uncertainty in modeling hydrogen reionization.

Figures (10)

• Figure 1: Rest-frame UV luminosity function of galaxies in the GRUMPY model with specific modifications for modeling reionization detailed in Wu.Kravtsov.2024Kravtsov.Belokurov.2024 (see Appendix \ref{['app:stochastic_params']}), each panel showing a redshift at $z\in[5, 16]$. Effects of dust are not included in the model LFs Wu.Kravtsov.2024. The different symbols show observational estimates of the UV LF in recent studies that used HST and JWST observations Bouwens.etal.2021Bouwens.etal.2022Finkelstein.etal.2022Bouwens.etal.2023aBouwens.etal.2023bDonnan.etal.2023Harikane.etal.2023Leung.etal.2023Harikane.etal.2024McLeod.etal.2024Perez.Gonzalez.etal.2024Robertson.etal.2024. Theoretical models are shown in dashed (Sun.etal.2023), dash-dotted (Kravtsov.Belokurov.2024) lines and colored regions Leung.etal.2023. Note that before reionization (i.e. $z \gtrsim 6$), the slope of the LF even at the faintest magnitudes remains as steep as the slope at $M_{1500}\approx -14$. For a single-panel comparison of UV LF evolution over redshift, see Fig. 2 of Wu.Kravtsov.2024.
• Figure 2: The $f_{\rm esc}$ distribution for galaxies in the SPHINX simulation, binned by maximum of the logarithm of the 10 Myr-averaged specific star formation rate $\rm sSFR_{10}$ measured over the past 50 Myr. The solid curves represent median $f_{\rm esc}$ values for different $\log_{10}{\rm sSFR_{\rm max,10}}$ at different redshifts, and shaded regions correspond to 68th and 84th percentiles for SPHINX galaxies at $z=6$ (the distributions at other $z$ are similar). The dashed thick line represents the median, and the thinner dotted lines represent the 68th and 84th percentiles of the distribution for the same galaxies, but with $\log_{10}(f_{\rm esc})$ modeled using the approximation described in § \ref{['subsec:fesc_models']}.
• Figure 3: Reionization histories represented by the average neutral fraction $1 - Q$ of the intergalactic medium as a function of redshift and cosmic time. The curves show predictions from integrating Eq. \ref{['eq:dqdz']} with three models for the ionizing photon escape fraction: a constant global $f_{\rm esc} = 0.1$ (blue); a model in which $f_{\rm esc} = f_{\rm esc}(M_{1500} = -21) \times 10 ^ {0.62(M_{1500} + 21)}$ increases monotonically for fainter galaxies (yellow), where $f_{\rm esc}(M_{1500} = -21) = 1.91\times 10^{-4}$; and lastly the model where $f_{\rm esc}$ depends on specific star formation rate (red, see § \ref{['subsec:fesc_models']}). All models integrate galaxies at each redshift across the full luminosity range.
• Figure 4: Hydrogen ionized fraction $Q_{\rm HII}(z)$ with redshift and cosmic time. The same curves representing $f_{\rm esc}$ models are shown as in Fig. \ref{['fig:log1Qz_fesc']} with the same colors. All models integrate galaxies at each redshift across the full luminosity range down to $M_{1500} < -5$. Observational measurements (points) and limits (arrows) are plotted from a compilation of Ly$\alpha$, QSO, and IGM temperature measurements Mason.etal.2019McGreer.etal.2015Ouchi.etal.2010Schenker.etal.2014Davies.etal.2018Durovcikova.etal.2020Greig.etal.2017Mason.etal.2018Kageura.etal.2025.
• Figure 5: Thomson optical depth $\tau(z)$ as a function of redshift for the three ionizing escape fraction models: a constant $f_{\rm esc} = 0.1$ integrated down to $M_{1500} < -5$ (blue), a model in which a model in which $f_{\rm esc}$ increases monotonically for fainter galaxies, and is normalized to 1 for the faintest galaxies (yellow), and the $f_{\rm esc}$ model depending on specific star formation rate (red). The colored bands shows the $2\sigma$ range of the opacity constraints measured by Planck.coll.2020 and Heinrich.Hu.2021's reanalysis.