Steep Redshift Evolution of the Ionizing Escape Fraction at $z = 5$--$12$: Empirical Constraints and Comparison with Simulations

Abstract

The ionizing photon escape fraction $f_{\rm esc}$ governs cosmic reionization yet remains observationally unconstrained as a function of halo mass. We present the first empirical constraints on $f_{\rm esc}(M_{\rm h},z)$ across the epoch of reionization, using a three-parameter power-law model $f_{\rm esc} = f_0\,(M/10^{10}M_\odot)^{α_M}\,[(1{+}z)/10]^{α_z}$, conditioned on HST and JWST UV luminosity functions at $z=5$--12, the Planck Thomson optical depth, seven neutral-fraction measurements, and one high-redshift prior. Using Schechter fits to the latest HST and JWST UV luminosity functions, abundance matching to link $M_{\rm UV}$ to halo mass, and a reionization ODE solver validated against Planck, we constrain the model via a dense grid scan and ensemble MCMC. The profile likelihood yields tight constraints: $f_0=0.061_{-0.023}^{+0.018}$, $α_M=0.18_{-0.30}^{+0.22}$, $α_z=1.98_{-0.42}^{+0.48}$. In contrast, the full marginal posterior is substantially broadened by a strong $f_0$--$α_M$--$α_z$ degeneracy ($α_z = 1.93_{-2.00}^{+2.09}$, $α_M = -0.52_{-0.69}^{+0.69}$). The population-averaged $\langle f_{\rm esc} \rangle(z)$ rises from $\sim$2\% at $z=5$ to $\sim$9\% at $z=12$, with sub-threshold halos contributing $>80\%$ of the ionizing budget at $z\geq10$. Comparing with THESAN, we find that the per-halo median $f_{\rm esc}$ shows steep evolution consistent with our profile result, while luminosity-weighted averaging systematically flattens the trend because massive halos dominate the ionizing budget at $z\lesssim7$. Robustness checks confirm $α_z>1.0$ at $>95\%$ confidence; the steep-evolution model predicts $τ_e=0.047$, consistent with Planck at $0.7σ$. We provide tabulated $f_{\rm esc}(M_{\rm h},z)$ posteriors as empirical inputs for reionization simulations.