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

The ionizing photon escape fraction $f_{\mathrm{e}\mathrm{s}\mathrm{c}}$ governs cosmic reionization yet remains observationally unconstrained as a function of halo mass. We present the first empirical constraints on $f_{\mathrm{e}\mathrm{s}\mathrm{c}}(M_{\mathrm{h}},z)$ across the epoch of reionization, using a three-parameter power-law model $f_{\mathrm{e}\mathrm{s}\mathrm{c}}=f_0(M\mathrm{/}{10}^{10}{M}_{\odot }{)}^{{\alpha }_M}[(1+z)\mathrm{/}10{]}^{{\alpha }_z}$, 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 $M_{\mathrm{U}\mathrm{V}}$ 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: $f_0=0.061_{-0.023}^{+0.018}$, ${\alpha }_M=0.18_{-0.30}^{+0.22}$, ${\alpha }_z=1.98_{-0.42}^{+0.48}$. In contrast, the full marginal posterior is substantially broadened by a strong $f_0$–${\alpha }_M$–${\alpha }_z$ degeneracy (${\alpha }_z=1.93_{-2.00}^{+2.09}$, ${\alpha }_M=-0.52_{-0.69}^{+0.69}$). The population-averaged $⟨f_{\mathrm{e}\mathrm{s}\mathrm{c}}⟩(z)$ rises from $\sim$2% at $z=5$ to $\sim$9% at $z=12$, with sub-threshold halos contributing $>80\mathrm{\%}$ of the ionizing budget at $z\ge 10$. Comparing with THESAN, we find that the per-halo median $f_{\mathrm{e}\mathrm{s}\mathrm{c}}$ shows steep evolution consistent with our profile result, while luminosity-weighted averaging systematically flattens the trend because massive halos dominate the ionizing budget at $z\lesssim 7$. Robustness checks confirm ${\alpha }_z>1.0$ at $>95\mathrm{\%}$ confidence; the steep-evolution model predicts ${\tau }_e=0.047$, consistent with Planck at $0.7\sigma$. We provide tabulated $f_{\mathrm{e}\mathrm{s}\mathrm{c}}(M_{\mathrm{h}},z)$ posteriors as empirical inputs for reionization simulations.