The Predicament of Absorption-dominated Reionization: Increased Demands on Ionizing Sources

The reionization epoch concludes when ionizing photons reach every corner of the Universe. Reionization has generally been assumed to be limited primarily by the rate at which galaxies produce ionizing photons, but the recent measurement of a surprisingly short ionizing photon mean free path of $0.75^{+0.65}_{-0.45}$ proper Mpc at $z = 6$ by Becker et al. (2021) suggests that absorption by residual neutral hydrogen in the otherwise ionized intergalactic medium may play a much larger role than previously expected. Here we show that consistency between this short mean free path and the coeval dark pixel fraction in the Ly$\alpha$ forest requires a cumulative output of $6.1^{+11}_{-2.4}$ ionizing photons per baryon by reionization's end. This represents a dramatic increase in the ionizing photon budget over previous estimates, greatly exacerbating the tension with measurements of the ionizing output from galaxies at later times. Translating this constraint into the instantaneous ionizing production from galaxies in our model, we find $\log_{10}f_{\rm esc}\xi_{\rm ion}/\text{(erg/Hz)}^{-1} =25.02_{-0.21}^{+0.45}$ at $z\sim6$. Even with optimistic assumptions about the ionizing production efficiency of early stellar populations, and assuming the galaxy luminosity function extends to extremely faint sources ($M_{\text{UV}}\leq-11$), complete reionization requires the escape fraction of ionizing photons to exceed $20\%$ across the galaxy population. This is far larger than observed in any galaxy population at lower redshifts, requiring rapid evolution in galaxy properties after the first billion years of cosmic time. This tension cannot be completely relieved within existing observational constraints on the hydrogen neutral fraction and mean free path.