New constraints on the galactic ionizing efficiency and escape fraction at 2.5 < z < 6 based on quasar absorption spectra

Measurements of the ionisation state of the intergalactic medium (IGM) can probe the sources of the extragalactic ionising background. We provide new measurements of the ionising emissivity of galaxies using measurements of the ionising background and ionising photon mean free path from high-redshift quasar spectra at $2.5 < z < 6$. Unlike most prior works, we account for radiative-transfer effects and possible neutral islands from the tail of reionisation at $z > 5$. We combine our results with measurements of the UV luminosity function to constrain the average escaping ionising efficiency of galaxies, $\langle f_{\rm esc} \xi_{\rm ion}\rangle_{L_{\rm UV}}$. Assuming galaxies with $M_{\rm UV} < -11$ emit ionising photons, we find $\log (\langle f_{\rm esc} \xi_{\rm ion}\rangle_{L_{\rm UV}}/{\rm erg^{-1}Hz}) = 24.47_{-0.17}^{+0.09}$ and $24.75_{-0.28}^{+0.15}$ at $z=5$ and $6$, and $1\sigma$ upper limits of $24.48$ and $24.31$ at $z = 2.5$ and $4$, respectively. We also estimate the population-averaged $f_{\rm esc}$ using measurements of intrinsic ionising efficiency from JWST. We find $\langle f_{\rm esc} \rangle = 0.126_{-0.041}^{+0.034}$ and $0.224_{-0.108}^{+0.098}$ at $z=5$ and $6$, and $1\sigma$ upper limits of $f_{\rm esc}< 0.138$ and $0.096$ at $z=2.5$ and $4$, respectively, for $M_{\rm UV} < -11$. Our findings are consistent with prior measurements of $f_{\rm esc} \lesssim 10\%$ at $z \leq 4$, but indicate a factor of several increase between $z = 4$ and $6$. The steepness of this evolution is sensitive to the highly uncertain mean free path and ionising background intensity at $z>5$. Lastly, we find $1.10^{+0.21}_{-0.39}$ photons per H atom are emitted into the IGM between $z=6$ and $=5.3$. This is $\approx 4\times$ more than needed to complete the last $20\%$ of reionisation absent recombinations, suggesting that reionisation's end was likely absorption-dominated.