A measurement of the escaping ionising efficiency of galaxies at redshift 5

Abstract

The escaping ionising efficiency from galaxies, $f_{\rm esc}\xi_{\rm ion}$, is a crucial ingredient for understanding their contribution to hydrogen reionisation, but both of its components, $f_{\rm{esc}}$ and $\xi_{\rm{ion}}$, are extremely difficult to measure. We measure the average escaping ionising efficiency $\langle f_{\rm{esc}} \xi_{\rm{ion}}\rangle$ of galaxies at $z=5$ implied by the mean level of ionisation in the intergalactic medium via the Lyman-$\alpha$ forest. We use the fact that $\dot{N}_{\rm{ion}} = \rho_{\rm{UV}} f_{\rm{esc}} \xi_{\rm{ion}}$, the product of the ionising output and the UV density $\rho_{\rm{UV}}$, can be calculated from the known average strength of the UV background and the mean free path of ionising photons. These quantities, as well as $\rho_{\rm{UV}}$, are robustly measured at $z\leq6$. We calculate the missing factor of $\langle f_{\rm{esc}} \xi_{\rm{ion}}\rangle$ at $z=5$, during a convenient epoch after hydrogen reionisation has completed and the intergalactic medium has reached ionisation equilibrium, but before bright quasars begin to dominate the ionising photon production. Intuitively, our constraint corresponds to the required escaping ionising production from galaxies in order to avoid over- or under-ionising the Lyman-$\alpha$ forest. We obtain a measurement of $\log \langle f_{\rm{esc}} \xi_{\rm{ion}}\rangle /$erg Hz$^{-1}$ $ = 24.28_{-0.20}^{+0.21}$ at $z=5$ when integrating $\rho_\text{UV}$ down to a limiting magnitude $M_\text{lim}=-11$. Our measurement of the escaping ionising efficiency of galaxies is in rough agreement with both observations and most models.