Model-independent constraints on the hydrogen-ionizing emissivity at z > 6

Modelling reionization often requires significant assumptions about the properties of ionizing sources. Here, we infer the total output of hydrogen-ionizing photons (the ionizing emissivity, $\dot{N}_\textrm{ion}$) at $z=4-14$ from current reionization constraints, being maximally agnostic to the properties of ionizing sources. We use a Bayesian analysis to fit for a non-parametric form of $\dot{N}_\textrm{ion}$, allowing us to flexibly explore the entire prior volume. We infer a declining $\dot{N}_\textrm{ion}$ with redshift at $z>6$, which can be used as a benchmark for reionization models. Model-independent reionization constraints from the CMB optical depth and Ly$\alpha$ and Ly$\beta$ forest dark pixel fraction produce $\dot{N}_\textrm{ion}$ evolution ($d\log_{10}\dot{N}_\textrm{ion}/dz|_{z=6\rightarrow8} = -0.31\pm0.35$ dex) consistent with the declining UV luminosity density of galaxies, assuming constant ionizing photon escape fraction and efficiency. Including measurements from Ly$\alpha$ damping of galaxies and quasars produces a more rapid decline: $d\log_{10}\dot{N}_\textrm{ion}/dz|_{z=6\rightarrow8} =-0.44\pm0.22$ dex, steeper than the declining galaxy luminosity density (if extrapolated beyond $M_\mathrm{UV} \lesssim -13$), and constrains the mid-point of reionization to $z = 6.93\pm0.14$.