ABSTRACT
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 cosmic microwave background (CMB) optical depth and Ly α and Ly β forest dark pixel fraction produce $\dot{N}_\textrm {ion}$ evolution ($\mathrm{ d}\log _{10}\dot{\mathbf {N}}_{\bf ion}/\mathrm{ d}z|_{z=6\rightarrow 8} = -0.31\pm 0.35$ dex) consistent with the declining UV luminosity density of galaxies, assuming constant ionizing photon escape fraction and efficiency. Including measurements from Ly α damping of galaxies and quasars produces a more rapid decline: $\mathrm{ d}\log _{10}\dot{\mathbf {N}}_{\bf ion}/\mathrm{ d}z|_{z=6\rightarrow 8} =-0.44\pm 0.22$ dex, steeper than the declining galaxy luminosity density (if extrapolated beyond $M_\rm{\small UV}\gtrsim -13$), and constrains the mid-point of reionization to z = 6.93 ± 0.14.
Model-independent constraints on the hydrogen-ionizing emissivity at z > 6