Inferring reionization and galaxy properties from the patchy kinetic Sunyaev-Zel'dovich signal

The patchy kinetic Sunyaev-Zel'dovich (kSZ) signal is an integral probe of the timing and morphology of the epoch of reionization (EoR). Recent observations have claimed a low signal-to-noise (S/N) measurement, with a dramatic increase in S/N expected in the near future. In this work, we quantify what we can learn about the EoR from the kSZ signal. We perform Bayesian inference by sampling galaxy properties and using forward-models of the kSZ as well as other EoR and galaxy observations in the likelihood. Including the recent kSZ measurement obtained by the South Pole Telescope ($\mathcal{D}_{3000}^{\rm{pkSZ}} = 1.1_{-0.7}^{+1.1} \mu$K$^2$) shifts the posterior distribution in favor of faster and later reionization models, resulting in lower values of the optical depth to the CMB: $\tau_e = 0.052_{-0.008}^{+0.009}$ with a 68$\%$ confidence interval (C.I.). The combined EoR and UV luminosity function observations also imply a typical ionizing escape fraction of $0.04_{-0.03}^{+0.05}$ (95$\%$ C.I.), without a strong dependence on halo mass. We show how the patchy kSZ power from our posterior depends on the commonly-used parameters of reionization. For a given midpoint and duration, the EoR morphology only has a few percent impact on the patchy kSZ power in our posterior. However, a physical model is needed to obtain tight constraints from the current low S/N patchy kSZ measurement, as it allows us to take advantage of complimentary high-$z$ observations. Future high S/N detections of the patchy kSZ should decrease the current uncertainties on the timing of the EoR by factors of $\sim$2 - 3.