Reconstructing the redshift evolution of escaped ionizing flux from early galaxies with Planck and HST observations

Abstract

While galaxies at $6\lesssim z\lesssim 10$ are believed to dominate the epoch of cosmic reionization, the escape fraction of ionizing flux $f_{\mathrm{esc}}$ and the photon production rate ${\dot{n}}_{\gamma }$ from these galaxies must vary with redshift to simultaneously match CMB and low-redshift observations. We constrain $f_{\mathrm{esc}}(z)$ and ${\dot{n}}_{\gamma }(z)$ with Planck 2015 measurements of the Thomson optical depth $\tau$, recent low multipole E-mode polarization measurements from Planck 2016, SDSS BAO data, and $3\lesssim z\lesssim 10$ galaxy observations. We compare different galaxy luminosity functions that are calibrated to HST observations, using both parametric and non-parametric statistical methods that marginalize over the effective clumping factor $C_{\mathrm{HII}}$, the LyC production efficiency ${\xi }_{\mathrm{ion}}$, and the time-evolution of the UV limiting magnitude $d{M}_{\mathrm{SF}}/dz$. Using a power-law model, we find $f_{\mathrm{esc}}\lesssim 0.5$ at $z=8$ with slope $\beta \gtrsim 2.0$ at $68\%$ confidence with little dependence on the galaxy luminosity function or data, although there is non-negligible probability for no redshift evolution $\beta \sim 0$ or small escape fraction $f_{\mathrm{esc}}\sim 10^{-2}$. A non-parametric form for $f_{\mathrm{esc}}(z)$ evolves significantly with redshift, yielding $f_{\mathrm{esc}}\sim 0.2,0.3,0.6$ at $z=6,9,12$, respectively. However, a model-independent reconstruction of ${\dot{n}}_{\gamma }(z)$ predicts a suppressed escaped photon production rate at $z=9$ for the latest Planck data compared to the other models, implying a quicker period of reionization. We find evidence for redshift evolution in the limiting magnitude of the galaxy luminosity function for empirical models of the galaxy luminosity function.

12 pages, 6 figures, 2 tables

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