Reconstructing the redshift evolution of escaped ionizing flux from   early galaxies with Planck and HST observations
  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 $dM_\mathrm{SF}/dz$. 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. 
Layne C. Price and Hy Trac and Renyue Cen
astro-ph.CO astro-ph.GA