Full-Data Results of Hubble Frontier Fields: UV Luminosity Functions at $z\sim 6-10$ and a Consistent Picture of Cosmic Reionization

Abstract

We present UV luminosity functions of dropout galaxies at $z\sim 6-10$ with the complete Hubble Frontier Fields data. We obtain a catalog of $\sim 450$ dropout-galaxy candidates (350, 66, and 40 at $z\sim 6-7$, 8, and 9, respectively), whose UV absolute magnitudes reach $\sim -14$ mag, $\sim 2$ mag deeper than the Hubble Ultra Deep Field detection limits. We carefully evaluate number densities of the dropout galaxies by Monte-Carlo simulations, including all lensing effects such as magnification, distortion, and multiplication of images as well as detection completeness and contamination effects in a self-consistent manner. We find that UV luminosity functions at $z\sim 6-8$ have steep faint-end slopes, $\alpha \sim -2$, and likely steeper slopes, $\alpha \lesssim -2$ at $z\sim 9-10$. We also find that the evolution of UV luminosity densities shows a non-accelerated decline beyond $z\sim 8$ in the case of $M_{\mathrm{trunc}}=-15$, while an accelerated in the case of $M_{\mathrm{trunc}}=-17$. We examine whether our results are consistent with the Thomson scattering optical depth from the Planck satellite and the ionized hydrogen fraction $Q_{\mathrm{HII}}$ at $z\lesssim 7$ based on the standard analytic reionization model. We find that there exist reionizaiton scenarios that consistently explain all the observational measurements with the allowed parameters of $f_{\mathrm{esc}}=0.17_{-0.03}^{+0.07}$ and $M_{\mathrm{trunc}}>-14.0$ for $\log {\xi }_{\mathrm{ion}}/[{\mathrm{erg}}^{-1}\mathrm{Hz}]=25.34$, where $f_{\mathrm{esc}}$ is the escape fraction, $M_{\mathrm{trunc}}$ is the faint limit of the UV luminosity function, and ${\xi }_{\mathrm{ion}}$ is the conversion factor of the UV luminosity to the ionizing photon emission rate. The length of the reionization period is estimated to be $\Delta z=3.9_{-1.6}^{+2.0}$ (for $0.1<Q_{\mathrm{HII}}<0.99$), consistent with the recent estimate from Planck.

21 pages, 10 figures. Accepted for publication in ApJ