Full-Data Results of Hubble Frontier Fields: UV Luminosity Functions at $z\sim6-10$ and a Consistent Picture of Cosmic Reionization

Masafumi Ishigaki, Ryota Kawamata, Masami Ouchi, Masamune Oguri, Kazuhiro Shimasaku

Published 2017-02-16Version 1

We present UV luminosity functions of star-forming galaxies at $z\sim6-10$ derived with the full-data set of the Hubble Frontier Fields (HFF) program consisting of 6 lensing-cluster and parallel-field data. We obtain a catalog of $\sim400$ dropout galaxy candidates at $z\sim6-10$ whose UV absolute magnitudes reach $\sim-14$ mag. 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. We find that UV luminosity functions at $z\sim6-8$ have steep faint end slopes, $\alpha\sim-2$, and the evolution of UV luminosity densities show a smooth decline toward high redshift. We examine whether our HFF results consistently explain cosmic reionization with the Thomson scattering optical depth $\tau_{\rm e}$ measurement from the Planck satellite and the ionized hydrogen fraction $Q_{\rm HII}$ estimates at $z\lesssim7$ from the literature. We conduct $\chi^2$ minimization fitting of the model to the observational measurements, introducing three free parameters; the escape fraction $f_{\rm esc}$, the conversion factor of the UV luminosity to the ionizing photon emission rate $\xi_{\rm ion}$, and the faint limit of the galaxy UV luminosity function $M_{\rm trunc}$. We find that there exist reionizaiton scenarios that consistently explain all of the observational measurements with the allowed parameters of $f_{\rm esc} = 0.15^{+0.06}_{-0.02}$ and $M_{\rm trunc} > -12.5$ for $\log \xi_{\rm ion}/[{\rm erg}^{-1}{\rm Hz}] = 25.34$. Our results indicate that the length of the reionization period is $\Delta z = 4.1\pm1.7$ (for $0.1 < Q_{\rm HII} < 0.99$), which is consistent with the Planck's kinetic Sunyaev-Zel'dovich effect estimate.