Full-data Results of Hubble Frontier Fields: UV Luminosity Functions at z similar to 6-10 and a Consistent Picture of Cosmic Reionization

We present UV luminosity functions of dropout galaxies at z similar to 6-10 with the complete Hubble Frontier Fields data. We obtain a catalog of similar to 450 dropout-galaxy candidates (350, 66, and 40 at z similar to 6-7, 8, and 9, respectively), with UV absolute magnitudes that reach similar to-14 mag, similar to 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 similar to 6-8have steep faint-end slopes, alpha similar to -2, and likely steeper slopes, alpha less than or similar to -2 at z similar to 9-10. We also find that the evolution of UV luminosity densities shows a non-accelerated decline beyond z similar to 8 in the case of M-trunc = -15, but an accelerated one in the case of M-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(H II) at z less than or similar to 7 based on the standard analytic reionization model. We find that reionization scenarios exist that consistently explain all of the observational measurements with the allowed parameters of f(esc) = 0.17(-0.03)(+0.07) and M-trunc > -14.0 for log xi(ion)/[erg(-1) Hz]= 25.34 , where f(esc) is the escape fraction, M-trunc is the faint limit of the UV luminosity function, and xi(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(H) (II) < 0.99), consistent with the recent estimate from Planck.