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Description
We present UV luminosity functions of dropout galaxies at z~6-10 with the complete Hubble Frontier Fields data. We obtain a catalog of ~450 dropout-galaxy candidates (350, 66, and 40 at z~6-7, 8, and 9, respectively), with UV absolute magnitudes that reach ~-14mag, ~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~6-8 have steep faint-end slopes, {alpha}~-2, and likely steeper slopes, {alpha}<~-2 at z~9-10. We also find that the evolution of UV luminosity densities shows a non-accelerated decline beyond z~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_HII_ at z<~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, Mtrunc 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_HII_<0.99), consistent with the recent estimate from Planck.
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