Аннотация
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 $\tau_e$ measurement from the Planck
satellite and the ionized hydrogen fraction $Q_HII$ estimates at
$złesssim7$ from the literature. We conduct $\chi^2$ minimization fitting of
the model to the observational measurements, introducing three free parameters;
the escape fraction $f_esc$, the conversion factor of the UV luminosity
to the ionizing photon emission rate $\xi_ion$, and the faint limit of
the galaxy UV luminosity function $M_trunc$. We find that there exist
reionizaiton scenarios that consistently explain all of the observational
measurements with the allowed parameters of $f_esc =
0.15^+0.06_-0.02$ and $M_trunc > -12.5$ for $\xi_ion/\rm
erg^-1Hz = 25.34$. Our results indicate that the length of the
reionization period is $\Delta z = 4.1\pm1.7$ (for $0.1 < Q_HII < 0.99$),
which is consistent with the Planck's kinetic Sunyaev-Zel'dovich effect
estimate.
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