Hubble Frontier Fields First Complete Cluster Data: Faint Galaxies at
  $z\sim 5-10$ for UV Luminosity Functions and Cosmic Reionization
  We present the comprehensive analyses of faint dropout galaxies up to
$z\sim10$ with the first full-depth data set of Abell 2744 lensing cluster and
parallel fields observed by the Hubble Frontier Fields (HFF) program. We
identify $54$ dropouts at $z\sim5-10$ in the HFF fields, and enlarge the size
of $z\sim9$ galaxy sample obtained to date. Although the number of highly
magnified ($\mu\sim10$) galaxies is small due to the tiny survey volume of
strong lensing, our study reaches the galaxies' intrinsic luminosities
comparable to the deepest-field HUDF studies. We derive UV luminosity functions
with these faint dropouts, carefully evaluating the combination of
observational incompleteness and lensing effects in the image plane by
intensive simulations including magnification, distortion, and multiplication
of images, with the evaluations of mass model dependences. Our results confirm
that the faint-end slope, $\alpha$, is as steep as $-2$ at $z\sim6-8$, and
strengthen the evidence of the rapid decrease of UV luminosity densities,
$\rho_\mathrm{UV}$, at $z>8$ from the large $z\sim9$ sample. We examine whether
the rapid $\rho_\mathrm{UV}$ decrease trend can reconcile with the large
Thomson scattering optical depth, $\tau_\mathrm{e}$, measured by CMB
experiments allowing a large space of free parameters such as average ionizing
photon escape fraction and stellar-population dependent conversion factor. No
parameter set can reproduce both the rapid $\rho_\mathrm{UV}$ decrease and the
large $\tau_\mathrm{e}$. It is possible that the $\rho_\mathrm{UV}$ decrease
moderates at $z\gtrsim11$, that the free parameters significantly evolve
towards high-$z$, or that there exist additional sources of reionization such
as X-ray binaries and faint AGNs.
