Great Optically Luminous Dropout Research Using Subaru HSC (GOLDRUSH).
  I. UV Luminosity Functions at $z \sim 4-7$ Derived with the Half-Million
  Dropouts on the 100 deg$^2$ Sky
  We study the UV luminosity functions (LFs) at $z\sim 4$, $5$, $6,$ and $7$
based on the deep large-area optical images taken by the Hyper Suprime-Cam
(HSC) Subaru strategic program (SSP). On the 100 deg$^2$ sky of the HSC SSP
data available to date, we make enormous samples consisting of a total of
579,565 dropout candidates at $z\sim 4-7$ by the standard color selection
technique, 358 out of which are spectroscopically confirmed by our follow-up
spectroscopy and other studies. We obtain UV LFs at $z \sim 4-7$ that span a
very wide UV luminosity range of $\sim 0.002 - 100 \, L_{\rm UV}^\ast$ ($-26 <
M_{\rm UV} < -14$ mag) by combining LFs from our program and the ultra-deep
Hubble Space Telescope legacy surveys. We derive three parameters of the
best-fit Schechter function, $\phi^\ast$, $M_{\rm UV}^\ast$, and $\alpha$, of
the UV LFs in the magnitude range where the AGN contribution is negligible, and
find that $\alpha$ and $\phi^\ast$ decrease from $z\sim 4$ to $7$ with no
significant evolution of $M_{\rm UV}^\ast$. Because our HSC SSP data bridge the
LFs of galaxies and AGNs with great statistical accuracy, we carefully
investigate the bright end of the galaxy UV LFs that are estimated by the
subtraction of the AGN contribution either aided with spectroscopy or the
best-fit AGN UV LFs. We find that the bright end of the galaxy UV LFs cannot be
explained by the Schechter function fits at $> 2 \sigma$ significance, and
require either double power-law functions or modified Schechter functions that
consider a magnification bias due to gravitational lensing.
