Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs). V. Quasar
  Luminosity Function and Contribution to Cosmic Reionization at z = 6
  We present new measurements of the quasar luminosity function (LF) at $z \sim
6$, over an unprecedentedly wide range of the rest-frame ultraviolet luminosity
$M_{1450}$ from $-30$ to $-22$ mag. This is the fifth in a series of
publications from the Subaru High-$z$ Exploration of Low-Luminosity Quasars
(SHELLQs) project, which exploits the deep multi-band imaging data produced by
the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey. The LF was
calculated with a complete sample of 110 quasars at $5.7 \le z \le 6.5$, which
includes 48 SHELLQs quasars discovered over 650 deg$^2$, and 63 brighter
quasars discovered by the Sloan Digital Sky Survey and the Canada-France-Hawaii
Quasar Survey (including one overlapping object). This is the largest sample of
$z \sim 6$ quasars with a well-defined selection function constructed to date,
and has allowed us to detect significant flattening of the LF at its faint end.
A double power-law function fit to the sample yields a faint-end slope $\alpha
= -1.23^{+0.44}_{-0.34}$, a bright-end slope $\beta = -2.73^{+0.23}_{-0.31}$, a
break magnitude $M_{1450}^* = -24.90^{+0.75}_{-0.90}$, and a characteristic
space density $\Phi^* = 10.9^{+10.0}_{-6.8}$ Gpc$^{-3}$ mag$^{-1}$. Integrating
this best-fit model over the range $-18 < M_{1450} < -30$ mag, quasars emit
ionizing photons at the rate of $\dot{n}_{\rm ion} = 10^{48.8 \pm 0.1}$
s$^{-1}$ Mpc$^{-3}$ at $z = 6.0$. This is less than 10 % of the critical rate
necessary to keep the intergalactic medium ionized, which indicates that
quasars are not a major contributor to cosmic reionization.
