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 ̃ 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 multiband imaging data produced by the Hyper Suprime-Cam Subaru Strategic Program survey. The LF was calculated with a complete sample of 110 quasars at 5.7 ≤ z ≤ 6.5, which includes 48 SHELLQs quasars discovered over 650 deg2 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 ̃ 6 quasars with a well-defined selection function constructed to date, which 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 α =-{1.23}-0.34+0.44, a bright-end slope β =-{2.73}-0.31+0.23, a break magnitude {M}1450* =-{24.90}-0.90+0.75, and a characteristic space density {{{Φ }}}* ={10.9}-6.8+10.0 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}}ion}={10}48.8+/- 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