The Pan-STARRS1 $\mathbf{z>5.6}$ Quasar Survey: III. The $\mathbf{z\approx6}$ Quasar Luminosity Function

We present the $z\!\approx\!6$ type-1 quasar luminosity function (QLF) based on the Pan-STARRS1 (PS1) quasar survey. The PS1 sample includes 125 quasars at $z\approx5.7-6.2$ with $-28\lesssim M_{1450}\lesssim-25$. Complemented by 48 fainter quasars from the SHELLQs survey, we evaluate the $z\approx6$ QLF over $-28\lesssim M_{1450}\lesssim-22$. Adopting a double power law with an exponential evolution of the quasar density ($Φ(z)\propto10^{k(z-6)}$; $k=-0.7$), we use a maximum likelihood method to model our data. We find a break magnitude of $M^*=-26.38_{-0.60}^{+0.79}\,\text{mag}$, a faint end slope of $α=-1.70_{-0.19}^{+0.29}$, and a steep bright end slope with $β=-3.84_{-1.21}^{+0.63}$. Based on our new QLF model we determine the quasar comoving spatial density at $z\!\approx\!6$ to be $n( M_{1450}<-26)=1.16_{-0.12}^{+0.13}\,\text{cGpc}^{-3}$. In comparison with the literature, we find the quasar density to evolve with a constant value of $k\approx-0.7$ from $z\approx7$ to $z\approx4$. Additionally, we derive an ionizing emissivity of $ε_{912}(z=6) =7.23_{-1.02}^{+1.65}\times 10^{22}\,\text{erg}\,\text{s}^{-1}\text{Hz}^{-1}\text{cMpc}^{-3}$ based on the QLF measurement. Given standard assumptions and the recent measurement of the mean free path of Becker et al. (2021) at $z\approx6$ we calculate an HI photoionizing rate of $Γ_{\text{HI}}(z{=}6) \approx 6 \times10^{-16}\,\text{s}^{-1}$, strongly disfavoring a dominant role of quasars in hydrogen reionization.