The Pan-STARRS1 $\mathbf{z}>\mathbf{5.6}$ Quasar Survey: III. The $\mathbf{z}\approx \mathbf{6}$ Quasar Luminosity Function

We present the $z\text{\hspace{0.17em}⁣}\approx \text{\hspace{0.17em}⁣}6$ type-1 quasar luminosity function (QLF) based on the Pan-STARRS1 (PS1) quasar survey. The PS1 sample includes 125 quasars at $z\approx 5.7-6.2$ with $-28\lesssim M_{1450}\lesssim -25$. Complemented by 48 fainter quasars from the SHELLQs survey, we evaluate the $z\approx 6$ QLF over $-28\lesssim M_{1450}\lesssim -22$. Adopting a double power law with an exponential evolution of the quasar density ($\mathrm{\Phi }(z)\propto {10}^{k(z-6)}$; $k=-0.7$), we use a maximum likelihood method to model our data. We find a break magnitude of $M^{\ast }=-26.38_{-0.60}^{+0.79}\text{mag}$, a faint end slope of $\alpha =-1.70_{-0.19}^{+0.29}$, and a steep bright end slope with $\beta =-3.84_{-1.21}^{+0.63}$. Based on our new QLF model we determine the quasar comoving spatial density at $z\text{\hspace{0.17em}⁣}\approx \text{\hspace{0.17em}⁣}6$ 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 $z\approx 7$ to $z\approx 4$. Additionally, we derive an ionizing emissivity of ${\epsilon }_{912}(z=6)=7.23_{-1.02}^{+1.65}\times {10}^{22}\text{erg}{\text{s}}^{-1}{\text{Hz}}^{-1}{\text{cMpc}}^{-3}$ based on the QLF measurement. Given standard assumptions and the recent measurement of the mean free path of Becker et al. (2021) at $z\approx 6$ we calculate an HI photoionizing rate of ${\mathrm{\Gamma }}_{\text{HI}}(z=6)\approx 6\times {10}^{-16}{\text{s}}^{-1}$, strongly disfavoring a dominant role of quasars in hydrogen reionization.