The Pan-STARRS1 z > 5.6 Quasar Survey. III. The z ≈ 6 Quasar Luminosity Function

We present the z ≈ 6 type-1 quasar luminosity function (QLF), based on the Pan-STARRS1 (PS1) quasar survey. The PS1 sample includes 125 quasars at z ≈ 5.7-6.2, with -28 ≲ M ₁₄₅₀ ≲ -25. With the addition of 48 fainter quasars from the SHELLQs survey, we evaluate the z ≈ 6 QLF over -28 ≲ M ₁₄₅₀ ≲ -22. Adopting a double power law with an exponential evolution of the quasar density (Φ(z) ∝ 10 ^k(z-6); k = -0.7), we use a maximum likelihood method to model our data. We find a break magnitude of ${M}^{* }=-{26.38}_{-0.60}^{+0.79}\,\mathrm{mag}$ , a faint-end slope of $\alpha =-{1.70}_{-0.19}^{+0.29}$ , and a steep bright-end slope of $\beta =-{3.84}_{-1.21}^{+0.63}$ . Based on our new QLF model, we determine the quasar comoving spatial density at z ≈ 6 to be $n({M}_{1450}\lt -26)={1.16}_{-0.12}^{+0.13}\,{\mathrm{cGpc}}^{-3}$ . In comparison with the literature, we find the quasar density to evolve with a constant value of k ≈ -0.7, from z ≈ 7 to z ≈ 4. Additionally, we derive an ionizing emissivity of ${\epsilon }_{912}(z=6)={7.23}_{-1.02}^{+1.65}\times {10}^{22}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{Hz}}^{-1}\,{\mathrm{cMpc}}^{-3}$ , based on the QLF measurement. Given standard assumptions, and the recent measurement of the mean free path by Becker et al. at z ≈ 6, we calculate an H I photoionizing rate of Γ_{H I}(z = 6) ≈ 6 × 10^-16 s^-1, strongly disfavoring a dominant role of quasars in hydrogen reionization.