2016ApJ...833..222J

We present the discovery of nine quasars at z∼6 identified in the Sloan Digital Sky Survey (SDSS) imaging data. This completes our survey of z∼6 quasars in the SDSS footprint. Our final sample consists of 52 quasars at 5.7<z\leqslant6.4, including 29 quasars with z_AB\leqslant20 mag selected from 11,240 deg² of the SDSS single-epoch imaging survey (the main survey), 10 quasars with 20\leqslantz_AB\leqslant20.5 selected from 4223 deg² of the SDSS overlap regions (regions with two or more imaging scans), and 13 quasars down to z_AB~22 mag from the 277 deg² in Stripe 82. They span a wide luminosity range of -29.0\leqslantM₁₄₅₀\leqslant-24.5. This well-defined sample is used to derive the quasar luminosity function (QLF) at z∼6. After combining our SDSS sample with two faint (M₁₄₅₀\geqslant-23 mag) quasars from the literature, we obtain the parameters for a double power-law fit to the QLF. The bright-end slope β of the QLF is well constrained to be β=-2.8±0.2. Due to the small number of low-luminosity quasars, the faint-end slope α and the characteristic magnitude M₁₄₅₀^* are less well constrained, with α=-1.90_–0.44^+0.58 and M^*=-25.2_–3.8^+1.2 mag. The spatial density of luminous quasars, parametrized as ρ(M₁₄₅₀←26,z)=ρ(z=6)10^k(z–6), drops rapidly from z∼5 to 6, with k=-0.72±0.11. Based on our fitted QLF and assuming an intergalactic medium (IGM) clumping factor of C = 3, we find that the observed quasar population cannot provide enough photons to ionize the z∼6 IGM at ∼90% confidence. Quasars may still provide a significant fraction of the required photons, although much larger samples of faint quasars are needed for more stringent constraints on the quasar contribution to reionization.