A survey of z ∼ 6 Quasars in the sloan digital sky survey deep stripe. I. A flux-limited sample at z_AB < 21

We present the discovery of five quasars at z 6 selected from 260 deg ² of the Sloan Digital Sky Survey (SDSS) southern survey, a deep imaging survey obtained by repeatedly scanning a stripe along the celestial equator. The five quasars with 20 < z_AB < 21 are 1-2 magnitudes fainter than the luminous z 6 quasars discovered in the SDSS main survey. One of them was independently discovered by the UKIRT Infrared Deep Sky Survey. These quasars, combined with another z 6 quasar known in this region, make a complete flux-limited quasar sample at z_AB < 21. The sample spans the redshift range 5.85 ≤ z ≤ 6.12 and the luminosity range -26.5 ≤ M ₁₄₅₀ ≤ -25.4 (H ₀ = 70 km s^-1 Mpc ^-1, Ω_m = 0.3, and Ω_Λ = 0.7). We use the 1/V_a method to determine that the comoving quasar spatial density at 〈z〉 = 6.0 and 〈M ₁₄₅₀〉 = -25.8 is (5.0 2.1) × 10^-9 Mpc^-3 mag^-1. We model the bright-end quasar luminosity function (QLF) at z 6 as a power law Φ(L ₁₄₅₀) L ^β ₁₄₅₀. The slope β calculated from a combination of our sample and the luminous SDSS quasar sample is -3.1 0.4, significantly steeper than the slope of the QLF at z 4. Based on the derived QLF, we find that the quasar/active galactic nucleus (AGN) population cannot provide enough photons to ionize the intergalactic medium (IGM) at z 6 unless the IGM is very homogeneous and the luminosity (L*₁₄₅₀) at which the QLF power law breaks is very low.