A Survey of z > 5.8 Quasars in the Sloan Digital Sky Survey. I. Discovery of Three New Quasars and the Spatial Density of Luminous Quasars at z ∼ 6^{* **}

We present the results from a survey of i-dropout objects selected from ∼1550 deg² of multicolor imaging data from the Sloan Digital Sky Survey to search for luminous quasars at z ≳ 5.8. Objects with i*-z* > 2.2 and z* < 20.2 are selected, and follow-up J-band photometry is used to separate L- and T-type cool dwarfs from high-redshift quasars. We describe the discovery of three new quasars, SDSSp J083643.85+005453.3 (z = 5.82), J130608.26+035626.3 (z = 5.99), and J103027.10+052455.0 (z = 6.28). The quasar SDSSp J083643.85+005453.3 is a radio source with flux of 1.1 mJy at 20 cm. The spectra of all three quasars show strong and broad Lyα + N V emission lines and very strong Lyα forest absorption, with a mean continuum decrement D_A > 0.90. The ARC 3.5 m spectrum of SDSSp J103027.10+052455.0 shows that over a range of ∼300 Å immediately blueward of the Lyα emission, the average transmitted flux is only 0.003 ± 0.020 times that of the continuum level, consistent with zero flux over a ∼300 Å range of the Lyα forest region and suggesting a tentative detection of the complete Gunn-Peterson trough. The existence of strong metal lines in the quasar spectra suggests early metal enrichment in the quasar environment. The three new objects, together with the previously published z = 5.8 quasar SDSSp J104433.04-012502.2, form a complete color-selected flux-limited sample at z ≳ 5.8. We estimate the selection function of this sample, taking into account the estimated variations in the quasar spectral energy distribution, as well as observational photometric errors. We find that at z = 6, the comoving density of luminous quasars at M₁₄₅₀ < -26.8 (H₀ = 50 km s^-1 Mpc^-1, Ω = 1) is 1.1 × 10^-9 Mpc^-3. This is a factor of ∼2 lower than that at z ∼ 5 and is consistent with an extrapolation of the observed quasar evolution at z < 5. Using the current sample, we discuss the constraint on the shape of the quasar luminosity function and the implications for the contribution of quasars to the ionizing background at z ∼ 6. The luminous quasars discussed in the paper have central black hole masses of several times 10⁹ M_⊙ by the Eddington argument, with likely dark halo masses on the order of 10¹³ M_⊙. Their observed space density provides a sensitive test of models of quasar and galaxy formation at high redshift.