High-Redshift Quasars Found in Sloan Digital Sky Survey Commissioning Data. IV. Luminosity Function from the Fall Equatorial Stripe Sample

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Abstract
This is the fourth paper in a series aimed at finding high-redshift quasars from five-color (u'g'r'i'z') imaging data taken along the celestial equator by the Sloan Digital Sky Survey during its commissioning phase. In this paper, we use the color-selected sample of 39 luminous high-redshift quasars presented in Paper III to derive the evolution of the quasar luminosity function over the range 3.6 < z < 5.0 and -27.5 < M1450 < -25.5 (Ω = 1, H0 = 50 km s-1 Mpc-1). We use the selection function derived in Paper III to correct for sample incompleteness. The luminosity function is estimated using three different methods: (1) the 1/Va estimator; (2) a maximum likelihood solution, assuming that the density of quasars depends exponentially on redshift and as a power law in luminosity; and (3) Lynden-Bell's nonparametric C- estimator. All three methods yield consistent results. The luminous quasar density decreases by a factor of ~6 from z = 3.5 to z = 5.0, consistent with the decline seen from several previous optical surveys at z < 4.5. The luminosity function follows ψ(L) ∝ L-2.5 for z ~ 4 at the bright end, significantly flatter than the bright-end luminosity function ψ(L) ∝ L-3.5 found in previous studies for z < 3, suggesting that the shape of the quasar luminosity function evolves with redshift as well, and that the quasar evolution from z = 2 to z = 5 cannot be described as pure luminosity evolution. Possible selection biases and the effect of dust extinction on the redshift evolution of the quasar density are also discussed.