A SURVEY of LUMINOUS HIGH-REDSHIFT QUASARS with SDSS and WISE. II. the BRIGHT END of the QUASAR LUMINOSITY FUNCTION at z ∼ 5

This is the second paper in a series on a new luminous z ∼ 5 quasar survey using optical and near-infrared colors. Here we present a new determination of the bright end of the quasar luminosity function (QLF) at z ∼ 5. Combining our 45 new quasars with previously known quasars that satisfy our selections, we construct the largest uniform luminous z ∼ 5 quasar sample to date, with 99 quasars in the range of 4.7 ≤ z < 5.4 and -29 < M ₁₄₅₀ ≤ -26.8, within the Sloan Digital Sky Survey (SDSS) footprint. We use a modified 1/V _a method including flux limit correction to derive a binned QLF, and we model the parametric QLF using maximum likelihood estimation. With the faint-end slope of the QLF fixed as α = -2.03 from previous deeper samples, the best fit of our QLF gives a flatter bright end slope β = -3.58 ± 0.24 and a fainter break magnitude = -26.98 ± 0.23 than previous studies at similar redshift. Combined with previous work at lower and higher redshifts, our result is consistent with a luminosity evolution and density evolution model. Using the best-fit QLF, the contribution of quasars to the ionizing background at z ∼ 5 is found to be 18%-45% with a clumping factor C of 2-5. Our sample suggests an evolution of radio loud fraction with optical luminosity but no obvious evolution with redshift.