Gravitational lensing of the sloan digital sky survey high-redshift quasars

We predict the effects of gravitational lensing on the color-selected flux-limited samples of z_s ∼ 4.3 and z_s≳5.8 quasars, recently published by the Sloan Digital Sky Survey (SDSS). Our main findings are the following: (1) The lensing probability should be 1-2 orders of magnitude higher than for conventional surveys. The expected fraction of multiply imaged quasars is highly sensitive to redshift and the uncertain slope of the bright end of the luminosity function, β_h. For β_h = 2.58 (3.43) we find that at z_s ∼ 4.3 and i* < 20.0 the fraction is ∼4% (13%), while at z_s ∼ 6 and z* < 20.2 the fraction is ∼7% (30%). (2) The distribution of magnifications is heavily skewed; sources having the redshift and luminosity of the SDSS z_s≳5.8 quasars acquire median magnifications of med(μ_obs) ∼ 1.1-1.3 and mean magnifications of (μ _obs) ∼ 5-50. Estimates of the quasar luminosity density at high redshift must therefore filter out gravitationally lensed sources. (3) The flux in the Gunn-Peterson trough of the highest redshift (z_s = 6.28) quasar is known to be fλ < 3 × 10^-19 ergs s ^-1 cm^-2 Å^-1. Should this quasar be multiply imaged, we estimate a 40% chance that light from the lens galaxy would have contaminated the same part of the quasar spectrum with a higher flux. Hence, spectroscopic studies of the epoch of reionization need to account for the possibility that a lens galaxy, which boosts the quasar flux, also contaminates the Gunn-Peterson trough. (4) Microlensing by stars should result in ∼1/3 of multiply imaged quasars in the Z_s≳5.8 catalog varying by more than 0.5 mag over the next decade. The median emission-line equivalent width of multiply imaged quasars would be lowered by ∼20% with respect to the intrinsic value because of differential magnification of the continuum and emission-line regions.