Gravitational Lensing of the SDSS High-Redshift Quasars

We predict the effects of gravitational lensing on the color-selected flux-limited samples of zs ∼ 4.3 and zs & 5.8 quasars, recently published by the Sloan Digital Sky Survey (SDSS). Our main findings are: (i) 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, βh. For βh = 2.58 (3.43) we find that at zs ∼ 4.3 and i ∗ < 20.0 the fraction is ∼ 4% (13%) while at zs ∼ 6 and z ∗ < 20.2 the fraction is ∼ 7% (30%). (ii) The distribution of magnifications is heavily skewed; sources having the redshift and luminosity of the SDSS zs & 5.8 quasars acquire median magnifications of med(μobs) ∼ 1.1–1.3 and mean magnifications of 〈μobs〉 ∼ 5–50. Estimates of the quasar luminosity density at high redshift must therefore filter out gravitationally-lensed sources. (iii) The flux in the Gunn-Peterson trough of the highest redshift (zs = 6.28) quasar is known to be fλ < 3 × 10 erg sec cmÅ. 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. (iv) Microlensing by stars should result in ∼ 1/3 of multiply imaged quasars in the zs & 5.8 catalog varying by more than 0.5 magnitudes 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 due to differential magnification of the continuum and emission-line regions. Subject headings: gravitational lenses: lens statistics, microlensing Quasars: luminosity function