Gravitational Lensing of the Sloan Digital Sky Survey High‐Redshift Quasars

We predict the effects of gravitational lensing on the color-selectedflux-limited samples of z~4.3 and z>5.8 quasars, recently published by theSloan Digital Sky Survey (SDSS). Our main findings are: (i) The lensingprobability should be 1-2 orders of magnitude higher than for conventionalsurveys. The expected fraction of multiply-imaged quasars is highly sensitiveto redshift and the uncertain slope of the bright end of the luminosityfunction, beta_h. For beta_h=2.58 (3.43) we find that at z~4.3 and i*<20.0 thefraction is ~4% (13%) while at z~6 and z*<20.2 the fraction is ~7% (30%). (ii)The distribution of magnifications is heavily skewed; sources having theredshift and luminosity of the SDSS z>5.8 quasars acquire median magnificationsof med(mu_obs)~1.1-1.3 and mean magnifications of ~5-50. Estimates ofthe quasar luminosity density at high redshift must therefore filter outgravitationally-lensed sources. (iii) The flux in the Gunn-Peterson trough ofthe highest redshift (z=6.28) quasar is known to be f_lambda<3 10^-19erg/sec/cm^2/Angstrom. Should this quasar be multiply imaged, we estimate a 40%chance that light from the lens galaxy would have contaminated the same part ofthe quasar spectrum with a higher flux. Hence, spectroscopic studies of theepoch 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 thez>5.8 catalog varying by more than 0.5 magnitudes over the next decade. Themedian equivalent width would be lowered by ~20% with respect to the intrinsicvalue due to differential magnification of the continuum and emission-lineregions.Comment: 27 pages, 10 figures. Expansion on the discussion in astro-ph/0203116. Replaced with version accepted for publication in Ap