The effects of BCGs on the statistics of large-separation lensed quasars by clusters

We study the statistics of large-separation multiply-imag ed quasars lensed by clusters of galaxies. In particular, we examine how the observed brightest cluster galaxies (BCGs) affect the predicted numbers of wide-separation lenses. We model the lens as an NFW-profiled dark matter halo with a truncated sing ular isothermal sphere to represent the BCG in its center. We mainly make predictions for the Sloan Digital Sky Survey Quasar Lens Search (SQLS) sample from the Data Release 5 (DR5) in two standardCDM cosmological models: a model with matter density M = 0.3 and �8 = 0.9, as is usually adopted in the literature (�CDM1), and a model suggested by the WMAP seven-year (WMAP7) data withM = 0.266 and�8 = 0.801. We also study the lensing properties for the WMAP3 cosmology in order to compare with the previous work. We find that BCGs in the centers of clusters sig nificantly enhance the lensing efficiency by a factor of 2 ∼ 3 compared with that of NFW-profiled pure dark matter halos. In addition, the dependence of mass ratios of BCGs to their host halos on the host halo masses reduces the lensing rate by ∼ 20% from assuming a constant ratio as in previous studies, but considering the evolution of this ratio with redshift out to z ∼ 1 would reduce it by ∼ 3%. Moreover, we predict that the numbers of lensed quasars with image separations larger than 10 '' in the statistical sample of SQLS from DR5 are 1.22 and 0.47, respectively forCDM1 and WMAP7 and0.73 and 0.33 for separations between 10 '' and 20 '' , which are consistent with the only observed cluster lens with such a large separation in the complete SQLS sample.