ENVIRONMENTAL-EFFECT ON THE ASSOCIATIONS OF BACKGROUND QUASARS WITH FOREGROUND OBJECTS .2. NUMERICAL SIMULATIONS

Using numerical simulations of cluster formation in the standard cold dark matter (CDM) model and in a low-density, flat CDM model with a co smological constant, we investigate the gravitational lensing explanat ion for the reported associations between background quasars and foreg round clusters. Under the thin-lens approximation and the unaffected-b ackground hypothesis, we show that the recently detected quasar overde nsity around clusters of galaxies on scales of similar to 10' cannot b e interpreted as a result of gravitational lensing by cluster matter o r by their environmental and projected matter along the line of sight, which is consistent with the analytical result based on the observed cluster and galaxy correlations. It appears very unlikely that uncerta inties in the modeling of the gravitational lensing can account for th e disagreement between the theoretical predictions and the observation s. We conclude that either the detected signal of the quasar-cluster a ssociations is a statistical fluke or the associations are generated b y mechanisms other than the magnification bias.