Abstract
To examine the effect of neighboring galaxies on the gravitational lensing statistics, we performed numerical simulations of lensing by many galaxies. The models consist of a galaxy in the rich cluster like Coma, or a galaxy surrounded by field galaxies in $\Omega_0 = 1$ universe with $\Omega_{gal} = 0.1,\;\Omega_{gal} = 0.3\;or\;\Omega_{gal}=1.0\;,\;where\;\Omega_{gal}$ is the total mass in galaxies. Field galaxies either have the same mass or follow Schechter luminosity function and luminosity-velocity relation. Each lensing galaxy is assumed to be singular isothermal sphere (SIS) with finite cutoff radius. In most simulations, the lensing is mainly due to the single galaxy. But in $\Omega_{gal} = 3$ universe, one out of five simulations have 'collective lensing' event in which more than two galaxies collectively produce multiple images. These cases cannot be incorporated into the simple 'standard' lensing statistics calculations. In cases where 'collective lensing' does not occur, distribution of image separation changes from delta function to bimodal distribution due to shear induced by the surrounding galaxies. The amount of spread in the distribution is from a few $\%\;up\;to\;50\%$ of the mean image separation in case when the galaxy is in the Coma-like cluster or when the galaxy is in the field with $\Omega_{gal} = 0.1\;or\;\Omega_{gal}=0.3.$ The mean of the image separation changes less than $5\%$ compared with a single lens case. Cross section for multiple image lensing turns out to be relatively insensitive to the presence of the neighboring galaxies, changing less than $5\%$ for Coma-like cluster and $\Omega_{gal}=0.1,\;0.3$ universe cases. So we conclude that Coma-like cluster or field galaxies whose total mass density $\Omega_{gal}<0.3$ do not significantly affect the probability of multiple image lensing if we exclude the 'collective lensing' cases. However, the distribution of the image separations can be significantly affected especially if the 'collective lensing' cases are included. Therefore, the effects of surrounding galaxies may not be negligible when statistics of lensing is used to deduce the cosmological informations.