What Fraction of Gravitational Lens Galaxies Lie in Groups?

We predict how the observed variations in galaxy populations with environment affect the number and properties of gravitational lenses in different environments. Two trends dominate: lensing strongly favors early-type galaxies, which tend to lie in dense environments, but dense environments tend to have a larger ratio of dwarf to giant galaxies than the field. The two effects nearly cancel, and the distribution of environments for lens and non-lens galaxies are not substantially different (lens galaxies are slightly less likely than non-lens galaxies to lie in groups and clusters). We predict that about 20% of lens galaxies are in bound groups (defined as systems with a line-of-sight velocity dispersion sigma in the range 200 < sigma < 500 km/s), and another roughly 3% are in rich clusters (sigma > 500 km/s). Therefore at least roughly 25% of lenses are likely to have environments that significantly perturb the lensing potential. If such perturbations do not significantly increase the image separation, we predict that lenses in groups have a mean image separation that is about 0.2'' smaller than that for lenses in the field and estimate that 20-40 lenses in groups are required to test this prediction with significance. The tail of the distribution of image separations is already illuminating. Although lensing by galactic potential wells should rarely produce lenses with image separations theta >~ 6'', two such lenses are seen among 49 known lenses, suggesting that environmental perturbations of the lensing potential can be significant. Further comparison of theory and data will offer a direct probe of the dark halos of galaxies and groups and reveal the extent to which they affect lensing estimates of cosmological parameters.