2004ApJ...612..660K

It is suspected that many strong gravitational lens galaxies lie in poor groups or rich clusters of galaxies, which modify the lens potentials. Unfortunately, little is actually known about the environments of most lenses, so environmental effects in lens models are often unconstrained and sometimes ignored. We show that such poor knowledge of environments introduces significant biases and uncertainties into a variety of lensing applications. Specifically, we create a mock poor group of 13 galaxies that resembles real groups, generate a sample of mock lenses associated with each member galaxy, and then analyze the lenses with standard techniques. We find that standard models of two-image (double) lenses, which neglect environment, grossly overestimate both the ellipticity of the lens galaxy (Δe/e∼0.5) and the Hubble constant (Δh/h∼0.22). Standard models of four-image (quad) lenses, which approximate the environment as a tidal shear, recover the ellipticity reasonably well (|Δe/e|≲0.24) but overestimate the Hubble constant (Δh/h∼0.15) and have significant (∼30%) errors in the millilensing analyses used to constrain the amount of substructure in dark matter halos. For both doubles and quads, standard models slightly overestimate the velocity dispersion of the lens galaxy (Δσ/σ∼0.06) and underestimate the magnifications of the images (Δµ/µ~-0.25). Standard analyses that use the statistics of lens populations to place limits on the dark energy overestimate Ω_Λ(by 0.05-0.14) and underestimate the ratio of quads to doubles (by a factor of 2). The systematic biases related to environment help explain some long-standing puzzles (such as the high observed quad/double ratio) but aggravate others (such as the low value of H₀inferred from lensing). Most of the biases are caused by neglect of the convergence (gravitational focusing) from the mass associated with the environment, but additional uncertainty is introduced by neglect of higher order terms in the lens potential. Fortunately, we show that directly observing and modeling lens environments should make it possible to remove the biases and reduce the uncertainties. Such sophisticated lensing analyses will require finding the other galaxies that are members of the lensing groups and measuring the group centroids and velocity dispersions, but they should reduce systematic effects associated with environments to the few percent level.