Quantifying Environmental and Line-of-Sight Effects in Models of Strong
  Gravitational Lens Systems
  Matter near a gravitational lens galaxy or projected along the line of sight
(LOS) can affect strong lensing observables by more than contemporary
measurement errors. We simulate lens fields with realistic three-dimensional
mass configurations (self-consistently including voids), and then fit mock
lensing observables with increasingly complex lens models to quantify biases
and uncertainties associated with different ways of treating the lens
environment (ENV) and LOS. We identify the combination of mass, projected
offset, and redshift that determines the importance of a perturbing galaxy for
lensing. Foreground structures have a stronger effect on the lens potential
than background structures, due to nonlinear effects in the foreground and
downweighting in the background. There is dramatic variation in the net
strength of ENV/LOS effects across different lens fields; modeling fields
individually yields stronger priors for $H_0$ than ray tracing through $N$-body
simulations. Models that ignore mass outside the lens yield poor fits and
biased results. Adding external shear can account for tidal stretching from
galaxies at redshifts $z \ge z_{\rm lens}$, but it requires corrections for
external convergence and cannot reproduce nonlinear effects from foreground
galaxies. Using the tidal approximation is reasonable for most perturbers as
long as nonlinear redshift effects are included. Even then, the scatter in
$H_0$ is limited by the lens profile degeneracy. Asymmetric image
configurations produced by highly elliptical lens galaxies are less sensitive
to the lens profile degeneracy, so they offer appealing targets for precision
lensing analyses in future surveys like LSST and Euclid.
