Strong gravitational lensing provides an independent measurement of the
Hubble parameter (H0). One remaining systematic is a bias from the
additional mass due to a galaxy group at the lens redshift or along the
sightline. We quantify this bias for more than 20 strong lenses that have
well-sampled sightline mass distributions, focusing on the convergence κ
and shear γ. In 23% of these fields, a lens group contributes a ≥1%
convergence bias; in 57%, there is a similarly significant line-of-sight group.
For the nine time delay lens systems, H0 is overestimated by 11−2+3%
on average when groups are ignored. In 67% of fields with total κ≥
0.01, line-of-sight groups contribute ≳2× more convergence than
do lens groups, indicating that the lens group is not the only important mass.
Lens environment affects the ratio of four (quad) to two (double) image
systems; all seven quads have lens groups while only three of 10 doubles do,
and the highest convergences due to lens groups are in quads. We calibrate the
γ-κ relation: log(κtot)=(1.94±0.34)log(γtot)+(1.31±0.49) with a rms scatter of 0.34 dex.
Shear, which, unlike convergence, can be measured directly from lensed images,
can be a poor predictor of κ; for 19% of our fields, κ is
≳2γ. Thus, accurate cosmology using strong gravitational lenses
requires precise measurement and correction for all significant structures in
each lens field.Comment: 34 pages, 11 figures, accepted for publication in Ap