A Spectroscopic Survey of the Fields of 28 Strong Gravitational Lenses: Implications for H ₀

Strong gravitational lensing provides an independent measurement of the Hubble parameter (H ₀). 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 ≥1% convergence bias; in 57%, there is a similarly significant line-of-sight group. For the nine time-delay lens systems, H ₀ is overestimated by % on average when groups are ignored. In 67% of fields with total , line-of-sight groups contribute 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 3 of 10 doubles do, and the highest convergences due to lens groups are in quads. We calibrate the γ-κ relation: log(κ_tot) =(194 ±0.34)log (γ_tot)+(1.31 ±0.49) with an rms scatter of 0.34 dex. Although shear can be measured directly from lensed images, unlike convergence, it can be a poor predictor of convergence; 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.