A Spectroscopic Survey of the Fields of 28 Strong Gravitational Lenses: Implications for &ITH&IT0

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 kappa and shear gamma. 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 11(-2)(+3)% on average when groups are ignored. In 67% of fields with total kappa >= 0.01, line-of-sight groups contribute greater than or similar to 2x 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 gamma-kappa relation: log(kappa(tot)) = (1.94 +/- 0.34)log(gamma(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, kappa is greater than or similar to 2 gamma. Thus, accurate cosmology using strong gravitational lenses requires precise measurement and correction for all significant structures in each lens field.