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 {11}_-2⁺³% on average when groups are ignored. In 67% of fields with total κ ≥slant 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 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})=(1.94+/- 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.