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 $kappa$ and shear $gamma$. In 23% of these fields, a lens group contributes a $ge$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$^{+3}_{-2}$% on average when groups are ignored. In 67% of fields with total $kappa ge$ 0.01, line-of-sight groups contribute $gtrsim 2times$ 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 $gamma$-$kappa$ relation: $log(kappa_{rm{tot}}) = (1.94 pm 0.34) log(gamma_{rm{tot}}) + (1.31 pm 0.49)$ 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 $kappa$; for 19% of our fields, $kappa$ is $gtrsim 2gamma$. Thus, accurate cosmology using strong gravitational lenses requires precise measurement and correction for all significant structures in each lens field.