2002ApJ...578...25K

Gravitational lens time delays depend on the Hubble constant, the observed image positions, and the surface mass density of the lens in the annulus between the images. Simple time delay lenses like PG 1115+80, SBS 1520+530, B1600+434, PKS 1830-211, and HE 2149-2745 have H₀=A(1-<κ>)+B<κ>(η-1), where the two coefficients A≃90 km.s^–1.Mpc^–1 and B≃10 km.s^–1.Mpc^–1 depend on the measured delays and the observed image positions, <κ> is the mean surface density in the annulus between the images, and there is a small correction from the logarithmic slope η≃2 of the density profile, κ∝R^1–η, in the annulus. These five systems are very homogeneous since for fixed H₀=100 h km.s^–1.Mpc^–1 they must have the same surface density, <κ≥1.11-1.22h±0.04, with an upper bound of σ_κ<0.07 on any dispersion in <κ> beyond those due to the measurement errors. If the lenses have their expected dark halos, <κ≥∼0.5 and H₀≃51±5 km.s^–1.Mpc^–1, while if they have constant mass-to-light ratios, <κ≥∼0.1-0.2 and H₀≃73±8 km.s^–1.Mpc^–1. More complicated lenses with multiple components or strong perturbations from nearby clusters, like RX J0911+0551 and Q0957+561, are easily recognized because they have significantly different coefficients.