Radial density profiles of time-delay lensing galaxies

We present nonparametric radial mass profiles for 10 QSO strong-lensing galaxies. Five of the galaxies have profiles close to ρ(r) ∝ r ^-2, while the rest are closer to r^-1, consistent with an NFW profile. The former are all relatively isolated early types and dominated by their stellar light. The latter-although the modeling code did not know this-are either in clusters, or have very high mass-to-light ratios, suggesting dark matter-dominant lenses (one is actually a pair of merging galaxies). The same models give H₀^-1 = 15.2_-1.7^+2.5 Gyr (H₀ = 64_-8⁺⁹ km s^-1 Mpc ^-1 ), consistent with a previous determination. When tested on simulated lenses taken from a cosmological hydrodynamical simulation, our modeling pipeline recovers both H₀ and ρ(r) within estimated uncertainties. Our result is contrary to some recent claims that lensing time delays imply either a low H⁰ or galaxy profiles much steeper than r^-2. We diagnose these claims as resulting from an invalid modeling approximation: that small deviations from a power-law profile have a small effect on lensing time delays. In fact, as we show using both perturbation theory and numerical computation from a galaxy formation simulation, a first-order perturbation of an isothermal lens can produce a zeroth-order change in the time delays.