Radial density profiles of time-delay lensing galaxies

Abstract

We present non-parametric radial mass profiles for ten QSO strong lensing galaxies. Five of the galaxies have profiles close to $ρ(r)\propto r^{-2}$, 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 --though the modeling code did not know this-- are either in clusters, or have very high mass-to-light, suggesting dark-matter dominant lenses (one is a actually pair of merging galaxies). The same models give $H_0^{-1} = 15.2_{-1.7}^{+2.5}\Gyr$ ($H_0 = 64_{-9}^{+8} \legacy$), consistent with a previous determination. When tested on simulated lenses taken from a cosmological hydrodynamical simulation, our modeling pipeline recovers both H_0 and $ρ(r)$ within estimated uncertainties. Our result is contrary to some recent claims that lensing time delays imply either a low H_0 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 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.