Radial Density Profiles of Time‐Delay Lensing Galaxies

Abstract

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 H = 15.2 Gyr (H0 = 64 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.