A simple analysis of halo density profiles using gravitational lensing time delays

Gravitational lensing time delays depend upon the Hubble constant and the density distribution of the lensing galaxies. This allows one to either model the lens and estimate the Hubble constant, or to use a prior on the Hubble constant from other studies and investigate what the preferred density distribution is. Some studies have required compact dark matter halos (constant M/L ratio) in order to reconcile gravitational lenses with the HST/WMAP value of the Hubble constant (72 ± 8 km s-1 Mpc-1 and 72 ± 5 km s-1 Mpc-1, respectively). This is in direct contradiction with X-ray, stellar dynamical, and weak lensing studies, which all point towards extended halos and isothermal density profiles. In this work, we examine an up-to-date sample of 13 lensing galaxies resulting in a data set consisting of 21 time delays. We select systems in which there is a single primary lensing galaxy (e.g. excluding systems undergoing mergers). Analysis is performed using analytic models based upon a power-law density profile ($\rho\propto r^{-\eta}$) of which the isothermal profile is a special case (η = 2). This yields a value of η = 2.11 ± 0.12 (3σ) for the mean profile when modeling with a prior on the Hubble constant, which is only consistent with isothermality within 3σ. Note that this is a formal error from our calculations, and does not include the impact of sample selection or simplifications in the lens modeling. We conclude that time delays are a useful probe of density profiles, in particular as a function of the environment in which the lens resides, when combined with a prior on the Hubble constant.