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 \pm 8 km s ^ { -1 } Mpc ^ { -1 } and 72 \pm 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 ( \eta = 2 ) .
This yields a value of \eta = 2.11 \pm 0.12 ( 3 \sigma ) for the mean profile when modeling with a prior on the Hubble constant , which is only consistent with isothermality within 3 \sigma .
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 .