Self‐similar Models for the Mass Profiles of Early‐Type Lens Galaxies

We introduce a self-similar mass model for early-type galaxies and constrain it using the aperture mass-radius relations determined from the geometries of 22 gravitational lenses. The model consists of two components: a concentrated component, which traces the light distribution, and a more extended power-law component (ρ ∝ r - n ), which represents the dark matter. We find that lens galaxies have total mass profiles that are nearly isothermal, or slightly steeper, on the several-kiloparsec radial scale spanned by the lensed images. In the limit of a single-component, power-law radial profile, the model implies n = 2.07 ± 0.13, consistent with isothermal ( n = 2). Models in which mass traces light are excluded at higher than 99% confidence. An n = 1 cusp (such as the Navarro-Frenk-White profile) requires a projected dark matter mass fraction of f cdm = 0.22 ± 0.10 inside two effective radii. These are the best statistical constraints yet obtained on the mass profiles of lenses and provide clear evidence for a small but nonzero dark matter mass fraction in the inner regions of early-type galaxies. In addition, we derive the first strong-lensing constraint on the relation between the stellar mass-to-light ratio ϒ and galaxy luminosity L , ϒ ∝ L , which is consistent with the relation suggested by the fundamental plane. Finally, we apply our self-similar mass models to current problems regarding the interpretation of time delays and flux ratio anomalies in gravitational lens systems.