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

We introduce a self-similar mass model for early-type galaxies, and constrainit using the aperture mass-radius relations determined from the geometries of22 gravitational lenses. The model consists of two components: a concentratedcomponent which traces the light distribution, and a more extended power-lawcomponent (rho propto r^-n) which represents the dark matter. We find that lensgalaxies have total mass profiles which are nearly isothermal, or slightlysteeper, on the several-kiloparsec radial scale spanned by the lensed images.In the limit of a single-component, power-law radial profile, the model impliesn=2.07+/-0.13, consistent with isothermal (n=2). Models in which mass traceslight are excluded at >99 percent confidence. An n=1 cusp (such as theNavarro-Frenk-White profile) requires a projected dark matter mass fraction off_cdm = 0.22+/-0.10 inside 2 effective radii. These are the best statisticalconstraints yet obtained on the mass profiles of lenses, and provide clearevidence for a small but non-zero dark matter mass fraction in the innerregions of early-type galaxies. In addition, we derive the first strong lensingconstraint on the relation between stellar mass-to-light ratio (Upsilon) andgalaxy luminosity (L): Upsilon propto L^[0.14 (+0.16)(-0.12)], which isconsistent with the relation suggested by the fundamental plane. Finally, weapply our self-similar mass models to current problems regarding theinterpretation of time delays and flux ratio anomalies in gravitational lenssystems.Comment: 30 pages including 6 figures, to be published in Ap