The Sloan Lens ACS Survey. VII. Elliptical Galaxy Scaling Laws from Direct Observational Mass Measurements

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Abstract
We use a sample of 53 massive early-type strong gravitational lens galaxies with well-measured redshifts (ranging from z = 0.06 to 0.36) and stellar velocity dispersions (between 175 and 400 km s−1) from the Sloan Lens ACS (SLACS) Survey to derive numerous empirical scaling relations. The ratio between central stellar velocity dispersion and isothermal lens-model velocity dispersion is nearly unity within errors. The SLACS lenses define a fundamental plane (FP) that is consistent with the FP of the general population of early-type galaxies. We measure the relationship between strong-lensing mass Mlens within one-half effective radius (Re/2) and the dimensional mass variable Mdim ≡ G−1σe22(Re/2) to be log (Mlens/1011 M☉) = (1.03 ± 0.04) log (Mdim/1011 M☉) + (0.54 ± 0.02) (where σe2 is the projected stellar velocity dispersion within Re/2). The near-unity slope indicates that the mass-dynamical structure of massive elliptical galaxies is independent of mass and that the "tilt" of the SLACS FP is due entirely to variation in total (luminous plus dark) mass-to-light ratio with mass. Our results imply that dynamical masses serve as a good proxies for true masses in massive elliptical galaxies. Regarding the SLACS lenses as a homologous population, we find that the average enclosed two-dimensional (2D) mass profile goes as log [M(< R)/Mdim] = (1.10 ± 0.09) log (R/Re) + (0.85 ± 0.03) , consistent with an isothermal (flat rotation curve) model when deprojected into three dimensions (3D). This measurement is inconsistent with the slope of the average projected aperture luminosity profile at a confidence level greater than 99.9%, implying a minimum dark matter fraction of fDM = 0.38 ± 0.07 within 1 effective radius. We also present an analysis of the angular mass structure of the lens galaxies, which further supports the need for dark matter inside one effective radius.
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