The Sloan Lens ACS Survey. VII. Elliptical galaxy scaling laws from direct observational mass measurements

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 M-lens within one-half effective radius (R-e/2) and the dimensional mass variable M-dim equivalent to G(-1) sigma(2)(e2)(R-e/2) to be log (M-lens/10(11) M-circle dot) = (1.03 +/- 0.04) log (M-dim/10(11) M-circle dot)+ (0.54 +/- 0.02) (where sigma(e2) is the projected stellar velocity dispersion within R-e/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)/M-dim]=(1.10 +/- 0.09)log(R/ R-e)+(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 f(DM) = 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.