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 _ { \mathrm { lens } } within one-half effective radius ( R _ { e } / 2 ) and the dimensional mass variable M _ { \mathrm { dim } } \equiv G ^ { -1 } \sigma _ { e 2 } ^ { 2 } ( R _ { e } / 2 ) to be \log _ { 10 } [ M _ { \mathrm { lens } } / 10 ^ { 11 } M _ { \odot } ] = ( 1.03 \pm 0.04 ) \log _ { 10 } [ M _ { % \mathrm { dim } } / 10 ^ { 11 } M _ { \odot } ] + ( 0.54 \pm 0.02 ) ( where \sigma _ { e 2 } 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 2D mass profile goes as \log _ { 10 } [ M ( < R ) / M _ { \mathrm { dim } } ] = ( 1.10 \pm 0.09 ) \log _ { 10 } [ R / R _ { e } ] + ( 0.85 % \pm 0.03 ) , consistent with an isothermal ( flat rotation curve ) model when de-projected into 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 _ { \mathrm { DM } } = 0.38 \pm 0.07 within one 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 .