We investigate in massive early-type galaxies the variation of their two-dimensional central fraction of dark over total mass and dark matter density as a function of stellar mass , central stellar velocity dispersion , effective radius , and central surface stellar mass density .
We use a sample of approximately 1.7 \times 10 ^ { 5 } galaxies from the Sloan Digital Sky Survey Data Release Seven ( SDSS DR7 ) at redshift smaller than 0.33 .
We apply conservative photometric and spectroscopic cuts on the SDSS DR7 and the MPA/JHU value-added galaxy catalogs , to select galaxies with physical properties similar to those of the lenses studied in the Sloan Lens ACS ( SLACS ) Survey .
The values of the galaxy stellar and total mass projected inside a cylinder of radius equal to the effective radius are obtained , respectively , by fitting the SDSS multicolor photometry with stellar population synthesis models , under the assumption of a Chabrier stellar initial mass function ( IMF ) , and adopting a one-component isothermal total mass model with effective velocity dispersion approximated by the central stellar velocity dispersion .
The plausibility of an isothermal model to represent the galaxy total mass distribution is supported by independent gravitational lensing and stellar dynamical analyses performed in the lens subsample , which is found here to represent nicely the entire galaxy sample .
We find that within the effective radius the stellar mass estimates differ from the total ones by only a relatively constant proportionality factor .
In detail , we observe that the values of the projected fraction of dark over total mass and the logarithmic values of the central surface dark matter density ( measured in M _ { \odot } \mathrm { kpc } ^ { -2 } ) have almost Gaussian probability distribution functions , with median values of 0.64 ^ { +0.08 } _ { -0.11 } and 9.1 ^ { +0.2 } _ { -0.2 } , respectively .
We discuss the observed correlations between these quantities and other galaxy global parameters and show that our results disfavor an interpretation of the tilt of the Fundamental Plane ( FP ) in terms of differences in the galaxy dark matter content and give useful information on the possible variations of the galaxy stellar IMF and dark matter density profile .
Finally , we provide some observational evidence on the likely significant contribution of dry minor mergers , feedback from active galactic nuclei , and/or coalescence of binary black holes on the formation and evolution of massive early-type galaxies .