Projected central dark matter fractions and densities in massive early-type galaxies from the sloan digital sky survey

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 ~ 1.7 x 10^5 galaxies from the SDSS DR7 at redshift smaller than 0.33. We apply conservative photometric and spectroscopic cuts to select galaxies with physical properties similar to those of the lenses studied in the 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 IMF, and adopting a one-component isothermal total mass model with effective velocity dispersion approximated by the central stellar velocity dispersion. 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_{Sun} 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. Our results disfavor an interpretation of the tilt of the 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.