Modelling mass distribution in elliptical galaxies: mass profiles and their correlation with velocity dispersion profiles

We assemble a statistical set of global mass models for similar to 2000 nearly spherical Sloan Digital Sky Survey (SDSS) galaxies at a mean redshift of << z >> = 0.12 based on their aperture velocity dispersions and newly derived luminosity profiles in conjunction with published velocity dispersion profiles and empirical properties and relations of galaxy and halo parameters. When two-component (i.e. stellar plus dark) mass models are fitted to the SDSS aperture velocity dispersions, the predicted velocity dispersion profile (VP) slopes within the effective (i.e. projected half-light) radius R-eff match well the distribution in observed elliptical galaxies. From a number of input variations the models exhibit for the radial range 0.1R(eff) < r < R-eff a tight correlation <> = (1.865 +/- 0.008) + (-4.93 +/- 0.15)<> where <> is the mean slope absolute value of the total mass density and <> is the mean slope of the velocity dispersion profile, which leads to a super-isothermal <> = 2.15 +/- 0.04 for <> = -0.058 +/- 0.008 in observed elliptical galaxies. Furthermore, the successful two-component models appear to imply a typical slope curvature pattern in the total mass profile because for the observed steep luminosity (stellar mass) profile and the weak lensing inferred halo profile at large radii a total mass profile with monotonically varying slope would require too high dark matter density in the optical region giving rise to too large aperture velocity dispersion and too shallow VP.