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 ~2,000 nearly
spherical SDSS galaxies at a mean redshift of 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 radius R_eff match
well the distribution in observed elliptical galaxies. In contrast, the
single-component models cannot reproduce the VP slope distribution. From a
number of input variations the models exhibit for the radial range 0.1 R_eff <
r < R_eff a tight correlation <gamma_e>=(1.865+/-0.008)+(-4.93+/-0.15)<eta>
where <gamma_e> is the mean slope absolute value of the total mass density and
<eta> is the mean slope of the velocity dispersion profile, which leads to a
super-isothermal <gamma_e> = 2.15+/-0.04 for <eta>=-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 DM density in the optical region giving
rise to too large aperture velocity dispersion and too shallow VP.
