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

Abstract

We assemble a statistical set of global mass models for ̃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 Reff match well the distribution in observed elliptical galaxies. From a number of input variations the models exhibit for the radial range 0.1Reff < r < Reff a tight correlation 〈γe〉 = (1.865 ± 0.008) + (-4.93 ± 0.15)〈γrlang; where 〈γe〉 is the mean slope absolute value of the total mass density and 〈γ〉 is the mean slope of the velocity dispersion profile, which leads to a super-isothermal 〈γe〉 = 2.15 ± 0.04 for 〈γ〉 = -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. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.