Dark matter in elliptical galaxies - I. Is the total mass density profile of the NFW form or even steeper?

Elliptical galaxies are modelled as Sersic luminosity distributions with density profiles (DPs) for the total mass adopted from the DPs of haloes within dissipationless ACDM (cold dark matter) N-body simulations. Ellipticals turn out to be inconsistent with cuspy low-concentration NFW models representing the total mass distribution, neither are they consistent with a steeper -1.5 inner slope, nor with the shallower models proposed by Navarro et al., nor with NFW models 10 times more concentrated than predicted, as deduced from several X-ray observations - the mass models, extrapolated inwards, lead to local mass-to-light ratios that are smaller than the stellar value inside an effective radius (R-e), and to central aperture velocity dispersions that are much smaller than observed. This conclusion remains true as long as there is no sharp steepening (slope < -2) of the dark matter DPs just inside 0.01 virial radii. The very low total mass and velocity dispersion produced within R-e by an NFW-like total mass profile suggests that the stellar component should dominate the dark matter component out to at least R-c. It should then be difficult to kinematically constrain the inner slope of the DP of ellipticals. The high-concentration parameters deduced from X-ray observations appear to be a consequence of fitting an NFW model to the total mass DP made up of a stellar component that dominates inside and a dark matter component that dominates outwards. An appendix gives the virial mass dependence of the concentration parameter, central density and total mass of the Navarro et al. model. In a second appendix are given single integral expressions for the velocity dispersions averaged along the line of sight, in circular apertures and in thin slits, for general luminosity density and mass distributions, with isotropic orbits.