Dark matter in elliptical galaxies - II. Estimating the mass within the virial radius

Elliptical galaxies are modelled with a four-component model: Sersic stars, Lambda-cold dark matter (Lambda CDM), a beta-model for the hot gas and a central black hole, with the aim of establishing how accurately can one measure the total mass within their virial radii. Dark matter (DM) is negligible in the inner regions, which are dominated by stars and the central black hole. This prevents any kinematic estimate (using a Jeans analysis) of the inner slope of the DM density profile. The gas fraction rises, but the baryon fraction decreases with radius, at least out to 10 effective radii (R-e). Even with line-of-sight velocity dispersion (VD) measurements at 4 or with 20 km s(-1) accuracy and perfectly known velocity anisotropy, the total mass within the virial radius (r(v)equivalent to r(200)) is uncertain by a factor of over 3. The DM distributions found in Lambda CDM simulations appear inconsistent with the low VDs measured by Romanowsky et al. of planetary nebulae between 2 and 5R(e). Some of Romanowsky et al.'s orbital solutions for NGC 3379 imply a dark matter content at least as large as cosmologically predicted, and the lower M/L values of most of their solutions lead to a baryonic fraction within r(v) that is larger than the universal value. Replacing the Navarro-Frenk-White (NFW) DM model by the new model of Navarro et al. decreases the VD slightly at a given radius. So, given the observed VD measured at 5R(e), the inferred M/L within r(v) is 40 per cent larger than that predicted by the NFW model. Folding in the slight (strong) radial anisotropy found in Lambda CDM (merger) simulations, which is well modelled (much better than with the Osipkov-Merritt formula) with, the inferred M/L within r(v) is 1.6 (2.4) times higher than for the isotropic NFW model. Thus, the DM model and radial anisotropy can partly explain the low planetary nebula VDs, but not in full. The logarithmic slope of the VD at radii of 1-5R(e), which is insensitive to radius, is another measure of the DM mass within the virial radius, but it is similarly affected by the a priori unknown DM mass profile and stellar velocity anisotropy. In an appendix, single integral expressions are derived for the VDs in terms of general radial profiles for the tracer density and total mass, for various anisotropic models (general constant anisotropy, radial, Osipkov-Merritt and the model above).