A simple recipe for estimating masses of elliptical galaxies and clusters of galaxies

We discuss a simple and robust procedure to evaluate the mass/circular velocity of massive elliptical galaxies and clusters of galaxies. It relies only on the surface density and the projected velocity dispersion profiles of tracer particles and therefore can be applied even in case of poor or noisy observational data. Stars, globular clusters or planetary nebulae can be used as tracers for mass determination of elliptical galaxies. For clusters the galaxies themselves can be used as tracer particles. The key element of the proposed procedure is the selection of a “sweet” radiusRsweet , where the sensitivity to the unknown anisotropy of the tracers’ orbits is minimal. At this radius the surface density of tracers declines approximately as I(R) ∝ R, thus placing Rsweet not far from the half-light radius of the tracers Reff . The procedure was tested on a sample of cosmological simulations of individual galaxies and galaxy clusters and then applied to real observational data. Independently the total mass profile was derived from the hydrostatic equilibrium equation for the gaseous atmosphere. Mismatch in mass profiles obtained from optical and X-ray data is used to estimate the non-thermal contribution to the gas pressure and/or to constrain the distribution of tracers’ orbits.