Comparison of approximately isothermal gravitational potentials of elliptical galaxies based on X-ray and optical data

We analyse six X-ray bright elliptical galaxies, observed with Chandra and XMM-Newton, and approximate their gravitational potentials by isothermal spheres ϕ = v²_c logr over a range of radii from ~0.5 to ~25 kpc. We then compare the circular speed v_c derived from X-ray data with the estimators available from optical data. In particular, we discuss two simple and robust procedures for evaluating the circular speed of the galaxy using the observed optical surface brightness and the line-of-sight velocity dispersion profiles. The best-fitting relation between the circular speeds derived from optical observations of stars and X-ray observations of hot gas is v_c,opt ~= η v_c,X, where η = 1.10-1.15 (depending on the method), suggesting, albeit with large statistical and systematic uncertainties, that non-thermal pressure on average contributes ~20-30 per cent of the gas thermal pressure.