Comparison of an approximately isothermal gravitational potentials of
  elliptical galaxies based on X-ray and optical data
  We analyze six X-ray bright elliptical galaxies, observed with Chandra and
XMM-Newton, and approximate their gravitational potentials by isothermal
spheres phi(r)=v_c^2 ln(r) 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}~ \eta *
v_{c,X}, where \eta=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% of the gas thermal pressure.
