On the use of X-rays to determine dynamical properties of elliptical galaxies

Abstract

The extended and X-ray-emitting interstellar medium of early-type galaxies is often used as a tool to determine their total mass M and stellar orbital anisotropy β profiles, based on the hypothesis of hydrostatic equilibrium for the hot gas. Here we investigate the effects that deviations from equilibrium have on M and β estimates, by using simple analytical calculations and hydrodynamical simulations representative of gas-rich galaxies. We show that the deviations of the X-ray-determined βest and Mest from the true values are linked by a remarkably simple relation; in particular, M is underestimated if β is overestimated. Also, more radially anisotropic orbital distributions than the true one are deduced in presence of gas infall velocities of the order of the local stellar velocity dispersion (as are likely in the central regions of galactic cooling flows). The results of this analysis are applied to the most thoroughly investigated bright elliptical, NGC 4472. First we show that βest recently derived from X-rays corresponds to a galaxy that is unstable by radial orbit instability. Then, assuming as true β and M the optically derived values, we show that the differences βest - β and Mest - M agree with the predictions found here in the case of lack of hydrostatic equilibrium, which points to the latter as a possible explanation for the discrepancies. This analysis casts doubts on the possibility of using X-ray information to determine accurately the dynamical properties of bright X-ray-emitting ellipticals, at least within their Re.