  The 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 beta
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
beta estimates, by using simple analytical calculations and hydrodynamical
simulations representative of gas rich galaxies. We show that the deviations of
the X-ray determined beta^{est} and M^{est} from the true values are linked by
a remarkably simple relation; in particular, M is underestimated if beta is
overestimated, and more radially anisotropic orbital distributions than true
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, NGC4472. We show that beta^{est} recently
derived from X-rays corresponds to a galaxy that is unstable by radial orbit
instability. Then, assuming as true beta and M the optically derived values, we
show that the differences beta^{est}-beta and M^{est}-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
(abridged).
