2003ApJ...599..992M

We draw attention to the close relationship between the anisotropy parameter β(r) for stellar orbits in elliptical galaxies and the temperature T(r) of the hot interstellar gas. For nearly spherical galaxies, the gas density ρ can be accurately determined from X-ray observations, and the stellar luminosity density ℓ_*can be accurately found from the optical surface brightness. The Jeans equation and hydrostatic equilibrium establish a connection between β(r) and T(r) that must be consistent with the observed stellar velocity dispersion. Optical observations of the bright elliptical galaxy NGC 4472 indicate β(r)≲0.35 within the effective radius. However, the X-ray gas temperature profile T(r) for NGC 4472 requires significantly larger anisotropy, β~0.6-0.7, about twice as large as the optical value. This strong preference for radial stellar orbits must be understood in terms of the formation history of massive elliptical galaxies. Conversely, if the smaller, optically determined β(r) is indeed correct, we are led to the important conclusion that the temperature profile T(r) of the hot interstellar gas in NGC 4472 must differ from that indicated by X-ray observations, or that the hot gas is not in hydrostatic equilibrium.