Stellar orbits and the interstellar gas temperature in elliptical galaxies

We draw attention to the close relationship between the anisotropy parameter beta(r) for stellar orbits in elliptical galaxies and the temperature T(r) of the hot interstellar gas. For nearly spherical galaxies, the gas density rho 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 beta(r) and T(r) that must be consistent with the observed stellar velocity dispersion. Optical observations of the bright elliptical galaxy NGC 4472 indicate beta(r) less than or similar to 0.35 within the effective radius. However, the X-ray gas temperature pro. le T(r) for NGC 4472 requires significantly larger anisotropy, beta approximate to 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 beta(r) is indeed correct, we are led to the important conclusion that the temperature pro. le 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.