  Recent hydrostatic X-ray studies of the hot interstellar medium (ISM) in
early-type galaxies underestimate the gravitating mass as compared to stellar
dynamics, implying modest, but significant deviations from exact hydrostatic
equilibrium. We present a method for combining X-ray measurements and stellar
dynamical constraints in the context of Bayesian statistics that allows the
radial distribution of the implied nonthermal pressure or bulk motions in the
hot ISM to be constrained. We demonstrate the accuracy of the method with
hydrodynamical simulations tailored to produce a realistic galaxy model.
Applying the method to the nearby elliptical galaxy NGC4649, we find a
significant but subdominant nonthermal pressure fraction (0.27+/-0.06) in the
central (<5 kpc) part of the galaxy, similar to the level of deviations from
hydrostatic equilibrium expected in galaxy clusters. Plausible sources of
systematic error, if important, may reduce this fraction. This would imply >360
km/s random turbulence or a magnetic field B=(39+/-6)(n_e/0.1
cm^{-3})^{0.59+/-0.09} muG, whereas gas rotation alone is unlikely to explain
the detailed nonthermal profile. Future observations with Astro-H will allow
turbulence or gas rotation at this level to be detected.
