4TH MOMENTS AND THE DYNAMICS OF SPHERICAL SYSTEMS

Analysis of the projected density and line-of-sight velocity dispersion of spherical systems leaves significant ambiguity as to the underlying dynamics. Using the additional information in the fourth moment of the line-of-sight velocity distribution is shown to impose tighter limits on the range of dynamical models that are consistent with observation. If the gravitational potential is known, the fourth moment can be deprojected uniquely to yield the three intrinsic components via formulas analogous to the second moment deprojection. Two fourth moment analogs of the virial theorem follow from this result and provide additional constraints on the form of the gravitational potential. A simple application of these formulas for testing the validity of assuming a constant mass-to-light ratio is presented. Extension of these fourth moment results to successively higher orders would imply that the form of the underlying potential and the distribution of orbits are uniquely specified by quantities that are, in principle, observable. Investigation of the fourth moment of velocity data from the globular cluster ω Cen demonstrates that useful constraints can be obtained from a dataset of only ∼300 velocities. The fourth moment of this sample is shown to be inconsistent with an isotropic velocity distribution and suggests that the orbits become predominantly radial at large radii. A more complete analysis of this and other systems awaits larger and more homogeneous samples.