COLD DISSIPATIONLESS COLLAPSE OF SPHERICAL SYSTEMS - SENSITIVITY TO THE INITIAL DENSITY LAW

We investigate the collapse of cold, initially spherical systems with varying degrees of central condensation. Such models are subject to the radial orbit instability, which tends to produce a barlike final configuration. The main objective of our numerical experimentation is to discover how the final shape of a collapsing system depends on the initial density law. Our results are in general agreement with those of Aguilar and Merritt, although our final states are not so elongated. For an initial stellar number density rho is-proportional-to r(-n), where 0 less than or similar n less than or similar 2.5, the final, nearly prolate shape is given by a/c is-approximately-equal-to 1.28(1 + 0.16n), where a/c is the ratio of long to short axes of the inertia ellipsoid computed from the moment of inertia tensor of the most tightly bound 80% of the mass. We also study the properties associated with the final states in our computations. The collapsing systems develop an anisotropic halo dominated by radial orbits surrounding an isotropic core as predicted by Burkert. The isotropic core is an artifact of (1) the smoothing length in our (Barnes-Hut) model and (2) the degeneracy in the central regions caused by conservation of phase space from the initial state.