Cold dissipationless collapse of spherical systems - Sensitivity to the initial density law

The collapse of cold, initially spherical systems with varying degrees of central condensation is investigated. The way in which the final shape of a collapsing system depends on the initial density law is examined. For an initial stellar number density rho varies as r exp -n, where n is in the range 0-2.5, the final, nearly prolate shape is given by a/c is approximately equal to 1.28(1 + 0.16 n), 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 percent of the mass. The properties associated with the final states in the present computations are also studied. The collapsing systems develop an anisotropic halo dominated by radial orbits surrounding an isotropic core as predicted by Burkert (1990).