Dynamical constraints during violent relaxation and their effects on the final state

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Abstract
A previous paper (Van Albada) described a series of N–body models of the collapse of collisionless stellar systems from roughly spherical initial conditions. In the present paper, these models are used to illustrate how certain properties of the final states may be related to dynamical constraints during the phase of violent relaxation. For example, Paper I showed that initially clumpy systems tend to approach a universal final density profile close to the observed r1/4 law, while initially homogeneous spheres do not. This difference arises because there is an additional constraint in the latter case: the angular momenta of individual particles are largely conserved during collapse in a spherically symmetric system. Secondly, all the models in Paper I showed a flattening-out of the density profile below the r1/4 law in the inner parts. This too may be related to a dynamical constraint: it seems to be a consequence of the conservation of fine-grained phase density imposed by the collisionless Boltzmann equation. Both the constraints discussed here arise from special aspects of the initial conditions which are unlikely to pertain to a real protogalaxy, and this supports the assertion of Paper I that only collapse simulations starting from the most general initial conditions can produce realistic final states.

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