Scaling up Tides in Numerical Models of Galaxy- and Halo-Formation
Résumé
The purpose of this article is to show that when dynamically cold, dissipationless self-gravitating systems collapse, their evolution is a strong function of the symmetry in the initial distribution. We explore with a set of pressure-less homogeneous fluids the time-evolution of ellipsoidal distributions and map the depth of potential achieved during relaxation as function of initial ellipsoid axis ratios. We then perform a series of N-body numerical simulations and contrast their evolution with the fluid solutions. We verify an analytic relation between collapse factor calC and particle number N in spherical symmetry, such that calCproptoN1/3. We sought a similar relation for axisymmetric configurations, and found an empirical scaling relation such that calCproptoN1/6 in these cases. We then show that when mass distributions do not respect spherical- or axial-symmetry, the ensuing gravitational collapse deepens with increasing particle number N but only slowly: 86% of triaxial configurations may collapse by a factor of no more than 40 as Ntoinfty. For Napprox105 and larger, violent relaxation develops fully under the Lin-Mestel-Shu instability such that numerical N-body solutions now resolve the different initial morphologies adequately.
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