SIMBAD references

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 pressureless 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 C and particle number N in spherical symmetry, such that C∝N^1/3. We sought a similar relation for axisymmetric configurations, and found an empirical scaling relation such that C∝N^1/6 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 per cent of triaxial configurations may collapse by a factor of no more than 40 as N ⟶∞. For N~10⁵ 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.