Scaling up tides in numerical models of galaxy and halo formation |
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| Authors: | C M Boily † E Athanassoula P Kroupa |
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| Institution: | Astronomisches Rechen-Institut, Mönchhofstrasse 12-14, D-69120 Heidelberg, Germany,; Observatoire de Marseille, 2 Place LeVerrier, Marseille Cedex 47000, France and; Institut für Theoretische Physik und Astrophysik der UniversitäKiel, D-24098 Kiel, Germany |
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| Abstract: | 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  and particle number N in spherical symmetry, such that ∝ N 1/3 . We sought a similar relation for axisymmetric configurations, and found an empirical scaling relation such that ∝ 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. |
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| Keywords: | galaxies: formation galaxies: haloes dark matter |
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