[1011.0614] Cold uniform spherical collapse revisited

Authors:  M. Joyce, B. Marcos, F. Sylos Labini
Abstract:  We report results of a study of the Newtonian dynamics of N self-gravitating particles which start in a quasi-uniform spherical configuration, without initial velocities. These initial conditions would lead to a density singularity at the origin at a finite time when N \rightarrow \infty, but this singularity is regulated at any finite N (by the associated density fluctuations). While previous studies have focussed on the behaviour as a function of N of the minimal size reached during the contracting phase, we examine in particular the size and energy of the virialized halo which results. We find the unexpected result that the structure decreases in size as N increases, scaling in proportion to N^{-1/3}, a behaviour which is associated with an ejection of kinetic energy during violent relaxation which grows in proportion to N^{1/3}. This latter scaling may be qualitatively understood, and if it represents the asymptotic behaviour in N implies that this ejected energy is unbounded above. We discuss also tests we have performed which indicate that this ejection is a mean-field phenomenon (i.e. a result of collisionless dynamics).
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Syksy Rasanen
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Joined: March 02 2005
Affiliation: University of Helsinki

[1011.0614] Cold uniform spherical collapse revisited

Post by Syksy Rasanen » November 15 2010

This paper looks at the formulation of the fluid limit of [tex]N[/tex]-body systems, a topic on which the authors and their collaborators have done interesting work before (and which seems strangely neglected in the wider cosmology community).

They distribute points randomly inside a sphere with zero initial velocity, and study the evolution. One interesting issue is the large amount of mass lost in the collapse: the fraction of particles ejected increases with [tex]N[/tex], and varies from 15% to 30% for the range of [tex]N[/tex] studied. In terms of energy, the situation is even more dramatic: the amount of energy ejected from the system grows roughly like [tex]N^{1/3}[/tex], and for the largest [tex]N[/tex] the kinetic energy carried away by the ejecta is almost ten times the original energy of the system. (Since the Newtonian gravitational potential is unbounded from below, there is in principle no upper limit to the amount you can extract from a self-gravitating system.)

This calls into question the issue of how the fluid limit should be formulated (since just taking [tex]N[/tex] naively to infinity is obviously wrong). The authors note that this should be done by keeping the fluctuations fixed above some length scale [tex]l[/tex] as [tex]N[/tex] increases.

It is not clear what is the importance of the ejection process for a realistic system, and the authors say they will follow up with a study of a system where the particles have non-zero initial velocities.

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