### [1011.0614] Cold uniform spherical collapse revisited

Posted:

**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.

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.