A numerical comparison of theories of violent relaxation

I. Arad; P. H. Johansson

doi:10.1111/j.1365-2966.2005.09293.x

paper

A numerical comparison of theories of violent relaxation

arXiv:astro-ph/0501619 · doi:10.1111/j.1365-2966.2005.09293.x

Abstract

Using N-body simulations with a large set of massless test particles we compare the predictions of two theories of violent relaxation, the well known Lynden-Bell theory and the more recent theory by Nakamura. We derive ``weaken'' versions of both theories in which we use the whole equilibrium coarse-grained distribution function as a constraint instead of the total energy constraint. We use these weaken theories to construct expressions for the conditional probability $K_{i} (τ)$ that a test particle initially at the phase-space coordinate $τ$ would end-up in the $i$ 'th macro-cell at equilibrium. We show that the logarithm of the ratio $R_{ij} (τ) \equiv K_{i} (τ) / K_{j} (τ)$ is directly proportional to the initial phase-space density $f_{0} (τ)$ for the Lynden-Bell theory and inversely proportional to $f_{0} (τ)$ for the Nakamura theory. We then measure $R_{ij} (τ)$ using a set of N-body simulations of a system undergoing a gravitational collapse to check the validity of the two theories of violent relaxation. We find that both theories are at odds with the numerical results, qualitatively and quantitatively.

arXiv commentReplaced with a revised version, which is now accepted to MNRAS. LaTeX, 12 pages, 6 figures

A numerical comparison of theories of violent relaxation

Abstract

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