Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Density Profiles of Collisionless Equilibria. I. Spherical Isotropic
  Systems   We investigate the connection between collisionless equilibria and the
phase-space relation between density $\rho$ and velocity dispersion $\sigma$
found in simulations of dark matter halo formation, $F=\psd \propto
r^{-\alpha}$. Understanding this relation will shed light on the physics
relevant to collisionless collapse and on the subsequent structures formed. We
show that empirical density profiles that provide good fits to N-body halos
also happen to have nearly scale-free \psd distributions when in equilibrium.
We have also done a preliminary investigation of variables other than $r$ that
may match or supercede the correlation with $F$. In the same vein, we show that
$\rho/\sigma^m$, where $m=3$ is the most appropriate combination to use in
discussions of the power-law relationship. Since the mechanical equilibrium
condition that characterizes the final systems does not by itself lead to
power-law $F$ distributions, our findings prompt us to posit that dynamical
collapse processes (such as violent relaxation) are responsible for the radial
power-law nature of the \psd distributions of virialized systems.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: math
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg