Saturn and its ring: equilibrium states of rotating self-gravitating systems

Condensed Matter, abstract
cond-mat/0307335

From: Iaroslav Ispolatov [view email]

Date: Mon, 14 Jul 2003 20:21:14 GMT   (48kb)

Authors:
I. Ispolatov

Comments: 7 pages, 2 figures

Subj-class: Statistical Mechanics

Low-energy or core-halo equilibrium states of self-gravitating systems with
finite angular momentum are studied. Core structure of such states is found to
be similar to the structure of the corresponding ground (zero-temperature)
states. Introduction of a physically relevant constraint that cores are
supported only gravitationally and do not come in contact with container walls
excludes the previously observed highest entropy asymmetric single-core
structures in which the core slides along the container equator. With such
constraint, the ground state of a rotating system is shown to consist of a
central core and an equatorial ring. The mass of the ring varies continuously
between zero for vanishing rotation and the full system mass for the maximum
angular momentum $L_{max}$ which the gravitationally self-supported localized
system can carry. The value of $L_{max}$ scales as $sqrt{ln(1/x_0)}$, where
$x_0$ is a ratio of the range of a short-distance regularization and the system
size. An example of soft-core potential regularization is considered; the
conclusions made for this example are shown to be valid for other forms of
short-range regularization as well.

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