Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2003-07-14
Phys. Rev. E 72, 026115 (2005)
Physics
Condensed Matter
Statistical Mechanics
6 pages, 3 figures
Scientific paper
10.1103/PhysRevE.72.026115
Low energy states of self-gravitating systems with finite angular momentum are considered. A constraint is introduced to confine cores and other condensed objects within the system boundaries by gravity alone. This excludes previously observed astrophysically irrelevant asymmetric configurations with a single core. We show that for an intermediate range of a short-distance cutoff and small angular momentum, the equilibrium configuration is an asymmetric binary. For larger angular momentum or for a smaller range of the short distance cutoff, the equilibrium configuration consists of a central core and an equatorial ring. The mass of the ring varies between zero for vanishing rotation and the full system mass for the maximum angular momentum $L_{max}$ a localized gravitationally bound system can have. The value of $L_{max}$ scales as $\sqrt{\ln(1/x_0)}$, where $x_0$ is a ratio of a short-distance cutoff range to the system size. An example of the soft gravitational potential is considered; the conclusions are shown to be valid for other forms of short-distance regularization.
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