Binaries and core-ring structures in self-gravitating systems

TL;DR

This paper investigates the equilibrium configurations of self-gravitating systems with finite angular momentum, revealing conditions under which binary or core-ring structures form, influenced by short-distance cutoff and angular momentum.

Contribution

It introduces a confinement constraint that excludes asymmetric configurations and characterizes the transition between binary and core-ring structures based on angular momentum and cutoff parameters.

Findings

Binary configurations occur at intermediate cutoff and low angular momentum.

Core-ring structures form at higher angular momentum or smaller cutoff ranges.

Maximum angular momentum scales as the square root of the logarithm of the cutoff ratio.

Abstract

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.