Binaries and core-ring structures in self-gravitating systems

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 square root of ((ln(1/x0)), where x0 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.