  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.
