Equilibrium stellar systems with spindle singularities

We construct equilibrium sequences of axisymmetric Newtonian clusters that tend toward singular states. The distribution functions are chosen to be of the form f = f(E, J_z). The numerical method then determines the density and gravitational potential self-consistently to satisfy Poisson's equation. For the prolate models, spindle singularities arise from the depletion of angular momentum near the symmetry axis. While the resulting density enhancement is confined to the region near the axis, the influence of the spindle extends much further out through its tidal gravitational field. Centrally condensed prolate clusters may contain strong-field regions even though the spindle mass is small and the mean cluster eccentricity is not extreme. While the calculations performed here are entirely Newtonian, the issue of singularities is an important tonic in general relativity. Equilibrium solutions for relativistic star clusters can provide a testing ground for exploring this issue. The methods used in this paper for building nonspherical clusters can be extended to relativistic systems.