  We describe the dynamics and thermodynamics of collisionless particle disks
orbiting a massive central body, in the case where the disk mass is small
compared to the central mass, the self-gravity of the disk dominates the
non-Keplerian force, and the spread in semi-major axes is small. We show that
with plausible approximations such disks have logarithmic two-body interactions
and a compact phase space, and therefore exhibit thermodynamics that are
simpler than most other gravitating systems, which require a confining box and
artificial softening of the potential at small scales to be thermodynamically
well-behaved. We solve for the microcanonical axisymmetric thermal equilibria
and demonstrate the existence of a symmetry-breaking bifurcation into lopsided
equilibria. We discuss the relation between thermal and dynamical instability
in these systems and draw connections to astrophysical settings, as well as to
the wider subject of the statistical mechanics of particles with logarithmic
long-range interactions, such as point vortices in two-dimensional fluids.
