The statistical mechanics of self-gravitating Keplerian disks

TL;DR

This paper explores the thermodynamics and equilibrium states of collisionless, self-gravitating Keplerian disks with small mass relative to the central body, revealing symmetry-breaking bifurcations and connections to other long-range interacting systems.

Contribution

It introduces a simplified thermodynamic model for Keplerian disks with logarithmic interactions, analyzing equilibrium solutions and stability, and linking astrophysical disks to broader statistical mechanics contexts.

Findings

Existence of microcanonical axisymmetric equilibria.

Demonstration of symmetry-breaking bifurcation into lopsided states.

Connection to long-range systems like point vortices.

Abstract

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.