Thermodynamics of gravitational systems

Abstract

The thermodynamics of self-gravitating systems play an essential role for explaining the formation and evolution of stellar objects and clusters. Due to the infinite range and singularity of the gravitational force, it is difficult to directly apply the standard methods of statistical physics to self-gravitating systems. Unusual phenomena can occur, such as a negative heat capacity, unbounded mass, or the gravothermal catastrophe where there is no equilibrium state for the system, and the entropy is unbounded. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems of either point masses, or rotating mass shells of different dimension. We also take into account that, the sum of the squares of the individual angular momenta is an integral of motion in the case of spherical symmetry. We establish a direct connection between the spherically symmetric equilibrium states of a self-gravitating point mass system and a shell model of dimension 3 that we utilize in the N-body simulations. We show that different constraints on the internal angular momentum exchange result in different thermodynamic behavior. In the most general case, where angular momentum exchange is allowed, gravothermal catastrophe is present ( L 2 model). In contrast, by ensuring a centrifugal barrier ( l 2 model), a first order phase transition can be observed between ¿quasi-uniform¿ and ¿core-halo¿ states. We also carried out N-body simulations using the rotating shell model to verify the equilibrium properties, dynamical evolution, and finite size effects in these models. We study the relaxation, fluctuations, and temporal and positional correlations for both the gravitational phase transition in the l 2 model and the gravothermal catastrophe in the L 2 model. Surprisingly, a sharp gravitational phase transition can be present in small-size systems, which is essential for explaining clustering. Due to the lack of fluctuations with sufficient size in large N clusters, the system can remain ¿supercooled¿ or ¿superheated¿. In addition, we study the dynamics and the long-time evolution of the gravothermal catastrophe for the L 2 model. After the initial collapse of the core and the development of a ¿core-halo¿ structure, core-oscillation with increasing amplitude dominate the system's dynamics.