Angular-momentum-induced phase transition in spherical gravitational systems: N-body simulations

Area of Science:

• Astrophysics
• Statistical Mechanics
• Computational Physics

Background:

• The role of thermodynamics in purely gravitational systems remains unclear due to the nature of Newtonian gravity.
• Astronomical observations hint at distinct thermodynamic phases in systems like globular clusters.
• Standard thermodynamic techniques are challenging to apply to gravitational systems.

Purpose of the Study:

• To investigate a model gravitational system exhibiting a phase transition in the mean-field limit.
• To explore the evolution and equilibrium properties of isolated, rotating mass shells under gravitational forces.
• To compare simulation results with mean-field theory, considering finite-size scaling.

Main Methods:

• Dynamical simulations of a model system composed of rotating, concentric mass shells with fixed angular momentum.
• Analysis of systems in the transition region, at the critical point, and within distinct thermodynamic phases.
• Time averaging to determine equilibrium properties and comparison with mean-field predictions.

Main Results:

• A first-order phase transition was observed between 'quasi-uniform' and 'core-halo' states, consistent with mean-field theory when finite-size scaling is applied.
• Equilibration follows power-law behavior and is notably slow in the transition region, indicating metastable states.
• Long-lived collective oscillations were detected in the supercritical region.

Conclusions:

• The model gravitational system successfully demonstrates a phase transition, validating mean-field predictions with corrections for finite-size effects.
• The slow dynamics and metastability in the transition region are significant features of gravitational systems.
• Evidence of collective oscillations suggests complex emergent behavior in these systems.