Nonequilibrium Stationary States of 3D Self-Gravitating Systems

Three-dimensional self-gravitating systems do not evolve to thermodynamic equilibrium but become trapped in nonequilibrium quasistationary states. In this Letter, we present a theory which allows us to a priori predict the particle distribution in a final quasistationary state to which a self-gravitating system will evolve from an initial condition which is isotropic in particle velocities and satisfies a virial constraint $2K=-U$, where $K$ is the total kinetic energy, and $U$ is the potential energy of the system.

Figure 1

Distribution function in energy and angular momentum for the QSS for an initial water-bag distribution, Eq. (18), satisfying the VC.

Figure 2

Theoretically predicted density (left) and momentum (right) distributions (solid lines) for the QSS for the initial water-bag distribution. The symbols (black dots) are the results of MD simulations. The initial $t=0$ density and momentum distributions are plotted with dashed lines—an initial water-bag distribution is given by Eq. (18).

Figure 3

Solid lines are the theoretically predicted density (left) and momentum (right) distributions for the QSS for initial distribution (dashed lines) given by Eq. (22). The symbols (black dots) are the results of MD simulations.

Figure 4

Comparison between the density, left panel, and momentum, right panel, distributions calculated using LB statistics and the present theory. Initial distribution is the water-bag in momentum and position, Eq. (18), satisfying the VC. Solid curves are the results of the present theory, dashed curves are the predictions of the LB theory, and the solid circles are the results of MD simulations.