Self-organized relaxation in a collisionless gravitating system.

We propose the self-organized relaxation process which drives a collisionless self-gravitating system to the equilibrium state satisfying local virial (LV) relation. During the violent relaxation process, particles can move widely within the time interval as short as a few free-fall times, because of the effective potential oscillations. Since such particle movement causes further potential oscillations, it is expected that the system approaches the critical state where such particle activities, which we call gravitational fugacity, is independent of the local position as much as possible.

Local virial relation for self-gravitating system.

We demonstrate that the quasi-equilibrium state in a self-gravitating N-body system after cold collapse is uniquely characterized by the local virial relation using numerical simulations. Conversely, assuming the constant local virial ratio and Jeans equation for a spherically steady-state system, we investigate the full solution space of the problem under the constant anisotropy parameter and obtain some relevant solutions. Specifically, the local virial relation always provides a solution which has a power-law density profile in both the asymptotic regions r --> 0 and infinity.

Universal non-Gaussian velocity distribution in violent gravitational processes.

We study the velocity distribution in spherical collapses and cluster-pair collisions by use of N -body simulations. Reflecting the violent gravitational processes, the velocity distribution of the resultant quasistationary state generally becomes non-Gaussian. Through the strong mixing of the violent process, there appears a universal non-Gaussian velocity distribution, which is a democratic (equal-weighted) superposition of many Gaussian distributions (DT distribution).

Stationary state in N-body system with power law interaction.

Many self-gravitating systems often show scaling properties in their mass density, system size, velocities, and so on. In order to clarify the origin of these scaling properties, we consider the stationary state of N-body system with inverse power law interaction. As a simple case, we consider the self-similar stationary solution in the collisionless Boltzmann equation with power law potential and investigate its stability in terms of a linear symplectic perturbation.