Origin of scaling structure and non-gaussian velocity distribution in self-gravitating ring model

Fractal structures and non-Gaussian velocity distributions are characteristic properties commonly observed in virialized self-gravitating systems such as galaxies or interstellar molecular clouds. We study the origin of these properties using the one-dimensional ring model which we newly propose in this paper. In this simple model, $N$ particles are moving, on a circular ring fixed in the three dimensional space, with mutual interaction of gravity. This model is suitable for accurate symplectic integration method by which we find the phase transition in this system from extended-phase to collapsed-phase through an interesting phase (\halo-phase) which has negative specific heat. In this intermediate energy scale, there appear scaling properties, non-thermal and non-Gaussian velocity distributions. In contrast, these peculiar properties are never observed in other \gas and \core phases. Particles in each phase have typical time scales of motion determined by the cutoff length $\xi$, the ring radius $R$ and the total energy $E$. Thus all relaxation patterns of the system are determined by these three time scales.Comment: 21pages,11figure

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 quasi-stationary 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). This is deeply related with the local virial equilibrium and the linear mass-temperature relation which characterize the system. We show the robustness of this distribution function against various initial conditions which leads to the violent gravitational process. The DT distribution has a positive correlation with the energy fluctuation of the system. On the other hand, the coherent motion such as the radial motion in the spherical collapse and the rotation with the angular momentum suppress the appearance of the DT distribution.Comment: 11 pages, 19 eps figures, RevTex, submitted to PRE, Revised version, minor change

Local virial relation for self-gravitating system

We demonstrate that the quasi-equilibrium state in self-gravitating $N$-body system after cold collapse are uniquely characterized by the local virial relation using numerical simulations. Conversely assuming the constant local virial ratio and Jeans equation for spherically steady state system, we investigate the full solution space of the problem under the constant anisotropy parameter and obtain some relevant solutions. Especially, the local virial relation always provides a solution which has a power law density profile in both the asymptotic regions $r\to 0$ and $\infty$. This type of solutions observed commonly in many numerical simulations. Only the anisotropic velocity dispersion controls this asymptotic behavior of density profile.Comment: 9 pages, 15 eps figures, RevTex, submitted to PR

Chaos in Static Axisymmetric Spacetimes I : Vacuum Case

We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a mingle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyze several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos. Although some test particles which do not satisfy the first criterion show chaotic behavior in some spacetimes, these can be accounted for the second criterion. April, 1995 (a) electronic mail : [email protected] (b) electronic mail : [email protected] (c) electronic mail : [email protected] 1 Introduction Chaos has become one of the most important ideas used to understand various non-linear phenomena in nature. We know many features of chaos in the Newtonian dynamics. However, we do not know, so far, so much about those in general relativity (GR). ..