Evolution of the Velocity Dispersion of Self-Gravitating Particles in Disc Potentials

Abstract

The ratio of the vertical velocity dispersion to radial one (sigma_z / sigma_R) of self-gravitating bodies in various disc potentials is investigated through two different numerical methods (statistical compilation of two-body encounters and N-body simulations). The velocity dispersion generated by two-body relaxation is considered. The ratio is given as a function of a disc potential parameter, kappa/Omega, where kappa and Omega are the epicycle and circular frequencies (the parameters kappa/Omega=1 and 2 correspond to Kepler rotation and solid-body rotation). For 1 <= kappa/Omega <~ 1.5, the velocity dispersion increases keeping some anisotropy (sigma_z / sigma_R ~ 0.5-0.7) if the amplitude of radial excursion is larger than tidal radius, while sigma_z / sigma_R << 1 for smaller amplitude. On the other hand, for 1.5 <~ kappa/Omega <= 2.0, we found isotropic state (sigma_z / sigma_R ~ 1) in the intermediate velocity regime, while anisotropic state (sigma_z / sigma_R < 1) still exists for higher and lower velocity regimes. The range of the intermediate velocity regime expands with kappa/Omega. In the limit of solid-body rotation, the regime covers all over the velocity space. Thus, the velocity dispersion generally has two different anisotropic states for each disc potential (1 <= kappa/Omega < 2) and one isotropic state for 1.5 <~ kappa/Omega < 2 where the individual states correspond to different amplitude of velocity dispersion, while in the limit of solid-body rotation (kappa/Omega = 2.0), entire velocity space is covered by the isotropic state.

arXiv commentAccepted by MNRAS. 16 pages, 16 figures. pLaTeX in the MN style

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