Partial suppression of the radial orbit instability in stellar systems

It is well known that the simple criterion originally proposed by Polyachenko and Shukhman in their 1981 paper for the onset of the radial orbit instability, although generally a useful tool, faces significant exceptions for both mildly anisotropic systems ( with some that can be proved to be unstable) and strongly anisotropic models ( with some that can be shown to be stable). In this paper we address two issues: Are there processes of collisionless collapse that can lead to equilibria of the exceptional type? And what is the intrinsic structural property that is responsible for the sometimes-noted exceptional stability behavior? To clarify these issues, we have performed a series of simulations of collisionless collapse that start from homogeneous, highly symmetrized, cold initial conditions and, because of such special conditions, are characterized by very little mixing. For these runs, the end states can be associated with large values of the global pressure anisotropy parameter up to 2K(r)/K-T approximate to 2.75. The highly anisotropic equilibrium states thus constructed show no significant traces of radial anisotropy in their central region, with a very sharp transition to a radially anisotropic envelope occurring well inside the half-mass radius ( around 0.2 r(M)). To check whether the existence of such an almost perfectly isotropic "nucleus'' might be responsible for the apparent suppression of the radial orbit instability, we could not resort to equilibrium models with the above characteristics and with analytically available distribution function. Instead, we studied and confirmed the stability of configurations with those characteristics by initializing N-body approximate equilibria ( with given density and pressure anisotropy profiles) with the help of the Jeans equations.