Partial Suppression of the Radial Orbit Instability in Stellar Systems

It is well known that the simple criterion proposed originally by Polyachenkoand Shukhman (1981) for the onset of the radial orbit instability, althoughbeing generally a useful tool, faces significant exceptions both on the side ofmildly anisotropic systems (with some that can be proved to be unstable) and onthe side of strongly anisotropic models (with some that can be shown to bestable). In this paper we address two issues: Are there processes ofcollisionless collapse that can lead to equilibria of the exceptional type?What is the intrinsic structural property that is responsible for the sometimesnoted exceptional stability behavior? To clarify these issues, we haveperformed a series of simulations of collisionless collapse that start fromhomogeneous, highly symmetrized, cold initial conditions and, because of suchspecial conditions, are characterized by very little mixing. For these runs,the end-states can be associated with large values of the global pressureanisotropy parameter up to 2K_r/K_T \approx 2.75. The highly anisotropicequilibrium states thus constructed show no significant traces of radialanisotropy in their central region, with a very sharp transition to a radiallyanisotropic envelope occurring well inside the half-mass radius (around 0.2r_M). To check whether the existence of such almost perfectly isotropic"nucleus" might be responsible for the apparent suppression of the radial orbitinstability, we could not resort to equilibrium models with the abovecharacteristics and with analytically available distribution function; instead,we studied and confirmed the stability of configurations with thosecharacteristics by initializing N-body approximate equilibria (with givendensity and pressure anisotropy profiles) with the help of the Jeans equations.Comment: 26 pages, 9 figures, accepted for publication in The Astrophysical Journa