Radially anisotropic systems with r-α forces - II: radial-orbit instability

We continue to investigate the dynamics of collisionless systems of particles interacting via additive r-α interparticle forces. Here we focus on the dependence of the radial-orbit instability on the force exponent α. By means of direct N-body simulations, we study the stability of equilibrium radially anisotropic Osipkov-Merritt spherical models with Hernquist density profile and with 1 ≤ α < 3. We determine, as a function of α, the minimum value for stability of the anisotropy radius ras and of the maximum value of the associated stability indicator ξs. We find that for decreasing α, ras decreases and ξs increases, i.e. longer range forces are more robust against radial-orbit instability. The isotropic systems are found to be stable for all the explored values of α. The end products of unstable systems are all markedly triaxial with minor-to-major axial ratio >0.3, so they are never flatter than an E7 system.