The stability of radially anisotropic rotating stellar systems with a central density cusp

We investigate the interplay between radial velocity anisotropy and internal rotation in self-gravitating systems characterised by initial spherical symmetry and a moderate density cusp. We study the stability properties of such configurations to disentangle the impact of anisotropy, rotation, and density structure on the formation of triaxial stellar systems. We perform a set of collisionless N-body simulations starting from initial equilibria with a phase space distribution function of the class introduced by Osipkov and Merritt, modified to impose a net global angular momentum with the Lynden-Bell daemon protocol. We analyse the growth of the density and phase space distribution modes, as well as the axial ratios and triaxiality index of the final configurations. We find that internal rotation has a mitigating effect on the strength of the radial orbit instability in radially anisotropic models with Fridman-Polyachenko-Shukhman index close to its value for consistency, while it slightly enhances the onset of the instability in nearly stable models. From the analysis of the growth rate of the density modes, we also find that an inner bar, though unstable for maximally rotating initial conditions, is formed even in systems with initial profiles with a central density cusp.