Radial-orbit instability of a family of anisotropic Hernquist models with and without a supermassive black hole

We present a method to investigate the non-radial stability of a spherical anisotropic system that hosts a central supermassive black hole (SBH). Such systems have never been tested before for stability, although high anisotropies have been considered in the dynamical models that were used to estimate the masses of the central putative SBHs. A family of analytical anisotropic spherical Hernquist models with and without a black hole were investigated by means of N-body simulations. A clear trend emerges that the SBH has a significant effect on the overall stability of the system, that is, an SBH with a mass of a few per cent of the total mass of the galaxy can prevent or reduce the bar instabilities in anisotropic systems. Its mass determines not only the strength of the instability reduction, but also the time in which this occurs. These effects are most significant for models with strong radial anisotropies. Furthermore, our analysis shows that unstable systems with similar SBHs but with different anisotropy radii evolve differently: highly radial systems become oblate, while more isotropic models tend to form into prolate structures. In addition to this study, we also present a Monte Carlo algorithm to generate particles in spherical anisotropic systems.