  We present a method to investigate the 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 supermassive black holes. 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
supermassive black hole has a significant effect on the overall stability of
the system, i.e. an SBH with a mass of a few percent of the total mass of the
galaxy can prevent or reduce the bar instabilities in anisotropic systems. Its
mass not only determines 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 SBH 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.

Astrophysics