A completely analytical family of dynamical models for spherical galaxies and bulges with a central black hole

We present a family of spherical models for elliptical galaxies and bulges consisting of a stellar component and a central black hole. All models in this family share the same stellar density profile, which has a steep central cusp. The gravitational potential of each model is a linear combination of the potential generated self-consistently by the stars and the potential of a central black hole. The relative importance of these two contributions is a free parameter in the models. Assuming an isotropic dynamical structure, almost all kinematical properties of these models can be calculated analytically. In particular, they form the first simple dynamical models for galaxies with a central black hole where the distribution function and differential energy distribution can be written completely in terms of elementary functions only. We also present various extensions of this family to models with anisotropic orbital structures. Also for these dynamical models, the distribution function and its moments can be expressed completely in terms of elementary functions. This family is useful for a large range of applications, in particular to generate initial conditions for N-body and hydrodynamical simulations to model galactic nuclei with a central black hole.