Analytical Models For Galactic Nuclei

I present a general family of dynamical models with simple analytical potential-density pairs suited to model galactic bulges and nuclei with double power-law radial density profiles and an optional central black hole. Analytical expressions for the potential and velocity dispersion of these models are given in the spherical case. Many previously known analytical spherical models, including also the recent $\gamma / \eta$-models by Dehnen (1993) and Tremaine et al. (1994), are special cases of this family. This family also forms a complete set for constructing general galaxy models or solving Poisson's equation in the non-spherical case. In particular, a generalized Clutton-Brock (1973) and Hernquist-Ostriker (1992) orthogonal basis set is given.