Density-potential pairs for spherical stellar systems with Sérsic light profiles and (optional) power-law cores

Popular models for describing the luminosity-density profiles of dynamically hot stellar systems (e.g. Jaffe, Hernquist, Dehnen) were constructed with the desire to match the deprojected form of an R^1/4 light profile. Real galaxies, however, are now known to have a range of different light-profile shapes that scale with mass. Consequently, although highly useful, the above models have implicit limitations, and this is illustrated here through their application to a number of real galaxy density profiles. On the other hand, the analytical density profile given by Prugniel & Simien closely matches the deprojected form of Sérsic R^1/n light profiles - including deprojected exponential light profiles. It is thus applicable for describing bulges in spiral galaxies, dwarf elliptical galaxies, and both ordinary and giant elliptical galaxies. Moreover, the observed Sérsic quantities define the parameters of the density model. Here we provide simple equations, in terms of elementary and special functions, for the gravitational potential and force associated with this density profile. Furthermore, to match galaxies with partially depleted cores, and better explore the supermassive black hole/galaxy connection, we have added a power-law core to this density profile and derived similar expressions for the potential and force of this hybrid profile. Expressions for the mass and velocity dispersion, assuming isotropy, are also given. These spherical models may also prove appropriate for describing the dark matter distribution in haloes formed from ACDM cosmological simulations.