  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 (1997) closely matches
the deprojected form of Sersic 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. 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 models may also prove appropriate for describing the dark matter
distribution in halos formed from LCDM cosmological simulations.
