  The dynamical properties of spherically symmetric galaxy models, where a
Jaffe (1983) stellar density profile is embedded in a total mass density
decreasing as $r^{-3}$ at large radii, are presented. The orbital structure of
the stellar component is described by the Osipkov--Merritt anisotropy; the dark
matter halo is isotropic, and a black hole is added at the center of the
galaxy. First, the conditions for a nowhere negative and monotonically
decreasing dark matter halo density profile are derived; this profile can be
made asymptotically coincident with a NFW profile at the center and at large
radii. Then the minimum value of the anisotropy radius for phase-space
consistency is derived as a function of the galaxy parameters. The Jeans
equations for the stellar component are solved analytically; the projected
velocity dispersion at the center and at large radii is also obtained, for
generic values of the anisotropy radius. Finally, analytical expressions for
the terms entering the Virial Theorem are derived, and the fiducial anisotropy
limit required to prevent the onset of Radial Orbit Instability is determined
as a function of the galaxy parameters. The presented models, built following
an approach already adopted in our previous works, can be a useful starting
point for a more advanced modeling of the dynamics of elliptical galaxies, and
can be easily implemented in numerical simulations requiring a realistic
dynamical model of a galaxy.
