  Dynamical properties of two-component galaxy models whose stellar density
distribution is described by a gamma-model while the total density distribution
has a pure r^(-2) profile, are presented. The orbital structure of the stellar
component is described by Osipkov-Merritt anisotropy, while the dark matter
halo is isotropic. After a description of minimum halo models, the positivity
of the phase-space density (the model consistency) is investigated, and
necessary and sufficient conditions for consistency are obtained analytically
as a function of the stellar inner density slope gamma and anisotropy radius.
The explicit phase-space distribution function is recovered for integer values
of gamma, and it is shown that while models with gamma>4/17 are consistent when
the anisotropy radius is larger than a critical value (dependent on gamma), the
gamma=0 models are unphysical even in the fully isotropic case. The Jeans
equations for the stellar component are then solved analytically; in addition,
the projected velocity dispersion at the center and at large radii are also
obtained analytically for generic values of the anisotropy radius, and it is
found that they are given by remarkably simple expressions. The presented
models, even though highly idealized, can be useful as starting point for more
advanced modeling of the mass distribution of elliptical galaxies in studies
combining stellar dynamics and gravitational lensing.
