Radially anisotropic systems with $r^{-\alpha}$ forces: equilibrium
  states
  We continue the study of collisionless systems governed by additive
$r^{-\alpha}$ interparticle forces by focusing on the influence of the force
exponent $\alpha$ on radial orbital anisotropy. In this preparatory work we
construct the radially anisotropic Osipkov-Merritt phase-space distribution
functions for self-consistent spherical Hernquist models with $r^{-\alpha}$
forces and $1\leq\alpha<3$. The resulting systems are isotropic at the center
and increasingly dominated by radial orbits at radii larger than the anisotropy
radius $r_a$. For radially anisotropic models we determine the minimum value of
the anisotropy radius $r_{ac}$ as a function of $\alpha$ for phase-space
consistency (such that the phase-space distribution function is nowhere
negative for $r_a\geq r_{ac}$). We find that $r_{ac}$ decreases for decreasing
$\alpha$, and that the amount of kinetic energy that can be stored in the
radial direction relative to that stored in the tangential directions for
marginally consistent models increases for decreasing $\alpha$. In particular,
we find that isotropic systems are consistent in the explored range of
$\alpha$. By means of direct $N$-body simulations we finally verify that the
isotropic systems are also stable.
