Asymmetric Velocity Distributions from Halo Density Profiles in the
  Eddington Approach
  In the present paper we show how obtain the energy distribution f(E) in our
vicinity starting from WIMP density profiles in a self consistent way by
employing the Eddington approach and adding reasonable angular momentum
dependent terms in the expression of the energy. We then show how we can obtain
the velocity dispersion and the asymmetry parameter {\beta} in terms of the
parameters describing the angular momentum dependence. From this expression for
f(E) we proceed to construct an axially symmetric WIMP velocity distributions,
which for a gravitationally bound system automatically has an velocity upper
bound and is characterized by the the same asymmetries. This approach is tested
and clarified by constructing analytic expressions in a simple model, with
adequate structure. We then show how such velocity distributions can be used in
determining the event rates, including modulation, both in the standard as well
directional WIMP searches. find that some density profiles lead to approximate
Maxwell-Boltzmann distributions, which are automatically defined in a finite
domain, i.e. the escape velocity need not be put by hand. The role of such
distributions in obtaining the direct WIMP detection rates, including the
modulation, is studied in some detail and, in particular, the role of the
asymmetry is explored.
