Dark matter searches employing asymmetric velocity distributions obtained via the Eddington approach

•Construction of a factorization phase space function for the energy and angular momentum of dark matter.•Use of the phase space function to obtain the velocity dispersion and the anisotropy parameter β.•Velocity distribution effects on the events rates on WIMP searches.•The modulation effects both in the standard and in directional WIMP searches.

Starting from WIMP density profiles, in the framework of the Eddington approach, we obtain the energy distribution f(E  ) of dark matter in our vicinity. Assuming a factorizable phase space function, f(E,L)=F(E)FL(L),f(E,L)=F(E)FL(L), we obtain the velocity dispersions and the anisotropy parameter β in terms of the parameters describing the angular momentum dependence. By employing the derived expression f(E) we construct axially symmetric WIMP velocity distributions. The obtained distributions automatically have a velocity upper bound, as a consequence of the fact that they are associated with a gravitationally bound system, and are characterized by an anisotropy parameter β. 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.