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In the present paper we obtain the WIMP velocity distribution in our vicinitystarting from spherically symmetric WIMP density profiles in a self consistentway by employing the Eddington approach. By adding a reasonable angularmomentum dependent term in the expression of the energy, we obtain axiallysymmetric WIMP velocity distributions as well. We find that some densityprofiles lead to approximate Maxwell-Boltzmann distributions, which areautomatically defined in a finite domain, i.e. the escape velocity need not beput by hand. The role of such distributions in obtaining the direct WIMPdetection rates, including the modulation, is studied in some detail and, inparticular, the role of the asymmetry is explored.

Halo Density Profiles Consistent with Asymmetric M-B Velocity Distributions-Implications on Direct Dark Matter Searches