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The velocity distribution of dark matter near the Earth is important for anaccurate analysis of the signals in terrestrial detectors. This distribution istypically extracted from numerical simulations. Here we address the possibilityof deriving the velocity distribution function analytically. We derive adifferential equation which is a function of radius and the radial component ofthe velocity. Under various assumptions this can be solved, and we compare thesolution with the results from controlled numerical simulations. Our findingscomplement the previously derived tangential velocity distribution. We herebydemonstrate that the entire distribution function, below 0.7 v_esc, can bederived analytically for spherical and equilibrated dark matter structures.

Analytical derivation of the radial distribution function in spherical dark matter halos