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We present a new determination of the local dark matter phase-space density.This result is obtained implementing, in the limit of isotropic velocitydistribution and spherical symmetry, Eddington's inversion formula, which linksunivocally the dark matter distribution function to the density profile, andapplying, within a Bayesian framework, a Markov Chain Monte Carlo algorithm tosample mass models for the Milky Way against a broad and variegated sample ofdynamical constraints. We consider three possible choices for the dark matterdensity profile, namely the Einasto, NFW and Burkert profiles, finding that thevelocity dispersion, which characterizes the width in the distribution, tendsto be larger for the Burkert case, while the escape velocity depends veryweakly on the profile, with the mean value we obtain being in very goodagreement with estimates from stellar kinematics. The derived dark matterphase-space densities differ significantly--most dramatically in the highvelocity tails--from the model usually taken as a reference in dark matterdetection studies, a Maxwell-Boltzmann distribution with velocity dispersionfixed in terms of the local circular velocity and with a sharp truncation at agiven value of the escape velocity. We discuss the impact of astrophysicaluncertainties on dark matter scattering rates and direct detection exclusionlimits, considering a few sample cases and showing that the most sensitive onesare those for light dark matter particles and for particles scatteringinelastically. As a general trend, when adopting a self-consistent phase-spacedensity, we find that rates are larger, and hence exclusion limits stronger,than with the standard Maxwell-Boltzmann approximation. Tools for applying ourresult on the local dark matter phase-space density to other dark mattercandidates or experimental setups are provided.

The local dark matter phase-space density and impact on WIMP direct detection