  We present a new determination of the local dark matter phase-space density.
This result is obtained implementing, in the limit of isotropic velocity
distribution and spherical symmetry, Eddington's inversion formula, which links
univocally the dark matter distribution function to the density profile, and
applying, within a Bayesian framework, a Markov Chain Monte Carlo algorithm to
sample mass models for the Milky Way against a broad and variegated sample of
dynamical constraints. We consider three possible choices for the dark matter
density profile, namely the Einasto, NFW and Burkert profiles, finding that the
velocity dispersion, which characterizes the width in the distribution, tends
to be larger for the Burkert case, while the escape velocity depends very
weakly on the profile, with the mean value we obtain being in very good
agreement with estimates from stellar kinematics. The derived dark matter
phase-space densities differ significantly--most dramatically in the high
velocity tails--from the model usually taken as a reference in dark matter
detection studies, a Maxwell-Boltzmann distribution with velocity dispersion
fixed in terms of the local circular velocity and with a sharp truncation at a
given value of the escape velocity. We discuss the impact of astrophysical
uncertainties on dark matter scattering rates and direct detection exclusion
limits, considering a few sample cases and showing that the most sensitive ones
are those for light dark matter particles and for particles scattering
inelastically. As a general trend, when adopting a self-consistent phase-space
density, we find that rates are larger, and hence exclusion limits stronger,
than with the standard Maxwell-Boltzmann approximation. Tools for applying our
result on the local dark matter phase-space density to other dark matter
candidates or experimental setups are provided.
