  In this work we characterize the distribution of Dark Matter (DM) in the
Milky Way (MW), and its uncertainties, adopting the well known "Rotation Curve"
method. We perform a full marginalization over the uncertainties of the
Galactic Parameters and over the lack of knowledge on the morphology of the
baryonic components of the Galaxy. The local DM density rho0 is constrained to
the range 0.3 - 0.8 GeV/cm3 at the 2 sigma level, and has a strong positive
correlation to R0, the local distance from the Galactic Center (GC). The not
well-known value of R0 is thus, at the moment, a major limitation in
determining rho0. Similarly, we find that the inner slope of the DM profile,
gamma, is very weakly constrained, showing no preference for a cored profile
(gamma~0) or a cuspy one (gamma~[1.0,1.4]). Some combination of parameters can
be, however, strongly constrained. For example the often used standard rho0=0.3
GeV/cm3, R0=8.5 kpc is excluded at more than 4 sigma. We release the full
likelihood of our analysis in a tabular form over a multidimensional grid in
the parameters characterizing the DM distribution, namely the scale radius Rs,
the scale density rhos, the inner slope of the profile gamma, and R0. The
likelihood can be used to include the effect of the DM distribution uncertainty
on the results of searches for an indirect DM signal in gamma-rays or
neutrinos, from the GC, or the Halo region surrounding it. As one example, we
study the case of the GC excess in gamma rays. Further applications of our
tabulated uncertainties in the DM distribution involve local DM searches, like
direct detection and anti-matter observations, or global fits combining local
and GC searches.
