Handling the uncertainties in the Galactic Dark Matter distribution for particle Dark Matter searches

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 rho(0) is constrained to the range 0.3-0.8 GeV/cm(3) at the 2 sigma level, and has a strong positive correlation to R-0, the local distance from the Galactic Center. The not well-known value of R-0 is thus, at the moment, a major limitation in determining rho(0). Similarly, we find that the inner slope of the DM profile, gamma, is very weakly constrained, showing no preference for a cored profile (gamma similar or equal to 0) or a cuspy one (gamma similar or equal to [1.0, 1.4]). Some combination of parameters can be, however, strongly constrained. For example the often used standard rho(0) = 0.3 GeV/cm(3), R-0 = 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 R-s, the scale density rho(s), the inner slope of the profile gamma, and R-0. 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 Galactic Center (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.