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 \simeq 0 ) or a cuspy one ( \gamma \simeq [ 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 .