Determination of the Local Dark Matter Density in our Galaxy

The rotation curve, the total mass and the gravitational potential of the Galaxy are sensitive measurements of the dark matter halo profile. In this publication cuspy and cored DM halo profiles are analysed with respect to recent astronomical constraints in order to constrain the shape of the Galactic DM halo and the local DM density. All Galactic density components (luminous matter and DM) are parametrized. Then the total density distribution is constrained by astronomical observations: 1) the total mass of the Galaxy, 2) the total matter density at the position of the Sun, 3) the surface density of the visible matter, 4) the surface density of the total matter in the vicinity of the Sun, 5) the rotation speed of the Sun and 6) the shape of the velocity distribution within and above the Galactic disc. The mass model of the Galaxy is mainly constrained by the local matter density (Oort limit), the rotation speed of the Sun and the total mass of the Galaxy from tracer stars in the halo. It is shown from a statistical chi^2 fit to all data that the local DM density is strongly positively (negatively) correlated with the scale length of the DM halo (baryonic disc). Since these scale lengths are poorly constrained the local DM density can vary from 0.2 to 0.4 GeV/cm^3 (0.005 - 0.01 M_sun/pc^3) for a spherical DM halo profile and allowing total Galaxy masses up to 2 * 10^12 M_sun. For oblate DM halos and dark matter discs, as predicted in recent N-body simulations, the local DM density can be increased significantly.