  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.
