Luminous and dark matter in the Milky Way

Axisymmetric models of the Milky Way exhibit strong interrelations between the Galactic constants [the Sun's distance to the Galactic Centre ( R 0 ), and the local rotation speed (θ 0 )], the local stellar column density [Σ∗( R 0 )] and the shortest‐to‐longest axis ratio of the dark matter halo ( q ). In this paper we present simple analytical approximations that allow for an efficient search through the vastness of parameter space, and apply this approximation to investigate the consequences of the uncertain gaseous velocity dispersion ( σ g ) on the constraints imposed by the thickness of the Milky Way's gas layer. The extra degree of freedom does not significantly alter the conclusions drawn in a previous paper on the shape of the Milky Way's dark matter halo. A significant contribution to the total gas pressure by cosmic rays and magnetic fields beyond the optical disc is thus ruled out. We find that the Milky Way's dark halo is close to spherical if R 0 ≳7.1 kpc , while a significantly flattened dark matter halo is possible only if our distance to the Galactic Centre is smaller than ∼6.8 kpc. Thus, if R 0 is larger than ∼7 kpc, or θ 0 ≳170 km s −1 , we can rule out two dark matter candidates that require a highly flattened dark matter halo: (1) decaying massive neutrinos, and (2) a disc of cold molecular hydrogen. It is possible to construct a self‐consistent axisymmetric model of the Galaxy based on the IAU‐recommended values for the Galactic constants (R 0 =8.5 kpc , θ 0 =220 km s −1 ) only in the unlikely case that the effective gaseous velocity dispersion is ∼19 per cent larger than observed, and if the local stellar column density is less than about 18 M ⊙  pc −2 . If we assume that the halo is oblate and a value of Σ∗ of 35±5 M ⊙  pc −2 , we can rule out Galactic models with R 0 ≳8.0 kpc and θ 0 ≳200 km s −1 . Combining the best kinematical and star‐count estimates of Σ∗, we conclude that Σ∗ probably lies between 25 and 45 M ⊙  pc −2 . We find that Kuijken & Gilmore's determination of the column density of matter within 1.1 kpc of the plane is robust and valid over a wide range of Galactic constants. Our mass models show that, largely owing to the uncertainty in the Galactic light distribution, the dark matter density in the Galactic Centre is uncertain by up to three orders of magnitude. In the solar neighbourhood this uncertainty is much reduced: our models imply a dark matter density of some 0.42 GeV/ c 2 per cubic centimetre, or (11±5) mM ⊙  pc −3 – roughly 15 per cent of the total mass density.