Two measures of the shape of the dark halo of the Milky Way

In order to test the reliability of determinations of the shapes of dark-matter haloes of the galaxies, we have made such measurements for the Milky Way by two independent methods. First, we have combined the measurements of the overall mass distribution of the Milky Way derived from its rotation curve and the measurements of the amount of dark matter in the solar neighbourhood obtained from stellar kinematics to determine the flattening of the dark halo. Secondly, we have used the established technique based on the variation in thickness of the Milky Way's H I layer with radius: by assuming that the H I gas is in hydrostatic equilibrium in the gravitational potential of a galaxy, one can use the observed flaring of the gas layer to determine the shape of the dark halo. These techniques are found to produce a consistent estimate for the flattening of the dark-matter halo, with a shortest-to-longest axis ratio of q similar to 0.8, but only if one adopts somewhat non-standard values for the distance to the Galactic centre, R-0, and the local Galactic rotation speed, Theta(0). For consistency, one requires values of R-0 less than or similar to 7.6 kpc and Theta(0) less than or similar to 190 km s(-1). The results depend on the Galactic constants because the adopted values affect both distance measurements within the Milky Way and the shape of the rotation curve, which, in turn, alter the inferred halo shape. Although differing significantly from the current IAU-sanctioned values, these upper limits are consistent with all existing observational constraints. If future measurements confirm these lower values for the Galactic constants, then the validity of the gas-layer-flaring method will be confirmed. Further, dark-matter candidates such as cold molecular gas and massive decaying neutrinos, which predict very flat dark haloes with q less than or similar to 0.2, will be ruled out. Conversely, if the Galactic constants were found to be close to the more conventional values, then there would have to be some systematic error in the methods for measuring dark halo shapes, so the existing modelling techniques would have to be viewed with some scepticism.