  In order to test the reliability of determinations of the shapes of galaxies'
dark matter halos, we have made such measurements for the Milky Way by two
independent methods, which make use of the stellar kinematics in the solar
neighbourhood and the observed flaring of the Galactic HI layer to estimate the
flattening of the Galactic dark halo. These techniques are found to produce a
consistent estimate for the halo shape, with a shortest-to-longest axis ratio
of q ~ 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 < 7.6 kpc and Theta_0 <
190 km/s. 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 halos with q < 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 modeling techniques
would have to be viewed with some scepticism.
