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 ( \Theta _ { 0 } ) ] , the local stellar columndensity ( \Sigma _ { * } ( 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 ( \sigma _ { 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 disk is thus ruled out .
We find that the Milky Way ’ s dark halo is close to spherical if \mbox { $R _ { 0 } $ } \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } % } \hbox { $ > $ } } } 7.1 kpc , while a significantly flattened dark matter halo is only possible if our distance to the Galactic centre is smaller than \sim 6.8 kpc .

Thus , if R _ { 0 } is larger than \sim 7 kpc , or \Theta _ { 0 } \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } } } 170 \mbox { 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 disk of cold molecular hydrogen .

It is only 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 , \Theta _ { 0 } = 220 \mbox { km s } ^ { -1 } ) in the unlikely case that the effective gaseous velocity dispersion is \sim 19 % larger than observed , and if the local stellar columndensity is less than about 18 M _ { \odot } { pc } ^ { -2 } .
If we assume that the halo is oblate and a value of \Sigma _ { * } of 35 \pm 5 M _ { \odot } { pc } ^ { -2 } [ ] , we can rule out Galactic models with \mbox { $R _ { 0 } $ } \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } % } \hbox { $ > $ } } } 8.0 kpc and \mbox { $ \Theta _ { 0 } $ } \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $% \sim$ } } } \hbox { $ > $ } } } 200 \mbox { km s } ^ { -1 } .

Combining the best kinematical and star-count estimates of \Sigma _ { * } , we conclude that \Sigma _ { * } probably lies between 25 and 45 M _ { \odot } { pc } ^ { -2 } .
We find that Kuijken & Gilmore ’ s ( 1991 ) determination of the columndensity 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 due 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 \pm 5 ) m M _ { \odot } { pc } ^ { -3 } – roughly 15 % of the total mass density .