The 3D geometry of Dark Matter Halos

The thickness of the neutral hydrogen layer, coupled with the rotation curve, traces the outer dark matter potential. We estimate the amplitude of the flaring in spiral galaxies from a 3D model of the HI gas. Warps in particular are explicitly parametrized in the form of an harmonical density wave. Applying our method to the galaxy NGC 891, the only model that could fit the observations, and in particular the HI at large height above the plane, includes a strong warp with a line of node almost coinciding with the line of sight. This high-Z HI is not observed at the most extreme velocity channels, those corresponding to high rotational velocities. This is accounted for by the model, since orbits in the tilted planes are not circular, but elongated, with their minor axis in the galaxy plane. Their velocity on the major axis (i.e. at their maximal height above the plane) is then 30% less than in the plane. We finally connect the modelled vertical outer gaseous distribution to the dark matter through hydrodynamical and gravitational equations. Under the assumption of isotropy of the gaseous velocity dispersion, we conclude on a very flattened halo geometry for the galaxy NGC 891 (q approximate to 0.2), while a vertical velocity dispersion smaller that the radial one would lead to a less flattened Dark Matter Halo (q approximate to 0.4 - 0.5). Both results however suggest that dark matter is dissipative or has been strongly influenced by the gas dynamics.