The Shape of Dark Matter Haloes III. Kinematics and Structure of the HI disc

We present a new strategy for fitting the structure and kinematics of the HI in edge-on galaxies using a fit to the terminal-velocity channel maps of a HI data cube. The strategy can deal with self-absorbing HI gas and the presence of warps. The method is first tested on a series of models. We demonstrate that fitting optically thin models to real galaxies will lead to an overestimation of the thickness and velocity dispersion, and to a serious underestimation of the HI face-on column densities. We subsequently fit both self-absorption and optically thin models to the HI data of six edge-on galaxies. In three of these we have also measured the velocity dispersion. On average 27 \pm 6 % of the total HI mass of edge-on galaxies is hidden by self-absorption. This implies that the HI mass, thickness and velocity dispersion of galaxies is typically underestimated in the literature.