The dark matter halo shape of edge-on disk galaxies - IV. UGC 7321
This is the fourth paper in a series in which we attempt to put constraints on the flattening of dark halos in disk galaxies. We observed for this purpose the HI in edge-on galaxies, where it is in principle possible to measure the force field in the halo vertically and radially from gas layer flaring and rotation curve decomposition respectively. We have analysed the HI channel maps to accurately measure all four functions that describe the HI kinematics and 3D distribution: the radial HI surface density, the HI vertical thickness, the rotation curve and the HI velocity dispersion. In this paper we analyse these data for the edge-on galaxy UGC7321. We measured the stellar mass distribution ($M=3\times10^8$ \msun with $M/L_R\lesim0.2$), finding that the vertical force of the gas disk dominates the stellar disk at all radii. We find that the vertical force puts a much stronger constraint on the stellar mass-to-light ratio than rotation curve decomposition. Fitting of the vertical force field derived from the flaring and velocity dispersion of the HI revealed that UGC7321 has a spherical halo density distribution with a flattening of $q = c/a = 1.0 \pm 0.1$.