In the previous papers in this series , we have measured the stellar and HI content in a sample of edge-on galaxies .
In the present paper , we perform a simultaneous rotation curve and vertical force field gradient decomposition for five of these edge-on galaxies .
The rotation curve decomposition provides a measure of the radial dark matter potential , while the vertical force field gradient provide a measure of the vertical dark matter potential .
We fit dark matter halo models to these potentials .
Using our HI self-absorption results , we find that a typical dark matter halo has a less dense core ( 0.094 \pm 0.230 M _ { \odot } /pc ^ { 3 } ) compared to an optically thin HI model ( 0.150 \pm 0.124 M _ { \odot } /pc ^ { 3 } ) .
The HI self-absorption dark matter halo has a longer scale length R _ { c } of 1.42 \pm 3.48 kpc , versus 1.10 \pm 1.81 kpc for the optically thin HI model .
The median halo shape is spherical , at q = 1.0 \pm 0.6 ( self-absorbing HI ) , while it is prolate at q = 1.5 \pm 0.6 for the optically thin .
Our best results were obtained for ESO 274-G001 and UGC 7321 , for which we were able to measure the velocity dispersion in Paper III .
These two galaxies have drastically different halo shapes , with one oblate and one strongly prolate .
Overall , we find that the many assumptions required make this type of analysis susceptible to errors .