Estimating the Oblateness of Dark Matter Halos Using Neutral Hydrogen Velocity Dispersion

We derive the oblateness parameter q of the dark matter halo of a sample of gas-rich, face-on disk galaxies. We have assumed that the halos are triaxial in shape but their axes in the disk plane (a and b) are equal, so that q = c/a measures the halo flattening. We have used the H i velocity dispersion, derived from the stacked H i emission lines and the disk surface density, determined from the H i flux distribution, to determine the disk potential and the halo shape at the R25 and 1.5R25 radii. We have applied our model to 20 nearby galaxies, of which six are large disk galaxies with M(stellar) > 1010, eight have moderate stellar masses, and six are low-surface-brightness dwarf galaxies. Our most important result is that gas-rich galaxies that have M(gas)/M(baryons) > 0.5 have oblate halos (q < 0.55), whereas stellar-dominated galaxies have a range of q values from 0.21 ± 0.07 in NGC4190 to 1.27 ± 0.61 in NGC5194. Our results also suggest a positive correlation between the stellar mass and the halo oblateness q, which indicates that galaxies with massive stellar disks have a higher probability of having halos that are spherical or slightly prolate, whereas low-mass galaxies have oblate halos (q < 0.55).