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 R <SUB>25</SUB> and 1.5R <SUB>25</SUB> radii. We have applied our model to 20 nearby galaxies, of which six are large disk galaxies with M(stellar) &gt; 10<SUP>10</SUP>, 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) &gt; 0.5 have oblate halos (q &lt; 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 &lt; 0.55).