Dynamical measurement of the stellar surface density of face-on galaxies

The DiskMass survey recently provided measurements of the vertical velocity dispersions of disk stars in a sample of nearly face-on galaxies. By setting the disk scale-heights to be equal to those of edge-on galaxies with similar scale-lengths, it was found that these disks must be sub-maximal, with surprisingly low K-band mass-to-light ratios of the order of $M_\star/L_K \simeq 0.3 M_\odot/L_\odot$. This study made use of a simple relation between the disk surface density and the measured velocity dispersion and scale height of the disk, neglecting the shape of the rotation curve and the dark matter contribution to the vertical force, which can be especially important in the case of sub-maximal disks. Here, we point out that these simplifying assumptions led to an overestimation of the stellar mass-to-light ratios. Relaxing these assumptions, we compute even lower values than previously reported for the mass-to-light ratios, with a median $M_\star/L_K \simeq 0.18 M_\odot/L_\odot$, where 14 galaxies have $M_\star/L_K < 0.11$. Invoking prolate dark matter halos made only a small difference to the derived $M_\star/L_K$, although extreme prolate halos ($q>1.5$ for the axis ratios of the potential) might help. The cross-terms in the Jeans equation are also generally negligible. These deduced K-band stellar mass-to-light ratios are even more difficult to reconcile with stellar population synthesis models than the previously reported ones.