The DiskMass Survey. VIII. On the Relationship Between Disk Stability
  and Star Formation
  We study the relationship between the stability level of late-type galaxy
disks and their star-formation activity using integral-field gaseous and
stellar kinematic data. Specifically, we compare the two-component (gas+stars)
stability parameter from Romeo & Wiegert (Q_RW), incorporating stellar
kinematic data for the first time, and the star-formation rate estimated from
21cm continuum emission. We determine the stability level of each disk
probabilistically using a Bayesian analysis of our data and a simple dynamical
model. Our method incorporates the shape of the stellar velocity ellipsoid
(SVE) and yields robust SVE measurements for over 90% of our sample. Averaging
over this subsample, we find a meridional shape of sigma_z/sigma_R =
0.51^{+0.36}_{-0.25} for the SVE and, at 1.5 disk scale lengths, a stability
parameter of Q_RW = 2.0 +/- 0.9. We also find that the disk-averaged
star-formation-rate surface density (Sigma-dot_e,*) is correlated with the
disk-averaged gas and stellar mass surface densities (Sigma_e,g and Sigma_e,*)
and anti-correlated with Q_RW. We show that an anti-correlation between
Sigma-dot_e,* and Q_RW can be predicted using empirical scaling relations, such
that this outcome is consistent with well-established statistical properties of
star-forming galaxies. Interestingly, Sigma-dot_e,* is not correlated with the
gas-only or star-only Toomre parameters, demonstrating the merit of calculating
a multi-component stability parameter when comparing to star-formation
activity. Finally, our results are consistent with the Ostriker et al. model of
self-regulated star-formation, which predicts
Sigma-dot_e,*/Sigma_e,g/sqrt(Sigma_e,*). Based on this and other theoretical
expectations, we discuss the possibility of a physical link between disk
stability level and star-formation rate in light of our empirical results.
