A Test of Star Formation Laws in Disk Galaxies. II. Dependence on dynamical properties

We use observed radial profiles of mass surface densities of total, $\Sigma_g$, & molecular, $\Sigma_{\rm H2}$, gas, rotation velocity & star formation rate (SFR) surface density, $\Sigma_{\rm sfr}$, of the molecular-rich ($\Sigma_{\rm H2}\ge\Sigma_{\rm HI}/2$) regions of 16 nearby disk galaxies to test several star formation laws: a Kennicutt-Schmidt law, $\Sigma_{\rm sfr}=A_g\Sigma_{g,2}^{1.5}$; a Constant Molecular law, $\Sigma_{\rm sfr}=A_{\rm H2}\Sigma_{\rm H2,2}$; the turbulence-regulated laws of Krumholz & McKee (KM05) and Krumholz et al. (KMT09), a Gas-$\Omega$ law, $\Sigma_{\rm sfr}=B_\Omega\Sigma_g\Omega$; and a shear-driven GMC Collision law, $\Sigma_{\rm sfr}=B_{\rm CC}\Sigma_g\Omega(1-0.7\beta)$, where $\beta\equiv d {\rm ln} v_{\rm circ}/d {\rm ln} r$. If allowed one free normalization parameter for each galaxy, these laws predict the SFR with rms errors of factors of 1.4 - 1.8. If a single normalization parameter is used by each law for the entire galaxy sample, then rms errors range from factors of 1.5 - 2.1. Although the Constant Molecular law gives the smallest errors, the improvement over KMT, Kennicutt-Schmidt & GMC Collision laws is not especially significant, particularly given the different observational inputs that the laws utilize and the scope of included physics, which ranges from empirical relations to detailed treatment of interstellar medium processes. We next search for variation of star formation law parameters with local & global galactic dynamical properties of disk shear rate (related to $\beta$), rotation speed & presence of a bar. We demonstrate with high significance that higher shear rates enhance star formation efficiency per local orbital time. Such a trend is expected if GMC collisions play an important role in star formation, while an opposite trend would be expected if development of disk gravitational instabilities is the controlling physics.