CARMA Survey Toward Infrared-bright Nearby Galaxies (STING) II: Molecular Gas Star Formation Law and Depletion Time Across the Blue Sequence

We present an analysis of the relationship between molecular gas and current star formation rate surface density at sub-kpc and kpc scales in a sample of 14 nearby star-forming galaxies. Measuring the relationship in the bright, high molecular gas surface density ($\Shtwo\gtrsim$20 \msunpc) regions of the disks to minimize the contribution from diffuse extended emission, we find an approximately linear relation between molecular gas and star formation rate surface density, $\nmol\sim0.96\pm0.16$, with a molecular gas depletion time $\tdep\sim2.30\pm1.32$ Gyr. We show that, in the molecular regions of our galaxies there are no clear correlations between \tdep\ and the free-fall and effective Jeans dynamical times throughout the sample. We do not find strong trends in the power-law index of the spatially resolved molecular gas star formation law or the molecular gas depletion time across the range of galactic stellar masses sampled (\mstar $\sim$$10^{9.7}-10^{11.5}$ \msun). There is a trend, however, in global measurements that is particularly marked for low mass galaxies. We suggest this trend is probably due to the low surface brightness CO, and it is likely associated with changes in CO-to-H2 conversion factor.