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 ( \hbox { $ \Sigma _ { H 2 } $ } \gtrsim 20 M _ { \odot } pc ^ { -2 } ) 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 , \hbox { $ N _ { mol } $ } \sim 0.96 \pm 0.16 , with a molecular gas depletion time , \hbox { $ \tau _ { dep } ^ { mol } $ } \sim 2.30 \pm 1.32 Gyr .
We show that , in the molecular regions of our galaxies there are no clear correlations between \tau _ { dep } ^ { mol } 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 ( M _ { \ast } \sim 10 ^ { 9.7 } -10 ^ { 11.5 } M _ { \odot } ) .
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 { \it J } = 1 - 0 } , and it is likely associated with changes in CO-to-H _ { 2 } conversion factor .