We compare the structure of molecular gas at 40 pc resolution to the ability of gas to form stars across the disk of the spiral galaxy M51 .
We break the PAWS survey into 370 pc and 1.1 kpc resolution elements , and within each we estimate the molecular gas depletion time ( \tau _ { Dep } ^ { mol } ) , the star formation efficiency per free fall time ( \epsilon _ { ff } ) , and the mass-weighted cloud-scale ( 40 pc ) properties of the molecular gas : surface density , \Sigma , line width , \sigma , and b \equiv \Sigma / \sigma ^ { 2 } \propto \alpha _ { vir } ^ { -1 } , a parameter that traces the boundedness of the gas .
We show that the cloud-scale surface density appears to be a reasonable proxy for mean volume density .
Applying this , we find a typical star formation efficiency per free-fall time , \mbox { $ \epsilon _ { ff } \left ( \mbox { $ \left < \Sigma _ { 40 pc } \right > $ } \right ) $ } % \sim 0.3 { - } 0.36 \% , lower than adopted in many models and found for local clouds .
More , the efficiency per free fall time anti-correlates with both \Sigma and \sigma , in some tension with turbulent star formation models .
The best predictor of the rate of star formation per unit gas mass in our analysis is b \equiv \Sigma / \sigma ^ { 2 } , tracing the strength of self gravity , with \tau _ { Dep } ^ { mol } \propto b ^ { -0.9 } .
The sense of the correlation is that gas with stronger self-gravity ( higher b ) forms stars at a higher rate ( low \tau _ { Dep } ^ { mol } ) .
The different regions of the galaxy mostly overlap in \tau _ { Dep } ^ { mol } as a function of b , so that low b explains the surprisingly high \tau _ { Dep } ^ { mol } found towards the inner spiral arms found by by Meidt et al .
( 2013 ) .