Cloud Scale ISM Structure and Star Formation in M51

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 ($tau_{rm Dep}^{rm mol}$), the star formation efficiency per free fall time ($epsilon_{rm ff}$), and the mass-weighted cloud-scale (40 pc) properties of the molecular gas: surface density, $Sigma$, line width, $sigma$, and $bequivSigma/sigma^2proptoalpha_{rm vir}^{-1}$, 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, $epsilon_{ff} left( left< Sigma_{40pc} right> right) sim 0.3{-}0.36%$, 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 $tau_{rm Dep}^{rm mol} propto b^{-0.9}$. The sense of the correlation is that gas with stronger self-gravity (higher $b$) forms stars at a higher rate (low $tau_{rm Dep}^{rm mol}$). The different regions of the galaxy mostly overlap in $tau_{rm Dep}^{rm mol}$ as a function of $b$, so that low $b$ explains the surprisingly high $tau_{rm Dep}^{rm mol}$ found towards the inner spiral arms found by by Meidt et al. (2013).