Abstract

The processes regulating star formation in galaxies are thought to act across a hierarchy of spatial scales. To connect extragalactic star formation relations from global and kiloparsec-scale measurements to recent cloud-scale resolution studies, we have developed a simple, robust method that quantifies the scale dependence of the relative spatial distributions of molecular gas and recent star formation. In this paper, we apply this method to eight galaxies with similar to 1 ''. resolution molecular gas imaging from the Physics at High Angular resolution in Nearby GalaxieS-ALMA (PHANGS-ALMA) survey and PdBI Arcsecond Whirlpool Survey (PAWS) that have matched resolution, high-quality narrowband H alpha imaging. At a common scale of 140 pc, our massive (log(M-*[M-circle dot]) = 9.3-10.7), normally star-forming (SFR[M(circle dot)yr(-1)] = 0.3-5.9) galaxies exhibit a significant reservoir of quiescent molecular gas not associated with star formation as traced by H alpha emission. Galactic structures act as backbones for both molecular gas and H II region distributions. As we degrade the spatial resolution, the quiescent molecular gas disappears, with the most rapid changes occurring for resolutions up to similar to 0.5 kpc. As the resolution becomes poorer, the morphological features become indistinct for spatial scales larger than similar to 1 kpc. The method is a promising tool to search for relationships between the quiescent or star-forming molecular reservoir and galaxy properties, but requires a larger sample size to identify robust correlations between the star-forming molecular gas fraction and global galaxy parameters.