2019ApJ...887...49S

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 ∼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 Hα imaging. At a common scale of 140 pc, our massive (log(M_*[M_☉]) = 9.3-10.7), normally star-forming (SFR[M_☉ yr^–1] = 0.3-5.9) galaxies exhibit a significant reservoir of quiescent molecular gas not associated with star formation as traced by Hα 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 ∼0.5 kpc. As the resolution becomes poorer, the morphological features become indistinct for spatial scales larger than ∼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.