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The processes regulating star formation in galaxies are thought to act acrossa hierarchy of spatial scales. To connect extragalactic star formationrelations from global and kpc-scale measurements to recent cloud-scaleresolution studies, we have developed a simple, robust method that quantifiesthe scale dependence of the relative spatial distributions of molecular gas andrecent star formation. In this paper, we apply this method to eight galaxieswith roughly 1 arcsec resolution molecular gas imaging from the PHANGS-ALMA andPAWS surveys that have matched resolution, high quality narrowband Halphaimaging. At a common scale of 140pc, our massive (log(Mstar/Msun)=9.3-10.7),normally star-forming (SFR/Msun/yr=0.3-5.9) galaxies exhibit a significantreservoir of quiescent molecular gas not associated with star formation astraced by Halpha emission. Galactic structures act as backbones for bothmolecular and HII region distributions. As we degrade the spatial resolution,the quiescent molecular gas disappears, with the most rapid changes occurringfor resolutions up to about 0.5kpc. As the resolution becomes poorer, themorphological features become indistinct for spatial scales larger than about1kpc. The method is a promising tool to search for relationships between thequiescent or star-forming molecular reservoir and galaxy properties, butrequires a larger sample size to identify robust correlations between thestar-forming molecular gas fraction and global galaxy parameters.

The Gas-Star Formation Cycle in Nearby Star-Forming Galaxies I. Assessment of Multi-scale Variations