We investigate the relationship between the star formation rate (SFR) and dense molecular gas mass in the nuclei of galaxies. To do this, we utilize the observed 850 micron luminosity as a proxy for the infrared luminosity and SFR, and correlate this with the observed CO (J=3-2) luminosity. We find tentative evidence that the LIR-CO (J=3-2) index is similar to the Kennicutt-Schmidt (KS) index (N ~ 1.5) in the central ~1.7 kpc of galaxies, and flattens to a roughly linear index when including emission from the entire galaxy. This result may imply that the volumetric Schmidt relation is the underlying driver behind the observed SFR-dense gas correlations, and provides tentative confirmation for recent numerical models. While the data exclude the possibility of a constant LIR-CO (J=3-2) index for both galaxy nuclei and global measurements at the ~80% confidence level, the considerable error bars cannot preclude alternative interpretations.
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