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 \mu m luminosity as a proxy for the infrared luminosity ( L _ { IR } ) and SFR , and correlate this with the observed CO ( J=3-2 ) luminosity .
We find tentative evidence that the L _ { IR } -CO ( J=3-2 ) index is similar to the Kennicutt-Schmidt ( KS ) index ( N \approx 1.5 ) in the central \sim 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 L _ { IR } -CO ( J=3-2 ) index for both galaxy nuclei and global measurements at the \sim 80 % confidence level , the considerable error bars can not preclude alternative interpretations .