2016ApJ...824...29S

In a survey of 65 galaxies, Gao & Solomon found a tight linear relation between the infrared luminosity (L_IR, a proxy for the star formation rate) and the HCN(1-0) luminosity ( L_{HCN} ). Wu et al. found that this relation extends from these galaxies to the much less luminous Galactic molecular high-mass star-forming clumps (∼1 pc scales), and posited that there exists a characteristic ratio L_IR/ L_{HCN} for high-mass star-forming clumps. The Gao-Solomon relation for galaxies could then be explained as a summation of large numbers of high-mass star-forming clumps, resulting in the same L_IR/ L_{HCN} ratio for galaxies. We test this explanation and other possible origins of the Gao-Solomon relation using high-density tracers (including HCN(1-0), N₂H⁺(1-0), HCO⁺(1-0), HNC(1-0), HC₃N(10-9), and C₂H(1-0)) for ∼300 Galactic clumps from the Millimetre Astronomy Legacy Team 90 GHz (MALT90) survey. The MALT90 data show that the Gao-Solomon relation in galaxies cannot be satisfactorily explained by the blending of large numbers of high-mass clumps in the telescope beam. Not only do the clumps have a large scatter in the L_IR/ L_{HCN} ratio, but also far too many high-mass clumps are required to account for the Galactic IR and HCN luminosities. We suggest that the scatter in the L_IR/ L_{HCN} ratio converges to the scatter of the Gao-Solomon relation at some size-scale >=1 kpc. We suggest that the Gao-Solomon relation could instead result from of a universal large-scale star formation efficiency, initial mass function, core mass function, and clump mass function.