Linking Dense Gas from the Milky Way to External Galaxies
  In a survey of 65 galaxies, Gao & Solomon (2004) found a tight linear relation between the infrared luminosity ($L_{\rm{IR}}$, a proxy for the star formation rate) and the HCN(1-0) luminosity ($L_{\rm{HCN}}$). Wu et al. (2005, 2010) found that this relation extends from these galaxies to the much less luminous Galactic molecular high-mass star-forming clumps ($\sim$1 pc scales), and posited that there exists a characteristic ratio $L_{\rm{IR}}$ /$L_{\rm{HCN}}$ 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 $L_{\rm{IR}}$ /$L_{\rm{HCN}}$ ratio for galaxies. We test this explanation and other possible origins of the Gao-Solomon relation using high-density tracers (including HCN(1-0), N$_2$H$^+$(1-0), HCO$^+$(1-0), HNC(1-0), HC$_3$N(10-9), and C$_2$H(1-0)) for $\sim$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 $L_{\rm{IR}}$/$L_{\rm{HCN}}$ 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 $L_{\rm{IR}}$/$L_{\rm{HCN}}$ ratio converges to the scatter of the Gao-Solomon relation at some size-scale $\gtrsim$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. 
Ian W. Stephens, James M. Jackson, J. Scott Whitaker, Yanett   Contreras, Andr\'es E. Guzm\'an, Patricio Sanhueza, Jonathan ...
astro-ph.GA