The Star Formation Rate - Dense Gas Relation in Galaxies as Measured by   HCN (3-2) Emission
  We present observations made with the 10m Heinrich Hertz Sub-Millimeter Telescope of HCN (3-2) emission from a sample of 30 nearby galaxies ranging in infrared luminosity from 10^10 - 10^12.5 L_sun and HCN (3-2) luminosity from 10^6 - 10^9 K km s^-1 pc^2. We examine the correlation between the infrared luminosity and HCN (3-2) luminosity and find that the best fit linear regression has a slope (in log-log space) of 0.74+/-0.12. Including recently published data from Gracia-Carpio et al. tightens the constraints on the best-fit slope to 0.79+/-0.09. This slope below unity suggests that the HCN (3-2) molecular line luminosity is not linearly tracing the amount of dense gas. Our results are consistent with predictions from recent theoretical models that find slopes below unity when the line luminosity depends upon the average gas density with a power-law index greater than a Kennicutt-Schmidt index of 1.5. 
R. S. Bussmann, D. Narayanan, Y. L. Shirley, S. Juneau, J. Wu, P. M.   Solomon, P. A. Vanden Bout, J. Moustakas, C. K. Walker