The Star Formation Rate-Dense Gas Relation in Galaxies as Measured by HCN(3-2) Emission

We present observations made with the 10 m Heinrich Hertz Submillimeter Telescope of HCN(3-2) emission from a sample of 30 nearby galaxies ranging in infrared luminosity from 10 super(10) to 10 super(12.5) L and HCN(3-2) luminosity from 10 super(6) to 10 super(9) K km s super(-1) pc super(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 plus or minus 0.12. Including recently published data from Gracia-Carpio et al. tightens the constraints on the best-fit slope to 0.79 plus or minus 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 on the average gas density with a power-law index greater than a Kennicutt-Schmidt index of 1.5.