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 \pm 0.12 .
Including recently published data from Gracia-Carpio et al .
tightens the constraints on the best-fit slope to 0.79 \pm 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 .