HCN ( 1–0 ) emission traces dense gas and correlates very strongly with star formation rates ( SFRs ) on scales from small Milky Way clouds to whole galaxies .
The observed correlation offers strong constraints on the efficiency of star formation in dense gas , but quantitative interpretation of this constraint requires a mapping from HCN emission to gas mass and density .
In this paper we provide the required calibration by post-processing high-resolution simulations of dense , star-forming clouds to calculate their HCN emission ( L _ { \mathrm { HCN } } ) and to determine how that emission is related to the underlying gas density distribution and star formation efficiency .
We find that HCN emission traces gas with a luminosity-weighted mean number density of 0.8 - 1.7 \times 10 ^ { 4 } \mbox { cm } ^ { -3 } and that HCN luminosity is related to mass of dense gas of \gtrsim 10 ^ { 4 } \mbox { cm } ^ { -3 } with a conversion factor of \alpha _ { HCN } \approx 14 \mathrm { M } _ { \odot } / ( \mathrm { K km s ^ { -1 } pc ^ { 2 % } } ) .
We also measure a new empirical relationship between the star formation rate per global mean freefall time ( \mathrm { \epsilon _ { ff } } ) and the SFR–HCN relationship , SFR/ L _ { \mathrm { HCN } } \approx 2.0 \times 10 ^ { -7 } ( \mathrm { \epsilon _ { ff } } / 0.01 ) ^ { 1.1 } % \mathrm { M } _ { \odot } \mathrm { yr ^ { -1 } } / ( \mathrm { K km s ^ { -1 } pc ^ { 2 } } ) .
The observed SFR–HCN correlation constrains \mathrm { \epsilon _ { ff } } \approx 1 \mathrm { \% } with a factor of \sim 3 systematic uncertainty .
The scatter in \mathrm { \epsilon _ { ff } } from cloud to cloud within the Milky Way is a factor of a few .
We conclude that L _ { \mathrm { HCN } } is an effective tracer of dense gas and that the IR–HCN correlation is a significant diagnostic of the microphysics of star formation in dense gas .