Numerical calibration of the HCN-star formation correlation

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-HCN) and 10 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 x 10(4) cm(-3) and that HCN luminosity is related to mass of dense gas of greater than or similar to 10(4) cm(-3) with a conversion factor of alpha(HCN) approximate to 14 M-circle dot (K km s(-1) pc(2)) We also measure a new empirical relationship between the SFR per global mean free-fall time (epsilon(ff)) and the SFR-HCN relationship, SFR/L-HCN approximate to 2.0 x 10(-7) (epsilon(ff)/0.01)(1.1) M-circle dot yr(-1)/ (K km s(-1) pc(2)). The observed SFR-HCN correlation constrains epsilon(ff) approximate to 1 per cent with a factor of similar to 3 systematic uncertainty. The scatter in epsilon(ff) from cloud-to-cloud within the Milky Way is a factor of a few. We conclude that L-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.