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 (LHCN) 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 × 10⁴ cm^-3 and that HCN luminosity is related tomass of dense gas of ≳10⁴ cm^-3 with a conversion factor of α_HCN ≈ 14M_⊙/(K km s^-1 pc²). We also measure a new empirical relationship between the SFR per global mean free-fall time (ε_ff) and the SFR-HCN relationship, SFR/L_HCN ≈ 2.0 × 10^-7 (ε_ff/0.01)1.1M_⊙ yr^-1/(K km s^-1 pc²). The observed SFR-HCN correlation constrains ε_ff ≈ 1 per cent with a factor of ~3 systematic uncertainty. The scatter in ε_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.