Does the HCN/CO Ratio Trace the Star-forming Fraction of Gas? I. A Comparison with Analytical Models of Star Formation

We use archival ALMA observations of the HCN and CO J = 1–0 transitions, in addition to the radio continuum at 93 GHz, to assess the relation between dense gas, star formation, and gas dynamics in 10 nearby (ultra)luminous IR galaxies (U)LIRGs and late-type galaxy centers. We frame our results in the context of turbulent and gravoturbulent models of star formation to assess whether the HCN/CO ratio tracks the gravitationally bound star-forming gas in molecular clouds (f grav) at subkiloparsec scales in nearby galaxies. We confirm that the HCN/CO ratio is a tracer of gas above n SF ≈ 104.5 cm−3, but the subkiloparsec variations in HCN/CO do not universally track f grav. We find strong evidence for the use of varying star formation density-threshold models, which are able to reproduce trends observed in t dep and ϵ ff that fixed-threshold models do not reproduce. Composite lognormal and power-law models outperform pure lognormal models in reproducing the observed trends, even when a fixed power-law slope is used. The ability of the composite models to better reproduce the star formation properties of the gas provides additional indirect evidence that the star formation efficiency per freefall time is proportional to the fraction of gravitationally bound gas.