Does the HCN/CO ratio trace the star-forming fraction of gas?

II. Variations in CO and HCN emissivity

¹ Leiden Observatory, Leiden University, PO Box 9513 2300 RA, Leiden, The Netherlands
² Department of Physics & Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada
³ Waterloo Centre for Astrophysics, University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada
⁴ Department of Physics & Astronomy, McMaster University, 1280 Main St W, Hamilton, ON L8S 4M1, Canada
⁵ Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany

^⋆ Corresponding author; abemis@uwaterloo.ca

Received: 5 September 2023
Accepted: 30 September 2024

Abstract

We modeled emissivities of the HCN and CO J = 1–0 transitions across a grid of molecular cloud models encapsulating observed properties that span from normal star-forming galaxies to more extreme merging systems. These models are compared with archival observations of the HCN and CO J = 1–0 transitions, in addition to the radio continuum at 93 GHz, for ten nearby galaxies. We combined these model emissivities with the predictions of gravoturbulent models of star formation presented in the first paper in this series. In particular, we explored the impact of excitation and optical depth on CO and HCN emission and assess if the HCN/CO ratio tracks the fraction of gravitationally bound dense gas, f_grav, in molecular clouds. We find that our modeled HCN/CO ratios are consistent with the measurements within our sample, and our modeled HCN and CO emissivities are consistent with the results of observational studies of nearby galaxies and clouds in the Milky Way. CO emission shows a wide range of optical depths across different environments, ranging from optically thick in normal galaxies to moderately optically thin in more extreme systems. HCN appears only moderately optically thick and shows significant subthermal excitation in both normal and extreme galaxies. We find an anticorrelation between HCN/CO and f_grav, which implies that the HCN/CO ratio is not a reliable tracer of f_grav. Instead, this ratio appears to best track gas at moderate densities (n > 10^3.5 cm⁻³), which is below the typically assumed dense gas threshold of n > 10^4.5 cm⁻³. We also find that variations in CO emissivity depend strongly on optical depth, which is a product of variations in the dynamics of the cloud gas. HCN emissivity is more strongly dependent on excitation, as opposed to optical depth, and thus does not necessarily track variations in CO emissivity. We further conclude that a single line ratio, such as HCN/CO, will not consistently track the fraction of gravitationally bound, star-forming gas if the critical density for star formation varies in molecular clouds. This work highlights important uncertainties that need to be considered when observationally applying an HCN conversion factor in order to estimate the dense (i.e., n > 10^4.5 cm⁻³) gas content in nearby galaxies.