Dust, CO, and [C I]: cross-calibration of molecular gas mass tracers in metal-rich galaxies across cosmic time

Abstract

We present a self-consistent cross-calibration of the three main molecular gas mass tracers in galaxies, namely the ¹²CO(1-0), [C I](³P₁-³P₀) lines, and the submm dust continuum emission, using a sample of 407 galaxies, ranging from local discs to submillimetre-selected galaxies (SMGs) up to z ≈ 6. A Bayesian statistical method is used to produce galaxy-scale universal calibrations of these molecular gas indicators, that hold over 3-4 orders of magnitude in infrared luminosity, L_IR. Regarding the dust continuum, we use a mass-weighted dust temperature, T_mw, determined using new empirical relations between temperature and luminosity. We find the average L/M_mol gas mass conversion factors (including He) to be ${\alpha _{850}}=6.9\times 10^{12}\, \rm W\, Hz^{-1}\, M_{\odot }^{-1}$, α_CO = 4.0 M_⊙ (κ km s^-1 pc²)^-1, and $\alpha _{\rm C\, I}$ = 17.0 M_⊙ (κ km s^-1 pc²)^-1, based on the assumption that the mean dust properties of the sample (κ_H = gas-to-dust ratio/dust emissivity) will be similar to those of local metal rich galaxies and the Milky Way. The tracer with the least intrinsic scatter is [C I](1-0), while CO(1-0) has the highest. The conversion factors show a weak but significant correlation with L_IR which is not apparent when T_mw is held constant. Assuming dust properties typical of metal-rich galaxies, we infer a neutral carbon abundance ${X_{\rm C\, I}}=\rm [C^0/\rm{H_2}]=1.6\times 10^{-5}$, similar to that in the Milky Way. We find no evidence for bi-modality of α_CO between main-sequence (MS) galaxies and those with extreme star-formation intensity, i.e. ultraluminous infrared galaxies (ULIRGs) and SMGs. The means of the three conversion factors are found to be similar between MS galaxies and ULIRGs/SMGs, to within 10-20 per cent. The overarching conclusion of our work is that, for metal-rich galaxies, near-universal average values for α_CO, $X_{\rm C\, I}$, and κ_H are adequate for global molecular gas estimates within the expected uncertainties. The 1σ scatter in our optimized values for α_CO, $X_{\rm C\, I}$, and κ_H are 0.14, 0.11, and 0.15 dex, respectively.