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

We present a self-consistent cross-calibration of the three main molecular gas mass tracers in galaxies, the ${}^{12}\mathrm{C}\mathrm{O}$(1-0), CI lines, and the submm dust continuum emission, using a sample of 407 galaxies, ranging from local disks to submillimetre-selected galaxies (SMGs) up to $z\approx 6$. A Bayesian 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, $L_{\mathrm{I}\mathrm{R}}$. Regarding the dust continuum, we use a mass-weighted dust temperature, $T_{\mathrm{m}\mathrm{w}}$, determined using new empirical relations between temperature and luminosity. We find the average $L\mathrm{/}{M}_{\mathrm{m}\mathrm{o}\mathrm{l}}$ gas mass conversion factors to be ${\alpha }_{850}=6.9\times {10}^{12}\mathrm{W}\mathrm{H}{\mathrm{z}}^{-1}{\mathrm{M}}_{\odot }^{-1}$, ${\alpha }_{\mathrm{C}\mathrm{O}}=4{\mathrm{M}}_{\odot }(\mathrm{K}\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}\mathrm{p}{\mathrm{c}}^2{)}^{-1}$ and ${\alpha }_{\mathrm{C}\mathrm{I}}=17.0{\mathrm{M}}_{\odot }(\mathrm{K}\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}\mathrm{p}{\mathrm{c}}^2{)}^{-1}$, based on the assumption that the mean dust properties of the sample (${\kappa }_H$ = gas-to-dust ratio/dust emissivity) will be similar to those of local metal rich galaxies and the MW. The tracer with the least intrinsic scatter is CI, while CO(1-0) has the highest. The conversion factors show a weak but significant correlation with $L_{\mathrm{I}\mathrm{R}}$. Assuming dust properties typical of metal-rich galaxies, we infer a neutral carbon abundance $X_{\mathrm{C}\mathrm{I}}=[C^0\mathrm{/}\mathrm{m}\mathrm{o}\mathrm{l}]=1.6\times {10}^{-5}$, similar to that in the MW. We find no evidence for bimodality of ${\alpha }_{\mathrm{C}\mathrm{O}}$ between main-sequence (MS) galaxies and those with extreme star-formation intensity, i.e. 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%. We show that for metal-rich galaxies, near-universal average values for ${\alpha }_{\mathrm{C}\mathrm{O}}$, $X_{\mathrm{C}\mathrm{I}}$ and ${\kappa }_H$ are adequate for global molecular gas estimates.