VALES: III. The calibration between the dust continuum and interstellar gas content of star-forming galaxies

We present the calibration between the dust continuum luminosity and interstellar gas content obtained from the Valpara\'{i}so ALMA Line Emission Survey (VALES) sample of 67 main-sequence star-forming galaxies at 0.02<$z$<0.35. We use CO(1-0) observations from the Atacama Large Millimetre/submillimetre Array (ALMA) to trace the molecular gas mass, $M_{\mathrm{H}_{2}}$, and estimate the rest-frame monochromatic luminosity at 850 $\mu$m, $L_{\nu_{850}}$, by extrapolating the dust continuum from MAGPHYS modelling of the far-ultraviolet to submillimetre spectral energy distribution sampled by the Galaxy And Mass Assembly (GAMA) survey. Adopting $\alpha_{\rm CO}$ = 6.5 (K km s$^{-1}$ pc$^{2}$)$^{-1}$, the average ratio of $L_{\nu_{850}}/M_{\mathrm{H}_{2}}$ = (6.4$\pm$1.4)$\times10^{19}$ erg s$^{-1}$ Hz$^{-1}$ $\mathrm{M}_{\odot}^{-1}$, in excellent agreement with literature values. We obtain a linear fit of $\log_{10}$ ($M_{\mathrm{H}_{2}}/\mathrm{M}_{\odot}$) = (0.92$\pm$0.02) $\log_{10}$ ($L_{\nu_{850}}$/erg s$^{-1}$ Hz$^{-1}$)-(17.31$\pm$0.59). We provide relations between $L_{\nu_{850}}$, $M_{\mathrm{H}_{2}}$ and $M_{\mathrm{ISM}}$ when combining the VALES and literature samples, and adopting a Galactic $\alpha_{\rm CO}$ value.