Deriving a multivariate αCO conversion function using the [C II]/CO (1-0) ratio and its application to molecular gas scaling relations

We present Herschel PACS observations of the [C II] 158 μm emission line in a sample of 24 intermediate mass (9 <log M*/M⊙ <10) and low metallicity (0.4 < Z/Z⊙ <1.0) galaxies from the xCOLD GASS survey. In combination with IRAM CO (1-0) measurements, we establish scaling relations between integrated and molecular region L_{[C II]}/LCO (1-0) ratios as a function of integrated galaxy properties. A Bayesian analysis reveals that only two parameters, metallicity and offset from the main sequence, Δ(MS), are needed to quantify variations in the luminosity ratio; metallicity describes the total dust content available to shield CO from UV radiation, while Δ(MS) describes the strength of this radiation field. We connect the L_{[C II]}/LCO (1-0) ratio to the CO-to-H2 conversion factor and find a multivariate conversion function, which can be used up to z ˜ 2.5. This function depends primarily on metallicity, with a second-order dependence on Δ(MS). We apply this to the full xCOLD GASS and PHIBSS1 surveys and investigate molecular gas scaling relations. We find a flattening of the relation between gas mass fraction and stellar mass at log M* <10.0. While the molecular gas depletion time varies with sSFR, it is mostly independent of mass, indicating that the low LCO/SFR ratios long observed in low-mass galaxies are entirely due to photodissociation of CO and not to an enhanced star formation efficiency.