Deriving a multivariate CO-to-H$_2$ conversion function using the [CII]/CO(1-0) ratio and its application to molecular gas scaling relations

2017 
We present Herschel PACS observations of the [CII] 158 micron emission line in a sample of 24 intermediate mass (9conversion factor and find a multivariate conversion function $\alpha_{CO}$, which can be used up to z~2.5. This function depends primarily on metallicity, with a second order dependence on $\Delta$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 logM$_\ast$/M$_\odot$<10. While the molecular gas depletion time varies with sSFR, it is mostly independent of mass, indicating that the low L$_{CO}$/SFR ratios long observed in low mass galaxies are entirely due to photodissociation of CO, and not to an enhanced star formation efficiency.
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