Radiative transfer meets Bayesian statistics: where does a galaxy's [C II] emission come from?

[C-II] 158 mu m emission line can arise in all phases of the interstellar medium (ISM), therefore being able to disentangle the different contributions is an important yet unresolved problem when undertaking galaxy-wide, integrated [C-II] observations. We present a new multiphase 3D radiative transfer interface that couples STARBURST99, a stellar spectrophotometric code, with the photoionization and astrochemistry codes MOCASSIN and 3D-PDR. We model entire star-forming regions, including the ionized, atomic, and molecular phases of the ISM, and apply a Bayesian inference methodology to parametrize how the fraction of the [C-II] emission originating from molecular regions, f([C II],mol), varies as a function of typical integrated properties of galaxies in the local Universe. The main parameters responsible for the variations of f([CII],mol) are specific star formation rate (SSFR), gas phase metallicity, HII region electron number density (n(e)), and dust mass fraction. For example, f([C II],mol) can increase from 60 to 80 per cent when either n(e) increases from 10(1.5) to 10(2.5) cm (3), or SSFR decreases from 10 (9.6) to 10 (10.6) yr (1). Our model predicts for the Milky Way that f([C II], mol) = 75.8 +/- 5.9 per cent, in agreement with the measured value of 75 per cent. When applying the new prescription to a complete sample of galaxies from the Herschel Reference Survey, we find that anywhere from 60 to 80 per cent of the total integrated [C-II] emission arises from molecular regions.