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

Abstract: The [CII] 158$\mu$m emission line can arise in all phases of the ISM, therefore being able to disentangle the different contributions is an important yet unresolved problem when undertaking galaxy-wide, integrated [CII] observations. We present a new multi-phase 3D radiative transfer interface that couples Starburst99, a stellar spectrophotometric code, with the photoionisation and astrochemistry codes Mocassin and 3D-PDR. We model entire star forming regions, including the ionised, atomic and molecular phases of the ISM, and apply a Bayesian inference methodology to parametrise how the fraction of the [CII] emission originating from molecular regions, $f_{[CII],mol}$, 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, $f_{[CII],mol}$ can increase from 60% to 80% 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_{[CII],mol}$$=75.8\pm5.9$%, in agreement with the measured value of 75%. When applying the new prescription to a complete sample of galaxies from the Herschel Reference Survey (HRS), we find that anywhere from 60 to 80% of the total integrated [CII] emission arises from molecular regions.