[CII] Emission in a Self-Regulated Interstellar Medium

The [CII] 157.74 $\mu$m fine structure transition is one of the brightest and most well-studied emission lines in the far-infrared (FIR), produced in the interstellar medium (ISM) of galaxies. We study its properties in sub-pc resolution hydrodynamical simulations for an ISM patch with gas surface density of $\Sigma_{\rm{g}}=10\;M_{\odot}\;\rm{pc}^{-2}$, coupled with time-dependent chemistry, far-ultraviolet (FUV) dust and gas shielding, star formation, photoionization and supernova (SN) feedback, and full line-radiative transfer. We find a [CII]-to-H$_2$ conversion factor that scales weakly with metallicity $X_{\rm{[CII]}}=6.31\times 10^{19} \;Z^{\prime\;0.17}\; \rm{cm}^{-2}\;(\rm{K}\;\rm{km}\;\rm{s}^{-1})^{-1}$, where $Z^{\prime}$ is the normalized metallicity relative to solar. {The majority of [CII] originates from atomic gas with hydrogen number density $n\sim 10~{\rm cm^{-3}}$.} The [CII] line intensity positively correlates with the star formation rate (SFR), with a normalization factor that scales linearly with metallicity. We find that this is broadly consistent with $z\sim0$ observations. As such, [CII] is a good SFR tracer even in metal-poor environments where molecular lines might be undetectable. Resolving the clumpy structure of the dense ($n=10-10^3\;\rm{cm}^{-3}$) interstellar medium (ISM) is important as it dominates [CII] 157.74 $\mu$m emission. We compare our full radiative transfer computation with the optically-thin limit and find that the [CII] line becomes marginally optically thick only at super-solar metallicity for our assumed gas surface density.