[CII] 158 m emission as an indicator of galaxy star formation rate

Observations of local star-forming galaxies (SFGs) show a tight correlation between their singly ionized carbon line luminosity (L-[C II]) and star formation rate (SFR), suggesting that L-[C II] may be a useful SFR tracer for galaxies. Some other galaxy populations, however, are found to have lower L-[C II]/SFR than local SFGs, including the infrared (IR)-luminous, starburst galaxies at low and high redshifts as well as some moderately SFGs at the epoch of re-ionization (EoR). The origins of this '[C II] deficit' is unclear. In this work, we study the L-[C II]-SFR relation of galaxies using a sample of z = 0-8 galaxies with M-* approximate to 10(7) - 5 x10(11) M circle dot extracted from cosmological volume and zoom-in simulations from the Feedback in Realistic Environments (FIRE) project. We find a simple analytic expression for L-[C II]/SFR of galaxies in terms of the following parameters: mass fraction of [C II]-emitting gas (f([C II])), gas metallicity (Z(gas)), gas density (n(gas)), and gas depletion time (t(dep) = M-gas/SFR). We find two distinct physical regimes: H-2-rich galaxies, where t dep is the main driver of the [C II] deficit and H-2-poor galaxies where Z(gas) is the main driver. The observed [C II] deficit of IR-luminous galaxies and early EoR galaxies, corresponding to the two different regimes, is due to short gas depletion time and low gas metallicity, respectively. Our result indicates that the [C II] deficit is a common phenomenon of galaxies, and caution needs to be taken when applying a constant L-[C II]-to-SFR conversion factor derived from local SFGs to estimate cosmic SFR density at high redshifts and interpret data from upcoming [C II] line intensity mapping experiments.