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ABSTRACT Observations of local star-forming galaxies (SFGs) show a tight correlation between their singly ionized carbon line luminosity (L ₂\, ₈₈) and star formation rate (SFR), suggesting that L ₂\, ₈₈ may be a useful SFR tracer for galaxies. Some other galaxy populations, however, are found to have lower L ₂\, ₈₈/ 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 ₂\, ₈₈–SFR relation of galaxies using a sample of z = 0–8 galaxies with M_* 10⁷-5 10^11\, M_ extracted from cosmological volume and zoom-in simulations from the Feedback in Realistic Environments (fire) project. We find a simple analytic expression for L ₂\, ₈₈/SFR of galaxies in terms of the following parameters: mass fraction of C\, II-emitting gas (f ₂\, ₈₈), gas metallicity (Zgas), gas density (ngas), and gas depletion time (t ₃₄=M ₆₀ₒ/ SFR). We find two distinct physical regimes: H₂-rich galaxies, where tdep is the main driver of the C\, II deficit and H₂-poor galaxies where Zgas 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 ₂\, ₈₈-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.
Liang et al. (Mon,) studied this question.