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_*≈ 10⁷-5× 10¹¹\, 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_ [C\, II]/SFR of galaxies in terms of the following parameters: mass fraction of [C\, II]-emitting gas (f_ [C\, II]), gas metallicity (Zgas), gas density (ngas), and gas depletion time (tdep=Mgas/ 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_ [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.
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Liang et al. (2023) studied this question.
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