$[{\mathrm{C}}_{\mathrm{II}}]$ 158 $\hat{\mathrm{I}}¼\mathrm{m}$ emission as an indicator of galaxy star formation rate

Abstract

Observations of local star-forming galaxies (SFGs) show a tight correlation between their singly ionized carbon line luminosity ($L_{[{\mathrm{C}}_{\mathrm{II}}]}$) and star formation rate (SFR), suggesting that $L_{[{\mathrm{C}}_{\mathrm{II}}]}$ may be a useful SFR tracer for galaxies. Some other galaxy populations, however, are found to have lower $L_{[{\mathrm{C}}_{\mathrm{II}}]}/\mathrm{SFR}$ than the local SFGs, including the infrared-luminous, starburst galaxies at low and high redshifts, as well as some moderately star-forming galaxies at the epoch of re-ionization (EoR). The origin of this `$[{\mathrm{C}}_{\mathrm{II}}]$ deficit' is unclear. In this work, we study the $L_{[{\mathrm{C}}_{\mathrm{II}}]}$-SFR relation of galaxies using a sample of $z=0-8$ galaxies with $M_{\ast }\approx 10^7-5\times 10^{11}{M}_{\odot }$ extracted from cosmological volume and zoom-in simulations from the Feedback in Realistic Environments (FIRE) project. We find a simple analytic expression for $L_{[{\mathrm{C}}_{\mathrm{II}}]}$/SFR of galaxies in terms of the following parameters: mass fraction of $[{\mathrm{C}}_{\mathrm{II}}]$-emitting gas ($f_{[{\mathrm{C}}_{\mathrm{II}}]}$), gas metallicity ($Z_{\mathrm{gas}}$), gas density ($n_{\mathrm{gas}}$) and gas depletion time ($t_{\mathrm{dep}}=M_{\mathrm{gas}}/\mathrm{SFR}$). We find two distinct physical regimes, where $t_{\mathrm{dep}}$ ($Z_{\mathrm{gas}}$) is the main driver of the $[{\mathrm{C}}_{\mathrm{II}}]$ deficit in ${\mathrm{H}}_2$-rich (${\mathrm{H}}_2$-poor) galaxies. The observed $[{\mathrm{C}}_{\mathrm{II}}]$ 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 $[{\mathrm{C}}_{\mathrm{II}}]$ deficit is a common phenomenon of galaxies, and caution needs to be taken when applying a constant $L_{[{\mathrm{C}}_{\mathrm{II}}]}$-to-SFR conversion factor derived from local SFGs to estimate cosmic SFR density at high redshifts and interpret data from upcoming $[{\mathrm{C}}_{\mathrm{II}}]$ line intensity mapping experiments.

44 page, 24 figures, 8 tables and 8 appendices, accepted for publication in MNRAS. Key figures: fig. 16 & 17. Comments are welcome