[C <scp>ii</scp>] 158 μm emission as an indicator of galaxy star formation rate
Lichen Liang, Robert Feldmann, Norman Murray, Desika Narayanan, Christopher C. Hayward, Daniel Anglés‐Alcázar, Luigi Bassini, Alexander J. Richings, Claude‐André Faucher‐Giguère, Dongwoo T. Chung, Jennifer Y H Chan, D. Tolgay, Onur Çatmabacak, Dušan Kereš, Philip F. Hopkins
Abstract
ABSTRACT Observations of local star-forming galaxies (SFGs) show a tight correlation between their singly ionized carbon line luminosity ($L_{\rm [C\, {\small II}]}$) and star formation rate (SFR), suggesting that $L_{\rm [C\, {\small II}]}$ may be a useful SFR tracer for galaxies. Some other galaxy populations, however, are found to have lower $L_{\rm [C\, {\small II}]}{}/{}\rm SFR$ 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 ‘$\rm [C\, {\small II}]$ deficit’ is unclear. In this work, we study the $L_{\rm [C\, {\small II}]}$–SFR relation of galaxies using a sample of z = 0–8 galaxies with $M_*\approx 10^7-5\times 10^{11}\, \mathrm{M}_\odot$ extracted from cosmological volume and zoom-in simulations from the Feedback in Realistic Environments (fire) project. We find a simple analytic expression for $L_{\rm [C\, {\small II}]}$/SFR of galaxies in terms of the following parameters: mass fraction of $\rm [C\, {\small II}]$-emitting gas ($f_{\rm [C\, {\small II}]}$), gas metallicity (Zgas), gas density (ngas), and gas depletion time ($t_{\rm dep}{}={}M_{\rm gas}{}/{}\rm SFR$). We find two distinct physical regimes: $\rm H_2$-rich galaxies, where tdep is the main driver of the $\rm [C\, {\small II}]$ deficit and $\rm H_2$-poor galaxies where Zgas is the main driver. The observed $\rm [C\, {\small II}]$ 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 $\rm [C\, {\small II}]$ deficit is a common phenomenon of galaxies, and caution needs to be taken when applying a constant $L_{\rm [C\, {\small II}]}$-to-SFR conversion factor derived from local SFGs to estimate cosmic SFR density at high redshifts and interpret data from upcoming $\rm [C\, {\small II}]$ line intensity mapping experiments.