Tracing Molecular Gas in z $\simeq$ 6 Galaxies with [C$\mathrm{II}$]

Abstract

We investigate the fine-structure [C$\mathrm{II}$] line at $158\mu$m as a molecular gas tracer by analyzing the relationship between molecular gas mass ($M_{\mathrm{mol}}$) and [C$\mathrm{II}$] line luminosity ($L_{[\mathrm{CII}]}$) in 11,125 $z\simeq 6$ star-forming, main sequence galaxies from the SIMBA simulations, with line emission modeled by SÍGAME. Though most ($\sim 50-100\%$) of the gas mass in our simulations is ionized, the bulk ($>50\%$) of the [C$\mathrm{II}$] emission comes from the molecular phase. We find a sub-linear (slope $0.78\pm 0.01$) $\log L_{[\mathrm{CII}]}-\log M_{\mathrm{mol}}$ relation, in contrast with the linear relation derived from observational samples of more massive, metal-rich galaxies at $z\lesssim 6$. We derive a median [C$\mathrm{II}$]-to-$M_{\mathrm{mol}}$ conversion factor of ${\alpha }_{[\mathrm{CII}]}\simeq 18{\mathrm{M}}_{\odot }/{\mathrm{L}}_{\odot }$. This is lower than the average value of $\simeq 30{\mathrm{M}}_{\odot }/{\mathrm{L}}_{\odot }$ derived from observations, which we attribute to lower gas-phase metallicities in our simulations. Thus, a lower, luminosity-dependent, conversion factor must be applied when inferring molecular gas masses from [C$\mathrm{II}$] observations of low-mass galaxies. For our simulations, [C$\mathrm{II}$] is a better tracer of the molecular gas than CO $J=1-0$, especially at the lowest metallicities, where much of the gas is 'CO-dark'. We find that $L_{[\mathrm{CII}]}$ is more tightly correlated with $M_{\mathrm{mol}}$ than with star-formation rate ($\mathrm{SFR}$), and both the $\log L_{[\mathrm{CII}]}-\log M_{\mathrm{mol}}$ and $\log L_{[\mathrm{CII}]}-\log \mathrm{SFR}$ relations arise from the Kennicutt-Schmidt relation. Our findings suggest that $L_{[\mathrm{CII}]}$ is a promising tracer of the molecular gas at the earliest cosmic epochs.

13 pages, 9 figures. Accepted for publication in ApJ

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