Ionized Carbon in Galaxies: The [C II] 158 $\mu$m Line as a Total Molecular Gas Mass Tracer Revisited

In this paper we present a statistical study of the [C II] 158 $\mu$m line and the CO(1-0) emission for a sample of $\sim$200 local and high-$z$ (32 sources with $z>1$) galaxies with much different physical conditions. We explore the correlation between the luminosities of [C II] and CO(1-0) lines, and obtain a strong linear relationship, confirming that [C II] is able to trace total molecular gas mass, with a small difference between (U)LIRGs and less-luminous galaxies. The tight and linear relation between [C II] and CO(1-0) is likely determined by the average value of the observed visual extinction $A_V$ and the range of $G_0/n$ in galaxies. Further investigations into the dependence of $L_{\mathrm{[CII]}}/L_{\mathrm{CO(1-0)}}$ on different physical properties show that $L_{\mathrm{[CII]}}/L_{\mathrm{CO(1-0)}}$ (1) anti-correlates with $\Sigma_{\mathrm{IR}}$, and the correlation becomes steeper when $\Sigma_{\mathrm{IR}} \gtrsim 10^{11}$ $L_\odot\,\mathrm{kpc}^{-2}$; (2) correlates positively with the distance from the main sequence $\Delta(\mathrm{MS})$ when $\Delta(\mathrm{MS})\lesssim 0$; and (3) tends to show a systematically smaller value in systems where the [C II] emission is dominated by ionized gas. Our results imply that caution needs to be taken when applying a constant [[C II]-to-$M_{\mathrm{H_2}}$ conversion factor to estimate the molecular gas content in extreme cases, such as galaxies having low-level star formation activity or high SFR surface density.