Tight correlation of star formation with [Ci] and CO lines across cosmic time

TL;DR

This study combines 885 literature sources to investigate how star formation rates scale with cold molecular gas tracers CO(1-0) and [CI](1-0), and with [CII], across 0 < z < 6.5. Using two regression frameworks, the authors derive near-linear to mildly superlinear SFR–line luminosity relations for CI and CO and quantify the [CII]-SFR relation, while carefully correcting for gravitational lensing and converting CO(2-1) to CO(1-0). They find that CI and CO trace similar molecular gas contents across cosmic time, with CI often yielding higher inferred H2 masses than CO unless abundances and conversion factors are adjusted; [CII] remains a valid but more uncertain SFR tracer due to scatter and possible deficits at high SFR or low metallicity. Overall, the results indicate little strong evolution in these relations with cosmic time and support CI as a robust molecular gas tracer alongside CO, with implications for interpreting gas content in high-redshift galaxies.

Abstract

Context. Cold molecular gas tracers, such as CI and CO lines, have been widely used to infer specific characteristics of the ISM and to derive star-formation relations among galaxies. Aims. However, there is still a lack of systematic studies of the star-formation scaling relation of CO and [CI] lines across cosmic time on multiple physical scales. Methods. We used observations of the ground state transitions of [CI], CO, and [CII], for 885 sources collected from the literature, to infer possible correlations between line luminosities of $\rm L^{'}_{[CI](1-0)}, \rm L^{'}_{CO(1-0)}$, and $\rm L^{'}_{[CII]}$ with star formation rates (SFR). With linear regression, we fit the relations between SFR and molecular mass derived from CO, CI, and CII lines. Results. The relation between [CI] and CO-based total molecular masses is weakly superlinear. Nevertheless, they can be calibrated against each other. For $\rm α_{CO} = 0.8$ and $4.0\ \rm {M}_{\odot}\,({K}\,{km}\,{s}^{-1}\,{pc}^2)^{-1}$ we derive $α_{\rm [CI]} = 3.9$ and $\sim$$17\ \rm {M}_{\odot}\,({K}\,{km}\,{s}^{-1}\,{pc}^2)^{-1}$ , respectively. Using the \emph{lmfit} package, we derived relation slopes of SFR--$\rm L^{'}_{[CI](1-0)}$, SFR--$\rm L^{'}_{CO(1-0)}$, and SFR--$\rm L^{'}_{[CII](1-0)}$ to be $\rm β$ = 1.06 $\pm$ 0.02, 1.24 $\pm$ 0.02, and 0.74 $\pm$ 0.02, respectively. With a Bayesian-inference \emph{linmix} method, we find consistent results. Conclusions. Our relations for [CI](1-0) and CO(1-0) indicate that they trace similar molecular gas contents, across different redshifts and different types of galaxies. This suggests that these correlations do not have strong evolution with cosmic time.

Figures (5)

• Figure 1: Redshift distribution for our sample.
• Figure 2: $\rm M(H_2)^{[CI]}$ versus $\rm M(H_2)^{CO}$ plot. The best fit using the lmfit package (red dashed line), and the linmix package (thick black solid line) are presented in the figure. The 1-to-1 line is presented with a dashed black line. Finally, the relation derived in montoya2023sensitive ($\rm \log M(H_2)^{[CI]} = (1.21 \pm 2.42) + (0.91 \pm 0.25)\,\rm \log M(H_2)^{CO}$) is included with a dotted magenta line.
• Figure 3: $\rm L_{IR}$ versus $\rm L^{'}_{[CI](1-0)}$ (panel a), $\rm L^{'}_{CO(1-0)}$ (panel b) luminosities, $\rm L^{'}_{[CI](1-0)}$/$\rm L^{'}_{CO(1-0)}$ ratio against redshift (panel c), and $\rm L^{'}_{[CI](1-0)}$/$\rm L^{'}_{CO(1-0)}$ ratio against $\rm L_{IR}$ (panel d). The secondary y-axis represents the SFR and the secondary x-axis the total molecular masses computed using the corresponding tracer. We include the best fit using the Levenberg-Marquardt algorithm of the lmfit package (red dashed line), and the Bayesian approach to linear regression using the linmix package (solid black line). In panel (b) we include the relations presented in sargent2014regularity for main-sequence galaxies (thick black dashed line), and starburst galaxies (dashed-dotted line). In panels (a) and (b), the relations derived in montoya2023sensitive for CO(1-0) and [C i](1-0) line detections are presented (magenta dashed lines). Panels (c) and (d) include the lmfit and linmix method fits, with solid red and dashed black lines, respectively. In panel (d), the black dash-dotted line presents the mean $\rm L^{'}_{[CI](1-0)}$/$\rm L^{'}_{CO(1-0)}$ value and the scatter (gray shaded area) derived by gerin2000atomic.
• Figure 4: SFR versus $\rm L^{'}_{[CII]}$ for the samples of cormier2015herschel (green triangles), olsen2017sigame (orange triangles), bothwell2017alma (black squares) and glazer2024studying and references therein (red symbols and teal stars). The red solid line represents the best fit for the listed sample based on a Levenberg-Marquardt algorithm, and the thick black dashed line represents the Bayesian fitting. The gray, black, and blue dashed lines represent different best-fitting relations presented by herrera2015cpineda2014aherschel, and sutter2019using, respectively. In addition, we plot with solid black, blue, and green lines the de2014applicability Dwarf Galaxy Survey (DGS), the normal and high star formation efficiencies relations by herrera2018shining (HC+ 2018), respectively. Also, the relation given in bisbas2022origin is presented with a dashed magenta line. Finally, the relation that best fits the simulated data presented by olsen2017sigame is also included in the figure with a dashed-doted yellow line.
• Figure 5: SFR versus $\rm L^{'}_{line}$ relations color-coded with respect to redshift.