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

¹ I. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany
² Research Center for Astronomical Computing, Zhejiang Lab, Hangzhou 311100, China
³ School of Astronomy and Space Science, Nanjing University, Nanjing, China
⁴ Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University, Ministry of Education, Nanjing, China

^⋆ Corresponding authors: topkaras@ph1.uni-koeln.de; tbisbas@zhejianglab.com

Received: 26 June 2024
Accepted: 13 August 2025

Abstract

Context. Cold molecular gas tracers, such as C I and CO lines, have been widely used to infer specific characteristics of the interstellar medium (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 [C I] lines across cosmic time on multiple physical scales.

Methods. We used observations of the ground state transitions of [C I], CO, and [C II], for 885 sources collected from the literature, to infer possible correlations between line luminosities of L′_[CI](1−0), L′_{CO(1 − 0)}, and L′_[CII] with star formation rates (SFRs). With linear regression, we fit the relations between SFR and molecular mass derived from CO, C I, and C II lines.

Results. The relation between [C I]- and CO-based total molecular masses is weakly superlinear. Nevertheless, they can be calibrated against each other. For α_CO = 0.8 and 4.0 M_⊙(K km s⁻¹ pc²)⁻¹ we derived α_[CI] = 3.9 and ∼ 17 M_⊙(K km s⁻¹ pc²)⁻¹, respectively. Using the lmfit package, we derived relation slopes of SFR–L′_{[CI](1 − 0)}, SFR–L′_{CO(1 − 0)}, and SFR–L′_{[CII](1 − 0)} to be β = 1.06 ± 0.02, 1.24 ± 0.02, and 0.74 ± 0.02, respectively. With a Bayesian inference linmix method, we find consistent results.

Conclusions. Our relations for [C I](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.