2023A&A...673A..13M

We present a high sensitivity, ground-based spectral line survey of low-J carbon monoxide (CO(J_up → J_up - 1) with J_up = 1, 2, 3) and neutral carbon [CI] ³P₁-³P₀ ([CI](1-0)) in 36 local ultra-luminous infrared galaxies (ULIRGs) and 4 additional LIRGs, all of which have previous Herschel OH 119 μm observations. The study is based on new single-dish observations conducted with the Atacama Pathfinder Experiment (APEX) and complemented with archival APEX and Atacama Large Millimeter Array (ALMA and ACA) data. Our methods are optimized for a multi-tracer study of the total molecular line emission from these ULIRGs, including any extended low-surface-brightness components. We find a tight correlation between the CO and [CI] line luminosities, which suggests that the emission from CO(1-0) (and CO(2-1)) arises from similar regions as the [CI](1-0), at least when averaged over galactic scales. By using [CI] to compute molecular gas masses, we estimate a median CO-to-H₂ conversion factor of ⟨α_CO⟩ = 1.7 ± 0.5 M_⊙ (K km s^–1pc²)^–1 for ULIRGs. We derive median galaxy-integrated CO line ratios of $ \langle r_{21} \rangle = L^\prime_{{\rm CO(2-1)}}/L^\prime_{{\rm CO(1-0)}} = 1.09 $ , $ \langle r_{31} \rangle = L^\prime_{{\rm CO(3-2)}}/L^\prime_{{\rm CO(1-0)}} = 0.76 $ , and $ \langle r_{32} \rangle = L^\prime_{{\rm CO(3-2)}}/L^\prime_{{\rm CO(2-1)}} = 0.76 $ , significantly higher than normal star-forming galaxies, confirming the exceptional molecular gas properties of ULIRGs. We find that the r₂₁ and r₃₂ ratios are poor tracers of CO excitation in ULIRGs, while r₃₁ shows a positive trend with L_IR and star formation rates and a negative trend with the H₂ gas depletion timescales (τ_dep). Our investigation of CO line ratios as a function of gas kinematics shows no clear trends, except for a positive relation between r₂₁ and σ_v, which can be explained by CO opacity effects. These ULIRGs are also characterized by high $ L^\prime_{\rm [CI](1-0)}/L^\prime_{\rm CO(1-0)} $ ratios, with a measured median value of ⟨r_CICO⟩ = 0.18, higher than values from previous interferometric studies that were affected by missing [CI] line flux. The r_CICO values do not show a significant correlation with any of the galaxy properties investigated, including OH outflow velocities and equivalent widths. We find that the widths of [CI](1-0) lines are ∼10% smaller than those of CO lines, and that this discrepancy becomes more significant in ULIRGs with broad lines (σ_v > 150 km s^–1) and when considering the high-v wings of the lines. This suggests that the low optical depth of [CI] can challenge its detection in diffuse, low-surface-brightness outflows and, therefore, its use as a tracer of CO-dark H₂ gas in these components. Finally, we find that higher L_AGN are associated with longer τ_dep, consistent with the hypothesis that active galactic nucleus feedback may reduce the efficiency of star formation. Our study highlights the need for sensitive single-dish multi-tracer H₂ surveys of ULIRGs that are able to recover the flux that is missed by interferometers, especially in the high-frequency lines such as [CI]. The Atacama Large Aperture Submillimeter Telescope (AtLAST) will be transformational for this field.