We present a high sensitivity, ground-based spectral line survey of low-J carbon monoxide (CO(Jup → Jup − 1) with Jup = 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 ⟨αCO⟩ = 1.7 ± 0.5 M⊙ (K km s−1pc2)−1 for ULIRGs. We derive median galaxy-integrated CO line ratios of 〈r21〉 = LCO(2-1)′/LCO(1-0)′ = 1.09, 〈r31〉 = LCO(3-2)′/LCO(1-0)′ = 0.76, and 〈r32〉 = LCO(3-2)′/LCO(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 LIR and star formation rates and a negative trend with the H2 gas depletion timescales (τdep). Our investigation of CO line ratios as a function of gas kinematics shows no clear trends, except for a positive relation between r21 and σv, which can be explained by CO opacity effects. These ULIRGs are also characterized by high L[CI](1-0)′/LCO(1-0)′ ratios, with a measured median value of ⟨rCICO⟩ = 0.18, higher than values from previous interferometric studies that were affected by missing [CI] line flux. The rCICO 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 (σv > 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 LAGN are associated with longer τdep, 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.
