$L_{CO}^{\prime }/L_{FIR}$ relations with CO rotational ladders of galaxies across the Herschel spire archive

We present a catalog of all CO (J = 4−3 through J = 13−12), [C i], and [N ii] lines available from extragalactic spectra from the Herschel SPIRE Fourier Transform Spectrometer (FTS) archive combined with observations of the low-J CO lines from the literature and from the Arizona Radio Observatory. This work examines the relationships between L _FIR, $L_{CO}^{\prime }$, and L _CO/L _CO,1−0. We also present a new method for estimating probability distribution functions from marginal signal-to-noise ratio Herschel FTS spectra, which takes into account the instrumental "ringing" and the resulting highly correlated nature of the spectra. The slopes of log(L _FIR) versus log($L_{CO}^{\prime }$) are linear for all mid- to high-J CO lines and slightly sublinear if restricted to (ultra)luminous infrared galaxies ((U)LIRGs). The mid- to high-J CO luminosity relative to CO J = 1−0 increases with increasing L _FIR, indicating higher excitement of the molecular gas, although these ratios do not exceed ∼180. For a given bin in L _FIR, the luminosities relative to CO J = 1−0 remain relatively flat from J = 6−5 through J = 13−12, across three orders of magnitude of L _FIR. A single component theoretical photodissociation region (PDR) model cannot match these flat SLED shapes, although combinations of PDR models with mechanical heating added qualitatively match the shapes, indicating the need for further comprehensive modeling of the excitation processes of warm molecular gas in nearby galaxies.