Star formation relations and CO SLEDs across the J-ladder and redshift

We present FIR [50-300 mu m]-CO luminosity relations (i.e., log L-FIR = alpha log L'(CO) + beta) for the full CO rotational ladder from J = 1-0 up to J = 13-12 for a sample of 62 local (z <= 0.1) (Ultra) Luminous InfraredGalaxies (LIRGs; LIR[8-1000 mu m] > 10(11) L-circle dot) using data from Herschel SPIRE-FTS and ground-based telescopes. We extend our sample to high redshifts (z > 1) by including 35 submillimeter selected dusty star forming galaxies from the literature with robust CO observations, and sufficiently well-sampled FIR/submillimeter spectral energy distributions (SEDs), so that accurate FIR luminosities can be determined. The addition of luminous starbursts at high redshifts enlarge the range of the FIR-CO luminosity relations toward the high-IR-luminosity end, while also significantly increasing the small amount of mid-J/high-J CO line data (J = 5-4 and higher) that was available prior to Herschel. This new data set (both in terms of IR luminosity and J-ladder) reveals linear FIR-CO luminosity relations (i.e., a similar or equal to 1) for J = 1-0 up to J = 5-4, with a nearly constant normalization (beta similar to 2). In the simplest physical scenario, this is expected from the (also) linear FIR-(molecular line) relations recently found for the dense gas tracer lines (HCN and CS), as long as the dense gas mass fraction does not vary strongly within our (merger/starburst)-dominated sample. However, from J = 6-5 and up to the J = 13-12 transition, we find an increasingly sublinear slope and higher normalization constant with increasing J. We argue that these are caused by a warm (similar to 100 K) and dense (>10(4) cm(-3)) gas component whose thermal state is unlikely to be maintained by star-formation-powered far-UV radiation fields (and thus is no longer directly tied to the star formation rate). We suggest that mechanical heating (e.g., supernova-driven turbulence and shocks), and not cosmic rays, is the more likely source of energy for this component. The global CO spectral line energy distributions, which remain highly excited from J = 6-5 up to J = 13-12, are found to be a generic feature of the (U)LIRGs in our sample, and further support the presence of this gas component.