A theory for the excitation of CO in star-forming galaxies

Observations of molecular gas in high-z star-forming galaxies typically rely on emission from CO lines arising from states with rotational quantum numbers J > 1. Converting these observations to an estimate of the CO J = 1-0 intensity, and thus inferring H₂ gas masses, requires knowledge of theCOexcitation ladder or spectral line energy distribution (SLED). The few available multi-J CO observations of galaxies show a very broad range of SLEDs, even at fixed galaxy mass and star formation rate (SFR), making the conversion to J = 1-0 emission and hence molecular gas mass highly uncertain. Here, we combine numerical simulations of disc galaxies and galaxy mergers with molecular line radiative transfer calculations to develop a model for the physical parameters that drive variations in CO SLEDs in galaxies. An essential feature of our model is a fully self-consistent computation of the molecular gas temperature and excitation structure. We find that, while the shape of the SLED is ultimately determined by difficult-to-observe quantities such as the gas density, temperature and optical depth distributions, all of these quantities are well correlated with the galaxy's mean star formation rate surface density (∑SFR), which is observable. We use this result to develop a model for the CO SLED in terms of ∑SFR, and show that this model quantitatively reproduces the SLEDs of galaxies over a dynamic range of ∼200 in SFR surface density, at redshifts from z = 0 to 6. This model should make it possible to significantly reduce the uncertainty in deducing molecular gas masses from observations of high-J CO emission.