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 H-2 gas masses, requires knowledge of the CO excitation 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 (I (SFR)) pound, which is observable. We use this result to develop a model for the CO SLED in terms of I (SFR) pound, and show that this model quantitatively reproduces the SLEDs of galaxies over a dynamic range of similar to 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.