Understanding the H2/H I ratio in galaxies

We revisit the mass ratio eta(galaxy) between molecular hydrogen (H-2)and atomic hydrogen (H I) in different galaxies from a phenomenological and theoretical viewpoint. First, the local H, mass function (MF) is estimated from the local CO luminosity function (LF) of the FCRAO Extra-galactic CO Survey, adopting a variable CO-to-H-2 conversion fitted to nearby observations. This implies an average H-2 density Omega(H2) = (6.9 +/- 2.7) x 10(-5) h(-1) and Omega(H2)/Omega(H) (I) = 0.26 +/- 0.11 the local Universe. Secondly, we investigate the correlations between eta(galaxy) and global galaxy properties in a sample of 245 local galaxies. Based on these correlations we introduce four phenomenological models for eta(galaxy), which we apply to estimate H-2 masses for each H I galaxy in the HIPASS catalogue. The resulting H-2 MFs (one for each model for eta(galaxy)) are compared to the reference H-2 MF derived from the CO LF, thus allowing LIS to determine the Bayesian evidence of each model and to identify a clear best model, in which, for spiral galaxies, eta(galaxy) negatively correlates with both galaxy Hubble type and total gas mass. Thirdly, we derive a theoretical model for eta(galaxy) for regular galaxies based on an expression for their axially symmetric pressure profile dictating the degree of molecularization. This model is quantitatively similar to the best phenomenological one at redshift z = 0, and hence represents a consistent generalization while providing a physical explanation for the dependence of eta(galaxy) on global galaxy properties. Applying the best phenomenological model for eta(galaxy) to the HIPASS sample, we derive the first integral cold gas MF (H I + H-2) + helium) of the local universe.