We revisit the mass ratio R _ { mol } ^ { galaxy } between molecular hydrogen ( H _ { 2 } ) and atomic hydrogen ( HI ) in different galaxies from a phenomenological and theoretical viewpoint .
First , the local H _ { 2 } -mass function ( MF ) is estimated from the local CO-luminosity function ( LF ) of the FCRAO Extragalactic CO-Survey , adopting a variable CO-to-H _ { 2 } conversion fitted to nearby observations .
This implies an average H _ { 2 } -density \Omega _ { { H } _ { 2 } } = ( 6.9 \pm 2.7 ) \cdot 10 ^ { -5 } h ^ { -1 } and \Omega _ { { H } _ { 2 } } / \Omega _ { HI } = 0.26 \pm 0.11 in the local Universe .
Second , we investigate the correlations between R _ { mol } ^ { galaxy } and global galaxy properties in a sample of 245 local galaxies .
Based on these correlations we introduce four phenomenological models for R _ { mol } ^ { galaxy } , which we apply to estimate H _ { 2 } -masses for each HI-galaxy in the HIPASS catalog .
The resulting H _ { 2 } -MFs ( one for each model for R _ { mol } ^ { galaxy } ) are compared to the reference H _ { 2 } -MF derived from the CO-LF , thus allowing us to determine the Bayesian evidence of each model and to identify a clear best model , in which , for spiral galaxies , R _ { mol } ^ { galaxy } negatively correlates with both galaxy Hubble type and total gas mass .
Third , we derive a theoretical model for R _ { mol } ^ { 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 R _ { mol } ^ { galaxy } on global galaxy properties .
Applying the best phenomenological model for R _ { mol } ^ { galaxy } to the HIPASS sample , we derive the first integral cold gas-MF ( HI+H _ { 2 } +helium ) of the local Universe .