The HI- and H2-to-Stellar Mass Correlations of Late- and Early-Type Galaxies and their Consistency with the Observational Mass Functions

We compile and homogenize local galaxy samples with available information on morphology, and stellar, HI and/or H₂ masses. After taking into account non gas detections, we determine the HI- and H₂-to-stellar mass relations and their 1σ scatter for late- and early-type galaxies. These relations are fitted to single or double power laws. Late-type galaxies are significantly gas richer than early-type ones, especially at high masses. The H₂-to-HI mass ratios as a function of M_* are discussed. We constrain the distribution functions of the HI- and H₂-to-stellar mass ratios. We find that they can be described by a Schechter function for late types and a (broken) Schechter + uniform function for early types. Using the observed galaxy stellar mass function and the volumecomplete late-to-early-type galaxy ratio as a function of M_*, these distributions are mapped into HI and H₂ mass functions. The mass functions are consistent with those inferred from large surveys. The results presented here can be used to constrain models and simulations of galaxy evolution.