# The $HI$- and $H_{2}$-to-stellar mass correlations of late- and early-type galaxies and their consistency with the observational mass functions

## TL;DR

This study derives and analyzes the correlations between HI and H2 gas masses and stellar masses in local galaxies, providing empirical relations and mass functions for different galaxy types to inform galaxy evolution models.

## Contribution

It presents the first comprehensive, homogenized analysis of HI and H2 to stellar mass relations and their distributions for local late- and early-type galaxies, consistent with observed mass functions.

## Key findings

- Late-type galaxies are more gas-rich than early types.
- Gas-to-stellar mass relations are well fitted by power laws.
- Derived mass functions agree with large survey results.

## Abstract

We compile and carrefully homogenize local galaxy samples with available information on stellar, $\rm HI$ and/or $\rm H_{2}$ masses, and morphology. After processing the information on upper limits in the case of non gas detections, we determine the $\rm HI$- and $\rm H_{2}$-to-stellar mass relations and their $1\sigma$ scatter for both late- and early-type galaxies. The obtained relations are fitted to single or double power laws. Late-type galaxies are significantly gas richer than early-type ones, specially at high masses. The respective $\rm H_{2}$-to-$\rm HI$ mass ratios as a function of $M_{\ast}$ are discussed. Further, we constrain the full mass-dependent distribution functions of the $\rm HI$- and $\rm H_{2}$-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. By using the observed galaxy stellar mass function and the volume-complete late-to-early-type galaxy ratio as a function of $M_{\ast}$, these empirical distribution functions are mapped into $\rm HI$ and $\rm H_{2}$ mass functions. The obtained mass functions are consistent with those inferred from large surveys. The empirical gas-to-stellar mass relations and their distributions for local late- and early-type galaxies presented here can be used to constrain models and simulations of galaxy evolution.