The Stellar Mass Function of Gas-Rich Galaxies and the Underlying $M_{\mathrm{HI}}-M_{\mathrm{star}}$ Scaling Relation in the Local Universe

Abstract

We estimate the Galaxy Stellar Mass Function (GSMF) of HI gas-rich galaxies using the 100\% ALFALFA ($\alpha$) catalog, $\sim 98\%$ of which have optical counterparts in the Sloan Digital Sky Survey (SDSS) and a subset of them have counterparts in GALEX SDSS WISE Legacy Catalogue-2(GSWLC-2). We use the mass estimates from this subset which combines UV, optical and IR bands with individual dust corrections to recalibrate optical stellar mass estimates. We use a non-parametric method to estimate the GSMF of these gas-rich galaxies. The resulting, HI-selected GSMF is consistent with a single Schechter function with best-fit parameters $\left\{{\varphi }_{\ast }(10^{-3}{h}_{70}^3{\mathrm{Mpc}}^{-3}{\mathrm{dex}}^{-1}),{\log }_{10}(M_{\ast }/M_{\odot })+2{\log }_{10}{h}_{70},\alpha \right\}=\left\{2.30_{-0.12}^{+0.12},10.83_{-0.01}^{+0.01},-1.14_{-0.02}^{+0.02}\right\}$. Additionally, the red and blue populations are each well described by a single Schechter function. After correcting for selection effects, we find that the red population accounts for only $\sim 18\%$ of gas-rich galaxies by number, yet contributes $\sim 54\%$ of the total stellar mass, with the blue population accounting for the rest. Using an optically selected sample and a joint optical-HI sample, we find gas-rich galaxies represent $\sim 33\%$ of the total stellar mass density and $\sim 39\%$ of the total galaxy number counts in the local Universe. We use the GSMF and the HI mass function (HIMF) of the HI-selected sample to obtain the $M_{\mathrm{HI}}-M_{\mathrm{star}}$ relation, which is free from selection bias.

22 pages, 14 figues