The Stellar Mass Function of Gas-Rich Galaxies and the Underlying M HI-M star Scaling Relation in the Local Universe

We estimate the Galaxy Stellar Mass Function (GSMF) of HI gas-rich galaxies using the 100% ALFALFA (alpha) catalog, about 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 phi* (10-3, h 70 cubed, Mpc-3, dex-1), 10 (M*/M) + 2 10 h 70, alpha = 2.30+0.12-0.12,,10.83+0.01-0.01,, -1.14+0.02-0.02. 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 about18% of gas-rich galaxies by number, yet contributes about54% 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 about 33% of the total stellar mass density and about 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 HI-M star relation, which is free from selection bias.