The Distribution of Neutral Hydrogen in the Color-Magnitude Plane of Galaxies

We present the conditional HI (neutral hydrogen) Mass Function (HIMF) conditioned on observed optical properties, $M_{\text{r}}$ ($r$-band absolute magnitude) and $C_{\text{ur}}$ ($u-r$ color), for a sample of 7709 galaxies from ALFALFA (40% data release - $\alpha.40$) which overlaps with a common volume in SDSS DR7. Based on the conditional HIMF we find that the luminous red, luminous blue and faint blue populations dominate the total HIMF at the high-mass end, knee and the low-mass end respectively. We use the conditional HIMF to derive the underlying distribution function of $\Omega_{\text{HI}}$ (HI density parameter), $p(\Omega_{\text{HI}})$, in the color-magnitude plane of galaxies. The distribution, $p(\Omega_{\text{HI}})$, peaks in the blue cloud at $M_{\text{r}}^{\text{max}}=$ $-19.25, C_{\text{ur}}^{\text{max}}=1.44$ but is skewed. It has a long tail towards faint blue galaxies and luminous red galaxies. We argue that $p(\Omega_{\text{HI}})$ can be used to reveal the underlying relation between cold gas, stellar mass and the star formation rate (SFR) in an unbiased way; that is the derived relation does not suffer from survey or sample selection.