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We present the neutral hydrogen mass ($M_{\text{HI}}$) function (HIMF) andvelocity width ($w_{50}$) function (HIWF) based on a sample of 7857 galaxiesfrom the 40% data release of the ALFALFA survey ($\alpha.40$). The low mass(velocity width) end of the HIMF (HIWF) is dominated by the blue population ofgalaxies whereas the red population dominates the HIMF (HIWF) at the high mass(velocity width) end. We use a deconvolution method to estimate the HIrotational velocity ($V_{\text{rot}}$) functions (HIVF) from the HIWF for thetotal, red, and blue samples. The HIWF and HIVF for the red and blue samplesare well separated at the knee of the function compared to their HIMFs. We thenuse recent stacking results from the ALFALFA survey to constrain the halo mass($M_{\text{h}}$) function of HI-selected galaxies. This allows us to obtainvarious scaling relations between $M_{\text{HI}} - w_{50} - V_{\text{rot}} -M_{\text{h}}$, which we present. The $M_{\text{HI}} - M_{\text{h}}$ relationhas a steep slope ~2.10 at small masses and flattens to ~0.34 at masses largerthan a transition halo mass, $\log_{10}(M_{\text{ht}}h^2_{70}/M_{\odot})=10.62$. Our scaling relation is robust and consistent witha volume-limited sample of $\alpha.40$. The $M_{\text{HI}} - M_{\text{h}}$relation is qualitatively similar to the $M_{\text{star}} - M_{\text{h}}$relation but the transition halo mass is smaller by ~1.4 dex compared to thatof the $M_{\text{star}} - M_{\text{h}}$ relation. Our results suggest thatbaryonic processes like heating and feedback in larger mass halos suppress HIgas on a shorter time scale compared to star-formation.

The Dark Matter Halos of HI Selected Galaxies