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The HI Mass Function and Velocity Width Function of Void Galaxies in the Arecibo Legacy Fast ALFA Survey

We measure the HI mass function (HIMF) and velocity width function (WF) across environments over a range of masses $7.2<\log(M_{HI}/M_{\odot})<10.8$, and profile widths $1.3\log(km/s)<\log(W)<2.9\log(km/s)$, using a catalog of ~7,300 HI-selected galaxies from the ALFALFA Survey, located in the region of sky where ALFALFA and SDSS (Data Release 7) North overlap. We divide our galaxy sample into those that reside in large-scale voids (void galaxies) and those that live in denser regions (wall galaxies). We find the void HIMF to be well fit by a Schechter function with normalization $Φ^*=(1.37\pm0.1)\times10^{-2} h^3Mpc^{-3}$, characteristic mass $\log(M^*/M_{\odot})+2\log h_{70}=9.86\pm0.02$, and low-mass-end slope $α=-1.29\pm0.02$. Similarly, for wall galaxies, we find best-fitting parameters $Φ^*=(1.82\pm0.03)\times10^{-2} h^3Mpc^{-3}$, $\log(M^*/M_{\odot})+2\log h_{70}=10.00\pm0.01$, and $α=-1.35\pm0.01$. We conclude that void galaxies typically have slightly lower HI masses than their non-void counterparts, which is in agreement with the dark matter halo mass function shift in voids assuming a simple relationship between DM mass and HI mass. We also find that the low-mass slope of the void HIMF is similar to that of the wall HIMF suggesting that there is either no excess of low-mass galaxies in voids or there is an abundance of intermediate HI mass galaxies. We fit a modified Schechter function to the ALFALFA void WF and determine its best-fitting parameters to be $Φ^*=0.21\pm0.1 h^3Mpc^{-3}$, $\log(W^*)=2.13\pm0.3$, $α=0.52\pm0.5$ and high-width slope $β=1.3\pm0.4$. For wall galaxies, the WF parameters are: $Φ^*=0.022\pm0.009 h^3Mpc^{-3}$, $\log(W^*)=2.62\pm0.5$, $α=-0.64\pm0.2$ and $β=3.58\pm1.5$. Because of large uncertainties on the void and wall width functions, we cannot conclude whether the WF is dependent on the environment.