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
$\Phi^*=(1.37\pm0.1)\times10^{-2} h^3Mpc^{-3}$, characteristic mass
$\log(M^*/M_{\odot})+2\log h_{70}=9.86\pm0.02$, and low-mass-end slope
$\alpha=-1.29\pm0.02$. Similarly, for wall galaxies, we find best-fitting
parameters $\Phi^*=(1.82\pm0.03)\times10^{-2} h^3Mpc^{-3}$,
$\log(M^*/M_{\odot})+2\log h_{70}=10.00\pm0.01$, and $\alpha=-1.35\pm0.01$. 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 $\Phi^*=0.21\pm0.1 h^3Mpc^{-3}$,
$\log(W^*)=2.13\pm0.3$, $\alpha=0.52\pm0.5$ and high-width slope
$\beta=1.3\pm0.4$. For wall galaxies, the WF parameters are:
$\Phi^*=0.022\pm0.009 h^3Mpc^{-3}$, $\log(W^*)=2.62\pm0.5$,
$\alpha=-0.64\pm0.2$ and $\beta=3.58\pm1.5$. Because of large uncertainties on
the void and wall width functions, we cannot conclude whether the WF is
dependent on the environment.
