Populating HI gas in dark matter halos: I. method
  We combine data from the Sloan Digital Sky Survey (SDSS) and the Arecibo
Legacy Fast ALFA Survey (ALFALFA) to establish an empirical model for the HI
gas content within dark matter halos. A cross-match between our SDSS DR7 galaxy
group sample and the ALFALFA HI sources provides a catalog of 16,520 HI-galaxy
pairs within 14,270 galaxy groups (halos). Using these matched pairs, we model
the HI gas mass distributions within halos using two components: 1) {\it in
situ} galaxy relations that involve the HI masses, colors $({\rm g-r})$ and
stellar masses 2) an {\it ex situ} dependence of the HI mass on the halo
mass/environment. We find that if we solely use galaxy associated scaling
relations to predict the HI gas distribution (solely component 1), the number
of HI detections is significantly over-predicted with respect the ALFALFA
observations. We introduce a concept for the survival of the HI masses/members
within halos of different masses labelled as the `efficiency' factor, in order
to describe the probability that a halo has in retaining its HI detections.
Taking the above consideration into account we construct a `halo based HI mass
model' which does not only predict the HI masses of galaxies, but also yields
similar number, stellar, halo mass and satellite fraction distributions to the
HI detections retrieved from observational data.
