How are Lyman $\alpha$ absorbers in the cosmic web related to gas-rich
  galaxies?
  We present the two-point cross-correlation function between Lyman $\alpha$
absorbers and HI galaxies in the nearby Universe ($0.01 \le z \le 0.057$). We
use absorbers from 21 QSO sightlines from the Survey of the Low-Redshift
Intergalactic Medium with HST/COS and the galaxy catalogs from the Arecibo
Legacy Fast ALFA survey and the New York University Value-Added Galaxy Catalog.
We find that Lyman $\alpha$ absorbers are strongly correlated to Lyman $\alpha$
galaxies at a projected separation of $\le$0.5 Mpc and velocity separation of
$\le 50~km~s^{-1}$. Lyman $\alpha$ absorbers are 7.6 times more likely to be
found near HI galaxies compared to a random distribution. The correlation
decreases as the projected and/or velocity separation increase. We also find
the correlation between Lyman $\alpha$ absorbers and HI galaxies to be stronger
than those observed between Lyman $\alpha$ absorbers and optically selected
galaxies. There is an enhancement in the number of absorbers at velocity
separations of $\le30~km~s^{-1}$ from HI galaxies at distances larger than
their viral radius. Combined with the fact that most of our galaxies are not
driving strong outflows, we conclude that the absorbers at low-velocity
separations are tracing cooler intergalactic gas around galaxies. This
conclusion is consistent with the predictions from cosmological simulations
where faint gas from the intergalactic medium flows into the disks of galaxies
leading to galaxy growth.
