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.