MUSEQuBES: Connecting HI absorption with Ly$\alpha$ emitters at $z \approx 3.3$

We present a comprehensive analysis of HI absorption around 96 lya emitters (LAEs) at $z\approx3.3$ (median lya luminosity $\approx10^{42}$ erg.s$^{-1}$). These LAEs were identified within 8 MUSE fields, each $1'\times1'$ on the sky and centered on a bright background quasar, as part of the MUSEQuBES survey. Using Voigt profile fitting for all HI absorbers detected within $\pm500$ km.$s^{-1}$ of these LAEs, we compiled a catalog of 800 HI absorption components. Our analysis shows that HI absorption is enhanced near the LAEs compared to the IGM. However, no trend is found between the column densities of HI absorbers and their impact parameters from the LAEs (spanning $\approx54$ to 260 pkpc). Additionally, all galaxies associated with Lyman-limit systems have impact parameters $>50$ pkpc from the quasar sightlines, suggesting that true absorber-hosts may be too faint to detect. The LAEs show an overall HI covering fraction (fc(HI)) of $\approx88\%$ for a threshold logN(HI)$=15$. Notably, at the same threshold, the pairs/group LAEs exhibit a $100\%$ HI covering fraction out to $\approx 250$ pkpc. In contrast, isolated LAEs consistently show a lower fc(HI) of $\approx80\%$. This environmental influence on fc(HI) is also evident up to $\approx 300$ km.$s^{-1}$ in differential bins of line-of-sight velocity. We find an anti-correlation between fc(HI) and the rest-frame lya-emission equivalent width (ew). Based on the lya-shell model, this could imply that gas-rich galaxies tend to reside in gas-rich environments or that the higher EW LAEs are more efficient at ionizing their surrounding medium.