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MUSEQuBES: Investigating the Physical and Chemical Properties of Circumgalactic Gas Around Ly$α$ Emitters at $z \approx 3.3$

We present a detailed study of the physical properties of absorbers associated with $z\approx3.3$ \lya\ emitters (LAEs) from the MUSEQuBES survey. Using \HI\ and ionic column densities derived from Voigt profile fitting, we determine the density and metallicity of 75 absorbers associated with 59 LAEs through a custom-built Bayesian framework. The overall sample shows a median density $\log\,(n_{\rm H}/{\rm cm^{-3}})=-2.7\pm0.7$ and metallicity \met$=-1.6^{+1.2}_{-0.9}$ with $\approx15\%$ ($\approx 40\%$ including upper limits) of systems showing metallicities consistent with the IGM at these redshifts (\met$\lesssim -2.8$). Intriguingly, absorbers with $\log\, N(\rm HI)/{\rm cm^{-2}} \gtrsim 16.5$, corresponding to an overdensity of $\sim 100$ at $z=3$, exhibit a bimodal metallicity distribution with peaks at \met$=-3.8\pm 0.2$ and $-1.8\pm 0.6$. The latter are observed at large impact parameters ($\gtrsim150$~pkpc) and often exhibit low-ionization species (e.g., \SiII, \AlII). We interpret the former as pristine inflowing gas from the cosmic web, while the latter likely traces metal-enriched CGM associated with outflows from faint galaxies not detected in Ly$α$ emission. We find no significant correlations between absorber metallicity or density and host galaxy properties, including redshift, impact parameter, SFR, Ly$α$ luminosity, or environment. Absorbers separated by $\lesssim500$~\kms\ show $\sim$1~dex metallicity and $\sim$0.5~dex density variations, indicating physical and chemical inhomogeneity of the medium around these LAEs.