The MUSE Ultra Deep Field: A 5 Mpc stretch of the z $\approx$ 4 cosmic web revealed in emission

We detect Ly$\alpha$ emission from a ~5 Mpc-long (comoving) portion of the cosmic web hosting an overdensity ($\delta \approx 25$) of 19 Ly$\alpha$ emitters (LAEs) at $z\approx 4$ within the MUSE Ultra Deep Field (MUDF), reaching an average surface brightness (SB) of $5\times 10^{-20}~\rm{erg~s^{-1}~ cm^{-2}~arcsec^{-2}}$. This large-scale structure has an average SB similar to the filament across the two MUDF quasars at $z\approx 3.22$. However, deep multiwavelength data do not show a clear presence of active galactic nuclei, suggesting that the emission is mainly regulated by the underlying gas density. We find $\approx 0.2$ dex higher star formation compared to control samples and a remarkable predominance (5/7) of blue-peaked emission lines in the spectra of the embedded LAEs, indicative of favorable conditions for gas accretion. Lastly, we quantify the contribution of intragalactic gas to the Ly$\alpha$ SB profile at large distances from LAEs. By studying samples of filaments detected in emission within diverse environments, we are finally gaining new insight into the physics of gas accretion within the cosmic web.