MUSE searches for galaxies near very metal-poor gas clouds at z~3: new constraints for cold accretion models

We report on the search for galaxies in the proximity of two very metal-poor gas clouds at z~3 towards the quasar Q0956+122. With a 5-hour MUSE integration in a ~500x500 kpc^2 region centred at the quasar position, we achieve a >80% complete spectroscopic survey of continuum-detected galaxies with m<25 mag and Ly{\alpha} emitters with luminosity L>3e41 erg/s. We do not identify galaxies at the redshift of a z~3.2 Lyman limit system (LLS) with log Z/Zsun = -3.35 +/- 0.05, placing this gas cloud in the intergalactic medium or circumgalactic medium of a galaxy below our sensitivity limits. Conversely, we detect five Ly{\alpha} emitters at the redshift of a pristine z~3.1 LLS with log Z/Zsun < -3.8, while ~0.4 sources were expected given the z~3 Ly{\alpha} luminosity function. Both this high detection rate and the fact that at least three emitters appear aligned in projection with the LLS suggest that this pristine cloud is tracing a gas filament that is feeding one or multiple galaxies. Our observations uncover two different environments for metal-poor LLSs, implying a complex link between these absorbers and galaxy halos, which ongoing MUSE surveys will soon explore in detail. Moreover, in agreement with recent MUSE observations, we detected a ~90 kpc Ly{\alpha} nebula at the quasar redshift and three Ly{\alpha} emitters reminiscent of a "dark galaxy" population.