We exploit wide-field Ly α imaging with Subaru to probe the environment around TN J1338-1942, a powerful radio galaxy with a > 100 kpc Ly α halo at z = 4.11. We used a sample of Ly α emitters (LAEs) down to log (LLyα[ erg s-1]) ~ 42.8 to measure the galaxy density around TN J1338-1942, compared to a control sample from a blank field taken with the same instrument. We found that TN J1338-1942 resides in a region with a peak overdensity of δLAE = 2.8 ± 0.5 on scales of 8 h -1 Mpc (on the sky) and 112 h -1 Mpc (line of sight) in comoving coordinates. Adjacent to this overdensity, we found a strong underdensity where virtually no LAEs are detected. We used a semi-analytical model of LAEs derived from the Millennium Simulation to compare our results with theoretical predictions. While the theoretical density distribution is consistent with the blank field, overdense regions such as that around TN J1338-1942 are very rare, with a number density of 6.4 × 10-8 Mpc-3 (comoving), corresponding to the densest < 0.4 percentile at z ≃ 4.1. We also found that the Ly a luminosity function in the TN J1338-1942 field differs from that in the blank field: the number of bright LAEs (log(LLyα[ergs-1]) ≳ 43.3) is enhanced, while the number of fainter LAEs is relatively suppressed. These results suggest that some powerful radio galaxies associated with Ly α nebulae reside in extreme overdensities on ~3-6 Mpc scales, where star formation and AGN activity may be enhanced via frequent galaxy mergers or high rates of gas accretion from the surroundings.
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