A multi-wavelength study of the proto-cluster surrounding the z=4.1 radio galaxy TN J1338-1942

We present a 1.2 mm (250 GHz) map obtained with MAMBO on the IRAM 30 m telescope of the central 25 arcmin(2) of the proto-cluster surrounding the z=4.1 radio galaxy TN J1338-1942. The map reaches a 1sigma sensitivity of 0.6 mJy in the central area, increasing to 1.2 mJy at the edges. We detect 10 candidate mm sources, of which 8 are also detected in a deep VLA 1.4 GHz map and/or a VLT R-band image. Three sources have a flux density S-1.2 mm>4.0 mJy, representing a 7sigma overdensity compared to random field surveys, which predict only 1 such source in our map area. We obtained SCUBA/JCMT 850 mum and 450 mum photometry of six radio/optically identified MAMBO sources, confirming 5 of them with S/N>4. Radio-to-mm and mm-to-submm redshift estimators cannot put strong constraints on the redshifts of these MAMBO sources, but 9 of them are consistent within the uncertainties (mean Deltaz=+2.6) with z=4.1. One faint MAMBO source is possibly identified with an extremely red object (R-K=6.1) at a likely spectroscopic redshift z=1.18. The four brightest MAMBO sources are all located north of the radio galaxy, while the densest area of companion Lyalpha excess and Lyman break galaxies is to the southeast. None of the 14 spectroscopically confirmed Lyalpha emitters in the MAMBO field are detected at 1.2 mm; their average 1.2 mm flux density is (S-1.2 mm)=0.25+/-0.24 mJy. If the mm sources lie at z=4.1, none of them show excess Lyalpha emission in our narrow-band images. Both populations thus show no apparent overlap, possibly due to dust quenching the Lyalpha emission. If the turn sources are part of the proto-cluster, our results suggest that galaxies with star formation rates of a few 1000 M-circle dot yr(-1) could be spread throughout the proto-cluster over projected scales of at least 2 Mpc.