We investigate various galaxy population properties of the massive X-ray luminous galaxy cluster XDCP J0044.0-2033 at z=1.58, which constitutes the most extreme matter density peak at this redshift currently known. We analyze deep VLT/HAWK-I NIR data in the J- and Ks-bands, complemented by Subaru imaging in i and V, Spitzer observations at 4.5 micron, and new spectroscopic observations with VLT/FORS2. We detect a cluster-associated excess population of about 90 galaxies, which follows a centrally peaked, compact NFW galaxy surface density profile with a concentration of c200~10. Based on the Spitzer 4.5 micron imaging data, we measure a stellar mass fraction of fstar,500=(3.3+-1.4)% consistent with local values. The total J- and Ks-band galaxy luminosity functions of the core region yield characteristic magnitudes J* and Ks* consistent with expectations from simple z_f=3 burst models. However, a detailed look at the morphologies and color distributions of the spectroscopically confirmed members reveals that the most massive galaxies are undergoing a very active mass assembly epoch through merging processes. Consequently, the bright end of the cluster red-sequence is not in place, while at intermediate magnitudes [Ks*,Ks*+1.6] a red-locus population is present, which is then sharply truncated at magnitudes fainter than Ks*+1.6. The dominant cluster core population comprises post-quenched galaxies transitioning towards the red-sequence at intermediate magnitudes, while additionally a significant blue cloud population of faint star-forming galaxies is present even in the densest central regions. Our observations lend support to the scenario in which the dominant effect of the dense z~1.6 cluster environment is an accelerated mass assembly timescale through merging activity that is responsible for driving core galaxies across the mass quenching threshold of log(Mstar/Msun)~10.4.
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