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Context. Recent observational progress has enabled the detection of galaxy clusters and groups out to very high redshifts and for the first time allows detailed studies of galaxy population properties in these densest environments in what was formerly known as the "redshift desert" at z> 1.5.

Aims. We aim to investigate various galaxy population properties of the massive X-ray luminous galaxy cluster XDCPJ0044.0-2033 at z = 1.58, which constitutes the most extreme currently known matter-density peak at this redshift.

Methods. We analyzed deep VLT/HAWK-I near-infrared data with an image quality of 0.5 ’’ and limiting Vega magnitudes (50% completeness) of 24.2 in J- and 22.8 in the Ks band, complemented by similarly deep Subaru imaging in i and V, Spitzer observations at 4.5 mu m, and new spectroscopic observations with VLT/FORS 2.

Results. We detect a cluster-associated excess population of about 90 galaxies, most of them located within the inner 30 ’’ (250 kpc) of the X-ray centroid, which follows a centrally peaked, compact NFW galaxy surface-density profile with a concentration of c(200) similar or equal to 10. Based on the Spitzer 4.5 mu m imaging data, we measure a total enclosed stellar mass of M*(500) similar or equal to (6.3 +/- 1.6) x 10(12) M-circle dot and a resulting stellar mass fraction of f(*, 500) = M-*,M- 500/M-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 a red-locus population is present at intermediate magnitudes [Ks*, Ks* + 1.6], which is then sharply truncated at magnitudes fainter than Ks* + 1.6. The dominant cluster-core population comprises post-quenched galaxies transitioning toward 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. Based on a color-color selection performed to separate different cluster galaxy types, we find that the blue star-forming population is concentrated in clumpy structures and dominates in particular at and beyond the R-500 radius. On the other hand, the fraction of post-starburst galaxies steadily increases toward the center, while the red-locus population and red-sequence transition galaxies seem to reach their peak fractions already at intermediate cluster-centric radii of about r similar to 200 kpc.

Conclusions. Our observations support the scenario in which the dominant effect of the dense z similar or equal to 1.6 cluster environment is an accelerated mass-assembly timescale (similar to 1 Gyr or shorter) through merging activity that is responsible for driving core galaxies across the mass-quenching threshold of log(M-*/M-circle dot) similar or equal to 10.4. Beyond this mass limit, star formation is suppressed on timescales of similar to 1 Gyr, while the direct environmental quenching process seems to be subdominant and is acting on significantly longer timescales (similar to 2-3 Gyr).