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Reversal or no reversal: the evolution of the star formation rate-density relation up to z~1.6

We investigate the evolution of the star formation rate (SFR)-density relation in the Extended Chandra Deep Field South (ECDFS) and the Great Observatories Origin Deep Survey (GOODS) fields up to z~1.6. In addition to the "traditional method", in which the environment is defined according to a statistical measurement of the local galaxy density, we use a "dynamical" approach, where galaxies are classified according to three different environment regimes: group, "filament-like", and field. Both methods show no evidence of a SFR-density reversal. Moreover, group galaxies show a mean SFR lower than other environments up to z~1, while at earlier epochs group and field galaxies exhibit consistent levels of star formation (SF) activity. We find that processes related to a massive dark matter halo must be dominant in the suppression of the SF below z~1, with respect to purely density-related processes. We confirm this finding by studying the distribution of galaxies in different environments with respect to the so-called Main Sequence (MS) of star-forming galaxies. Galaxies in both group and "filament-like" environments preferentially lie below the MS up to z~1, with group galaxies exhibiting lower levels of star-forming activity at a given mass. At z>1, the star-forming galaxies in groups reside on the MS. Groups exhibit the highest fraction of quiescent galaxies up to z~1, after which group, "filament-like", and field environments have a similar mix of galaxy types. We conclude that groups are the most efficient locus for star-formation quenching. Thus, a fundamental difference exists between bound and unbound objects, or between dark matter haloes of different masses.