We study the evolution of the total star formation (SF) activity, total stellar mass and halo occupation distribution in massive halos by using one of the largest X-ray selected sample of galaxy groups with secure spectroscopic identification in the major blank field surveys (ECDFS, CDFN, COSMOS, AEGIS). We provide an accurate measurement of SFR for the bulk of the star-forming galaxies using very deep mid-infrared Spitzer MIPS and far-infrared Herschel PACS observations. For undetected IR sources, we provide a well-calibrated SFR from SED fitting. We observe a clear evolution in the level of SF activity in galaxy groups. The total SF activity in the high redshift groups (0.5<z<1.1) is higher with respect to the low redshift (0.15<z<0.5) sample at any mass by 0.8+/-0.12 dex. A milder difference (0.35+/-0.1 dex) is observed between the low redshift bin and the groups at z~0. We show that the level of SF activity is declining more rapidly in the more massive halos than in the more common lower mass halos. We do not observe any evolution in the halo occupation distribution and total stellar mass- halo mass relations in groups. The picture emerging from our findings suggests that the galaxy population in the most massive systems is evolving faster than galaxies in lower mass halos, consistently with a halo downsizing scenario.
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