We present an analysis of the deepest Herschel images in four major extragalactic fields GOODS-North, GOODS-South, UDS, and COSMOS obtained within the GOODS-Herschel and CANDELS-Herschel key programs. The star formation picture provided by a total of 10 497 individual far-infrared detections is supplemented by the stacking analysis of a mass complete sample of 62 361 starforming galaxies from the Hubble Space Telescope (HST) H band-selected catalogs of the CANDELS survey and from two deep ground-based K s band-selected catalogs in the GOODS-North and the COSMOS-wide field to obtain one of the most accurate and unbiased understanding to date of the stellar mass growth over the cosmic history. We show, for the first time, that stacking also provides a powerful tool to determine the dispersion of a physical correlation and describe our method called "scatter stacking", which may be easily generalized to other experiments. The combination of direct UV and far-infrared UV-reprocessed light provides a complete census on the star formation rates (SFRs), allowing us to demonstrate that galaxies at z = 4 to 0 of all stellar masses (M * ) follow a universal scaling law, the so-called main sequence of star-forming galaxies. We find a universal close-to-linear slope of the log 10 (SFR)-log 10 (M * ) relation, with evidence for a flattening of the main sequence at high masses (log 10 (M * /M ) > 10.5) that becomes less prominent with increasing redshift and almost vanishes by z 2. This flattening may be due to the parallel stellar growth of quiescent bulges in star-forming galaxies, which mostly happens over the same redshift range. Within the main sequence, we measure a nonvarying SFR dispersion of 0.3 dex: at a fixed redshift and stellar mass, about 68% of star-forming galaxies form stars at a universal rate within a factor 2. The specific SFR (sSFR = SFR/M * ) of star-forming galaxies is found to continuously increase from z = 0 to 4. Finally we discuss the implications of our findings on the cosmic SFR history and on the origin of present-day stars: more than two-thirds of present-day stars must have formed in a regime dominated by the "main sequence" mode. As a consequence we conclude that, although omnipresent in the distant Universe, galaxy mergers had little impact in shaping the global star formation history over the last 12.5 billion years.

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It has been widely claimed that several lines of observational evidence point towards a ‘downsizing’ of the process of galaxy formation over cosmic time. This behaviour is sometimes termed ‘antihierarchical’, and contrasted with the ‘bottom‐up’ (small objects form first) assembly of the dark matter structures in cold dark matter (CDM) models. In this paper, we address three different kinds of observational evidence that have been described as ‘downsizing’: the stellar mass assembly (i.e. more massive galaxies assemble at higher redshift with respect to low‐mass ones), star formation rate (SFR) (i.e. the decline of the specific star formation rate is faster for more massive systems) and the ages of the stellar populations in local galaxies (i.e. more massive galaxies host older stellar populations). We compare a broad compilation of available data sets with the predictions of three different semi‐analytic models of galaxy formation within the ΛCDM framework. In the data, we see only weak evidence at best of ‘downsizing’ in stellar mass and in SFR. Despite the different implementations of the physical recipes, the three models agree remarkably well in their predictions. We find that, when observational errors on stellar mass and SFR are taken into account, the models acceptably reproduce the evolution of massive galaxies (M > 1011 M⊙ in stellar mass), over the entire redshift range that we consider (0 ≲z≲ 4). However, lower mass galaxies, in the stellar mass range 109–1011 M⊙, are formed too early in the models and are too passive at late times. Thus, the models do not correctly reproduce the downsizing trend in stellar mass or the archaeological downsizing, while they qualitatively reproduce the mass‐dependent evolution of the SFR. We demonstrate that these discrepancies are not solely due to a poor treatment of satellite galaxies but are mainly connected to the excessively efficient formation of central galaxies in high‐redshift haloes with circular velocities ∼100–200 km s−1. We conclude that some physical processes operating on these mass scales – most probably star formation and/or supernova feedback – are not yet properly treated in these models.