On the SFR-M* main sequence archetypal star-formation history and analytical models

From the evolution of the main sequence we can build the star formation history (SFH) of MS galaxies, assuming that they follow this relation all their life. We show that this SFH is not only a function of cosmic time but also involve the seed mass of the galaxy. We discuss the implications of this MS SFH on the stellar mass growth, and the entry in the passive region of the UVJ diagram, while the galaxy is still forming stars. We test the ability of different analytical SFH forms found in the literature to probe the SFR of all type of galaxies. Using a sample of GOODS-South galaxies, we show that these SFHs artificially enhance or create a gradient of age, parallel to the MS. A simple model of a MS galaxy, such as those expected from compaction or variation in gas accretion, undergoing some fluctuations provide does not predict such a gradient, that we show is due to SFH assumptions. We propose an improved analytical form, taking into account a flexibility in the recent SFH that we calibrate as a diagnostic to identify rapidly quenched galaxies from large photometric survey.