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In this paper we study the causes of the reported mass-dependence of theslope of SFR-M* relation, the so-called "Main Sequence" of star-forminggalaxies, and discuss its implication on the physical processes that shaped thestar formation history of massive galaxies over cosmic time. We use the CANDELSnear-IR imaging from the Hubble Space Telescope to perform the bulge-to-diskdecomposition of distant galaxies and measure for the first time the slope ofthe SFR-Mdisk relation at z=1. We find that this relation follows very closelythe shape of the SFR-M* correlation, still with a pronounced flattening at thehigh-mass end. This is clearly excluding, at least at z=1, the secular growthof quiescent bulges in star-forming galaxies as the main driver for the changeof slope of the Main Sequence. Then, by stacking the Herschel data available inthe CANDELS field, we estimate the total gas mass and the star formationefficiency at different positions on the SFR-M* relation. We find that therelatively low SFRs observed in massive galaxies (M* > 5e10 Msun) are caused bya decreased star formation efficiency, by up to a factor of 3 as compared tolower stellar mass galaxies, and not by a reduced gas content. The trend at thelowest masses is likely linked to the dominance of atomic over molecular gas.We argue that this stellar-mass-dependent SFE can explain the varying slope ofthe Main Sequence since z=1.5, hence over 70% of the Hubble time. The drop ofSFE occurs at lower masses in the local Universe (M* > 2e10 Msun) and is notpresent at z=2. Altogether this provides evidence for a slow downfall of thestar formation efficiency in massive Main Sequence galaxies. The resulting lossof star formation is found to be rising starting from z=2 to reach a levelcomparable to the mass growth of the quiescent population by z=1. We finallydiscuss the possible physical origin of this phenomenon.

Observational evidence of a slow downfall of star formation efficiency in massive galaxies during the last 10 Gyr