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[abridged] Building upon a previous study, we define a method to blindlyidentify galaxies that underwent, and may still be undergoing, a fast downfallof their star-formation activity, that is, a more than 80% drop instar-formation rate (SFR) occurring in less than 500 Myr. Modeling galaxies'SED with a delayed-$\tau$ star formation history (SFH), with and withoutallowing an instantaneous SFR drop within the last hundreds Myr, we isolate 102candidates out of a subsample of 6,680 galaxies classified as star-forming fromthe UVJ criterion in the ZFOURGE catalogues. These galaxies are mostly locatedin the lower part of the SFR-M$_*$ main sequence (MS) and extend up to a factor100 below it. They also lie close to the limit between the passive and activeregions on the UVJ diagram, indicating that they are in a transition phase. Weshow that the selected candidates have different physical properties comparedto galaxies with similar UVJ colors, namely, lower star-formation rates anddifferent stellar masses. The morphology of the candidates show no preferencefor a particular type. Among the 102 candidates, only 4 show signs of an AGNactivity (from X-ray luminosity or UV-IR SED fitting decomposition). This lowfraction of AGNs among the candidates implies that AGN activity may not be themain driver of the recent downfall, although timescale differences and dutycycle must be taken into account. We finally attempt to recover the pastposition of these galaxies on the SFR-M$_*$ plane, before the downfall of theirstar-formation and show that some of them were in the starburst region beforeand are back on the MS. These candidates constitute a promising sample thatneed more investigation in order to understand the different mechanisms at theorigin of the star formation decrease of the Universe since $z$$\sim$2.

Identification of galaxies that experienced a recent major drop of star formation