The intrinsic characteristics of galaxies on the SFR-stellar mass plane at 1.2<z<4: I. the correlation between stellar age, central density and position relative to the main sequence
We use the deep CANDELS observations in the GOODS North and South fields to revisit the correlations between stellar mass ($M_*$), star--formation rate (SFR) and morphology, and to introduce a fourth dimension, the mass-weighted stellar age, in galaxies at $1.2<z<4$. We do this by making new measures of $M_*$, $SFR$, and stellar age thanks to an improved SED fitting procedure that allows various star formation history for each galaxy. Like others, we find that the slope of the Main Sequence (MS) of star formation in the $(M_*;SFR)$ plane bends at high mass. We observe clear morphological differences among galaxies across the MS, which also correlate with stellar age. At all redshifts, galaxies that are quenching or quenched, and thus old, have high $Σ_1$ (the projected density within the central 1 kpc), while younger, star-forming galaxies span a much broader range of $Σ_1$, which includes the high values observed for quenched galaxies, but also extends to much lower values. As galaxies age and quench, the stellar age and the dispersion of $Σ_1$ for fixed values of $M_{*}$ shows two different regimes, one, at the low--mass end, where quenching might be driven by causes external to the galaxies; the other, at the high--mass end, where quenching is driven by internal causes, very likely the mass given the low scatter of $Σ_1$ (mass quenching). We suggest that the monotonic increase of central density as galaxies grow is one manifestation of a more general phenomenon of structural transformation that galaxies undergo as they evolve.