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Constraining the star formation and the assembly histories of normal and compact early-type galaxies at 1<z<2

[Abridged]We present a study based on a sample of 62 early-type galaxies (ETGs) at 0.9<z_spec<2 aimed at constraining their past star formation and mass assembly histories. The sample is composed of normal ETGs having effective radii comparable to the mean radius of local ones and of compact ETGs having effective radii from two to six times smaller. We do not find evidence of a dependence of the compactness of ETGs on their stellar mass. We find that the stellar mass of normal ETGs formed at z_form<3 while the stellar content of compact ETGs formed at 2<z_form<10 with a large fraction of them characterized by z_form>5. Earlier stars formed at z_form>5 are assembled in compact and more massive (M_*>10^11 M_sun) ETGs while stars later formed (z_form<3) or resulting from subsequent episodes of star formation are assembled both in compact and normal ETGs. Thus, the older the stellar population the higher the mass of the hosting galaxy but not vice versa. This suggests that the epoch of formation may play a role in the formation of massive ETGs rather than the mass itself. The possible general scheme in which normal <z>~1.5 ETGs are descendants of high-z compact spheroids enlarged through subsequent dry mergers is not compatible with the current models which predict a number of dry mergers two orders of magnitude lower than the one needed. Moreover, we do not find evidence supporting a dependence of the compactness of galaxies on their redshift of assembly. Finally, we propose a simple scheme of formation and assembly of the stellar mass of ETGs based on dissipative gas-rich merger which can qualitatively account for the co-existence of normal and compact ETGs observed at <z>~1.5 in spite of the same stellar mass, the lack of normal ETGs with high z_form and the absence of correlation between compactness, stellar mass and formation redshift.