The aim of our analysis is twofold. On the one hand we are interested in addressing whether a sample of ETGs morphologically selected differs from a sample of passive galaxies in terms of galaxy statistics. On the other hand we study how the relative abundance of galaxies, the number density and the stellar mass density for different morphological types change over the redshift range 0.6<z<2.5. From the 1302 galaxies brighter than Ks=22 selected from the GOODS-MUSIC catalogue, we classified the ETGs on the basis of their morphology and the passive galaxies on the basis of their sSFR. We proved how the definition of passive galaxy depends on the IMF adopted in the models and on the assumed sSFR threshold. We find that ETGs cannot be distinguished from the other morphological classes on the basis of their low sSFR, irrespective of the IMF adopted in the models. Using the sample of 1302 galaxies morphologically classified into spheroidal galaxies (ETGs) and not spheroidal galaxies (LTGs), we find that their fractions are constant over the redshift range 0.6<z<2.5 (20-30% ETGs vs 70-80% LTGs). However, at z<1 these fractions change among the population of the most massive (M*>=10^(11) M_sol) galaxies, with the fraction of massive ETGs rising up to 40% and the fraction of massive LTGs decreasing down to 60%. Moreover, we find that the number density and the stellar mass density of the whole population of massive galaxies increase almost by a factor of ~10 between 0.6<z<2.5, with a faster increase of these densities for the ETGs than for the LTGs. Finally, we find that the number density of the highest-mass galaxies (M*>3-4x10^(11) M_sol) both ETGs and LTGs do not increase since z~2.5, contrary to the lower mass galaxies. This suggests that the population of the most massive galaxies formed at z>2.5-3 and that the assembly of such high-mass galaxies is not effective at lower redshift.
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