The K20 survey -: VI.: The distribution of the stellar masses in galaxies up to z ≃ 2

We present a detailed analysis of the stellar mass content of galaxies up to z=2.5 as obtained from the K20 spectrophotometric galaxy sample. We have applied and compared two different methods to estimate the stellar mass M-* from broad-band photometry: a Maximal Age approach, where we maximize the age of the stellar population to obtain the maximal mass compatible with the observed R-K color, and a Best Fit model, where the best-fitting spectrum to the complete UBVRIzJK(s) multicolor distribution is used. We find that the M-*/L ratio decreases with redshift: in particular, the average M-*/L ratio of early type galaxies decreases with z, with a scatter that is indicative of a range of star-formation time-scales and redshift of formation. More important, the typical M-*/L ratio of massive early type galaxies is larger than that of less massive ones, suggesting that their stellar population formed at higher z. We show that the final K20 galaxy sample spans a range of stellar masses from M-*=10(9) M-circle dot to M-*=10(12) M-circle dot: massive galaxies (M-* greater than or equal to 10(11) M-circle dot) are common at 0.5<z<1, and are detected also up to zsimilar or equal to2. We compute the Galaxy Stellar Mass Function at various z, of which we observe only a mild evolution (i.e. by 20-30%) up to zsimilar or equal to1. At z>1, the evolution in the normalization of the GSMF appears to be much faster: at zsimilar or equal to2, about 35% of the present day stellar mass in objects with M-* similar or equal to 10(11) M-circle dot appear to have assembled. We also detect a change in the physical nature of the most massive galaxies: at zless than or similar to0.7, all galaxies with M>10(11) M-circle dot are early type, while at higher z a population of massive star-forming galaxies progressively appears. We finally analyze our results in the framework of Lambda-CDM hierarchical models. First, we show that the large number of massive galaxies detected at high z does not violate any fundamental Lambda-CDM constraint based on the number of massive DM halos. Then, we compare our results with the predictions of several renditions of both semianalytic as well as hydro-dynamical models. The predictions from these models range from severe underestimates to slight overestimates of the observed mass density at less than or equal to2. We discuss how the differences among these models are due to the different implementation of the main physical processes.