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 ${\it UBVRIzJK}_{\rm s}$ 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 $M_*=10^9~M_\odot$ to $M_*=10^{12}~M_\odot$: massive galaxies ($M_*\geq10^{11}~M_\odot$) are common at $0.5 1$, the evolution in the normalization of the GSMF appears to be much faster: at $z\simeq 2$, about 35% of the present day stellar mass in objects with $M_* \simeq 10^{11}~M_\odot$ appear to have assembled. We also detect a change in the physical nature of the most massive galaxies: at $z \la 0.7$, all galaxies with $M>10^{11}~M_\odot$ 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 Λ -CDM hierarchical models. First, we show that the large number of massive galaxies detected at high  z does not violate any fundamental Λ -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 ≤ 2. We discuss how the differences among these models are due to the different implementation of the main physical processes.