The Galaxy mass function up to z=4 in the GOODS-MUSIC sample:: into the epoch of formation of massive galaxies

Aims. The goal of this work is to measure the evolution of the Galaxy Stellar Mass Function and of the resulting Stellar Mass Density up to redshift similar or equal to 4, in order to study the assembly of massive galaxies in the high redshift Universe. Methods. We have used the GOODS-MUSIC catalog, containing similar to 3000 Ks- selected galaxies with multi-wavelength coverage extending from the U band to the Spitzer 8 mu m band, of which 27% have spectroscopic redshifts and the remaining fraction have accurate photometric redshifts. On this sample we have applied a standard fitting procedure to measure stellar masses. We compute the Galaxy Stellar Mass Function and the resulting Stellar Mass Density up to redshift similar or equal to 4, taking into proper account the biases and incompleteness effects. Results. Within the well known trend of global decline of the Stellar Mass Density with redshift, we show that the decline of the more massive galaxies may be described by an exponential timescale of similar or equal to 6 Gyr up to z similar or equal to 1.5, and proceeds much faster thereafter, with an exponential timescale of similar or equal to 0.6 Gyr. We also show that there is some evidence for a differential evolution of the Galaxy Stellar Mass Function, with low mass galaxies evolving faster than more massive ones up to z similar or equal to 1-1.5 and that the Galaxy Stellar Mass Function remains remarkably flat (i.e. with a slope close to the local one) up to z similar or equal to 1-1.3. Conclusions. The observed behaviour of the Galaxy Stellar Mass Function is consistent with a scenario where about 50% of present-day massive galaxies formed at a vigorous rate in the epoch between redshift 4 and 1.5, followed by a milder evolution until the present-day epoch.