The VIMOS VLT Deep Survey. The Assembly History of the Stellar Mass in Galaxies: from the Young to the Old Universe

18 pages with encapsulated figures. Submitted to A&AWe present a detailed analysis of the Galaxy Stellar Mass Function of galaxies up to z=2.5 as obtained from the VVDS. We estimate the stellar mass from broad-band photometry using 2 different assumptions on the galaxy star formation history and show that the addition of secondary bursts to a continuous star formation history produces systematically higher (up to 40%) stellar masses. At low redshift (z=0.2) we find a substantial population of low-mass galaxies (10^8 Msun at z=1), and a mild mass-dependent average evolution (`mass-downsizing'). In particular our data are consistent with mild/negligible (6x10^10 Msun). For less massive systems the no-evolution scenario is excluded. A large fraction (>=50%) of massive galaxies have been already assembled and converted most of their gas into stars at z=1, ruling out the `dry mergers' as the major mechanism of their assembly history below z=1. This fraction decreases to 33% at z=2. Low-mass systems have decreased continuously in number and mass density (by a factor up to 4) from the present age to z=2, consistently with a prolonged mass assembly also at z1.5 we note a flattening in the number and mass density of massive galaxies, compared to previous surveys, produced by a population with extremely red colours (MI-MK=0.8)