We analyze star formation (SF) as a function of stellar mass (M_*) and redshift z in the All Wavelength Extended Groth Strip International Survey (AEGIS), for star-forming field galaxies with M_* >~ 10^10 M_sun out to z=1.1. The data indicate that the high specific SF rates (SFR) of many less massive galaxies do not represent late, irregular or recurrent, starbursts in evolved galaxies. They rather seem to reflect the onset (initial burst) of the dominant SF episode of galaxies, after which SF gradually declines on Gyr timescales to z=0 and forms the bulk of a galaxys M_*. With decreasing mass, this onset of major SF shifts to decreasing z for an increasing fraction of galaxies (staged galaxy formation). This process may be an important component of the ``downsizing phenomenon. We find that the predominantly gradual decline of SFR (Noeske et al. 2007, this volume) can be reproduced by exponential SF histories (tau models), if less massive galaxies have systematically longer e-folding times tau, and a later onset of SF (z_f). Our model can provide a first parametrization of SFR as a function of M_* and z, and quantify mass-dependences of tau and z_f, from direct observations of M_* and SFR up to z>1. The observed evolution of SF in galaxies can plausibly reflect the dominance of gradual gas exhaustion. The data are also consistent with the history of cosmological accretion onto Dark Matter halos.
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