Star formation in AEGIS field galaxies since z=1.1:: The dominance of gradually declining star formation, and the main sequence of star-forming galaxies

We analyze star formation (SF) as a function of stellar mass (M-*) and redshift z in the All-Wavelength Extended M * Groth Strip International Survey. For 2905 field galaxies, complete to 10(10)(10(10.8)) M-circle dot at z < 0.7( 1), spectroscopic redshifts out to z = 1.1, we compile SF rates (SFRs) from emission lines, GALEX, and Spitzer MIPS 24 mu m photometry, optical-NIR M-* measurements, and HST morphologies. Galaxies with reliable signs of SF form a distinct "main sequence" (MS), with a limited range of SFRs at a given M-* and z (1 sigma less than or similar to +/- 0.3 dex), and log (SFR) approximately proportional to log M-*. The range of log (SFR) remains constant to z > 1, while the MS as a whole moves to higher SFR as z increases. The range of the SFR along the MS constrains the amplitude of episodic variations of SF and the effect of mergers on the SFR. Typical galaxies spend similar to 67%( 95%) of their lifetime since z = 1 within a factor of less than or similar to 2(4) of their average SFR at a given M-* and z. The dominant mode of the evolution z similar to 1 is apparently a gradual decline of the average SFR in most individual galaxies, not a decreasing frequency of starburst episodes, or a decreasing factor by which SFRs are enhanced in starbursts. LIRGs at z similar to 1 seem to mostly reflect the high SFR typical for massive galaxies at that epoch. The smooth MS may reflect that the same set of few physical processes governs SF prior to additional quenching processes. A gradual process like gas exhaustion may play a dominant role.