We study zCOSMOS-bright optical spectra for 609 Spitzer/MIPS 24 micron-selected galaxies with S(24um)> 0.30 mJy and I<22.5 (AB mag) over 1.5 sq. deg. of the COSMOS field. From emission-line diagnostics we find that: 1) star-formation rates (SFR) derived from the observed Halpha and Hbeta lines underestimate, on average, the total SFR by factors ~5 and 10, respectively; 2) both the Calzetti et al. and the Milky Way reddening laws are suitable to describe the extinction observed in infrared (IR) sources in most cases; 3) some IR galaxies at z<0.3 have low abundances, but many others with similar IR luminosities and redshifts are chemically enriched; 4) The average [OIII]/Hbeta ratios of nuLnu(24um)>10^11 Lsun galaxies at 0.6<z<0.7 are ~0.6 dex higher than the average ratio of all zCOSMOS galaxies at similar redshifts. Massive star formation and active galactic nuclei (AGN) could simultaneously be present in those galaxies with the highest ionising fluxes; 5) ~1/3 of the galaxies with metallicity measurements at 0.5<z<0.7 lie below the general mass-metallicity relation at the corresponding redshifts. The strengths of the 4000 Angstrom break and the Hdelta EW of our galaxies show that secondary bursts of star formation are needed to explain the spectral properties of most IR sources. The LIRG and ULIRG phases occur, on average, between 10^7 and 10^8 years after the onset of a starburst on top of underlying older stellar populations. These results are valid for galaxies of different IR luminosities at 0.6<z<1.0 and seem independent of the mechanisms triggering star formation.
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