We present ultra-deep mid-IR spectra of 48 infrared-luminous galaxies in the GOODS-South field obtained with the InfraRed Spectrograph (IRS) on the Spitzer Space Telescope. These galaxies are selected among faint infrared sources (0.14 - 0.5 mJy at 24 um) in two redshift bins (0.76-1.05 and 1.75-2.4) to sample the major contributors to the cosmic infrared background at the most active epochs. We estimate redshifts for 92% of the sample using PAH and Si absorption features. Only few of these galaxies (5% at z~1 and 12% at z~2) have their total infrared luminosity dominated by emission from AGN. The averaged mid-IR spectra of the z~1 LIRGs and of the z~2 ULIRGs are very similar to the averaged spectrum of local starbursts and HII-like ULIRGs, respectively. We find that 6.2um PAH equivalent widths reach a plateau of ~1 um for L(24 mu) < 1E11 L(sun). At higher luminosities, EW (6.2 mu) anti-correlates with L(24 um). Intriguingly, high-z ULIRGs and SMG lie above the local EW (6.2 um) - L(24 um) relationship suggesting that, at a given luminosity, high-z ULIRGs have AGN contributions to their dust emission lower than those of local counterparts. A quantitative analysis of their morphology shows that most of the luminous IR galaxies have morphologies similar to those of IR-quiet galaxies at the same redshift. All z~2 ULIRGs of our sample are IR-excess BzK galaxies and most of them have L(FIR)/L(1600A) ratios higher than those of starburst galaxies at a given UV slope. The ``IR excess (Daddi et al. 2007) is mostly due to strong 7.7 um PAH emission and under-estimation of UV dust extinction. On the basis of the AGN-powered L (6 um) continuum measured directly from the mid-IR spectra, we estimate an average intrinsic X-ray AGN luminosity of L(2-10 keV) = (0.1 +/- 0.6) 1E43 erg/s, a value substantially lower than the prediction by Daddi et al. (2007).
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