| Abstract
| - Models of galaxy evolution assume some connection between the AGN and star formation activity in galaxies. We use the multi-wavelength information of the CDFS to assess this issue. We select the AGNs from the 3 Ms XMM-Newton survey and measure the star-formation rates of their hosts using data that probe rest-frame wavelengths longward of 20 μm, predominantly from deep 100 μm and 160 μm Herschel observations, but also from Spitzer-MIPS-70 μm. Star-formation rates are obtained from spectral energy distribution fits, identifying and subtracting an AGN component. Our sample consists of sources in the z ≈ 0.5−4 redshift range, with star-formation rates SFR ≈ 10 1−10 3 M⊙ yr -1 and stellar masses M⋆ ≈ 10 10−10 11.5 M⊙. We divide the star-formation rates by the stellar masses of the hosts to derive specific star-formation rates (sSFR) and find evidence for a positive correlation between the AGN activity (proxied by the X-ray luminosity) and the sSFR for themost active systems with X-ray luminosities exceeding Lx ≃ 10 43 erg s -1 and redshifts z ≳ 1. We do not find evidence for such a correlation for lower luminosity systems or those at lower redshifts, consistent with previous studies. We do not find any correlation between the SFR (or the sSFR) and the X-ray absorption derived from high-quality XMM-Newton spectra either, showing that the absorption is likely to be linked to the nuclear region rather than the host, while the star-formation is not nuclear. Comparing the sSFR of the hosts to the characteristic sSFR of star-forming galaxies at the same redshift (the so-called “main sequence”) we find that the AGNs reside mostly in main-sequence and starburst hosts, reflecting the AGN-sSFR connection; however the infrared selection might bias this result. Limiting our analysis to the highest X-ray luminosity AGNs (X-ray QSOs with Lx > 10 44 erg s -1), we find that the highest-redshift QSOs (with z ≳ 2) reside predominantly in starburst hosts, with an average sSFR more than double that of the “main sequence”, and we find a few cases of QSOs at z ≈ 1.5 with specific star-formation rates compatible with the main-sequence, or even in the “quiescent” region. Finally, we test the reliability of the colour-magnitude diagram (plotting the rest-frame optical colours against the stellar mass) in assessing host properties, and find a significant correlation between rest-frame colour (without any correction for AGN contribution or dust extinction) and sSFR excess relative to the “main sequence” at a given redshift. This means that the most “starbursty” objects have the bluest rest-frame colours.
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