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 the most 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 sam
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