Spatial limits of the different surveys used in this work. The grey-scale image is the combined 2–10 keV 3 Ms image of the XMM-Newton observations, and the regions are the Herschel area (small rectangle), the 4 Ms Chandra area (solid circle), the XMM-Newton area used (dashed circle) and the E-CDFS Chandra area (large square). The radio and Spitzer areas used are all wider than the E-CDFS. The Herschel and the XMM-Newton areas are the boundaries of the “complete” and “broad” samples, respectively (see Sect. 3.3). The sources of the “broad” sample are marked with blue symbols, whereas the sources with FIR flux density upper limits in the “complete” sample are marked with red symbols.