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High-redshift sub-millimetre galaxies (SMGs) are usually assumed to be powered by star formation. However, it has been clear for some time that >20 per cent of such sourcesbrighter than ≈3 mJy host quasars. Here, we analyse a complete sample of 12 sub-mm LABOCA/ALMA 870-μm sources in the centre of the William Herschel Deep Field (WHDF) with multiwavelength data available from the X-ray to the radio bands. Previously, two sources were identified as X-ray-absorbed quasars at z = 1.32 and z = 2.12. By comparing their spectral energy distributions (SEDs) with unabsorbed quasars in the same field, we confirm that they are dust reddened although at a level significantly lower than implied by their X-ray absorption. Then, we compare the SEDs of all the sources to dust-reddened AGN and star-forming galaxy models. This optical/NIR comparison combined with Spitzer MIR colours and faint Chandra X-ray detections shows that 7/12 SMGs are best fitted with an obscured quasar model, a further 3/12 show no preference between AGN and star-forming templates, leaving only a z = 0.046 spiral galaxy and one unidentified source. So in our complete sample, the majority (10/12) of bright SMGs are at least as likely to fit an AGN as a star-forming galaxy template, although no claim is made to rule out the latter as SMG power sources. We then suggest modifications to a previous SMG number count model and conclude that obscured AGN in SMGs may still provide the dominant contribution to both the hard X-ray and sub-millimetre backgrounds. [ABSTRACT FROM AUTHOR]

High-redshift sub-millimetre galaxies (SMGs) are usually assumed to be powered by star formation. However, it has been clear for some time that >20 per cent of such sourcesbrighter than ≈3 mJy host quasars. Here, we analyse a complete sample of 12 sub-mm LABOCA/ALMA 870-μm sources in the centre of the William Herschel Deep Field (WHDF) with multiwavelength data available from the X-ray to the radio bands. Previously, two sources were identified as X-ray-absorbed quasars at z = 1.32 and z = 2.12. By comparing their spectral energy distributions (SEDs) with unabsorbed quasars in the same field, we confirm that they are dust reddened although at a level significantly lower than implied by their X-ray absorption. Then, we compare the SEDs of all the sources to dust-reddened AGN and star-forming galaxy models. This optical/NIR comparison combined with Spitzer MIR colours and faint Chandra X-ray detections shows that 7/12 SMGs are best fitted with an obscured quasar model, a further 3/12 show no preference between AGN and star-forming templates, leaving only a z = 0.046 spiral galaxy and one unidentified source. So in our complete sample, the majority (10/12) of bright SMGs are at least as likely to fit an AGN as a star-forming galaxy template, although no claim is made to rule out the latter as SMG power sources. We then suggest modifications to a previous SMG number count model and conclude that obscured AGN in SMGs may still provide the dominant contribution to both the hard X-ray and sub-millimetre backgrounds. [ABSTRACT FROM AUTHOR]