  We find that X-ray sources in the Extended Chandra Deep Field South are
strongly spatially correlated with LABOCA 870 micron sources. We investigate
the dependence of this correlation on X-ray flux, hardness ratio and column
density, finding that specifically faint and absorbed X-ray sources are
significant sub-mm emitters. In the X-ray source redshift subsample we confirm
the previous result that higher luminosity sources (L_X>10^44 ergs/s) have
greater 870um fluxes but we also find that this subsample selects against
absorbed sources, faint in X-ray flux. Overall, we find that X-ray sources
contribute 1.5 \pm 0.1 Jy/deg^2 to the sub-mm background, ~3% of the total, in
agreement with the prediction of an obscured AGN model which also gives a
reasonable fit to the bright sub-mm source counts. This non-unified model also
suggests that when Compton-thick, X-ray-undetected sources are included, then
the fractional AGN contribution to the sub-mm background would rise from ~3% to
a total of 25-40%, although in a unified model the AGN contribution would only
reach ~13%, because the sub-mm flux of the X-ray sources is then more
representative of the whole AGN population. Measurements of the dependence of
sub-mm flux on X-ray flux, luminosity and column density all agree well with
the predictions of the non-unified AGN model. Heavily absorbed,
X-ray-undetected AGN could explain the further cross-correlation we find
between sub-mm sources and z > 0.5 red galaxies. We conclude that sub-mm
galaxies may contain the long-sought absorbed AGN population needed to explain
the X-ray background.
