Characterising the Far-infrared Properties of Distant X-ray Detected
  AGNs: Evidence for Evolution in the Infrared--X-ray Luminosity Ratio
  (Abridged) We investigate the far-infrared properties of X-ray sources
detected in the Chandra Deep Field-South (CDF-S) survey using the ultra-deep
70um and 24um Spitzer observations taken in this field. We rely on stacking
analyses of the 70um data to characterise the average 70um properties of the
X-ray sources. Using Spitzer-IRS data of the Swift-BAT sample of z~0 active
galactic nuclei (hereafter, AGNs), we show that the 70um/24um flux ratio can
distinguish between AGN-dominated and starburst-dominated systems out to z~1.5.
  From stacking analysis we find that both high redshift and z~0 AGNs follow
the same tendency toward warmer 70um/24um colours with increasing X-ray
luminosity (L_X). We also show that the 70um flux can be used to determine the
infrared (8-1000um) luminosities of high redshift AGNs. We use this information
to show that L_X=10^{42-43} erg/s AGNs at high redshifts (z=1-2) have infrared
to X-ray luminosity ratios (hereafter, L_IR/L_X) that are, on average,
4.7_{-2.0}^{+10.2} and 12.7^{+7.1}_{-2.6} times higher than AGNs with similar
X-ray luminosities at z=0.5-1 and z~0, respectively. By comparison, we find
that the L_IR/L_X ratios of L_X=10^{43-44} erg/s AGNs remain largely unchanged
across this same redshift interval. We explore the consequences that these
results may have on the identification of distant, potentially Compton thick
AGNs using L_IR/L_X ratios. We discuss possible scenarios for the observed
increase in the L_IR/L_X ratio with redshift, including changes in the dust
covering factor of AGNs and/or the star formation rates of their host galaxies.
Finally, we show how deep observations to be undertaken by the Herschel Space
Observatory will enable us to discriminate between these proposed scenarios and
also identify Compton-thick AGNs at high redshifts.
