Confirmation of a correlation between the X-ray luminosity and spectral   slope of AGNs in the Chandra Deep Fields
  We present results from a statistical analysis of 173 bright radio-quiet AGNs selected from the Chandra Deep Field-North and Chandra Deep Field-South surveys (hereafter, CDFs) in the redshift range of 0.1 < z < 4. We find that the X-ray power-law photon index (Gamma) of radio-quiet AGNs is correlated with their 2-10 keV rest-frame X-ray luminosity (L_X) at the > 99.5 percent confidence level in two redshift bins, 0.3 < z < 0.96, and 1.5 < z < 3.3 and is slightly less significant in the redshift bin 0.96 < z < 1.5. We investigate the redshift evolution of the correlation between the power-law photon index and the hard X-ray luminosity and find that the slope and offset of a linear fit to the correlation change significantly (at the > 99.9 percent confidence level) between redshift bins of 0.3 < z < 0.96 and 1.5 < z < 3.3. We explore physical scenarios explaining the origin of this correlation and its possible evolution with redshift in the context of steady corona models focusing on its dependency on variations of the properties of the hot corona with redshift. 
C. Saez, G. Chartas, W. N. Brandt, B. D. Lehmer, F. E. Bauer, X. Dai,   G. P. Garmire