Confirmation of a correlation between the X-ray luminosity and spectral slope of active galactic nuclei in the Chandra deep fields

We present results from a statistical analysis of 173 bright radio-quiet active galactic nuclei (AGNs) selected from the Chandra Deep Field-North and Chandra Deep Field-South surveys (hereafter, CDFs) in the redshift range of 0.1 less than or similar to z less than or similar to 4. We find that the X-ray power-law photon index (G) of radio-quiet AGNs is correlated with their 2-10 keV rest-frame X-ray luminosity (LX) at the > 99.5% confidence level in two redshift bins: 0.3 less than or similar to z less than or similar to 0.96, and 1.5 less than or similar to z less than or similar to 3.3 and is slightly less significant in the redshift bin 0.96 less than or similar to z less than or similar to 1.5. The X-ray spectral slope steepens as the X-ray luminosity increases for AGNs in the luminosity range 10(42) to 10(45) erg s(-1). Combining our results from the CDFs with those from previous studies in the redshift range 1.5 less than or similar to z less than or similar to 3.3, we find that the Gamma-L-X correlation has a null-hypothesis probability of 1.6 x 10(-9). 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% confidence level) between redshift bins of 0.3 less than or similar to z less than or similar to 0.96 and 1.5 less than or similar to z less than or similar to 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 dependence on variations of the properties of the hot corona with redshift.