X-ray Spectral Index and Eddington Ratio Correlation in Radio-Quiet AGNs

Abstract This study presents a comprehensive X-ray spectroscopic analysis of 642 quasars, obtained by cross-matching the XMMNewtonSerendipitous Source Catalog (DR11) with the Sloan Digital Sky Survey (DR16) quasar catalog. After stringent quality filtering and automated spectral reduction, we derived reliable photon indices (Γ) and intrinsic 2–10 keV X-ray luminosities.Using multiwavelength data, sources were classified into 561 radio-quiet (RQ) and 81 radio-loud (RL) quasars. We estimate the bolometric luminosity and Eddington ratio (λEdd) from absorption-corrected X-ray measurements and virial black hole masses.Our primary objective is to establish and characterize the fundamental relationship between the photon index and Eddingtonratio for RQ population. We find that RQ quasars exhibit systematically higher Eddington ratios, peaking at logλEdd ≈ −1.2, and softer spectra with Γ ≈ 2.0. A statistically significant positive correlation between Γ and λEdd is detected in RQ quasars, supporting disk–corona coupling models. To validate our results within the broader context of AGN evolution, we further examine the dependence of λEdd on redshift (z) and black hole mass (MBH). For RQ quasars, λEdd increases with redshift and decreases with MBH, in strong agreement with recent results1, highlighting the universal nature of these accretion trends. By correlating spectral slope with accretion rate, this work provides new insights into the interplay between accretion physics, jet activity, and the cosmic evolution of quasars.