The X-ray photon index Eddington ratio relation in radio-quiet quasars from XMM-Newton and SDSS
This study presents a comprehensive X-ray spectroscopic analysis of 642 quasars, obtained by cross-matching the XMM-Newton Serendipitous 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 ($λ_{\mathrm{Edd}}$) 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 Eddington ratio for RQ population. We find that RQ quasars exhibit systematically higher Eddington ratios, peaking at $\log λ_{\mathrm{Edd}} \approx -1.2$, and softer spectra with $Γ\approx 2.0$. A statistically significant positive correlation between $Γ$ and $λ_{\mathrm{Edd}}$ 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 $λ_{\mathrm{Edd}}$ on redshift ($z$) and black hole mass ($M_{\mathrm{BH}}$). For RQ quasars, $λ_{\mathrm{Edd}}$ increases with redshift and decreases with $M_{\mathrm{BH}}$, in strong agreement with recent results \cite{aggarwal2024evidence}, 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.