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In this paper, we explained the observed $\Gamma_{\rm 2-10keV}-L_{\rmbol}/L_{\rm Edd}$ correlation in luminous active galactic nuclei within theframework of the condensation of the corona around a supermassive black hole(Liu et al. 2015; Qiao & Liu 2017). Specifically, we systemically test theeffects of black hole mass $M$, the viscosity parameter $\alpha$, and themagnetic parameter $\beta$ (with magnetic pressure $p_{\rmm}=B^2/{8\pi}=(1-\beta)p_{\rm tot}$, $p_{\rm tot}=p_{\rm gas}+p_{\rm m}$) onthe structure of the accretion disc and the corona, as well as thecorresponding emergent spectra. It is found that the hard X-ray photon index$\Gamma_{\rm 2-10keV}$ nearly does not change with changing black hole mass$M$, or changing magnetic parameter $\beta$. Meanwhile, it is found that thegeometry of the accretion flow, i.e., the relative configuration of the discand corona, as well as the emergent spectra can be strongly affected bychanging the value of $\alpha$. By comparing with a sample composed of 29luminous active galactic nuclei with well constrained X-ray spectra andEddington ratios, it is found that the observed $\Gamma_{\rm 2-10keV}-L_{\rmbol}/L_{\rm Edd}$ correlation can be well matched with a relatively biggervalue of $\alpha$, i.e., $\alpha \sim 1$, as previously also suggested byNarayan (1996) for luminous accreting black holes.

monthly notices of the royal astronomical society

A systematic study of the condensation of the corona and the application  for $\Gamma_{\rm 2-10keV}-L_{\rm bol}/L_{\rm Edd}$ correlation in luminous  active galactic nuclei