In this paper , we explained the observed \Gamma _ { 2 - 10 keV } - L _ { bol } / L _ { Edd } correlation in luminous active galactic nuclei within the framework of the condensation of the corona around a supermassive black hole \citep Liu2015 , Qiao2017 .
Specifically , we systemically test the effects of black hole mass M , the viscosity parameter \alpha , and the magnetic parameter \beta ( with magnetic pressure p _ { m } = B ^ { 2 } / { 8 \pi } = ( 1 - \beta ) p _ { tot } , p _ { tot } = p _ { gas } + p _ { m } ) on the structure of the accretion disc and the corona , as well as the corresponding emergent spectra .
It is found that the hard X-ray photon index \Gamma _ { 2 - 10 keV } nearly does not change with changing black hole mass M , or changing magnetic parameter \beta .
Meanwhile , it is found that the geometry of the accretion flow , i.e. , the relative configuration of the disc and corona , as well as the emergent spectra can be strongly affected by changing the value of \alpha .
By comparing with a sample composed of 29 luminous active galactic nuclei with well constrained X-ray spectra and Eddington ratios , it is found that the observed \Gamma _ { 2 - 10 keV } - L _ { bol } / L _ { Edd } correlation can be well matched with a relatively bigger value of \alpha , i.e. , \alpha \sim 1 , as previously also suggested by \citet [ ] Narayan1996 for luminous accreting black holes .