The condensation of the corona for the correlation between the hard X-ray photon index Γ and the reflection scaling factor R in active galactic nuclei

Observationally, it is found that there is a strong correlation between the hard X-ray photon index Gamma and the Compton reflection scaling factor R in active galactic nuclei. In this paper, we propose that the Gamma -R correlation can be explained within the framework of the condensation of the hot corona on to the cold accretion disc around a supermassive black hole. In the model, it is presumed that, initially, a vertically extended hot gas (corona) is supplied to the central supermassive black hole by capturing the interstellarmedium and stellar wind. In this scenario, when the initial mass accretion rate. M/M-Edd greater than or similar to 0.01, at a critical radius r(d), part of the hot gas begins to condense on to the equatorial disc plane of the black hole, forming an inner cold accretion disc. Then, the matter is accreted in the form of a disc-corona structure extending down to the innermost stable circular orbits of the black hole. The size of the inner disc is determined by the initial mass accretion rate. With the increase of the initial mass accretion rate, the size of the inner disc increases, which results in both the increase of the Compton reflection scaling factor Gamma and the increase of the hard X-ray photon index Gamma. By comparing with a sample of Seyfert galaxies with well-fitted X-ray spectra, it is found that our model can roughly explain the observations. Finally, we discuss the possibility of applying our model to high-mass X-ray binaries, which are believed to be fuelled by hot winds from the companion stars.