Hot Corona Properties of Swift/BAT detected AGN

Using a sample of 208 broad-line active galactic nuclei (AGNs) from Swift/BAT AGN Spectroscopic Survey in ultra-hard X-ray band (\(14-195\) keV), the hot corona properties are investigated, i.e. the fraction of gravitational energy dissipated in the hot corona and the hard X-ray photon index. The bolometric luminosity, \lb, is calculated from host-corrected luminosity at 5100 \AA. Virial supermassive black hole masses (SMBH, \mbh) are calculated from the \(\rm H\beta\) line width and the corresponding broad line region size-luminosity empirical relation at 5100 \AA. We find a strong anti-correlation between the fraction of energy released in corona (\(F_x \equiv L_{14-195 keV}/L_{\rm Edd}\)) and the Eddington ratio (\( \varepsilon \equiv L_{\rm Bol}/L_{\rm Edd}\)), \(F_x \propto \varepsilon^{-0.60\pm 0.1}\). It is found that this fraction also has a correlation with the SMBH mass, \(F_x \propto \varepsilon^{-0.74\pm 0.14} M_{\rm BH}^{-0.30\pm 0.03}\). Assuming that magnetic buoyancy and feild reconnection lead to the formation of a hot corona, our result favours the shear stress tensor being a proportion of the gas pressure. For our entire sample, it is found that the hard X-ray photon index \(\Gamma\) has a weak but significant correlation with the Eddington ratio, \( \Gamma=2.17+0.21\log \varepsilon\). However, this correlation is not robust because the relation is not statistically significant for its subsample of 32 RM AGNs with relatively reliable \(M_{\rm BH}\) or its subsample of 166 AGNs with single-epoch \(M_{\rm BH}\). We do not find a statistically significant relation between the photon index and the Eddington ratio taking into account an additional dependence on \(F_x\).