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 $rm Hbeta$ 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}$), $F_x propto varepsilon^{-0.60pm 0.1}$. It is found that this fraction also has a correlation with the SMBH mass, $F_x propto varepsilon^{-0.74pm 0.14} M_{rm BH}^{-0.30pm 0.03}$. 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+0.21log 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 $F_x$.
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