Revisiting the structure and spectrum of the magnetic-reconnection-heated corona in luminous AGNs

It is believed that the hard X-ray emission in the luminous active galactic nuclei (AGNs) is from the hot corona above the cool accretion disk. However, the formation of the corona is still debated. Liu et al. investigated the spectrum of the corona heated by the reconnection of the magnetic field generated by dynamo action in the thin disk and emerging into the corona as a result of buoyancy instability. In the present paper, we improve this model to interpret the observed relation of the hard X-ray spectrum becoming softer at higher accretion rate in luminous AGNs. The magnetic field is characterized by $\beta_{\rm 0}$, i.e., the ratio of the sum of gas pressure and radiation pressure to magnetic pressure in the disk ($\beta_{\rm 0}=(P_{\rm g,d}+P_{\rm r,d})/P_{\rm B}$). Besides, both the intrinsic disk photons and reprocessed photons by the disk are included as the seed photons for inverse Compton scattering. These improvements are crucial for investigating the effect of magnetic field on the accretion disk-corona when it is not clear whether the radiation pressure or gas pressure dominates in thin disk. We change the value of $\beta_{\rm 0}$ in order to constrain the magnetic field in the accretion disk. We find that the energy fraction released in the corona ($f$) gradually increases with the decrease of $\beta_{\rm 0}$ for the same accretion rate. When $\beta_{\rm 0}$ decreases to less than 50, the structure and spectrum of the disk-corona is independent on accretion rate, which is similar to the hard spectrum found in Liu et al.(2003). Comparing with the observational results of the hard X-ray bolometric correction factor in a sample of luminous AGNs, we suggest that the value of $\beta_{\rm 0}$ is about 100-200 for $\alpha=0.3$ and the energy fraction $f$ should be larger than $30\%$ for hard X-ray emission.