2023MNRAS.520..129T

Most active galactic nucleus (AGN) spectra show a soft X-ray excess above the 2-10 keV power law extrapolation. A warm corona has been widely used to explain the excess, but its observed radiation flux in the actually physical environment has yet to be further studied. For the first time, we calculate the relativistic warm coronal flux under the finite disc-corona thickness in high-accretion-rate systems. The numerical results show that the warm coronal flux generally rises first and then drops with increasing inclination. The flux rise is more significant for a compact and low-temperature warm corona and can reach 1-2 dexes. Meanwhile, the flux drop is significant if and only if the warm corona is heavily obscured due to the finite thickness. Our model can successfully explain the soft excess variance and the X-ray weak fraction in a high-accretion-rate AGN sample. In conclusion, our study indicates that when fitting the soft X-ray spectra of AGNs, the relativistic inclination dependence of warm coronal flux is essential, especially for the high-accretion-rate systems with thick warm coronae.