Model of a "Warm Corona" as the origin of the soft X-ray excess of active galactic nuclei.

This article focuses on modeling the warm corona as the origin of the soft X-ray excess observed in active galactic nuclei (AGNs). The warm corona is described as a scattering-dominated surface layer of an accretion disk around a supermassive black hole, with electron temperatures of approximately 0.1–0.3 keV and Compton y-parameters near unity, largely independent of black hole mass or accretion rate. The authors develop a vertical one-zone model incorporating anomalous heating and dominant Compton cooling to reproduce these observational features, explaining the stability and temperature regulation of the warm corona. The study also distinguishes the warm corona from the hot corona found in AGNs and addresses why soft X-ray excess is absent in stellar-mass black holes, attributing it to higher disk temperatures that inhibit effective Compton cooling. Limitations of the one-zone approximation and the need for multi-zone modeling and detailed magnetohydrodynamic simulations are noted for future research.