A generalized solution for advection-dominated accretion flow, standard disc, and slim disc
Liu, Mingjun; Liu, B. F.; Wang, Yilong; Cheng, Huaqing; Yuan, Weimin May 2025, Monthly Notices of the Royal Astronomical Society, Volume 539, Issue 1, pp.69-81
Aiming at a general description of four basic solutions describing the accretion processes, i.e. the Shakura-Sunyaev thin disc (SSD), the Shapiro-Lightman-Eardley (SLE) solution, the slim disc, and the advection-dominated accretion flow (ADAF), we present generalized axisymmetric height-averaged equations, where the entropy advection, the radiation pressure, and photon trapping effect are all included self-consistently. Our generalized solution can reproduce the ADAF, SLE, SSD, and slim disc branches in a wide range of accretion rates from sub- to super-Eddington accretion. An S-curve in the mdot-Sigma plane is also reproduced, representing the SSD branch, the radiation-pressure-dominant branch, and the slim disc branch. The solution gives a natural transition between SSD and slim disc when photon trapping occurs in the accretion flow, producing a radially hybrid SSD-slim disc structure in a certain range of accretion rates. The coexistence of ADAF and SSD below a critical accretion rate is clearly shown with distinct advection fraction of accretion energy. We also present the luminosity, radiation efficiency, and spectrum from the generalized solutions for a large range of accretion rates in stellar mass black holes.
