A generalized solution for advection-dominated accretion flow, standard disc, and slim disc

TL;DR

This paper develops a unified, axisymmetric model that captures various accretion flow solutions, including SSD, SLE, slim disc, and ADAF, across a wide range of accretion rates, incorporating key physical effects.

Contribution

It introduces a generalized set of equations that self-consistently include entropy advection, radiation pressure, and photon trapping, unifying multiple accretion flow solutions.

Findings

Reproduces ADAF, SLE, SSD, and slim disc solutions across accretion rates.

Shows a natural transition between SSD and slim disc with photon trapping.

Demonstrates coexistence of ADAF and SSD below a critical accretion rate.

Abstract

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 solution (SLE), 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 $\dot{m}-\Sigma$ 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.