A simplified global solution for an advection-dominated accretion flow

TL;DR

This paper introduces a simplified method for calculating global advection-dominated accretion flow solutions around black holes, making it easier to model radiation emission without complex boundary value problems.

Contribution

It replaces the radial momentum equation with an algebraic relation, enabling easier computation of approximate global solutions for ADAFs.

Findings

Approximate solutions match true global solutions closely.

Method works for a wide range of accretion rates and viscosity parameters.

Spectra from simplified solutions are very similar to those from full solutions.

Abstract

When we model black hole accretion sources such as active galactic nuclei and black hole X-ray binaries as advection-dominated accretion flows (ADAFs), it is neccesary to use the global solution to the equations rather than the simpler self-similar solution, since the latter is inaccurate in the region near the black hole where most of the radiation is emitted. However, technically, it is a difficult task to calculate the global solution because of the transonic nature of the flow, which makes it a two-point boundary value problem. In this paper we propose a simplified approach for calculating the global ADAF solution. We replace the radial momentum equation by a simple algebraic relation between the angular velocity of the gas and the Keplerian angular velocity, while keeping all other equations unchanged. It is then easy to solve the differential energy equations to obtain an approximate global solution. By adjusting the free parameters, we find that for almost any accretion rate and for $\alpha=0.1-0.3$ we can get good simplified global solutions. The predicted spectra from the approximate solutions are very close to the spectra obtained from the true global solutions.