Analytical solution for the structure of ADAFs

TL;DR

This paper presents self-similar analytical solutions for ADAFs that capture key properties of the flow, simplifying the study of these accretion structures without complex numerical methods.

Contribution

It introduces new analytical, self-similar solutions for ADAFs assuming dominant shear stress and negligible latitudinal velocity, aligning with numerical results.

Findings

Density and pressure decrease from equator to poles

Flow tends to spherical shape with increased energy advection

Solutions replicate key properties of numerical ADAF models

Abstract

The standard Advection-Dominated Accretion Flow (ADAF) is studied using a set of self-similar analytical solutions in the spherical coordinates. Our new solutions are useful for studying ADAFs without dealing with the usual mathematical complexity. We assume the $r\varphi$ component of the stress tensor dominates and the latitudinal component of the velocity is negligible. Moreover, the fluid is incompressible and the solutions are radially self-similar. We show that our analytical solutions display most of the important properties of ADAFs which have already been obtained by the detailed numerical solutions. According to our solutions, the density and the pressure of the flow decreases from the equator to the polar regions and this reduction depends on the amount of the advected energy. We also show analytically that an ADAF tends to a quasi-spherical configuration as more energy is advected with the radial flow.