Vertical structure of Advection dominated Accretion Flows

TL;DR

This paper analytically investigates the vertical structure of optically thin Advection Dominated Accretion Flows (ADAFs), revealing how key dynamical quantities vary with height and demonstrating thermal equilibrium without outflows.

Contribution

It provides an analytical solution for the vertical structure of ADAFs, showing the variation of the advection parameter and thermal balance in a self-similar, steady, axisymmetric disk.

Findings

Advection parameter varies with vertical angle and peaks near the axis.

Thermal equilibrium persists in no-outflow solutions, balancing viscous heating and advection cooling.

Analytical solutions describe the vertical profiles of flow quantities in ADAFs.

Abstract

We solve the set of hydrodynamic (HD) equations for optically thin Advection Dominated Accretion Flows (ADAFs) by assuming radially self-similar in spherical coordinate system $ (r, \theta, \phi) $. The disk is considered to be steady state and axi-symmetric. We define the boundary conditions at the pole and the equator of the disk and to avoid singularity at the rotation axis, the disk is taken to be symmetric with respect to this axis. Moreover, only the $ \tau_{r \phi} $ component of viscous stress tensor is assumed and we have set $ v_{\theta} = 0 $. The main purpose of this study is to investigate the variation of dynamical quantities of the flow in the vertical direction by finding an analytical solution. As a consequence, we found that the advection parameter, $ f^{adv} $, varies along the $ \theta $ direction and reaches to its maximum near the rotation axis. Our results also show that, in terms of no-outflow solution, thermal equilibrium still exists and consequently advection cooling can balance viscous heating.