Self-similar structure of magnetized ADAFs and CDAFs

TL;DR

This paper investigates how a global magnetic field influences the structure and dynamics of advection-dominated accretion flows (ADAFs) and convection-dominated accretion flows (CDAFs), extending previous models to include three magnetic field components and different viscosity prescriptions.

Contribution

It extends existing ADAF models by incorporating a three-component magnetic field and analyzing its effects on flow properties and convection, providing new relations between viscosity parameters.

Findings

Magnetic fields alter radial and azimuthal velocities depending on field strength and orientation.

The $ ho ext{-}r$ relation can be $ ho o r^{-1}$ or $r^{-2}$ in magnetized CDAFs.

Magnetic fields modify the $ ext{alpha}_c- ext{alpha}$ relation and flow structure.

Abstract

(Abridged) We study the effects of a global magnetic field on viscously-rotating and vertically-integrated accretion disks around compact objects using a self-similar treatment. We extend Akizuki & Fukue's work (2006) by discussing a general magnetic field with three components ($r, \phi, z$) in advection-dominated accretion flows (ADAFs). We also investigate the effects of a global magnetic field on flows with convection. For these purposes, we first adopt a simple form of the kinematic viscosity $\nu=\alpha c_{s}^{2}/\Omega_{K}$ to study magnetized ADAFs. Then we consider a more realistic model of the kinematic viscosity $\nu=\alpha c_{s}H$, which makes the infall velocity increase but the sound speed and toroidal velocity decrease. We next use two methods to study magnetized flows with convection, i.e., we take the convective coefficient $\alpha_{c}$ as a free parameter to discuss the effects of convection for simplicity. We establish the $\alpha_{c}-\alpha$ relation for magnetized flows using the mixing-length theory and compare this relation with the non-magnetized case. If $\alpha_{c}$ is set as a free parameter, then $|v_{r}|$ and $c_{s}$ increase for a large toroidal magnetic field, while $|v_{r}|$ decreases but $|v_{\phi}|$ increases (or decreases) for a strong and dominated radial (or vertical) magnetic field with increasing $\alpha_{c}$. In addition, the magnetic field makes the $\alpha_{c}-\alpha$ relation be distinct from that of non-magnetized flows, and allows the $\rho\propto r^{-1}$ or $\rho\propto r^{-2}$ structure for magnetized non-accreting convection-dominated accretion flows with $\alpha+g\alpha_{c}< 0$ (where $g$ is the parameter to determine the condition of convective angular momentum transport).