Time-Dependent of Accretion Flow with Toroidal Magnetic Field

TL;DR

This study models the time evolution of quasi-spherical accretion flows with toroidal magnetic fields, revealing how magnetic strength influences flow dynamics, disk thickness, and the position of the transonic point.

Contribution

It introduces a self-similar solution for time-dependent accretion flows with magnetic fields, extending previous steady models and providing new insights into magnetic effects on flow structure.

Findings

Magnetic field strength affects the transonic point location.

Increased magnetic pressure compresses the accretion disk.

Radial velocity depends solely on Alfvén velocity.

Abstract

In the present study time evolution of quasi-spherical polytropic accretion flow with toroidal magnetic field is investigated. The study especially focused the astrophysically important case in which the adiabatic exponent $\gamma=5/3$. In this scenario, it was assumed that the angular momentum transport is due to viscous turbulence and used $\alpha$-prescription for kinematic coefficient of viscosity. The equations of accretion flow are solved in a simplified one-dimensional model that neglects the latitudinal dependence of the flow. In order to solve the integrated equations which govern the dynamical behavior of the accretion flow, self-similar solution was used. The solution provides some insight into the dynamics of quasi-spherical accretion flow and avoids many of the strictures of the steady self-similar solution. The effect of the toroidal magnetic field is considered with additional variable $\beta[=p_{mag}/p_{gas}]$, where $p_{mag}$ and $p_{gas}$ are the magnetic and gas pressure, respectively. The solution indicates a transonic point in the accretion flow, that this point approaches to central object by adding strength of the magnetic field. Also, by adding strength of the magnetic field, the radial-thickness of the disk decreases and the disk compresses. It was analytically indicated that the radial velocity is only a function of Alfv'en velocity. The model implies that the flow has differential rotation and is sub-Keplerian at all radii.