Self-similar Evolutionary Solutions for Accreting Magneto-fluid around a Compact Object with Finite Electrical Conductivity

TL;DR

This paper develops self-similar solutions for the evolution of accreting magneto-fluids around compact objects, considering finite electrical conductivity and analyzing how conductivity and density influence disk structure.

Contribution

It introduces a simplified one-dimensional model with self-similar solutions to study the effects of finite electrical conductivity on accretion disk dynamics.

Findings

Electrical conductivity affects the radial thickness of the disk.

Radial velocity and pressure are sensitive to conductivity in inner regions.

Density behavior significantly influences physical quantities at small radii.

Abstract

In this paper, we investigate the time evolution an accreting magneto-fluid with finite conductivity. For the case of a thin disk, the fluid equations along with Maxwell equations are derived in a simplified, one-dimensional model that neglects the latitudinal dependence of the flow. The finite electrical conductivity is taken into account for the plasma through Ohm law; however, the shear viscous stress is neglected, as well as the self-gravity of the disk. In order to solve the integrated equations that govern the dynamical behaviour of the magneto-fluid, we have used a self-similar solution. We introduce two dimensionless variables, $S_0$ and $\epsilon_\rho$, which show the magnitude of electrical conductivity and the density behaviour with time, respectively. The effect of each of these on the structure of the disk is studied. While the pressure is obtained simply by solving an ordinary differential equation, the density, the magnetic field, the radial velocity and the rotational velocity are presented analytically. The solutions show that the $S_0$ and $\epsilon_\rho$ parameters affect the radial thickness of the disk. Also, the radial velocity and gas pressure are more sensitive to electrical conductivity in the inner regions of disk. Moreover, the $\epsilon_\rho$ parameter has a more significant effect on physical quantities in small radii.