Self‐similar evolutionary solutions for an accreting magneto‐fluid around a compact object with finite electrical conductivity

Abstract

AbstractIn this paper, we investigate the time evolution of an accreting magneto‐fluid with finite conductivity. For the case of a thin disk, the fluid equations along with Maxwell's equations are derived in a simplified, one‐dimensional model that neglects the latitudinal dependence of the flow. The finite electrical conductivity of the plasma is taken into account by Ohm's 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, S0 and εϱ, which represent the size of the 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 S0 and εϱ parameters affect the radial thickness of the disk. Also, radial velocity and gas pressure are more sensitive to the electrical conductivity in the inner regions of disk. Moreover, the parameter εϱ has a more significant effect on the physical quantities for small radii. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)