The dynamics of magnetized viscous-resistive ADAFs under a self-similar evolution

Abstract

In this paper, we explore the self-similarity time evolution of a hot accretion flow around a compact object in the presence of a toroidal magnetic field. We focus on a simplified model which is axisymmetric, rotating, unsteady viscous-resistive under an advection-dominated stage. In this work, we suppose that both the kinematic viscosity and the magnetic diffusivity to be a result of turbulence in the accretion flow. To describe such a flow, we apply magneto-hydrodynamics equations in spherical coordinates, [Formula: see text] and adopt unsteady self-similar solutions. By neglecting the latitudinal dependence of the flow, we obtain a set of one-dimensional differential equations governing the accretion system. In this research, we encounter two parameters related to the magnetic field; one of them is, [Formula: see text], defined as the ratio of the magnetic pressure to the gas pressure and the other one, [Formula: see text] applied in the magnetic diffusivity definition. Our results show that [Formula: see text] is a function of position, and increases towards outer layers. On the other hand, we examine different strength of magnetic field by choosing different value of [Formula: see text] which is the value of [Formula: see text] at the inner edge of disc. We see that both [Formula: see text] and [Formula: see text] have positive effect on growing the radial infall velocity but density and gas pressure decrease by larger values of these parameters. Moreover, the rotational velocity and temperature of accreting material reduce considerably under the influence of a stronger magnetic field. We also focus on the behavior of the mass accretion rate appearing as a descending function of position. Finally, our solutions confirm that the radial trend of the physical quantities in a dynamical accretion flow is different from the ones in a steady flow. However, the effect of various parameters on the physical quantities in our model is qualitatively consistent with similar steady models.