Structure of advection-dominated accretion discs with outflows: the role of toroidal magnetic fields

The main aim of this article is to study the effect of toroidal magnetic fields on the structure of advection-dominated accretion flows (ADAFs) in the presence of turbulence viscosity and diffusivity due to viscosity and magnetic field respectively. We use the self-similar assumption in the radial direction to solve the magnetohydrodynamic equations for a hot accretion disc. We use spherical coordinates (r, θ, ) to solve our equation. The toroidal component of magnetic field is considered and all three components of the velocity field are present in our work. We reduce the equations to a set of differential equations in θ and apply a symmetric boundary condition at the equatorial plane of the disc. Our results indicate that the outflow region, where the radial velocity becomes positive at a certain inclination angle θ0, always exists. The results illustrate that the stronger the magnetic field, the smaller the inclination angle θ0 becomes. This means that a magnetized disc is thinner compared with a non-magnetized disc. According to the work of Jiao & Wu, we can define three regions. The first is called the inflow region, which starts from the disc mid-plane and extends to a certain inclination θ0 where v r (θ0) = 0. In this region, the velocity has a negative value and the accretion material moves towards the central object. The outflow region, where v r (θ) > 0, is placed between θ0 and the surface of the disc, θ0 < θ < θs. In this area, the accretion flow moves away from the central object. The third region, which is located between the surface of the disc and the polar axis, is called the wind region. This area is very narrow and material is blown out from the surface in the form of wind. In this article, we consider two parameters to illustrate the magnetic field effects. These parameters are the ratio of gas pressure to magnetic pressure in the equatorial plane of the disc, β0, and also the magnetic diffusivity parameter, η0. Numerical calculations with our model have revealed that the toroidal component of magnetic field has a significant effect on the vertical structure of an accretion disc.