Structure of Advection-Dominated Accretion Disks with Outflows: Role of Toroidal Magnetic Field

The main aim of this paper is studying the effect of toroidal magnetic field on the structure of Advection-Dominated Accretion Flows (ADAF) in the presence of the turbulence viscosity and diffusivity due to viscosity and magnetic field respectively. We use self-similar assumption in radial direction to solve the magnetohydrodynamic (MHD) equations for hot accretion disk. We use spherical coordinate $ (r, \theta, \varphi) $ to solve our equation. The toroidal component of magnetic field is considered and all three components of the velocity field $ \mathbf{v}\equiv (v_{r}, v_{\theta}, v_{\varphi}) $ are present in our work. We reduce the equations to a set of differential equations about $ \theta $ and apply the symmetric boundary condition at the equatorial plane of the disk. Our results indicate that the outflow region, where the redial velocity becomes positive in a certain inclination angle $ \theta_{0} $, always exist. The results represent that the stronger the magnetic field, the smaller the inclination angle, $ \theta_{0} $ becomes. It means that a magnetized disk is thinner compared to a non-magnetized disk. According to the work by \citealt{jw}, we can define three regions. The first one is called inflow region, which starts from the disk midplane to a certain inclination $ \theta_0 $ where $ v_{r}(\theta_{0}) = 0 $. In this region, the velocity has a negative value and the accretion material moves toward the central object. The outflow region, where $ v_{r}(\theta) > 0 $, is placed between $ \theta_{0} $ and surface of the disk, $ \theta_{0} < \theta < \theta_{s} $. In this area, the accretion flow moves away from the central object. The third region, which is located between the surface of the disk and the polar axis, is called wind region.