We solve the two-dimensional magnetohydrodynamic (MHD) equations of black hole accretion with the presence of magnetic field. The field includes a turbulent component, whose role is represented by the viscosity, and a large-scale ordered component. The latter is further assumed to be evenly symmetric with the equatorial plane. The equations are solved in the r − θ plane of a spherical coordinate by assuming timesteady and radially self-similar. An inflow-wind solution is found. Around the equatorial plane, the gas is inflowing; while above and below the equatorial plane at a certain critical θ angle, θ ∼ 47 • , the inflow changes its direction of radial motion and becomes wind. The driving forces are analyzed and found to be the centrifugal force and the gradient of gas and magnetic pressure. The properties of wind are also calculated. The specific angular momentum of wind is found to be significantly larger than that of inflow, thus wind can transfer angular momentum outward. These analytical results are compared to those obtained by the trajectory analysis based on MHD numerical simulation data and good agreements are found.

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, θ, ϕ) to solve our equation. The toroidal component of magnetic field is considered and all three components of the velocity field v ≡ (v r , v θ , v ϕ ) are present in our work. We reduce the equations to a set of differential equations about θ 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 θ 0 , always exist. The results represent that the stronger the magnetic field, the smaller the inclination angle, θ 0 becomes. It means that a magnetized disk is thinner compared to a non-magnetized disk. According to the work by Jiao & Wu 2011, we can define three regions. The first one is called inflow region, which starts from the disk midplane to a certain inclination θ 0 where v r (θ 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 (θ) > 0, is placed between θ 0 and surface of the disk, θ 0 < θ < θ 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. This area is very narrow and the material is blown out from the surface in the form of wind. In this paper we consider two parameters to show the magnetic field effects. These parameters include ratio of gas pressure to magnetic pressure in the equatorial plane of the disk, β 0 , and also magnetic diffusivity parameter, η 0 . Numerical calculations of our model have revealed that the toroidal components of magnetic field has a significant effect on the vertical structure of accretion disk.Many theoretical models have been proposed. One of them is the standard accretion disk model presented by Shakura & Sunyaev 1973. In this model, the disk is assumed to be geometrically thin (H/r ≪ 1), optically thick in the vertical direction and the accreting matter moves with nearly Keplerian velocity. This model explains most of the observational features of X-ray binaries and active galactic nuclei in a highly convincing manner. However, standard disk models cannot reproduce high energy emissions, such as X-ray and gamma rays spectrum. One of the most important processes that is not considered in the standard accretion disk model is advective cooling. In this model, the accret-

We perform two-dimensional hydrodynamical simulations of slowly rotating accretion flows in the region of 0.01 − 7 pc around a supermassive black holes with M BH = 10 8 M . The accretion flow is irradiated by the photons from the central active galactic nucleus (AGN). In addition to the direct radiation from the AGN, we have also included the "re-radiation", i.e., the locally produced radiation by Thomson scattering, line and bremsstrahlung radiation. Compare to our previous work, we have improved the calculation of radiation force due to the Thomson scattering of X-ray photons from the central AGN. We find that this improvement can significantly increase the mass flux and velocity of outflow. We have compared the properties of outflow -including mass outflow rate, velocity, and kinetic luminosity of outflow -in our simulation with the observed properties of outflow in AGNs and found that they are in good consistency. This implies that the combination of line and re-radiation forces is the possible origin of observed outflow in luminous AGNs.

Context. Observations indicate that wind can be generated in hot accretion flow. By performing numerical simulations, Yuan et al. studied the detailed properties of wind generated from weakly magnetized accretion flow. However, properties of wind generated from strongly magnetized hot accretion flow have not been studied. Aims. In this paper, we study the properties of wind generated from both weakly and strongly magnetized accretion flow. We focus on how the magnetic field strength affects the wind properties. Methods. We solve time-steady two-dimensional magnetohydrodynamic (MHD) equations of black hole accretion in the presence of large-scale magnetic field. We assume self-similarity in radial direction. The magnetic field is assumed to be evenly symmetric with the equatorial plane. Results. We find that wind exists in both weakly and strongly magnetized accretion flow. When magnetic field is weak (magnetic pressure is more than 2 orders of magnitude smaller than gas pressure), wind is driven by gas pressure gradient and centrifugal forces. When magnetic field is strong (magnetic pressure is slightly smaller than gas pressure), wind is driven by gas pressure gradient and magnetic pressure gradient forces. The power of wind in strongly magnetized case is just slightly larger than that in weakly magnetized case. The power of wind lies in a range P W ∼ 10 −4 − 10 −3Ṁ in c 2 , withṀ in and c being mass inflow rate and speed of light, respectively. The possible role of wind in active galactic nuclei feedback is briefly discussed.

We solve the radiation-hydrodynamic (RHD) equations of supercritical accretion flows in the presence of radiation force and outflow by using self similar solutions. Compare with the pioneer works, in this paper we consider power-law function for mass inflow rate asṀ ∝ r s . We found that s = 1 when the radiative cooling term is included in the energy equation. Correspondingly, the effective temperature profile with respect to the radius was obtained as T eff ∝ r −1/2 . In addition, we investigated the influence of the outflow on the dynamics of the accretion flow. We also calculated the continuum spectrum emitted from the disk surface as well as the bolometric luminosity of the accretion flow. Furthermore, our results show that the advection parameter, f , strongly depends on mass inflow rate.

We have examined the structure of hot accretion flow with a large-scale magnetic field. The importance of outflow/wind and thermal conduction on the self-similar structure of a hot accretion flows has been investigated. In comparison to the accretion disk without winds/outflow, our results show that the radial and rotational velocities of the disk become faster however it become cooler because of the angular momentum and energy flux which are taking away by the winds/outflows. but thermal conduction opposes the effect of winds/outflows not only decrease the rotational velocity but also increase the radial velocity as well as the sound speed of the disk. In addition we have studied the effect of global magnetic field on the structure of the disk. We have found out that all three components of magnetic field have a noticeable effect on the structure of the disk such as velocities and vertical thickness of the disk.

We present the two-dimensional inflow-outflow solutions of radiation hydrodynamic (RHD) equations of supercritical accretion flows. Compared with prior studies, we include all components of the viscous stress tensor. We assume steady state flow and use self-similar solutions in the radial direction to solve the equations in r − θ domain of the spherical coordinates. The set of differential equations have been integrated from the rotation axis to the equatorial plane. We find that the self-similarity assumption requires that the radial profile of density is described by ρ(r) ∝ r −0.5 . Correspondingly, the radial profile of the mass inflow rate decreases with decreasing radii as Ṁin ∝ r. Inflow-outflow structure has been found in our solution. In the region θ > 65 • there exist inflow while above that flow moves outward and outflow could launch. The driving forces of the outflow are analyzed and found that the radiation force is dominant and push the gas particles outwards with poloidal velocity ∼ 0.25c. The properties of outflow are also studied. The results show that the mass flux weighted angular momentum of the inflow is lower than that of outflow, thus the angular momentum of the flow can be transported by the outflow. We also analyze the convective stability of the supercritical disk and find that in the absence of the magnetic field, the flow is convectively unstable. Our analytical results are fully consistent with the previous numerical simulations of the supercritical accretion flow.

Force due to the self-gravity of the disc in the vertical direction is considered to study its possible effects on the structure of a magnetized advection-dominated accretion disc. We present steady-sate self similar solutions for the dynamical structure of such a type of the accretion flows. Our solutions imply reduced thickness of the disc because of the self-gravity. It also imply that the thickness of the disc will increase by adding the magnetic field strength.