The 2D Disk Structure with Advective Transonic Inflow–Outflow Solutions around Black Holes

Abstract

Abstract We solved analytically viscous two-dimensional (2D) fluid equations for accretion and outflows in spherical polar coordinates (r, θ, ϕ) and obtained explicitly flow variables in r- and θ-directions around black holes (BHs). We investigated global transonic advection-dominated accretion flow (ADAF) solutions in an r-direction on an equatorial plane using Paczyński–Wiita potential. We used radial flow variables of ADAFs with symmetric conditions on the equatorial plane as initial values for integration in the θ-direction. In the study of 2D disk structure, we used two azimuthal components of viscous stress tensors—namely, and . Interestingly, we found that the whole advective disk does not participate in outflow generation, and the outflows form close to the BHs. Normally, outflow strength increased with increasing viscosity parameter (α 1), mass-loss parameter (s), and decreasing gas pressure ratio (β). The outflow region increased with increasing s, α 1 for and decreasing α 2 for . The is effective in angular momentum transportation at high latitude and outflows collimation along an axis of symmetry, since it changes polar velocity ( ) of the flow. The outflow emission is also affected by the ADAF size and decreases with it. Transonic surfaces formed for both inflows ( , very close to BH) and outflows ( ). We also explored no outflows, outflows, and failed outflows regions, which mainly depend on the viscosity parameters.