Two-dimensional Inflow-outflow Solution of Supercritical Accretion Flow

TL;DR

This paper develops a two-dimensional analytical model of supercritical accretion flows, revealing inflow-outflow structures, radiation-driven outflows, and convective instability, consistent with previous numerical simulations.

Contribution

It introduces a comprehensive 2D analytical solution including all viscous stress components for supercritical accretion flows, extending prior models.

Findings

Inflow occurs at angles > 65°, outflow is launched above that.

Radiation force dominates outflow acceleration with poloidal velocity ~0.25c.

Flow is convectively unstable without magnetic fields.

Abstract

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-\theta $ 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 $ \rho(r) \propto r^{-0.5} $. Correspondingly, the radial profile of the mass inflow rate decreases with decreasing radii as $ \dot{M}_\mathrm{in} \propto r $. Inflow-outflow structure has been found in our solution. In the region $ \theta > 65^{\circ} $ 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 $ \sim 0.25 c $. 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.