Two-dimensional inflow-wind solution of black hole accretion with an evenly symmetric magnetic field

TL;DR

This paper presents an analytical two-dimensional MHD model of black hole accretion, revealing an inflow-wind structure with wind carrying away angular momentum, consistent with numerical simulations.

Contribution

The study introduces a self-similar, steady-state analytical solution for magnetized black hole accretion with symmetric magnetic fields, highlighting the inflow-wind transition and angular momentum transfer.

Findings

Inflow occurs near the equator, wind at higher latitudes with a critical angle around 47°.

Wind carries significantly more angular momentum than inflow.

Analytical results agree well with numerical MHD simulation data.

Abstract

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 $r-\theta$ plane of a spherical coordinate by assuming time-steady 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 $\theta$ angle, $\theta\sim 47^{\circ}$, 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.