Steady General Relativistic Magnetohydrodynamic Inflow/Outflow Solution along Large-Scale Magnetic Fields that Thread a Rotating Black Hole

TL;DR

This paper presents the first semi-analytical, self-consistent solution for a cold, Poynting flux-dominated GRMHD flow along magnetic fields around a rotating black hole, passing all critical points along a parabolic streamline.

Contribution

It introduces a novel semi-analytical method to model steady GRMHD inflow/outflow solutions that can complement numerical simulations around rotating black holes.

Findings

Successfully models a self-consistent GRMHD flow passing all critical points.

Provides a method to constrain outflow solutions based on inflow properties.

Demonstrates agreement with previous numerical work by McKinney.

Abstract

General relativistic magnetohydrodynamic (GRMHD) flows along magnetic fields threading a black hole can be divided into inflow and outflow parts, according to the result of the competition between the black hole gravity and magneto-centrifugal forces along the field line. Here we present the first self-consistent, semi-analytical solution for a cold, Poynting flux-dominated (PFD) GRMHD flow, which passes all four critical (inner and outer, Alfven and fast magnetosonic) points along a parabolic streamline. By assuming that the dominating (electromagnetic) component of the energy flux per flux tube is conserved at the surface where the inflow and outflow are separated, the outflow part of the solution can be constrained by the inflow part. The semi-analytical method can provide fiducial and complementary solutions for GRMHD simulations around the rotating black hole, given that the black hole spin, global streamline, and magnetizaion (i.e., a mass loading at the inflow/outflow separation) are prescribed. For reference, we demonstrate a self-consistent result with the work by McKinney in a quantitative level.