Black hole jet power from impedance matching

TL;DR

This paper demonstrates that black hole jet power is linked to magnetic field line angular velocity, using an impedance-matching approach, and compares theoretical predictions with simulation results highlighting where the force-free approximation fails.

Contribution

It provides a streamlined proof of the typical ratio of magnetic field line angular velocity to horizon angular velocity using an impedance-matching argument and compares theory with GRMHD simulations.

Findings

Force-free magnetospheres have $ ext{Ω}_F/ ext{Ω}_H extapprox 0.5

Simulation confirms the theory in jet regions

Force-free approximation breaks near the equator in accretion flow

Abstract

Black hole jet power depends on the angular velocity of magnetic field lines, $\Omega_F$. Force-free black hole magnetospheres typically have $\Omega_F/\Omega_H \approx 0.5$, where $\Omega_H$ is the angular velocity of the horizon. We give a streamlined proof of this result using an extension of the classical black hole membrane paradigm. The proof is based on an impedance-matching argument between membranes at the horizon and infinity. Then we consider a general relativistic magnetohydrodynamic simulation of an accreting, spinning black hole and jet. We find that the theory correctly describes the simulation in the jet region. However, the field lines threading the horizon near the equator have much smaller $\Omega_F/\Omega_H$ because the force-free approximation breaks down in the accretion flow.