Two-dimensional Particle-in-Cell simulations of axisymmetric black hole magnetospheres: angular dependence of the Blandford-Znajek flux

TL;DR

This study uses 2D particle-in-cell simulations to explore the magnetic and energetic behavior of axisymmetric black hole magnetospheres, revealing how magnetic flux and energy extraction depend on accretion rates and magnetic reconnection.

Contribution

It provides new insights into the angular dependence of the Blandford-Znajek flux and the dynamics of magnetic islands near black holes using detailed PIC simulations.

Findings

Magnetic islands form and migrate, affecting flux expulsion.

Strong magnetic fields penetrate the horizon during flares.

Energy flux concentrates along specific magnetic field lines.

Abstract

We examine the temporary evolution of axisymmetric magnetospheres around rapidly rotating black holes (BHs), by applying our two-dimensional particle-in-cell simulation code. Assuming a stellar-mass BH, we find that the created pairs fail to screen the electric field along the magnetic field, provided that the mass accretion rate is much small compared to the Eddington limit. Magnetic islands are created by reconnection near the equator and migrate toward the event horizon, expelling magnetic flux tubes from the BH vicinity during a large fraction of time. When the magnetic islands stick to the horizon due to redshift and virtually vanish, a strong magnetic field penetrates the horizon, enabling efficient extraction of energy from the BH. During this flaring phase, a BH gap appears around the inner light surface with a strong meridional return current toward the equator within the ergosphere. If the mass accretion rate is 0.025 percent of the Eddington limit, the BH's spin-down luminosity becomes 16-19 times greater than its analytical estimate during the flares, although its long-term average is only 6 percent of it. We demonstrate that the extracted energy flux concentrates along the magnetic field lines threading the horizon in the middle latitudes. It is implied that this meridional concentration of the Poynting flux may result in the formation of limb-brightened jets from low-accreting BH systems.