Magnetosphere structure of a Kerr black hole: Marginally force-free equatorial boundary condition

Abstract

The role of equatorial boundary condition in the structure of a force-free black hole magnetosphere was rarely discussed, since previous studies have been focused on the field lines entering the horizon. However, recent high-accuracy force-free electrodynamics (FFE) simulations [1] show that there are both field lines entering the horizon and field lines ending up on the equatorial current sheet within the ergosphere for asymptotic uniform field configuration. For the latter field lines, the equatorial boundary condition is well approximated being marginally force-free, i.e., B 2 − E 2 ≈ 0, where B and E are the magnetic and electric field strength, respectively. In this paper, we revisit the uniform field solution to the Kerr BH magnetosphere structure and investigate the role of the marginally force-free equatorial boundary condition. We find this boundary condition plays an important role in shaping the BH magnetosphere in various aspects, including the shape of the light surface, the near-horizon field line configuration and the source of the Poynting flux. We also propose an algorithm for numerically solving the Grad-Shafranov equation and self-consistently imposing the marginally force-free equatorial condition. As a result, we find a good agreement between our numerical solutions and the high-accuracy FFE simulations. We also discuss the applicability of the marginally force-free boundary condition and the numerical algorithm proposed in this paper for general magnetic field configurations. arXiv:1807.05611v4 [astro-ph.HE]

Particle Acceleration Driven by Null Electromagnetic Fields Near a Kerr Black Hole

“…We consider the relation with those in the background field. In the Schwarzschild case, both the sign of the charge density and the direction of the outflow current are distinguished by only θ: ρ e < 0 in the range of 0 ≤ θ < arccos(3 −1/2 ), whereas ρ e > 0 in the range of arccos(3 −1/2 ) < θ < arccos(−3 −1/2 ) (see Equation (33).) In the left panel of Figure 4, a line of θ = arccos(3 −1/2 ) is plotted.…”

“…As described in Reference [13], part of the outward energy and angular momentum can be traced to the current sheet. The equatorial boundary condition is therefore important to determine the global solution [32,33]. Numerical simulations show that magnetic dominance (B 2 − E 2 > 0) tends to break down in the singular regions.…”

Conformal representation of Kerr space–time poloidal sub-manifolds

“…Nevertheless, when the field is not a purely radial field (more precisely if we do not have ∂ r A = 0 on the horizon), this property does not appear clearly in the ordinary field line representation of the poloidal magnetic field. In the literature focusing on black hole magnetosphere, Nathanail and Contopoulos [2014]; Pan [2018] or Mahlmann et al [2018], the field line representation of some solutions of the Grad-Shafranov equation (GSE) seems not enter in the horizon perpendicularly to it. This problem does not lie with the solution determination.…”

Particle acceleration driven by null electromagnetic fields near a Kerr black hole

“…As described in [13], part of the outward energy and angular momentum can be traced to the current sheet. The equatorial boundary condition is therefore important to determine the global solution [32,33]. Numerical simulations show that magnetic dominance (B 2 − E 2 > 0) tends to break down in the singular regions.…”