Black Hole Magnetospheres

Abstract

We investigate the structure of the steady-state force-free magnetosphere around a Kerr black hole in various astrophysical settings. The solution Ψ(r, θ) depends on the distributions of the magnetic field line angular velocity ω(Ψ) and the poloidal electric current I(Ψ). These are obtained self-consistently as eigenfunctions that allow the solution to smoothly cross the two singular surfaces of the problem, the Inner Light Surface (ILS) inside the ergosphere, and the Outer Light Surface (OLS), which is the generalization of the pulsar light cylinder. Magnetic field configurations that cross both singular surfaces (e.g. monopole, paraboloidal) are uniquely determined. Configurations that cross only one light surface (e.g. the artificial case of a rotating black hole embedded in a vertical magnetic field) are degenerate. We show that, similarly to pulsars, black hole magnetospheres naturally develop an electric current sheet that potentially plays a very important role in the dissipation of black hole rotational energy and in the emission of high-energy radiation.

Black hole magnetosphere with small-scale flux tubes

“…The black hole event horizon and the infinity are also singular surfaces/points of Equation (A2), but it turns out that the solution only needs to satisfy certain regularity conditions at these locations (e.g., Komissarov 2004;Uzdensky 2005;Nathanail & Contopoulos 2014). For our configurations, the field line angular velocity ω is given by the Keplerian angular velocity of the foot point on the disk, and B T (ψ) can be obtained from the smoothness condition (A3) at the light surface-each field line passes through one and only one light surface, which is just sufficient and necessary to constrain B T (ψ).…”

Spacetime approach to force-free magnetospheres

“…These expectations are borne out in numerical calculations that iteratively update guesses for the free functions until a sufficiently smooth match is achieved across all light surfaces. This approach to solving the stream equation in the presence of light surfaces was introduced by Contopoulos, Kazanas & Fendt (1999) and later used by several other authors (Uzdensky 2005;Timokhin 2006;Gruzinov 2006;Contopoulos, Kazanas & Papadopoulos 2013;Nathanail & Contopoulos 2014). For a pulsar magnetosphere, ΩF (ψ) may be fixed in advance to be the (constant) angular velocity of the star (cf.…”

The Cosmic Battery in Astrophysical Accretion Disks

“…If the central object is rotating, then the field lines of one polarity that have already reached it can extract its rotational energy (Blandford & Znajek 1977;Nathanail & Contopoulos 2014). In this paper, we are interested in showing the growth of the magnetic field, and therefore, we are not going to discuss this effect any further.…”