Relativistic Magnetic Reconnection in Kerr Spacetime

Abstract

The magnetic reconnection process is analyzed for relativistic magnetohydrodynamical plasmas around rotating black holes. A simple generalization of the Sweet-Parker model is used as a first approximation to the problem. The reconnection rate, as well as other important properties of the reconnection layer, have been calculated taking into account the effect of spacetime curvature. Azimuthal and radial current sheet configurations in the equatorial plane of the black hole have been studied, and the case of small black hole rotation rate has been analyzed. For the azimuthal configuration, it is found that the black hole rotation decreases the reconnection rate. On the other hand, in the radial configuration, it is the gravitational force created by the black hole mass that decreases the reconnection rate. These results establish a fundamental interaction between gravity and magnetic reconnection in astrophysical contexts.Introduction.-The rapid conversion of magnetic energy into plasma particle energy through the process of magnetic reconnection is of paramount importance in many astrophysical processes [1]. Magnetospheric substorms, coronal mass ejections, stellar and gamma-ray flares are just a few examples of pheneomena in which magnetic reconnection is thought to play a crucial role.In recent years, significant work has been undertaken to better understand magnetic reconnection in magnetically dominated environments, where relativistic effects become significant [2]. This has led to the generalization of the classical Sweet-Parker and Petschek reconnection models to the special relativistic regime [3,4]. Furthermore, many numerical campaigns have been devoted to the investigation of the reconnection rate [5][6][7][8][9][10][11][12] and the particle acceleration [13][14][15][16][17][18][19][20] in this regime. Relativistic reconnection has been found to be a very efficient mechanism of magnetic energy conversion and particle acceleration, making it a primary candidate to explain nonthermal emissions from pulsar wind nebulae, gamma-ray bursts, and active galactic nuclei.While special relativistic effects on the reconnection process are starting to become clear, the effects related to the spacetime curvature are far less explored and a detailed understanding is lacking. General relativistic magnetohydrodynamic simulations have repeatedly shown the formation of reconnection layers in proximity of blacks holes [21][22][23][24], where spacetime curvature effects can be important. However, the difficulties related to the spatial and temporal resolution of typical reconnection processes have been such to prevent their thorough study.A step forward in the comprehension of magnetic reconnection in curved spacetime could be taken by studying simple generalizations of known theoretical models. It is the purpose of this Letter to develop such theoretical study considering the contribution of the gravitational

Collisionless magnetic reconnection in curved spacetime and the effect of black hole rotation

“…implying that the outflow velocity and its Lorentz factor are both of order of unity, as was also shown for current sheet configurations around Kerr black holes in the absence of thermal-inertial effects [30]. Note that this conclusion is not affected by the rotation of the black hole.…”

“…We adopt a Sweet-Parker-like approach [12,22,30] in order to evaluate the reconnection rate and other quantities related to the magnetic reconnection layer. This approach is suitable to study magnetic reconnection within narrow quasi-two-dimensional current sheets, i.e.…”

“…In the azimuthal configuration [30], the reconnecting magnetic field is in the φ-direction. We indicate witĥ B in its magnitude in the ZAMO frame.…”

“…However, a detailed investigation of these reconnection layers by means of numerical simulations has not been possible so far, due to the stringent requirements on the spatial and temporal resolutions of typical reconnection processes in this setting. On the other hand, an advance in our theoretical understanding of magnetic reconnection in curved spacetime has been recently obtained by generalizing the collisional Sweet-Parker reconnection model in Kerr spacetime [30]. This approach allowed us to obtain a first estimation of the effects of the gravitational field arXiv:1801.06174v1 [astro-ph.HE] 18 Jan 2018 on the magnetic reconnection process in the collisional regime.…”

One-fluid Equations of General Relativistic Two-fluid Plasma with the Landau–Lifshitz Radiation Reaction Force in Curved Space

“…where we neglect the radiation reaction force acting on the proton due to its large mass Equation (82) could be changed to the following form in the ZAMO frame in the azimuthal direction along the neutral line (Asenjo & Comisso 2017) 1…”