Computational general relativistic force-free electrodynamics

Abstract

General relativistic force-free electrodynamics is one possible plasma-limit employed to analyze energetic outflows in which strong magnetic fields are dominant over all inertial phenomena. The amazing images of black hole (BH) shadows from the Galactic Center and the M87 galaxy provide a first direct glimpse into the physics of accretion flows in the most extreme environments of the universe. The efficient extraction of energy in the form of collimated outflows or jets from a rotating BH is directly linked to the topology of the surrounding magnetic field. We aim at providing a tool to numerically model the dynamics of such fields in magnetospheres around compact objects, such as BHs and neutron stars. To do so, we probe their role in the formation of high energy phenomena such as magnetar flares and the highly variable teraelectronvolt emission of some active galactic nuclei. In this work, we present numerical strategies capable of modeling fully dynamical force-free magnetospheres of compact astrophysical objects. We provide implementation details and extensive testing of our implementation of general relativistic force-free electrodynamics in Cartesian and spherical coordinates using the infrastructure of the EINSTEIN TOOLKIT. The employed hyperbolic/parabolic cleaning of numerical errors with full general relativistic compatibility allows for fast advection of numerical errors in dynamical spacetimes. Such fast advection of divergence errors significantly improves the stability of the general relativistic force-free electrodynamics modeling of BH magnetospheres.

Weak Alfvénic turbulence in relativistic plasmas. Part 2. current sheets and dissipation

“…the perpendicular component Bl ). The gradient of the guide field pressure (red line) is non-zero in the current sheet, which compensates for gas pressure that is absent in the force-free limit of MHD, and effectively working to sustain the evolving force-free current sheet by a locally balanced magnetic pressure at the location of the field reversal (similar to the stationary force-free current sheets analysed by Komissarov, Barkov & Lyutikov 2007;Del Zanna et al 2016;Mahlmann et al 2021b).…”

“…We outline the details of the numerical algorithms below. Mahlmann et al (2021a) introduced a scheme based on the infrastructure of the EINSTEIN TOOLKIT, 2 here dubbed ET-FFE, specifically designed for the high-order conservative modelling of the force-free electrodynamics equations (2.8)-(2.9). The charge density is evolved in a separate continuity equation and the algorithm relies on the fully consistent force-free current (2.10).…”

“…The combination of algebraic corrections and the consistent ideal force-free current does not require implicit steps in the time integrator. Therefore, employing MP7 (Suresh & Huynh 1997) spatial reconstruction and fourth-order accurate time integration results in very competitive convergence of the numerical diffusion and dispersion (Mahlmann et al 2021b). These properties are essential for the robustness of the results presented in this manuscript.…”

“…Compact object magnetospheres in particular can be so highly magnetized that the infinitely magnetized, or force-free, limit of relativistic MHD 1 is not only applicable (Goldreich & Julian 1969;Blandford & Znajek 1977) but also provides a more accurate numerical method. Although the force-free MHD limit technically cannot describe the physical effects of dissipation, it does capture the formation of a turbulent cascade (Thompson & Blaes 1998;Cho 2005;Li et al 2019) and of current sheets (Mahlmann et al 2021b). The force-free MHD limit admits two normal modes, an Alfvén wave and a fast wave.…”

“…We compare results from independent and different numerical methods to substantiate our findings. The algorithms we employ, the high-order force-free code ET-FFE (Mahlmann et al 2021a) and the force-free/relativistic MHD code BHAC (Porth et al 2017;Olivares et al 2019;Ripperda et al 2019a), are described in § 2. We explore the nonlinear modelling of continuously overlapping Alfvén waves in detail in § 3, where we provide an analysis of current sheet formation in developing weak turbulence.…”