We present 3D force-free electrodynamics simulations of magnetar magnetospheres that demonstrate the instability of certain degenerate, high energy equilibrium solutions of the Grad–Shafranov equation. This result indicates the existence of an unstable branch of twisted magnetospheric solutions and allows us to formulate an instability criterion. The rearrangement of magnetic field lines as a consequence of this instability triggers the dissipation of up to 30 per cent of the magnetospheric energy on a thin layer above the magnetar surface. During this process, we predict an increase of the mechanical stresses on to the stellar crust, which can potentially result in a global mechanical failure of a significant fraction of it. We find that the estimated energy release and the emission properties are compatible with the observed giant flare events. The newly identified instability is a candidate for recurrent energy dissipation, which could explain part of the phenomenology observed in magnetars.

One scenario for the generation of fast radio bursts (FRBs) is magnetic reconnection in a current sheet of the magnetar wind. Compressed by a strong magnetic pulse induced by a magnetar flare, the current sheet fragments into a self-similar chain of magnetic islands. Time-dependent plasma currents at their interfaces produce coherent radiation during their hierarchical coalescence. We investigate this scenario using 2D radiative relativistic particle-in-cell simulations to compute the efficiency of the coherent emission and to obtain frequency scalings. Consistent with expectations, a fraction of the reconnected magnetic field energy, f ∼ 0.002, is converted to packets of high-frequency fast magnetosonic waves, which can escape from the magnetar wind as radio emission. In agreement with analytical estimates, we find that magnetic pulses of 1047 erg s−1 can trigger relatively narrowband GHz emission with luminosities of approximately 1042 erg s−1, sufficient to explain bright extragalactic FRBs. The mechanism provides a natural explanation for a downward frequency drift of burst signals, as well as the ∼100 ns substructure recently detected in FRB 20200120E .

The study of the electrodynamics of static, axisymmetric and force-free Kerr magnetospheres relies vastly on solutions of the so called relativistic Grad-Shafranov equation (GSE). Different numerical approaches to the solution of the GSE have been introduced in the literature, but none of them has been fully assessed from the numerical point of view in terms of efficiency and quality of the solutions found. We present a generalization of these algorithms and give detailed background on the algorithmic implementation. We assess the numerical stability of the implemented algorithms and quantify the convergence of the presented methodology for the most established setups (split-monopole, paraboloidal, BH-disk, uniform).

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.

ABSTRACT Black hole – accretion disc systems are the central engines of relativistic jets from stellar to galactic scales. We numerically quantify the unsteady outgoing Poynting flux through the horizon of a rapidly spinning black hole endowed with a rotating accretion disc. The disc supports small-scale, concentric, flux tubes with zero net magnetic flux. Our general relativistic force-free electrodynamics simulations follow the accretion on to the black hole over several hundred dynamical time-scales in 3D. For the case of counter-rotating accretion discs, the average process efficiency reaches up to 〈ϵ〉 ≈ 0.43, compared to a stationary energy extraction by the Blandford/Znajek process. The process efficiency depends on the cross-sectional area of the loops, i.e. on the product l × h, where l is the radial loop thickness and h its vertical scale height. We identify a strong correlation between efficient electromagnetic energy extraction and the quasi-stationary setting of ideal conditions for the operation of the Blandford/Znajek process (e.g. optimal field line angular velocity and fulfillment of the so-called Znajek condition). Remarkably, the energy extraction operates intermittently (alternating episodes of high and low efficiency) without imposing any large-scale magnetic field embedding the central object. Scaling our results to supermassive black holes, we estimate that the typical variability time-scale of the system is of the order of days to months. Such time-scales may account for the longest variability scales of TeV emission observed, e.g. in M87.