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Polarization measurements by the Event Horizon Telescope from M87* and Sgr A* suggest that there is a dynamically strong, ordered magnetic field, typical of what is expected of a magnetically arrested accretion disc (MAD). In such discs, the strong poloidal magnetic field can suppress the accretion flow and cause episodic flux eruptions. Recent work shows that general relativistic magnetohydrodynamic (GRMHD) MAD simulations feature dynamics of turbulence and mixing instabilities that are becoming resolved at higher resolutions. We perform a convergence study of MAD states exceeding the status quo by an order of magnitude in resolution. We use existing 3D simulations performed with the H-AMR code, up to a resolution of 5376 × 2304 × 2304 in a logarithmic spherical-polar grid. We find consistent time-averaged disc properties across all resolutions. However, higher resolutions reveal signs of inward angular momentum transport attributed to turbulent convection, particularly evident when mixing instabilities occur at the surfaces of flux tubes during flux eruptions. Additionally, we see wave-like features in the jet sheath, which become more prominent at higher resolutions, that may induce mixing between the jet and disc. At higher resolutions, we observe the sheath to be thinner, resulting in increased temperature, reduced magnetization, and greater variability. Those differences could affect the dissipation of energy, which would eventually result in distinct observable radiative emission from high-resolution simulations. With higher resolutions, we can delve into crucial questions about horizon-scale physics and its impact on the dynamics and emission properties of larger-scale jets. [ABSTRACT FROM AUTHOR]

We apply the general relativistic resistive magnetohydrodynamics code bhac to perform a 2D study of the formation and evolution of a reconnection layer in between two merging magnetic flux tubes in Minkowski space–time. Small-scale effects in the regime of low resistivity most relevant for dilute astrophysical plasmas are resolved with very high accuracy due to the extreme resolutions obtained with adaptive mesh refinement. Numerical convergence in the highly non-linear plasmoid-dominated regime is confirmed for a sweep of resolutions. We employ both uniform resistivity and non-uniform resistivity based on the local, instantaneous current density. For uniform resistivity we find Sweet–Parker reconnection, from η = 10−2 down to η = 10−4, for a reference case of magnetization σ = 3.33 and plasma-β = 0.1. For uniform resistivity η = 5 × 10−5 the tearing mode is recovered, resulting in the formation of secondary plasmoids. The plasmoid instability enhances the reconnection rate to |$v$| rec ∼ 0.03 c compared to |$v$| rec ∼ 0.01 c for η = 10−4. For non-uniform resistivity with a base level η0 = 10−4 and an enhanced current-dependent resistivity in the current sheet, we find an increased reconnection rate of |$v$| rec ∼ 0.1 c. The influence of the magnetization σ and the plasma-β is analysed for cases with uniform resistivity η = 5 × 10−5 and η = 10−4 in a range 0.5 ≤ σ ≤ 10 and 0.01 ≤ β ≤ 1 in regimes that are applicable for black hole accretion discs and jets. The plasmoid instability is triggered for Lundquist numbers larger than a critical value of S c ≈ 8000. [ABSTRACT FROM AUTHOR]

We analyse particle acceleration in explosive reconnection events in magnetically dominated proton–electron plasmas. Reconnection is driven by large-scale magnetic stresses in interacting current-carrying flux tubes. Our model relies on development of current-driven instabilities on macroscopic scales. These tilt–kink instabilities develop in an initially force-free equilibrium of repelling current channels. Using magnetohydrodynamics (MHD) methods we study a 3D model of repelling and interacting flux tubes in which we simultaneously evolve test particles, guided by electromagnetic fields obtained from MHD. We identify two stages of particle acceleration; initially particles accelerate in the current channels, after which the flux ropes start tilting and kinking and particles accelerate due to reconnection processes in the plasma. The explosive stage of reconnection produces non-thermal energy distributions with slopes that depend on plasma resistivity and the initial particle velocity. We also discuss the influence of the length of the flux ropes on particle acceleration and energy distributions. This study extends previous 2.5D results to 3D setups, providing all ingredients needed to model realistic scenarios like solar flares, black hole flares and particle acceleration in pulsar wind nebulae: formation of strong resistive electric fields, explosive reconnection and non-thermal particle distributions. By assuming initial energy equipartition between electrons and protons, applying low resistivity in accordance with solar corona conditions and limiting the flux rope length to a fraction of a solar radius, we obtain realistic energy distributions for solar flares with non-thermal power-law tails and maximum electron energies up to 11 MeV and maximum proton energies up to 1 GeV. [ABSTRACT FROM AUTHOR]

Magnetic reconnection and non-thermal particle distributions associated with current-driven instabilities are investigated by means of resistive magnetohydrodynamics (MHD) simulations combined with relativistic test particle methods. We propose a system with two parallel, repelling current channels in an initially force-free equilibrium, as a simplified representation of flux ropes in a stellar magnetosphere. The current channels undergo a rotation and separation on Alfvénic time-scales, forming secondary islands and (up to tearing unstable) current sheets in which non-thermal energy distributions are expected to develop. Using the recently developed particle module of our open-source grid-adaptive MPI-AMRVAC software, we simulate MHD evolution combined with test particle treatments in MHD snapshots. We explore under which plasma-β conditions the fastest reconnection occurs in 2.5D scenarios, and in these settings, test particles are evolved. We quantify energy distributions, acceleration mechanisms, relativistic corrections to the particle equations of motion and effects of resistivity in magnetically dominated proton-electron plasmas. Due to large resistive electric fields and indefinite acceleration of particles in the infinitely long current channels, hard energy spectra are found in 2.5D configurations. Solutions to these numerical artefacts are proposed for both 2.5D setups and future 3D work. We discuss the MHD of an additional kink instability in 3D setups and the expected effects on energy distributions. The obtained results hold as a proof-of-principle for test particle approaches in MHD simulations, relevant to explore less idealized scenarios like solar flares and more exotic astrophysical phenomena, like black hole flares, magnetar magnetospheres and pulsar wind nebulae. [ABSTRACT FROM AUTHOR]