Black Hole Flares: Ejection of Accreted Magnetic Flux through 3D Plasmoid-mediated Reconnection

Magnetic reconnection can power bright, rapid flares originating from the inner magnetosphere of accreting black holes. We conduct extremely high-resolution (5376 × 2304 × 2304 cells) general-relativistic magnetohydrodynamics simulations, capturing plasmoid-mediated reconnection in a 3D magnetically arrested disk for the first time. We show that an equatorial, plasmoid-unstable current sheet forms in a transient, nonaxisymmetric, low-density magnetosphere within the inner few Schwarzschild radii. Magnetic flux bundles escape from the event horizon through reconnection at the universal plasmoid-mediated rate in this current sheet. The reconnection feeds on the highly magnetized plasma in the jets and heats the plasma that ends up trapped in flux bundles to temperatures proportional to the jet’s magnetization. The escaped flux bundles can complete a full orbit as low-density hot spots, consistent with Sgr A* observations by the GRAVITY interferometer. Reconnection near the horizon produces sufficiently energetic plasma to explain flares from accreting black holes, such as the TeV emission observed from M87. The drop in the mass accretion rate during the flare and the resulting low-density magnetosphere make it easier for very-high-energy photons produced by reconnection-accelerated particles to escape. The extreme-resolution results in a converged plasmoid-mediated reconnection rate that directly determines the timescales and properties of the flare.

Weak Alfvénic turbulence in relativistic plasmas. Part 1. Dynamical equations and basic dynamics of interacting resonant triads

Alfvén wave collisions are the primary building blocks of the non-relativistic turbulence that permeates the heliosphere and low- to moderate-energy astrophysical systems. However, many astrophysical systems such as gamma-ray bursts, pulsar and magnetar magnetospheres and active galactic nuclei have relativistic flows or energy densities. To better understand these high-energy systems, we derive reduced relativistic magnetohydrodynamics equations and employ them to examine weak Alfvénic turbulence, dominated by three-wave interactions, in reduced relativistic magnetohydrodynamics, including the force-free, infinitely magnetized limit. We compare both numerical and analytical solutions to demonstrate that many of the findings from non-relativistic weak turbulence are retained in relativistic systems. But, an important distinction in the relativistic limit is the inapplicability of a formally incompressible limit, i.e. there exists finite coupling to the compressible fast mode regardless of the strength of the magnetic field. Since fast modes can propagate across field lines, this mechanism provides a route for energy to escape strongly magnetized systems, e.g. magnetar magnetospheres. However, we find that the fast-Alfvén coupling is diminished in the limit of oblique propagation.

Exact nonlinear solutions for three-dimensional Alfvén-wave packets in relativistic magnetohydrodynamics

We show that large-amplitude, non-planar, Alfvén-wave (AW) packets are exact nonlinear solutions of the relativistic magnetohydrodynamic equations when the total magnetic-field strength in the local fluid rest frame ( $b$ ) is a constant. We derive analytic expressions relating the components of the fluctuating velocity and magnetic field. We also show that these constant- $b$ AWs propagate without distortion at the relativistic Alfvén velocity and never steepen into shocks. These findings and the observed abundance of large-amplitude, constant- $b$ AWs in the solar wind suggest that such waves may be present in relativistic outflows around compact astrophysical objects.

Gmunu: Paralleled, grid-adaptive, general-relativistic magnetohydrodynamics in curvilinear geometries in dynamical spacetimes

We present an update on the General-relativistic multigrid numerical (Gmunu) code, a parallelised, multi-dimensional curvilinear, general relativistic magnetohydrodynamics code with an efficient non-linear cell-centred multigrid elliptic solver, which is fully coupled with an efficient block-based adaptive mesh refinement module. To date, as described in this paper, Gmunu is able to solve the elliptic metric equations in the conformally flat condition approximation with the multigrid approach and the equations of ideal general-relativistic magnetohydrodynamics by means of high-resolution shock-capturing finite-volume method with reference metric formularised multi-dimensionally in Cartesian, cylindrical or spherical geometries. To guarantee the absence of magnetic monopoles during the evolution, we have developed an elliptical divergence cleaning method by using the multigrid solver. In this paper, we present the methodology, full evolution equations and implementation details of Gmunu and its properties and performance in some benchmarking and challenging relativistic magnetohydrodynamics problems.

General Relativistic Magnetohydrodynamic Source Terms in 3+1 Form

The main purpose of this paper is to study the general relativistic magnetohydrodynamics source terms in 3+1 form. In this paper a set of equations, which are suitable for numerical interpretation in full 3+1 dimensions is determined. Section 2 is devoted to electromagnetic source terms in 3+1 form. In the section 3 we have delineated the general relativistic magnetohydrodynamics and obtained a condition that 3+1 source terms are in the same form as that in flat space. In the end we have established a theorem regarding general relativistic magnetohydrodynamics.

Revisiting relativistic magnetohydrodynamics from quantum electrodynamics

We provide a statistical mechanical derivation of relativistic magnetohydrodynamics on the basis of (3 + 1)-dimensional quantum electrodynamics; the system endowed with a magnetic one-form symmetry. The conservation laws and constitutive relations are presented in a manifestly covariant way with respect to the general coordinate transformation. The method of the local Gibbs ensemble (or nonequilibrium statistical operator) combined with the path-integral formula for a thermodynamic functional enables us to obtain exact forms of constitutive relations. Applying the derivative expansion to exact formulas, we derive the first-order constitutive relations for nonlinear relativistic magnetohydrodynamics. Our results for the QED plasma preserving parity and charge-conjugation symmetries are equipped with two electrical resistivities and five (three bulk and two shear) viscosities. We also show that those transport coefficients satisfy the Onsager’s reciprocal relation and a set of inequalities, indicating semi-positivity of the entropy production rate consistent with the local second law of thermodynamics.