Force-free Electrodynamics Research Articles

Nonlinear Alfvén-wave Dynamics and Premerger Emission from Crustal Oscillations in Neutron Star Mergers

Neutron stars have solid crusts threaded by strong magnetic fields. Perturbations in the crust can excite nonradial oscillations, which can in turn launch Alfvén waves into the magnetosphere. In the case of a compact binary close to merger involving at least one neutron star, this can happen through tidal interactions causing resonant excitations that shatter the neutron star crust. We present the first numerical study that elucidates the dynamics of Alfvén waves launched in a compact binary magnetosphere. We seed a magnetic field perturbation on the neutron star crust, which we then evolve in fully general-relativistic force-free electrodynamics using a GPU-based implementation. We show that Alfvén waves steepen nonlinearly before reaching the orbital light cylinder, form flares, and dissipate energy in a transient current sheet. Our results predict radio and X-ray precursor emission from this process.

Force-free Wave Interaction in Magnetar Magnetospheres: Computational Modeling in Axisymmetry

Crustal quakes of highly magnetized neutron stars can disrupt their magnetospheres, triggering energetic phenomena like X-ray and fast radio bursts. Understanding plasma wave dynamics in these extreme environments is vital for predicting energy transport across scales to the radiation length. This study models relativistic plasma wave interaction in magnetar magnetospheres with force-free electrodynamics simulations. For propagation along curved magnetic field lines, we observe the continuous conversion of Alfvén waves to fast magnetosonic (FMS) waves. The conversion efficiency can be up to three times higher when counter-propagating Alfvén waves interact in the equatorial region. Alfvén waves generate FMS waves of twice their frequency during their first crossing of the magnetosphere. After the initial transient burst of FMS waves, Alfvén waves convert to FMS waves periodically, generating variations on timescales of the magnetospheric Alfvén wave crossing time. This decaying FMS wave tail carries a significant portion (half) of the total energy emitted. Plastic damping of “bouncing” Alfvén waves by the magnetar crust has minimal impact on the FMS efficiency. We discuss the implications of the identified wave phenomena for magnetar observations. Outgoing FMS waves can develop electric zones, potential sources of coherent radiation. Long wavelength FMS waves could generate FRBs through reconnection beyond the light cylinder.

Hybrid GRMHD and force-free simulations of black hole accretion

ABSTRACT We present a new approach for stably evolving general relativistic magnetohydrodynamic (GRMHD) simulations in regions where the magnetization $\sigma =b^2/\rho c^2$ becomes large. GRMHD codes typically struggle to evolve plasma above $\sigma \approx 100$ in simulations of black hole accretion. To ensure stability, GRMHD codes will inject mass density artificially to the simulation as necessary to keep the magnetization below a ceiling value $\sigma _{\rm max}$. We propose an alternative approach where the simulation transitions to solving the equations of general relativistic force-free electrodynamics (GRFFE) above a magnetization $\sigma _{\rm trans}$. We augment the GRFFE equations in the highly magnetized region with approximate equations to evolve the decoupled field-parallel velocity and plasma energy density. Our hybrid scheme is explicit and easily added to the framework of standard-volume GRMHD codes. We present a variety of tests of our method, implemented in the GRMHD code koral, and we show results from a 3D hybrid GRMHD + GRFFE simulation of a magnetically arrested disc (MAD) around a spinning black hole. Our hybrid MAD simulation closely matches the average properties of a standard GRMHD MAD simulation with the same initial conditions in low magnetization regions, but it achieves a magnetization $\sigma \approx 10^6$ in the evacuated jet funnel. We present simulated horizon-scale images of both simulations at 230 GHz with the black hole mass and accretion rate matched to M87*. Images from the hybrid simulation are less affected by the choice of magnetization cut-off $\sigma _{\rm cut}$ imposed in radiative transfer than images from the standard GRMHD simulation.

General relativistic force-free electrodynamics with a discontinuous Galerkin-finite difference hybrid method

General relativistic force-free electrodynamics with a discontinuous Galerkin-finite difference hybrid method

Safety First: Stability and Dissipation of Line-tied Force-free Flux Tubes in Magnetized Coronae

Magnetized plasma columns and extended magnetic structures with both footpoints anchored to a surface layer are an important building block of astrophysical dissipation models. Current loops shining in X-rays during the growth of plasma instabilities are observed in the corona of the Sun and are expected to exist in highly magnetized neutron star magnetospheres and accretion disk coronae. For varying twist and system sizes, we investigate the stability of line-tied force-free flux tubes and the dissipation of twist energy during instabilities using linear analysis and time-dependent force-free electrodynamics simulations. Kink modes (m = 1) and efficient magnetic energy dissipation develop for plasma safety factors q ≲ 1, where q is the inverse of the number of magnetic field line windings per column length. Higher-order fluting modes (m > 1) can distort equilibrium flux tubes for q > 1 but induce significantly less dissipation. In our analysis, the characteristic pitch μ˜0 of flux-tube field lines determines the growth rate ( ∝μ˜03 ) and minimum wavelength of the kink instability ( ∝μ˜0−1 ). We use these scalings to determine a minimum flux tube length for the growth of the kink instability for any given μ˜0 . By drawing analogies to idealized magnetar magnetospheres with varying regimes of boundary shearing rates, we discuss the expected impact of the pitch-dependent growth rates for magnetospheric dissipation in magnetar conditions.

An operator-splitting numerical scheme for relativistic magnetohydrodynamics

We describe a novel operator-splitting approach to numerical relativistic magnetohydrodynamics designed to expand its applicability to the domain of ultra-high magnetisation. In this approach, the electromagnetic field is split into the force-free component, governed by the equations of force-free degenerate electrodynamics (FFDE), and the perturbation component, governed by the perturbation equations derived from the full system of relativistic magnetohydrodynamics (RMHD). The combined system of the FFDE and perturbation equations is integrated simultaneously, for which various numerical techniques developed for hyperbolic conservation laws can be used. At the end of every time-step of numerical integration, the force-free and the perturbation components of the electromagnetic field are recombined and the result is regarded as the initial value of the force-free component for the next time-step, whereas the initial value of the perturbation component is set to zero. To explore the potential of this approach, we build a 3rd-order WENO code, which was used to carry out 1D and 2D test simulations. Their results show that this operator-splitting approach allows us to bypass the stiffness of RMHD in the ultra-high-magnetisation regime where the perturbation component becomes very small. At the same time, the code performs very well in problems with moderate and low magnetisation too.

Modeling the Multiwavelength Radiation Properties in Pulsar Dissipative Magnetospheres

We explore the multiwavelength radiation properties of the light curves and energy spectra in the dissipative magnetospheres of pulsars. The dissipative magnetospheres are simulated by the pseudo-spectral method with the combined force-free and Aristotelian electrodynamics, which can produce self-consistent accelerating electric fields mainly distributed in the equatorial current sheet outside the light cylinder. The multiwavelength light curves and spectra are computed by using the multiple emission mechanisms of both the primary particles accelerated by the accelerating electric fields in the equatorial current sheet and the secondary pairs with an assumed distribution spectrum. We then compare the predicted multiwavelength light curves and spectra with the observed data from the Crab, Vela, and Geminga pulsars. Our modeling results can systematically reproduce the observed trends of the multiwavelength light curves and the spectra for these three pulsars well.

The pulsar magnetosphere with machine learning: methodology

ABSTRACT In this study, we introduce a novel approach for deriving the solution of the ideal force-free steady-state pulsar magnetosphere in three dimensions. Our method involves partitioning the magnetosphere into the regions of closed and open field lines, and subsequently training two custom Physics Informed Neural Networks to generate the solution within each region. We periodically modify the shape of the boundary separating the two regions (the separatrix) to ensure pressure balance throughout. Our approach provides an effective way to handle mathematical contact discontinuities in force-free electrodynamics. We present preliminary results in axisymmetry, which underscore the significant potential of our method. Finally, we discuss the challenges and limitations encountered while working with Neural Networks, thus providing valuable insights from our experience.

Electromagnetic Precursors to Black Hole–Neutron Star Gravitational Wave Events: Flares and Reconnection-powered Fast Radio Transients from the Late Inspiral

The presence of magnetic fields in the late inspiral of black hole–neutron star binaries could lead to potentially detectable electromagnetic precursor transients. Using general-relativistic force-free electrodynamics simulations, we investigate premerger interactions of the common magnetosphere of black hole–neutron star systems. We demonstrate that these systems can feature copious electromagnetic flaring activity, which we find depends on the magnetic field orientation but not on black hole spin. Due to interactions with the surrounding magnetosphere, these flares could lead to fast-radio-burst-like transients and X-ray emission, with as an upper bound on the luminosity, where B * is the magnetic field strength on the surface of the neutron star.

Reconnection-Powered Fast Radio Transients from Coalescing Neutron Star Binaries.

It is an open question whether and how gravitational wave events involving neutron stars can be preceded by electromagnetic counterparts. This Letter shows that the collision of two neutron stars with magnetic fields well below magnetar-level strengths can produce millisecond fast-radio-burst-like transients. Using global force-free electrodynamics simulations, we identify the coherent emission mechanism that might operate in the common magnetosphere of a binary neutron star system prior to merger. We predict that the emission show have frequencies in the range of 10-20GHz for magnetic fields of B^{*}=10^{11} G at the surfaces of the stars.

Breakdown of force-free electrodynamics in electric zones

Abstract It is shown that force-free electrodynamics (FFE) breaks down in regions where B2 − E2 < 0 (electric zones) even if ${\boldsymbol E}\cdot {\boldsymbol B} =0$. Spontaneous creation of such regions will inevitably lead to plasma oscillations that will subsequently decay over a few periods via anomalous heating and, under certain conditions, emission of high-energy quanta, until the system relaxes to a state in which B2 − E2 ≲ 0. For M87, assuming pair plasma, the inverse Compton cooling time is estimated to be shorter than the dynamical time when E2/B2 − 1 > (104/σ)2 roughly, where σ is the magnetization. If the electric zone is weak, the global system will maintain a nearly force-free state, however, the force-free condition, FμνJν = 0, will be broken at the order of the excess electric field and cannot describe wave dynamics. Our analysis does not support recent claims, that creation of electric zones can trigger a transition to force-free turbulence which, when generated in the ergosphere of a Kerr black hole, can lead to extraction of the black hole rotational energy. Whether some secondary electromagnetic modes produced in the decaying electric zone can extract the BH energy is yet an open question.

Electromagnetic precursor flares from the late inspiral of neutron star binaries

ABSTRACT The coalescence of two neutron stars is accompanied by the emission of gravitational waves, and can also feature electromagnetic counterparts powered by mass ejecta and the formation of a relativistic jet after the merger. Since neutron stars can feature strong magnetic fields, the non-trivial interaction of the neutron star magnetospheres might fuel potentially powerful electromagnetic transients prior to merger. A key process powering those precursor transients is relativistic reconnection in strong current sheets formed between the two stars. In this work, we provide a detailed analysis of how the twisting of the common magnetosphere of the binary leads to an emission of electromagnetic flares, akin to those produced in the solar corona. By means of relativistic force-free electrodynamics simulations, we clarify the role of different magnetic field topologies in the process. We conclude that flaring will always occur for suitable magnetic field alignments, unless one of the neutron stars has a magnetic field significantly weaker than the other.

Blandford-Znajek monopole expansion revisited: novel non-analytic contributions to the power emission

The Blandford and Znajek (BZ) split-monopole serves as an important theoretical example of the mechanism that can drive the electromagnetic extraction of energy from Kerr black holes. It is constructed as a perturbative low spin solution of Force Free Electrodynamics (FFE). Recently, Armas et al. put this construction on a firmer footing by clearing up issues with apparent divergent asymptotics. This was accomplished by resolving the behavior around the outer light surface, a critical surface of the FFE equations.Building on this, we revisit the BZ perturbative expansion, and extend the perturbative approach to higher orders in the spin parameter of the Kerr black hole.We employ matched-asymptotic-expansions and semi-analytic techniques to extend the split-monopole solution to the sixth-order in perturbation theory. The expansion necessarily includes novel logarithmic contributions in the spin parameter.We show that these higher order terms result in non-analytic contributions to the power and angular momentum output. In particular, we compute for the first time the perturbative contributions to the energy extraction at seventh- and eighth-order in the spin parameter.The resulting formula for the energy extractionimproves the agreement with numerical simulations at finite spin.Moreover, we present a novel numerical procedure for resolving the FFE equations across the outer light surface, resulting in significantly faster convergence and greater accuracy, and extend this to higher orders as well.Finally, we include a general discussion of light surfaces as critical surfaces of the FFE equations.

Radio Emission of Pulsars. II. Coherence Catalyzed by Cerenkov-unstable Shear Alfvén Waves

This paper explores small-scale departures from force-free electrodynamics around a rotating neutron star, extending our treatment of resistive instability in a quantizing magnetic field. A secondary, Cerenkov instability is identified: relativistic particles flowing through thin current sheets excite propagating charge perturbations that are localized near the sheets. Growth is rapid at wavenumbers below the inverse ambient skin depth k p,ex. Small-scale Alfvénic wavepackets are promising sources of coherent curvature radiation. When the group Lorentz factor , where R c is the magnetic curvature radius, a fraction ∼10−3–10−2 of the particle kinetic energy is radiated into the extraordinary mode at a peak frequency ∼10−2 ck p,ex. Consistency with observations requires a high pair multiplicity (∼103–5) in the pulsar magnetosphere. Neither the primary, slow resistive instability nor the secondary, Alfvénic instability depend directly on the presence of magnetospheric gaps, and may activate where the mean current is fully supplied by outward drift of the corotation charge. The resistive mode is overstable and grows at a rate comparable to the stellar spin frequency; the model directly accommodates strong pulse-to-pulse radio flux variations and coordinated subpulse drift. Alfvén mode growth can track the local plasma conditions, allowing for lower-frequency emission from the outer magnetosphere. Beamed radio emission from charged packets with γ gr ∼ 50–100 also varies on submillisecond timescales. The modes identified here will be excited inside the magnetosphere of a magnetar, and may mediate Taylor relaxation of the magnetic twist.

Magnetar Bursts Due to Alfvén Wave Nonlinear Breakout

The most common form of magnetar activity is short X-ray bursts, with durations from milliseconds to seconds, and luminosities ranging from 1036–1043 erg s−1. Recently, an X-ray burst from the galactic magnetar SGR 1935+2154 was detected to be coincident with two fast radio burst (FRB) like events from the same source, providing evidence that FRBs may be linked to magnetar bursts. Using fully 3D force-free electrodynamics simulations, we show that such magnetar bursts may be produced by Alfvén waves launched from localized magnetar quakes: a wave packet propagates to the outer magnetosphere, becomes nonlinear, and escapes the magnetosphere, forming an ultra-relativistic ejecta. The ejecta pushes open the magnetospheric field lines, creating current sheets behind it. Magnetic reconnection can happen at these current sheets, leading to plasma energization and X-ray emission. The angular size of the ejecta can be compact, ≲1 sr if the quake launching region is small, ≲0.01 sr at the stellar surface. We discuss implications for the FRBs and the coincident X-ray burst from SGR 1935+2154.

Towards traversable wormholes from force-free plasmas

The near-horizon region of magnetically charged black holes can have very strong magnetic fields. A useful low-energy effective theory for fluctuations of the fields, coupled to electrically charged particles, is force-free electrodynamics. The low energy collective excitations include a large number of Alfven wave modes, which have a massless dispersion relation along the field worldlines. We attempt to construct traversable wormhole solutions using the negative Casimir energy of the Alfven wave modes, analogously to the recent construction using charged massless fermions. The behaviour of massless scalars in the near-horizon region implies that the size of the wormholes is strongly restricted and cannot be made large, even though the force free description is valid in a larger regime.

Effective description of non-equilibrium currents in cold magnetized plasma

The dynamics of cold strongly magnetized plasma -- traditionally the domain of force-free electrodynamics -- has recently been reformulated in terms of symmetries and effective field theory, where the degrees of freedom are the momentum and magnetic flux carried by a fluid of cold strings. In physical applications where the electron mass can be neglected one might expect the presence of extra light charged modes -- electrons in the lowest Landau level -- propagating parallel to the magnetic field lines. We construct an effective description of such electric charges, describing their interaction with plasma degrees of freedom in terms of a new collective mode that can be thought of as a bosonization of the electric charge density along each field line. In this framework QED phenomena such as charged pair production and the axial anomaly are described at the classical level. Formally, our construction corresponds to gauging a particular part of the higher form symmetry associated with magnetic flux conservation. We study some simple applications of our effective theory, showing that the scattering of magnetosonic modes generically creates particles and that the rotating Michel monopole is now surrounded by a cloud of electric charge.

Diffusivity in force-free simulations of global magnetospheres

ABSTRACT Assuming that the numerical diffusivity triggered by violations of the force-free electrodynamics constraints is a proxy for the physical resistivity, we examine its impact on the overall dynamics of force-free aligned pulsar magnetospheres endowed with an equatorial current sheet (ECS). We assess the constraint violations as a diffusivity source. The effects of modifications on electric fields used to restore force-free conditions are not confined to the ECS, but modify the magnetospheric dynamics on time-scales shorter than the pulsar rotational period. These corrections propagate especially via a channel that was unexplored, namely, changes induced to the electric charge density, ρ. We quantify the global consequences of diffusivity by comparing different techniques to model ρ. By default, we combine a conservative ρ-evolution with hyperbolic/parabolic cleaning of inaccuracies in the Maxwell equations. As an alternative, we enforce a constrained evolution, where ρ is directly computed as the electric field divergence. The conservative approach reduces the Poynting flux dissipated in the ECS by an order of magnitude, along with an increase of the pulsar luminosity driven by a shift of the Y-point location. The luminosity changes according to LY ∝ α0.11, where α is the ratio of diffusion to advection time-scales, controlling the amount of (numerical) diffusivity. Our models suggest interpreting the luminosity dependence on the Y-point location as differences in resistivities encountered at the ECS. Alternatively, they could be interpreted in terms of the pair formation multiplicity, κ, smaller diffusion being consistent with κ ≫ 1.

Operator lifetime and the force-free electrodynamic limit of magnetised holographic plasma

Using the framework of higher-form global symmetries, we examine the regime of validity of force-free electrodynamics by evaluating the lifetime of the electric field operator, which is non-conserved due to screening effects. We focus on a holographic model which has the same global symmetry as that of low energy plasma and obtain the lifetime of (non-conserved) electric flux in a strong magnetic field regime. The lifetime is inversely correlated to the magnetic field strength and thus suppressed in the strong field regime.

The non-null and force-free electromagnetic field

In this paper, we present a covariant formalism that connects solutions to force-free electrodynamics in the non-null case and foliations of spacetime. In doing so, we are also able to derive an expression of the general non-null current density vector. Just as in the null case, solutions in the non-null case can give rise to a dual solution, however, as is shown below, this can happen only when the solution describes a vacuum field. All theorems are illustrated with previously known solutions.