Magnetar magnetospheres are believed to be strongly twisted, due to shearing of the stellar crust by internal magnetic stresses. We present time-dependent axisymmetric simulations showing in detail the evolution of relativistic force-free magnetospheres subjected to slow twisting through large angles. When the twist amplitude is small, the magnetosphere moves quasi-statically through a sequence of equilibria of increasing free energy. At some twist amplitude the magnetosphere becomes tearing-mode unstable to forming a resistive current sheet, initiating large-scale magnetic reconnection in which a significant fraction of the magnetic free energy can be dissipated. This "critical" twist angle is insensitive to the resistive length scale. Rapid shearing temporarily stabilizes the magnetosphere beyond the critical angle, allowing the magnetosphere of a rapidly differentially rotating star to store, and dissipate, more free energy. In addition to these effects, shearing the surface of a rotating star increases the spindown torque applied to the star. If shearing is much slower than rotation, the resulting spikes in spindown rate can occur on timescales anywhere from the long twisting timescale to the stellar spin period or shorter, depending both on the stellar shear distribution and the existing distribution of magnetospheric twists. A model in which energy is stored in the magnetosphere, and released by a magnetospheric instability, therefore predicts large changes in the measured spindown rate before SGR giant flares.
In this poster we present the structure of an axisymmetric, force-free magnetosphere of a twisted, aligned rotating dipole within a corotating plasma-filled magnetosphere. We explore various profiles for the twist. We find that as the current increases more field lines cross the light cylinder leading to more efficient spin-down. Moreover, we notice that the twist cannot be increased indefinitely and after a finite twist of about $π/2$ the field becomes approximately radial. This could have implications for torque variations of magnetars related to outbursts.
The X-ray spectra observed in the persistent emission of magnetars are evidence for the existence of a magnetosphere. The high-energy part of the spectra is explained by resonant cyclotron upscattering of soft thermal photons in a twisted magnetosphere, which has motivated an increasing number of efforts to improve and generalize existing magnetosphere models. We want to build more general configurations of twisted, force-free magnetospheres as a first step to understanding the role played by the magnetic field geometry in the observed spectra. First we reviewed and extended previous analytica…
The magnetospheres of magnetars are believed to be filled with electron-positron plasma generated by electric discharge. We present a first direct numerical experiment showing how the plasma is created in an axisymmetric closed magnetosphere. The $e^\pm$ discharge occurs in response to twisting of the magnetic field lines by a shear deformation of the magnetar surface, which launches electric currents into the magnetosphere. The simulation shows the formation of an electric "gap" with unscreened electric field ($\mathbf{E}\cdot \mathbf{B}\neq 0$) that continually accelerates particles along th…
We consider magnetospheric structure of rotating neutron stars with internally twisted axisymmetric magnetic fields. The twist-induced and rotation-induced toroidal magnetic fields align/counter-align in different hemispheres. Using analytical and numerical calculations (with PHAEDRA code) we show that as a result the North-South symmetry is broken: the magnetosphere and the wind become "angled", of conical shape. Angling of the magnetosphere affects the spindown (making it smaller for mild twists), makes the return current split unequally at the Y-point, produces anisotropic wind and linear a…
The magnetic field of magnetars may be twisted compared with that of normal pulsars. Previous works mainly discussed magnetic energy release in the closed field line regions of magnetars. For a twisted magnetic field, the field lines will inflate in the radial direction. Similar to normal pulsars, the idea of light cylinder radius is introduced. More field lines will cross the light cylinder and become open for a twisted magnetic field. Therefore, magnetars may have a large polar cap, which may correspond to the hot spot during outburst. Particle flow in the open field line regions will result…
Anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are recognized as the most promising magnetar candidates, as indicated by their energetic bursts and rapid spin-downs. It is expected that the strong magnetic field leaves distinctive imprints on the emergent radiation both by affecting the radiative processes in atmospheres of magnetars and by scattering in the upper magnetospheres. We construct a self-consistent physical model that incorporates emission from the magnetar surface and its reprocessing in the three-dimensional (3D) twisted magnetosphere using a Monte Carlo techn…
We obtained the magnetic field configurations, including both poloidal and toroidal components, throughout the interior and exterior of magnetars using a realistic equation of state. We divided the magnetized star into the hydromagnetic equilibrium core, Hall equilibrium crust and twisted force-free magnetosphere. We systematically and simultaneously calculated these regions under various boundary conditions using the Green function relaxation method, and noted the following interesting characteristics of these numerical results. First, the strength and structure of core magnetic fields affect…
Magnetars are neutron stars characterized by strong surface magnetic fields generally exceeding the quantum critical value of 44.1 TeraGauss. High-energy photons propagating in their magnetospheres can be attenuated by QED processes like photon splitting and magnetic pair creation. In this paper, we compute the opacities due to photon splitting and pair creation by photons emitted anywhere in the magnetosphere of a magnetar. Axisymmetric, twisted dipole field configurations embedded in the Schwarzschild metric are treated. The paper computes the maximum energies for photon transparency that pe…
Soft Gamma-Ray Repeaters and Anomalous X-Ray Pulsars are extreme manifestations of the most magnetized neutron stars: magnetars. The phenomenology of their emission and spectral properties strongly support the idea that the magnetospheres of these astrophysical objects are tightly twisted in the vicinity of the star. Previous studies on equilibrium configurations have so far focused on either the internal or the external magnetic field configuration, without considering a real coupling between the two fields. Here we investigate numerical equilibrium models of magnetized neutron stars endowed …
We study the long-term quasi-steady evolution of the force-free magnetosphere of a magnetar coupled to its internal magnetic field. We find that magnetospheric currents can be maintained on long timescales of the order of thousands of years. Meanwhile, the energy, helicity and twist stored in the magnetosphere all gradually increase over the course of this evolution, until a critical point is reached, beyond which a force-free magnetosphere cannot be constructed. At this point, some large-scale magnetospheric rearrangement, possibly resulting in an outburst or a flare, must occur, releasing a …
The magnetar magnetosphere is gradually twisted by shearing from footpoint motion, and stored magnetic energy also increases at the same time. When a state exceeds a threshold, flares/outbursts manifest themselves as a result of a catastrophic transition. Axisymmetric static solutions for a relativistic force-free magnetosphere with dipole--quadrupole mixed fields at the surface have been calculated. The quadrupole component represents a kind of magnetic-field irregularity at a small scale. Locally twisted models are constructed by limiting current flow regions, where the small part originates…
We extend our previous study of equilibrium solutions of non-rotating force-free magnetospheres of neutron stars. We show that multiple solutions exist for the same sets of parameters, implying that the solutions are degenerate. We are able to obtain configurations with disconnected field lines, however, in nearly all cases these correspond to degenerate higher energy solutions. We carry out a wide parametric search in order to understand the properties of the solutions. We confirm our previous results that the lower energy solutions have up to $\sim 25\%$ more energy than the vacuum case, hel…
Magnetars are a class of highly magnetized, slowly rotating neutron stars, only a small fraction of which exhibit radio emission. We propose that the coherent radio curvature emission is generated by net charge fluctuations from a twist-current-carrying bundle (the j-bundle) in the scenario of magnetar-quake. Two-photon pair production is triggered, which requires a threshold voltage not too much higher than $10^9$ V in the current-carrying bundle, and which can be regarded as the `open field lines' of a magnetar. Continued untwisting of the magnetosphere maintains change fluctuations, and hen…
We present three-dimensional 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 to formulate an instability criterion. The rearrangement of magnetic field lines as a consequence of this instability triggers the dissipation of up to 30% of the magnetospheric energy on a thin layer above the magnetar surface. During this process, we predict an increase of th…
We propose that the magnetosphere reconfiguration induced by magnetic twists in the closed field line region can account for the mode-switching of intermittent pulsars. We carefully investigate the properties of axisymmetric force-free pulsar magnetospheres with magnetic twists in closed field line region around the polar caps. The magnetosphere with twisted closed lines leads to enhanced spin-down rates. The enhancement in spin-down rate depends on the size of region with twisted closed lines. Typically, it is increased by a factor of $\sim2$, which is consistent with the intermittent pulsars…
The close vicinity of neutron stars remains poorly constrained by observations. Although plenty of data are available for the peculiar class of pulsars we are still unable to deduce the underlying plasma distribution in their magnetosphere. In the present paper, we try to unravel the magnetospheric structure starting from basic physics principles and reasonable assumptions about the magnetosphere. Beginning with the monopole force-free case, we compute accurate general-relativistic solutions for the electromagnetic field around a slowly rotating magnetized neutron star. Moreover, here we addre…
We present a numerical model in which a cold pair plasma is ejected with relativistic speed through a polar cap region and flows almost radially outside the light cylinder. Stationary axisymmetric structures of electromagnetic fields and plasma flows are self-consistently calculated. In our model, motions of positively and negatively charged particles are assumed to be determined by electromagnetic forces and inertial terms, without pair creation and annihilation or radiation loss. The global electromagnetic fields are calculated by the Maxwell's equations for the plasma density and velocity, …
Neutron stars are compact objects rotating at high speed, up to a substantial fraction of the speed of light (up to 20\% for millisecond pulsars) and possessing ultra-strong electromagnetic fields (close to and sometimes above the quantum critical field of \numprint{4.4e9}~\SIunits{\tesla}). Moreover, due to copious $e^\pm$ pair creation within the magnetosphere, the relativistic plasma surrounding the star is forced into corotation up to the light cylinder where the corotation speed reaches the speed of light. The neutron star electromagnetic activity is powered by its rotation which becomes …
Pulsar magnetospheres are shaped by ultra-relativistic electron/positron plasmas flowing in a strong magnetic field and subject to strong gravitational fields. The former induces magnetospheric currents and space charges responsible for the distortion of the electromagnetic field based on pure electrodynamics. The latter induces other perturbations in these fields based on space-time curvature. The force-free approximation describes the response of this magnetosphere to the presence of currents and charges and has been investigated by many authors. In this context, general relativity has been …
We present a detailed analysis of the properties of twisted, force-free magnetospheres of non-rotating neutron stars, which are of interest in the modelling of magnetar properties and evolution. In our models the magnetic field smoothly matches to a current-free (vacuum) solution at some large external radius, and they are specifically built to avoid pathological surface currents at any of the interfaces. By exploring a large range of parameters, we find a few remarkable general trends. We find that the total dipolar moment can be increased by up to $40\%$ with respect to a vacuum model with t…
Magnetars exhibit a variety of transient high-energy phenomena in the form of bursts, outbursts, and giant flares. It is a common belief that these events originate in the sudden release of magnetic energy due to the rearrangement of a twisted magnetic field. We present global models of a 3D Force-Free (FF) non-linear twisted magnetar magnetosphere. We solve the FF equations following the Grad-Rubin approach in a compactified spherical domain. Appropriate boundary conditions are imposed at the surface of the star for the current distribution and the magnetic field. Our implementation is tested…
The phenomenology of the emission of pulsars and magnetars depends dramatically on the structure and properties of their magnetic field. In particular it is believed that the outbursting and flaring activity observed in AXPs and SRGs is strongly related to their internal magnetic field. Recent observations have moreover shown that charges are present in their magnetospheres supporting the idea that their magnetic field is tightly twisted in the vicinity of the star. In principle these objects offer a unique opportunity to investigate physics in a regime beyond what can be obtained in the labor…
There is an increasing theoretical and observational evidence that the external magnetic field of magnetars may contain a toroidal component, likely of the same order of the poloidal one. Such "twisted magnetospheres" are threaded by currents flowing along the closed field lines which can efficiently interact with soft thermal photons via resonant cyclotron scatterings (RCS). Actually, RCS spectral models proved quite successful in explaining the persistent ~1-10 keV emission from the magnetar candidates, the soft gamma-ray repeaters (SGRs) and the anomalous X-ray pulsars (AXPs). Moreover, it …
Magnetar magnetospheres gradually become twisted due to shearing by footpoint motion. The axisymmetric solutions for the force-free field with a power-law current model are calculated by taking into account general relativistic effects. Here we show how the magnetic energy and helicity are accumulated along a sequence of equilibria. In a strongly twisted case, a magnetic flux rope, in which a large amount of toroidal field is confined, detaches in the vicinity of the star. It is found this kind of magnetic field line structure is easily produced due to strong relativistic effects compared with…
Magnetar flares excite strong Alfvén waves in the magnetosphere of the neutron star. The wave energy can (1) dissipate in the magnetosphere, (2) convert to "fast modes" and possibly escape, and (3) penetrate the neutron star crust and dissipate there. We examine and compare the three options. Particularly challenging are nonlinear interactions between strong waves, which develop a cascade to small dissipative scales. This process can be studied in the framework of force-free electrodynamics (FFE). We perform three-dimensional FFE simulations to investigate Alfvén wave dissipation, how long it …
Electron-positron cascade in magnetospheres of supermassive Kerr black holes and the origin of relativistic AGN jets
University of Kansas（堪萨斯大学）；Massachusetts Institute of Technology（麻省理工学院）；Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文中心）
Instabilities in a neutron star can generate Alfvén waves in its magnetosphere. Propagation along the curved magnetic field lines strongly shears the wave, boosting its electric current $j_{\rm A}$. We derive an analytic expression for the evolution of the wave vector $\boldsymbol{k}$ and the growth of $j_{\rm A}$. In the strongly sheared regime, $j_{\rm A}$ may exceed the maximum current $j_{0}$ that can be supported by the background $e^{\pm}$ plasma. We investigate these "charge-starved" waves, first using a simplified two-fluid analytic model, then with first-principles kinetic simulations…
We present the first simulations of evolving, strongly twisted magnetar magnetospheres. Slow shearing of the magnetar crust is seen to lead to a series of magnetospheric expansion and reconnection events, corresponding to X-ray flares and bursts. The axisymmetric simulations include rotation of the neutron star and the magnetic wind through the light cylinder. We study how the increasing twist affects the spindown rate of the star, finding that a dramatic increase in spindown occurs. Particularly spectacular are explosive events caused by the sudden opening of large amounts of overtwisted magn…
The magnetosphere of, and electromagnetic (EM) radiation from pulsars are usually described in the framework of classical electrodynamics. For some pulsars, however, whose emission heights are relatively close to the surface of the neutron star, general relativistic effects might modify the emission from the pulsar. We consider a magnetic dipole model of a pulsar to investigate general relativistic effects on EM radiation from it. Our study includes general relativistic modifications applicable to some significant issues in pulsar astronomy, such as the magnetosphere structure and pulse profil…
We study global non-axisymmetric oscillation modes and instabilities in magnetosphere- disc systems, as expected in neutron star X-ray binaries and possibly also in accreting black hole systems. Our two-dimensional magnetosphere-disc model consists of a Keplerian disc in contact with an uniformly rotating magnetosphere with low plasma density. Two types of global overstable modes exist in such systems, the interface modes and the disc inertial-acoustic modes. We examine various physical effects and parameters that influence the properties of these oscillation modes, particularly their growth r…
We perform first-principles relativistic particle-in-cell simulations of aligned pulsar magnetosphere. We allow free escape of particles from the surface of a neutron star and continuously populate the magnetosphere with neutral pair plasma to imitate pair production. As pair plasma supply increases, we observe the transition from a charge-separated electrosphere solution with trapped plasma and no spin-down to a solution close to the ideal force-free magnetosphere with electromagnetically-dominated pulsar wind. We calculate the magnetospheric structure, current distribution and spin-down powe…
We describe a new scheme for evolving the equations of force-free electrodynamics, the vanishing-inertia limit of magnetohydrodynamics. This pseudospectral code uses global orthogonal basis function expansions to take accurate spatial derivatives, allowing the use of an unstaggered mesh and the complete force-free current density. The method has low numerical dissipation and diffusion outside of singular current sheets. We present a range of one- and two-dimensional tests, and demonstrate convergence to both smooth and discontinuous analytic solutions. As a first application, we revisit the al…
I argue that the problem of electromagnetically driven electron-positron cascades in magnetospheres of neutron stars must be addressed starting from first principles. I describe a general numerical algorithm for doing self-consistent kinetic simulations of electron-positron cascades - wherein particle acceleration, pair creation and screening of the electric field are calculated simultaneously - and apply it to model the Ruderman and Sutherland cascade in one dimension. I find that pair creation is quite regular and quasi-periodic. In each cycle a blob of ultrarelativistic electron-positron pl…
Pulsar magnetospheres are filled with relativistic pairs copiously emitting photons detected from the radio wavelengths up to high and very high energies, in the GeV and sometimes in the TeV range. Efficient particle acceleration converts the stellar rotational kinetic energy into radio, X-ray and gamma-ray photons. Force-free magnetospheres, being dissipationless, cannot operate this conversion. Some non ideal plasma effects must set in within the magnetosphere. In this paper, we compute numerical solutions of pulsar radiative magnetospheres in the radiation reaction limit, where radiation fu…
A magnetar's magnetosphere gradually evolves by the injection of energy and helicity from the interior. Axisymmetric static solutions for a relativistic force-free magnetosphere with a power-law current model are numerically obtained. They provide information about the configurations in which the stored energy is large. The energy along a sequence of equilibria increases and becomes sufficient to open the magnetic field. A magnetic flux rope, in which a large amount of toroidal field is confined, is formed in the vicinity of the star, for states exceeding the open field energy. These states ar…
Black holes are known to launch powerful relativistic jets and emit highly variable gamma radiation. How these jets are loaded with plasma remains poorly understood. Spark gaps are thought to drive particle acceleration and pair creation in the black-hole magnetosphere. In this paper, we perform 2D axisymmetric general-relativistic particle-in-cell simulations of a monopole black-hole magnetosphere with a realistic treatment of inverse Compton scattering and pair production. We find that the magnetosphere can self-consistently fill itself with plasma and activate the Blandford-Znajek mechanism…
We discuss stationary and axisymmetric trans-magnetosonic outflows in the magnetosphere of a rotating black hole (BH). Ejected plasma from the plasma source located near the BH is accelerated far away to form a relativistic jet. In this study, the plasma acceleration efficiency and conversion of fluid energy from electromagnetic energy are considered by employing the trans-fast magnetosonic flow solution derived by Takahashi & Tomimatsu (2008). Considering the parameter dependence of magnetohydrodynamical flows, we search for the parameters of the trans-magnetosonic outflow solution to the rec…
The main contribution to the pulsar power can be calculated by assuming a rotating magnetically-dominated magnetosphere described by the force-free approximation. Although this simple model has been used thoroughly to study pulsar magnetospheres in the flat spacetime regime, only few works have considered the relativistic corrections introduced by the curvature and frame-dragging effects induced by a rotating neutron star. Here we revisit the problem and describe pulsar magnetospheres within full General Relativity, quantifying the corrections as a function of the angular velocity, the compact…
We study the magnetosphere of a slowly rotating magnetized neutron star subject to toroidal oscillations in the relativistic regime. Under the assumption of a zero inclination angle between the magnetic moment and the angular momentum of the star, we analyze the Goldreich-Julian charge density and derive a second-order differential equation for the electrostatic potential. The analytical solution of this equation in the polar cap region of the magnetosphere shows the modification induced by stellar toroidal oscillations on the accelerating electric field and on the charge density. We also find…
We present solutions of force-free pulsar magnetospheres coupled with a uniform external magnetic field aligned with the dipole magnetic moment of the pulsar. The inclusion of the uniform magnetic field has the following consequences: The equatorial current sheet is truncated to a finite length, the fraction of field lines that are open increases, and the open field lines are confined within a cylindrical surface instead of becoming radial. A strong external magnetic field antiparallel to the dipole allows for solutions where the pulsar magnetic field is fully enclosed within an ellipsoidal su…
The study of magnetars is of particular relevance since these objects are the only laboratories where the physics in ultra-strong magnetic fields can be directly tested. Until now, spectroscopic and timing measurements at X-ray energies in soft gamma-repeaters (SGRs) and anomalous X-ray pulsar (AXPs) have been the main source of information about the physical properties of a magnetar and of its magnetosphere. Spectral fitting in the ~ 0.5-10 keV range allowed to validate the "twisted magnetosphere" model, probing the structure of the external field and estimating the density and velocity of th…
An energy extracting black hole magnetosphere can be defined by the location of its inner Alfvén surface, which determines the rate of black hole energy extraction along a given magnetic field line. We study how the location of the inner Alfvén surface can modify the structure of energy extracting black hole magnetospheres in the force-free limit. Hundreds of magnetospheres are numerically computed via a general relativistic extension of the Newtonian magnetofrictional method for a full range of black hole spins and flow parameters. We find that jet-like structures naturally form very close to…
Motivated by coronal mass ejection studies, we construct general relativistic models of a magnetar magnetosphere endowed with strong magnetic fields. The equilibrium states of the stationary, axisymmetric magnetic fields in the magnetar magnetosphere are obtained as solutions of the Grad-Shafranov equation in a Schwarzschild spacetime. To understand the magnetic energy buildup in the magnetar magnetosphere, a generalized magnetic virial theorem in the Schwarzschild metric is newly derived. We carefully address the question whether the magnetar magnetospheric magnetic field can build up suffici…
Like the solar corona, the external magnetic field of magnetars is twisted by surface motions of the star. The twist energy is dissipated over time. We discuss the theory of this activity and its observational status. (1) Theory predicts that the magnetosphere tends to untwist in a peculiar way: a bundle of electric currents (the "j-bundle") is formed with a sharp boundary, which shrinks toward the magnetic dipole axis. Recent observations of shrinking hot spots on magnetars are consistent with this behavior. (2) Continual discharge fills the j-bundle with electron-positron plasma, maintaining…
Accreting pulsars power relativistic jets, and display a complex spin phenomenology. These behaviours may be closely related to the large-scale configuration of the star's magnetic field, shaped by its interaction with the surrounding accretion disc. Here we present the first relativistic simulations of the interaction of a pulsar magnetosphere with an accretion flow. Our axisymmetric simulations treat the magnetospheric, or coronal, regions using a resistive extension of force-free electrodynamics. The magnetic field is also evolved inside the disc, which is a defined volume with a specified …
On the universality of the split monopole black hole magnetosphere
Columbia University（哥伦比亚大学）；Anton Pannekoek Institute（安东·潘内克研究所）；Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）；University of Toronto（多伦多大学）；Perimeter Institute for Theoretical Physics（基础理论物理研究所）；Flatiron Institute（平顿研究所）
Strong gravity and magnetic fields are key ingredients that power processes of accretion and ejection near compact objects. While the particular mechanisms that operate here are still discussed, it seems that the presence of an ordered magnetic field is crucial for the acceleration and collimation of relativistic jets of electrically charged particles on superhorizon length scales. In this context, we further study the effect of a large-scale magnetic field on the dynamics of charged particles near a rotating black hole. We consider a scenario in which the initially neutral particles on regula…
In this paper we consider relativistic effects of rotation in the magnetospheres of $γ$-ray pulsars. The paper reviews the progress achieved in this field during the last three decades. For this purpose we examine direct centrifugal acceleration of particles and corresponding limiting factors: constraints due to the curvature radiation and the inverse Compton scattering of electrons against soft photons. Based on the obtained results generation of parametrically excited Langmuir waves and the corresponding Landau-Langmuir-centrifugal drive is studied.
The nearly 100% linear polarization has been reported for a few fast radio bursts. This finding places severe limits on the emission mechanism. I argue that the totally polarized radiation could be generated in the course of relativistic magnetic reconnection in the outer magnetosphere of the magnetar. At the onset of the magnetar flare, a large scale magnetic perturbation forms a magnetic pulse, which propagates from the flare cite outwards. The pulse strongly compresses magnetospheric plasma and pushes it away. The high-frequency MHD waves are generated when the magnetic pulse reaches the cu…
According to current pulsar emission models, photons are produced within their magnetosphere or inside the current sheet outside the light-cylinder. Radio emission is favoured in the vicinity of the polar caps whereas the high-energy counterpart is presumably enhanced in regions around the light-cylinder, magnetosphere or/and wind. However, gravitational impacts on light-curves and their spectral properties have only been sparsely touched. In this paper, we present a new method to simulate the influence of the neutron star gravitational field on its emission according to general relativity. We…
