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 the mechanical stresses onto 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.
We couple internal torsional, magneto-elastic oscillations of highly magnetized neutron stars (magnetars) to their magnetospheres. The corresponding axisymmetric perturbations of the external magnetic field configuration evolve as a sequence of linear, force-free equilibria that are completely determined by the background magnetic field configuration and by the perturbations of the magnetic field at the surface. The perturbations are obtained from simulations of magneto-elastic oscillations in the interior of the magnetar. While such oscillations can excite travelling Alfvén waves in the exter…
In this paper we propose a new mechanism describing the initial spike of giant flares in the framework of the starquake model. We investigate the evolution of a plasma on a closed magnetic flux tube in the magnetosphere of a magnetar in the case of a sudden energy release and discuss the relationship with observations of giant flares. We perform one-dimensional numerical simulations of the relativistic magnetohydrodynamics in Schwarzschild geometry. We assume energy is injected at the footpoints of the loop by a hot star surface containing random perturbations of the transverse velocity. Alfvé…
Lyutikov (2002) predicted "radio emission from soft gamma-ray repeaters (SGRs) during their bursting activity". Detection of a Mega-Jansky radio burst in temporal coincidence with high energy bursts from a Galactic magnetar SGR 1935+2154 confirms that prediction. Similarity of this radio event with Fast Radio Bursts (FRBs) suggests that FRBs are produced within magnetar magnetospheres. We demonstrate that SGR 1935+2154 satisfies the previously derived constraints on the physical parameters at the FRBs' loci. Coherent radio emission is generated in the inner parts of the magnetosphere at $r< 10…
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 examine the possibility that fast radio bursts (FRBs) are emitted inside the magnetosphere of a magnetar. On its way out, the radio wave must interact with a low-density $e^\pm$ plasma in the outer magnetosphere at radii $R=10^9$-$10^{10}\,$cm. In this region, the magnetospheric particles have a huge cross section for scattering the wave. As a result, the wave strongly interacts with the magnetosphere and compresses it, depositing the FRB energy into the compressed field and the scattered radiation. The scattered spectrum extends to the $γ$-ray band and triggers $e^\pm$ avalanche, further b…
We investigate the conditions for radio emission in rotating and oscillating magnetars, by focusing on the main physical processes determining the position of their death-lines in the P-\dot{P} diagram, i.e. of those lines that separate the regions where the neutron star may be radio-loud or radio-quiet. After using the general relativistic expression for the electromagnetic scalar potential in the magnetar magnetosphere, we find that larger compactness parameters of the star as well as larger inclination angles between the rotation axis and the magnetic moment produce death-lines well above t…
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…
In this, paper we study the possibility of generation of electromagnetic waves in the magnetospheres of radio magnetars by means of the quasi-linear diffusion (QLD). Considering the magnetosphere composed of the so-called beam and the plasma components respectively, we argue that the frozen-in condition will inevitably lead to the generation of the unstable cyclotron modes. These modes, via the QLD, will in turn influence the particle distribution function, leading to certain values of the pitch angles, thus to an efficient synchrotron mechanism, producing radio photons. We show that for three…
When the magnetosphere of a magnetar is perturbed by crustal deformation, an electric field $E_\parallel$ parallel to the magnetic field line would appear via Alvfén waves in the charge starvation region. The electron-positron pair bunches will be generated via two-stream instability in the magnetosphere, and these pairs will undergo charge separation in the $E_\parallel$ and in the meantime emit coherent curvature radiation. Following the approach of Yang & Zhang (2018), we find that the superposed curvature radiation becomes narrower due to charge separation, with the width of spectrum depen…
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 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…
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…
At least some fast radio bursts (FRBs) are produced by magnetars. Even though mounting observational evidence points towards a magnetospheric origin of FRB emission, the question of the location for FRB generation continues to be debated. One argument suggested against the magnetospheric origin of bright FRBs is that the radio waves associated with an FRB may lose most of their energy before escaping the magnetosphere because the cross-section for $e^\pm$ to scatter large-amplitude EM waves in the presence of a strong magnetic field is much larger than the Thompson cross-section. We have inves…
Magnetars are the most luminous compact objects in the stellar mass range observed in the Milky Way, with giant flares of hard X-ray power ~10^45 erg/sec being detected from three soft gamma repeaters in the Galactic neighborhood. Periodicity seen in magnetar persistent emission, and a distinctive "spin-down" lengthening of this period, have driven the paradigm that strongly-magnetized neutron stars constitute these fascinating sources. The steady X-ray emission includes both thermal atmospheric components, and magnetospheric contributions that are manifested as hard X-ray "tails." This paper …
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 construct hydromagnetic neutron star equilibria which allow for a non-zero electric current distribution in the exterior. The novelty of our models is that the neutron star's interior field is in equilibrium with its magnetosphere, thus bridging the gap between previous work in this area which either solves for the interior assuming a vacuum exterior or solves for the magnetosphere without modelling the star itself. We consider only non-rotating stars in this work, so our solutions are most immediately applicable to slowly-rotating systems such as magnetars. Nonetheless, we demonstrate that…
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 compute electromagnetic wave propagation through the magnetosphere of a magnetar. The magnetosphere is modeled as the QED vacuum and a cold, strongly magnetized plasma. The background field and electromagnetic waves are treated nonperturbatively and can be arbitrarily strong. This technique is particularly useful for examining non-linear effects in propagating waves. Waves travelling through such a medium typically form shocks; on the other hand we focus on the possible existence of waves that travel without evolving. Therefore, in order to examine the nonlinear effects, we make a travellin…
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…
We study the coupling of the force-free magnetosphere to the long-term internal evolution of a magnetar. We allow the relation between the poloidal and toroidal stream functions - that characterizes the magnetosphere - to evolve freely without constraining its particular form. We find that, on time-scales of the order of kyr, the energy stored in the magnetosphere gradually increases, as the toroidal region grows and the field lines expand outwards. This continues until a critical point is reached beyond which force-free solutions for the magnetosphere can no longer be constructed, likely lead…
The recent discovery of a Galactic fast radio burst (FRB) occurring simultaneously with an X-ray burst (XRB) from the Galactic magnetar SGR J1935+2154 implies that at least some FRBs arise from magnetar activities. We propose that FRBs are triggered by crust fracturing of magnetars, with the burst event rate depending on the magnetic field strength in the crust. Since the crust fracturing rate is relatively higher in polar regions, FRBs are preferred to be triggered near the directions of multipolar magnetic poles. Crust fracturing produces Alfvén waves, forming a charge starved region in the …
Eight pulsars have low braking indices, which challenge the magnetic dipole braking of pulsars. 222 pulsars and 15 magnetars have abnormal distribution of frequency second derivatives, which also make contradiction with classical understanding. How neutron star magnetospheric activities affect these two phenomena are investigated by using the wind braking model of pulsars. It is based on the observational evidence that pulsar timing is correlated with emission and both aspects reflect the magnetospheric activities. Fluctuations are unavoidable for a physical neutron star magnetosphere. Young p…
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 …
We analyze the statistics of pulse arrival times in fast radio burst (FRB) 121102 and demonstrate that they are remarkably similar to statistics of magnetar high-energy short bursts. Motivated by this correspondence, we propose that repeating FRBs are generated during short bursts in the closed field line zone of magnetar magnetospheres via a pulsar-like emission mechanism. Crustal slippage events dislocate field line foot points, initiating intense particle acceleration and pair production, giving rise to coherent radio emission similar to that generated near pulsar polar caps. We argue that …
We discuss dissipative processes occurring during production and escape of Fast Radio Bursts (FRBs) from magnetars' magnetospheres, the presumed loci of FRBs. High magnetic fields are required in the emission region, both to account for the overall energetics of FRBs, and in order to suppress ``normal'' (non-coherent) radiative losses of radio emitting particles; this limits the emission radii to $\leq {\rm few} \times 10 R_{NS}$. Radiative losses by particles in the strong FRB pulse may occur in the outer regions of the magnetosphere for longer rotation periods, $P\geq 1$ second. These losses…
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…
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…
We attribute the rapid spindown of magnetar 1E 2259+586 observed by Archibald et al. (2013), termed the "anti-glitch", to partial opening of the magnetosphere during the X-ray burst, followed by changes of the structure of the closed field line region. To account for the observed spin decrease during the X- ray flare all that is needed is the transient opening, for just one period, of a relatively small fraction of the magnetosphere, of the order of only few percent. More generally, we argue that in magnetars all timing irregularities have magnetospheric origin and are induced either by (i) th…
1D PIC Simulations of Resonant Scattering-Driven Pair Cascades in Magnetar Magnetospheres
Dartmouth College（达特茅斯学院）；University of Maryland, College Park（马里兰大学帕克分校）；Stanford University（斯坦福大学）；Columbia University（哥伦比亚大学）；Max-Planck Institute for Astrophysics（马克斯·普朗克天体物理学研究所）；Center for Computational Astrophysics, Flatiron Institute（平顿研究所计算天体物理中心）
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 …
Sudden relaxation of the magnetic field in the core of a magnetar produces mechanical energy primarily in the form of shear waves which propagate to the surface and enter the magnetosphere as relativistic Alfvén waves. Due to a strong impedance mismatch, shear waves excited in the star suffer many reflections before exiting the star. If mechanical energy is deposited in the core and is converted {\em directly} to radiation upon propagation to the surface, the rise time of the emission is at least seconds to minutes, and probably minutes to hours for a realistic magnetic field geometry, at odds…
Magnetar X-ray flares as elementary reconnection events in a self-organized critical magnetosphere
Institute for Astronomy and Astrophysics, Jinggangshan University（井冈山大学天体物理与天文研究所）；Key Laboratory of Energy Conversion Optoelectronic Functional Materials of Jiangxi Education Institutes, School of Mathematics and Physics, Jinggangshan University（江西高校能量转换光电功能材料重点实验室，井冈山大学数学与物理学院）；School of Computer and Information, Dezhou University（德州大学计算机与信息学院）；Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；School of Astronomy and Space Sciences, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）；Department of Astronomy, Tsinghua University（清华大学天文系）；Institute of Astrophysics, Central China Normal University（华中师范大学天体物理研究所）；State Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所粒子天体物理国家重点实验室）
Radio-loud magnetars display a wide variety of radio-pulse phenomenology seldom seen among the population of rotation-powered pulsars. Spectropolarimetry of the radio pulses from these objects has the potential to place constraints on their magnetic topology and unveil clues about the magnetar radio emission mechanism. Here we report on eight observations of the magnetar Swift J1818.0$-$1607 taken with the Parkes Ultra-Wideband Low receiver covering a wide frequency range from 0.7 to 4 GHz over a period of 5 months. The magnetar exhibits significant temporal profile evolution over this period,…
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…
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…
Over the last four decades, persistent and flaring emission of magnetars observed by various telescopes has provided us with a suite of light curves and spectra in soft and hard X-rays, with no emission yet detected above around 1 MeV. Attenuation of such high-energy photons by magnetic pair creation and photon splitting is expected to be active in the magnetospheres of magnetars, possibly accounting for the paucity of gamma-rays in their signals. This paper explores polarization-dependent opacities for these two QED processes in static vacuum dipole magnetospheres of highly-magnetized neutron…
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…
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…
In this paper, we discuss our first attempts to model the broadband persistent emission of magnetars within a self consistent, physical scenario. We present the predictions of a synthetic model that we calculated with a new Monte Carlo 3-D radiative code. The basic idea is that soft thermal photons (e.g. emitted by the star surface) can experience resonant cyclotron upscattering by a population of relativistic electrons threated in the twisted magnetosphere. Our code is specifically tailored to work in the ultra-magnetized regime; polarization and QED effects are consistently accounted for, as…
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 …
The modification of the rotating vector model in the case of magnetars are calculated. Magnetars may have twisted magnetic field compared with normal pulsars. The polarization position angle of magnetars will change in the case of a twisted magnetic field. For a twisted dipole field, we found that the position angle will change both vertically and horizontally. During the untwisting process of the magnetar magnetosphere, the modifications of the position angle will evolve with time monotonously. This may explain the evolution of the position angle in magnetar PSR J1622-4950 and XTE J1810-197. …
