Magnetar flares generate Alfvén waves bouncing in the closed magnetosphere with energy up to $\sim 10^{46}$ erg. We show that on a 10-ms timescale the waves are transmitted into the star and form a compressed packet of high energy density. This packet strongly shears the stellar crust and initiates a plastic flow, heating the crust and melting it hundreds of meters below the surface. A fraction of the deposited plastic heat is eventually conducted to the stellar surface, contributing to the surface afterglow months to years after the flare. A large fraction of heat is lost to neutrino emission or conducted into the core of the neutron star.
The most common form of magnetar activity is short X-ray bursts, with durations from milliseconds to seconds, and luminosities ranging from $10^{36}$ to $10^{43}\ {\rm erg}\,{\rm s}^{-1}$. 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…
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 …
Using numerical simulations we show that low-amplitude Alfvén waves from a magnetar quake propagate to the outer magnetosphere and convert to "plasmoids" (closed magnetic loops) which accelerate from the star, driving blast waves into the magnetar wind. Quickly after its formation, the plasmoid becomes a thin relativistic pancake. It pushes out the magnetospheric field lines, and they gradually reconnect behind the pancake, generating a variable wind far stronger than the normal spindown wind of the magnetar. Repeating ejections drive blast waves in the amplified wind. We suggest that these ej…
The activity of magnetars is believed to be powered by colossal magnetic energy reservoirs. We sketch an evolutionary picture in which internal field evolution in magnetars generates a twisted corona, form which energy may be released suddenly in a single giant flare, or more gradually through smaller outbursts and persistent emission. Given the ages of magnetars and the energy of their giant flares, we suggest that their evolution is driven by a novel mechanism: magnetic flux transport/decay due to persistent plastic flow in the crust, which would invalidate the common assumption that the cru…
Quasi-Periodic Oscillations (QPOs) observed during Soft Gamma Repeaters giant flares are commonly interpreted as the torsional oscillations of magnetars. The oscillatory motion is influenced by the strong interaction between the shear modes of the crust and Alfven-like modes in the core. We study the dynamics which arises through this interaction, and present several new results: (1) We show that global {\it edge modes} frequently reside near the edges of the core Alfven continuum. (2) We compute the magnetar's oscillatory motion for realistic axisymmetric magnetic field configurations and cor…
(Abridged) The hyperaccreting neutron star or magnetar disks cooled via neutrino emission can be a candidate of gamma-ray burst (GRB) central engines. The strong field $\geq10^{15}-10^{16}$ G of the magnetar can play a significant role in affecting the disk properties and even lead to the funnel accretion process. We investigate the effects of strong fields on the disks around magnetars, and discuss implications of such accreting magnetar systems for GRB and GRB-like events. We discuss quantum effects of the strong fields on the disk, and use the MHD conservation equations to describe the beha…
We present a model for FRBs where a large amplitude Alfven wave packet is launched by a disturbance near the surface of a magnetar, and a substantial fraction of the wave energy is converted to coherent radio waves at a distance of a few tens of neutron star radii. The wave amplitude at the magnetar surface should be about 1011G in order to produce a FRB of isotropic luminosity 10$^{44}$ erg s$^{-1}$. An electric current along the static magnetic field is required by Alfven waves with nonzero component of transverse wave-vector. The current is supplied by counter-streaming electron-positron pa…
We advance a "Solar flare" model of magnetar activity, whereas a slow evolution of the magnetic field in the upper crust, driven by electron MHD (EMHD) flows, twists the external magnetic flux tubes, producing persistent emission, bursts and flares. At the same time the neutron star crust plastically relieves the imposed magnetic field stress, limiting the strain $ ε_t $ to values well below the critical strain $ ε_{crit}$ of a brittle fracture, $ ε_t \sim 10^{-2}ε_{crit} $. Magnetar-like behavior, occurring near the magnetic equator, takes place in all neutron stars, but to a different extent…
We compute the characteristic parameters of magnetic dipole radiation of a neutron star undergoing torsional seismic vibrations under the action of Lorentz restoring force about axis of a dipolar magnetic field experiencing decay. After brief outline of general theoretical background of the model of vibration powered neutron star, we present numerical estimates of basic vibration and radiation characteristics, such as the oscillation frequency, lifetime, luminosity of radiation, and investigate their time dependence upon magnetic field decay. The presented analysis suggests that gradual decrea…
A parametric study of population inversions in relativistic plasmas through nonresonant interactions with Alfvén waves and their applications to Fast Radio Bursts
The seismological dynamics of magnetars is largely determined by a strong hydro-magnetic coupling between the solid crust and the fluid core. In this paper we set up a "spectral" computational framework in which the magnetar's motion is decomposed into a series of basis functions which are associated with the crust and core vibrational eigenmodes. A general-relativistic formalism is presented for evaluation of the core Alfven modes in the magnetic-flux coordinates, as well for eigenmode computation of a strongly magnetized crust of finite thickness. By considering coupling of the crustal modes…
Asteroids orbiting into the highly magnetized and highly relativistic wind of a pulsar offer a favourable configuration for repeating fast radio bursts (FRB). The body in direct contact with the wind develops a trail formed of a stationary Alfvén wave, called an \textit{Alfvén wing}. When an element of wind crosses the Alfvén wing, it sees a rotation of the ambient magnetic field that can cause radio-wave instabilities. In the observer's reference frame, the waves are collimated in a very narrow range of directions, and they have an extremely high intensity. A previous work, published in 2014,…
We explore the interaction between Hall waves and mechanical failures inside a magnetar crust, using detailed one-dimentional models that consider temperature-sensitive plastic flow, heat transport and cooling by neutrino emission, as well as the coupling of the crustal motion to the magnetosphere. We find that the dynamics is enriched and accelerated by the fast, short-wavelength Hall waves that are emitted by each failure. The waves propagate and cause failures elsewhere, triggering avalanches. We argue that these avalanches are the likely sources of outbursts in transient magnetars.
This paper considers the yielding response of a neutron star crust to smooth, unbalanced Maxwell stresses imposed at the core-crust boundary, and the coupling of the dynamic crust to the external magnetic field. Stress buildup and yielding in a magnetar crust is a global phenomenon: an elastic distortion radiating from one plastically deforming zone is shown to dramatically increase the creep rate in distant zones. Runaway creep to dynamical rates is shown to be possible, being enhanced by in situ heating and suppressed by thermal conduction and shearing of an embedded magnetic field. A global…
Recently, a fast radio burst (FRB)-like event is found to be associated with a Galactic magnetar, SGR 1935+2154, accompanied by an X-ray burst. We find this radio burst challenges the typical emission mechanisms involving magnetars, which includes coherent curvature radiation from charged bunches, fast magnetosonic (FMS) wave, synchrotron maser from shocks, and the pulsar-like mechanism for low-twist magnetars. More specifically, we find that (1) the X-rays are most-likely to be produced inside the magnetosphere. (2) For the coherent curvature radiation from the decay of Alfvén wave, it will g…
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 …
In a realistic model of magneto-elastic oscillations in magnetars, we find that crustal shear oscillations, often invoked as an explanation of quasi-periodic oscillations (QPOs) seen after giant flares in soft gamma-ray repeaters (SGRs), are damped by resonant absorption on timescales of at most 0.2s, for a lower limit on the dipole magnetic field strength of 5 x 10^13 G. At higher magnetic field strengths (typical in magnetars) the damping timescale is even shorter, as anticipated by earlier toy-models. We have investigated a range of equations of state and masses and if magnetars are dominat…
We extend a general-relativistic ideal magneto-hydrodynamical code to include the effects of elasticity. Using this numerical tool we analyse the magneto-elastic oscillations of highly magnetised neutron stars (magnetars). In simulations without magnetic field we are able to recover the purely crustal shear oscillations within an accuracy of about a few per cent. For dipole magnetic fields between 5 x 10^13 and 10^15 G the Alfvén oscillations become modified substantially by the presence of the crust. Those quasi-periodic oscillations (QPOs) split into three families: Lower QPOs near the equat…
We study axisymmetric perturbations of neutron star endowed with a strong magnetic field (magnetars), considering the coupled oscillations of the fluid core with the solid crust. We recover discrete oscillations based mainly in the crust and a continuum in the core. We also confirm the presence of "discrete Alfvén modes" in the gap between two contiguous continua (see Van Hooven& Levin (2011)) and, in addition, we can resolve some of them also inside the continua. Our results can explain both the lower and the higher observed quasi periodical oscillations (QPOs) in SGR 1806-20 and SGR 1900+14 …
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 MHD equations and employ them to examine weak Alfvénic turbulence, dominated by three-wave interactions, in reduced relativistic magnetohydrodynamics, including the force-free, inf…
Very recently, an extremely bright fast radio burst (FRB) 200428 with two sub-millisecond pulses was discovered to come from the direction of the Galactic magnetar SGR 1935+2154, and an X-ray burst (XRB) counterpart was detected simultaneously. These observations favor magnetar-based interior-driven models. In this Letter, we propose a different model for FRB 200428 associated with an XRB from SGR 1935+2154, in which a magnetar with high proper velocity encounters an asteroid of mass $\sim10^{20}\,$g. This infalling asteroid in the stellar gravitational field is first possibly disrupted tidall…
We study the stability of Hall MHD with strong magnetic fields in which Landau quantization of electrons is important. We find that the strong-field Hall modes can be destabilized by the dependence of the differential magnetic susceptibility on magnetic field strength. This instability is studied using linear perturbation theory, and is found to have typical growth time of order $\lesssim 10^3$ yrs, with the growth time decreasing as a function of wavelength of the perturbation. The instability is self-limiting, turning off following a period of local field growth by a few percent of the initi…
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…
We use ideal axisymmetric relativistic magnetohydrodynamic simulations to calculate the spindown of a newly formed millisecond, B ~ 10^{15} G, magnetar and its interaction with the surrounding stellar envelope during a core-collapse supernova (SN) explosion. The mass, angular momentum, and rotational energy lost by the neutron star are determined self-consistently given the thermal properties of the cooling neutron star's atmosphere and the wind's interaction with the surrounding star. The magnetar drives a relativistic magnetized wind into a cavity created by the outgoing SN shock. For high s…
It is shown that depletion of the magnetic field pressure in a quaking neutron star undergoing Lorentz-force-driven torsional seismic vibrations about axis of its dipole magnetic moment is accompanied by the loss of vibration energy of the star that causes its vibration period to lengthen at a rate proportional to the rate of magnetic field decay. Highlighted is the magnetic-field-decay induced conversion of the energy of differentially rotational Alfvén vibrations into the energy of oscillating magneto-dipole radiation. A set of representative examples of magnetic field decay illustrating the…
We develop a model of the generation of coherent radio emission in the Crab pulsar, magnetars and Fast Radio Bursts (FRBs). Emission is produced by a reconnection-generated beam of particles via a variant of Free Electron Laser (FEL) mechanism, operating in a weakly-turbulent, guide-field dominated plasma. We first consider nonlinear Thomson scattering in a guide-field dominated regime, and apply to model to explain emission bands observed in Crab pulsar and in Fast Radio Bursts. We consider particle motion in a combined fields of the electromagnetic wave and thee lectromagnetic (Alfvenic) wig…
Interior Magnetic Fields in Magnetars and Radio Pulsars
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）；Department of Physics, University of Milan（米兰大学物理系）；INFN, Sezione di Milano（意大利国家核物理研究所米兰分部）；Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学理论物理研究所）
Spectral Evidence of Heavy Nuclei from the Neutron Star Crust in Magnetar Bursts
Central China Normal University（华中师范大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
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…
The radio pulsar GLEAM-X J162759.5-523504.3 has an extremely long spin period ($P = 1091.17\, \mbox{s}$), and yet seemingly continues to spin down rapidly ($\dot{P} < 1.2 \times 10^{-9}\, \mbox{ss}^{-1}$). The magnetic field strength that is implied, if the source is a neutron star undergoing magnetic dipole braking, could exceed $10^{16}\,\mbox{G}$. This object may therefore be the most magnetised neutron star observed to date. In this paper, a critical analysis of a magnetar interpretation for the source is provided. (i) A minimum polar magnetic field strength of $B \sim 5 \times 10^{15}\,\m…
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…
Magnetar bursts can be emitted by Alfvén waves growing in the outer magnetosphere to nonlinear amplitudes, $δB/B\sim 1$, and triggering magnetic reconnection. Similar magnetic flares should occur quasi-periodically in a magnetized neutron star binary nearing merger. In both cases, fast dissipation in the magnetic flare creates optically thick $e^\pm$ plasma, whose heat capacity is negligible compared with the generated radiation energy. Magnetic dissipation then involves photon viscosity and acts through Compton drag on the plasma bulk motions in the reconnection region. The effective temperat…
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…
Under normal conditions in a neutron-star crust, ions are locked in place in the crustal lattice and only electrons are mobile, and magnetic-field evolution is thus directly related to the electron velocity. The evolution, however, builds magnetic stresses that can become sufficiently large for the crust to exceed its elastic limit, and to flow plastically. We consider the nature of this plastic flow and the back-reaction on the crustal magnetic field evolution. We formulate a plane-parallel model for the local failure, showing that surface motions are inevitable once the crust yields, in the …
The neutron star (NS) merger GW170817 was followed over several days by optical-wavelength ("blue") kilonova (KN) emission likely powered by the radioactive decay of light r-process nuclei synthesized by ejecta with a low neutron abundance (electron fraction Ye ~ 0.25-0.35). While the composition and high velocities of the blue KN ejecta are consistent with shock-heated dynamical material, the large quantity is in tension with the results of numerical simulations. We propose an alternative ejecta source: the neutrino-heated, magnetically-accelerated wind from the strongly-magnetized hypermassi…
We study the effect of superfluidity on torsional oscillations of highly magnetised neutron stars (magnetars) with a microphysical equation of state by means of two-dimensional, magnetohydrodynamical- elastic simulations. The superfluid properties of the neutrons in the neutron star core are treated in a parametric way in which we effectively decouple part of the core matter from the oscillations. Our simulations confirm the existence of two groups of oscillations, namely continuum oscillations that are confined to the neutron star core and are of Alfvénic character, and global oscillations wi…
If the observed quasi-periodic oscillations in magnetar flares are partially confined to the crust, then the oscillation frequencies are unique probes of the nuclear physics of the neutron star crust. We study crustal oscillations in magnetars including corrections for a finite Alfven velocity. Our crust model uses a new nuclear mass formula that predicts nuclear masses with an accuracy very close to that of the finite range droplet model. This mass model for equilibrium nuclei also includes shell corrections and an updated neutron-drip line. We perturb our crust model to predict axial crust m…
The emission of intense radio pulses by flaring magnetars is investigated. Small-scale current gradients can be imprinted into a strongly magnetized outflow by the same processes that source fireball radiation in the closed magnetosphere. This structure arises from a combination of crustal yielding, internal tearing, and turbulent cascade. We consider the quasi-linear development of weak, small-scale currents as (i) they are stretched out and frozen by relativistic expansion and then (ii) pass through a shock. In particular, we derive the amplitudes of the ordinary and fast waves that emerge d…
Magnetic field evolution in neutron-star crusts is driven by the Hall effect and Ohmic dissipation, for as long as the crust is sufficiently strong to absorb Maxwell stresses exerted by the field and thus make the momentum equation redundant. For the strongest neutron-star fields, however, stresses build to the point of crustal failure, at which point the standard evolution equations are no longer valid. Here, we study the evolution of the magnetic field of the crust up to and beyond crustal failure, whence the crust begins to flow plastically. We perform global axisymmetric evolutions, explor…
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 $k_{p,\rm ex}$. Small-scale Alfvénic wavepackets are promising sources of coherent curvature radiation. When the group Lorentz factor $γ_{\rm gr} \lesssim (k_{p…
Magnetic energy around compact objects often dominates over plasma rest mass, and its dissipation can power the object luminosity. We describe a dissipation mechanism which works faster than magnetic reconnection. The mechanism involves two strong Alfvén waves with anti-aligned magnetic fields $\boldsymbol{B}_1$ and $\boldsymbol{B}_2$ that propagate in opposite directions along background magnetic field $\boldsymbol{B}_0$ and collide. The collision forms a thin current sheet perpendicular to $\boldsymbol{B}_0$, which absorbs the incoming waves. The current sheet is sustained by electric field …
We propose a scenario for the quasi-periodic oscillations observed in magnetar flares wherein a tangled component of the stellar magnetic field introduces nearly isotropic stress that gives the fluid core of the star an effective shear modulus. In a simple, illustrative model of constant density, the tangled field eliminates the problematic Alfvén continuum that would exist in the stellar core for an organized field. For a tangled field energy density comparable to that inferred from the measured dipole fields of $\sim 10^{15}$ G in SGRs 1806-20 and 1900+14, torsional modes exist with fundamen…
By means of two dimensional, general-relativistic, magneto-hydrodynamical simulations we investigate the oscillations of magnetized neutron star models (magnetars) including the description of an extended solid crust. The aim of this study is to understand the origin of the QPOs observed in the giant flares of SGRs. We confirm the existence of three different regimes: (a) a weak magnetic field regime B<5 x 10^13 G, where crustal shear modes dominate the evolution; (b) a regime of intermediate magnetic fields 5 x 10^13 G<B< 10^15 G, where Alfvén QPOs are mainly confined to the core of the neutr…
