The strong magnetic fields found on the surface of magnetars are known to have profound effects in the physics of atoms in magnetar envelopes. We argue that the Friedel oscillations in the Coulomb force between the ions due to electron shielding can, for certain values of the parameters, be the dominant effect determining the crystal structure in the outer crust of magnetars. We estimate the densities and magnetic fields for which this occurs, compute some of the elastic moduli and lattice phonon dispersion relations in this "Friedel crystal" phase.
The equation of state (EoS) of the outer crust of a cold non-accreting magnetar has been determined using the model of Lai and Shapiro (1991). For this purpose, we have made use of the latest experimental atomic mass data complemented with a Hartree-Fock-Bogoliubov (HFB) mass model. Magnetar crusts are found to be significantly different from the crusts of ordinary neutron stars.
Magnetic fields of order $10^{15}$ G have been measured at the surface of some neutron stars, and much stronger magnetic fields are expected to be present in the solid region beneath the surface. The effects of the magnetic field on the equation of state and on the composition of the crust due to Landau-Rabi quantization of electron motion are studied. Both the outer and inner crustal regions are described in a unified and consistent way within the nuclear-energy density functional theory.
Magnetars are neutron stars endowed with surface magnetic fields of the order of $10^{14}-10^{15}$~G, and with presumably much stronger fields in their interior. As a result of Landau quantization of electron motion, the neutron-drip transition in the crust of a magnetar is shifted to either higher or lower densities depending on the magnetic field strength. The impact of nuclear uncertainties is explored considering the recent series of Brussels-Montreal microscopic nuclear mass models. All these models are based on the Hartree-Fock-Bogoliubov method with generalized Skyrme functionals. They …
We investigate a thermo-resistive instability in the outer crusts of magnetars wherein a perturbation in temperature increases ohmic heating. We show that magnetars of characteristic age τ_{age} ~ 10^4 yr are unstable over timescales as short as days if strong current sheets are present in the outer crust. This instability could play an important role in the thermal and magnetic field evolution of magnetars, and may be related to bursting activity in magnetars.
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…
We propose a new heating mechanism in magnetar crusts. Magnetars' crustal magnetic fields are much stronger than their surface fields; therefore, magnetic pressure partially supports the crust against gravity. The crust loses magnetic pressure support as the field decays and must compensate by increasing the electron degeneracy pressure; the accompanying increase in the electron Fermi energy induces nonequilibrium, exothermic electron captures. The total heat released via field-decay electron captures is comparable to the total magnetic energy in the crust. Thus, field-decay electron captures …
We discuss outer and inner crusts of neutron stars in strong magnetic fields. Here, we demonstrate the effect of Landau quantization of electrons on the ground state properties of matter in outer and inner crusts in magnetars. This effect leads to the enhancement of the electron number density in strong magnetic fields with respect to the zero field case. For the outer crust, we adopt the magnetic Baym-Pethick-Sutherland model and obtain the sequence of nuclei and equation of state (EoS). The properties of nuclei in the inner crust in the presence of strong magnetic fields are investigated usi…
In this work we find that the at the high polar magnetic fields of magnetars, $B \sim 10^{14-15}$ G, the outermost crust ($ρ< 10^7$ gm/cc) of the star can become a transverse insulator and a filamentary crystal along the field direction. Also, the transverse conductivity in the crust goes inversely as the square of polar magnetic field (as $1/B^2$). At these high fields the transverse crustal currents associated with the polar magnetic field can then dissipate more effectively via Ohm's law.
We discuss the origin of strong crustal magnetic field in one of central compact objects (CCOs) --- a neutron star PSR J1852+0040 in the supernova remnant Kes 79. Taking into account its relatively long present day spin period we conclude that the field could not be generated via a dynamo mechanism. If this neutron star indeed is a magnetar with field submerged during a strong fall-back episode, then it argues against the dynamo field origin in magnetars. Otherwise, Kes 79 is not a close relative of normal magnetars. A discovery of an anti-magnetar with a millisecond period and strong crustal …
We study the influence of magnetised crusts on torsional shear mode oscillations of magnetars. In this context, we employ magnetised crusts whose ground state properties are affected by Landau quantisation of electrons. The shear modulus of magnetised crusts is enhanced in strong magnetic fields $\geq 10^{17}$ G. Though we do not find any appreciable change in frequencies of fundamental torsional shear modes, frequencies of first overtones are significantly affected in strong magnetic fields. Furthermore, frequencies of torsional shear modes calculated with magnetised crusts are in good agreem…
We show that ions at the low densities and high magnetic fields relevant to the outer crust of magnetars form a novel crystalline phase where ions are strongly coupled along the magnetic field and loosely coupled in the transverse direction. The underlying cause is the anisotropic screening of the Coulomb force by electrons in the presence of a strongly quantizing magnetic field which leads to Friedel oscillations in the ion-ion potential. In particular, the Friedel oscillations are much longer-ranged in the direction of the magnetic field than is the case in the absence of magnetic fields, a …
Strong magnetic fields have important effects on the crustal properties of magnetars. Here we study the magneto-elastic oscillations of magnetars taking into consideration the effect of strong magnetic fields on the crustal composition (magnetised crust). We calculate global magneto-elastic (GME) modes as well as modes confined to the crust (CME) only. The composition of the crust directly affects its shear modulus which we calculate using three different nucleon-nucleon interactions: SLy4, SkM and Sk272. The shear modulus of the crust is found to be enhanced in strong magnetic fields $\geq 10…
The presence of strong magnetic fields in neutron stars, such as in magnetars, may significantly affect their crust-core transition properties and the crust size. This knowledge is crucial in the correct interpretation of astrophysical phenomena involving magnetars, such as glitches in observed rotation frequencies, cooling, bursts and possibly tidal polarizabilities. A recently developed meta-modelling technique allows exploring the model dependence of density functional theory equation of state calculations. In this work, we extend this meta-model to investigate the effect of strong magnetic…
The persistent thermal luminosity of magnetars and their outbursts suggest the existence of some internal heat sources located in their outer crust. The compression of matter accompanying the decay of the magnetic field may trigger exothermic electron captures and, possibly, pycnonuclear fusions of light elements that may have been accreted onto the surface from the fallback of supernova debris, from a disk or from the interstellar medium. This scenario bears some resemblance to deep crustal heating in accreting neutron stars, although the matter composition and the thermodynamic conditions ar…
If a magnetar interior $B$-field exceeds $10^{15}$~G, it will unpair the proton superconductor in the stellar core by inducing diamagnetic currents that destroy the Cooper pair coherence. Then, the $P$-wave neutron superfluid in these non-superconducting regions will couple to the stellar plasma by scattering of protons off the quasiparticles that are confined in the cores of neutron vortices by the strong (nuclear) force. The dynamical timescales associated with this interaction span from several minutes at the crust-core interface to a few seconds in the deep core. We show that (a) the rapid…
The activity of magnetars is powered by their intense and dynamic magnetic fields and has been proposed as the trigger to extragalactic Fast Radio Bursts. Here we estimate the frequency of crustal failures in young magnetars, by computing the magnetic stresses in detailed magneto-thermal simulations including Hall drift and Ohmic dissipation. The initial internal topology at birth is poorly known but is likely to be much more complex than a dipole. Thus, we explore a wide range of initial configurations, finding that the expected rate of crustal failures varies by orders of magnitude depending…
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…
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 …
Magnetar activity is generated by shear motions of the neutron star surface, which relieve internal magnetic stresses. An analogy with earthquakes and faults is problematic, as the crust is permeated by strong magnetic fields, which greatly constrain crustal displacements. We describe a new deformation mechanism that is specific to strongly magnetized neutron stars. The magnetically stressed crust begins to move because of a thermoplastic instability, which launches a wave that shears the crust and burns its magnetic energy. The propagating wave front resembles the deflagration front in combus…
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…
The equilibrium properties of the outer crust of cold nonaccreting magnetars (i.e. neutron stars endowed with very strong magnetic fields) are studied using the latest experimental atomic mass data complemented with a microscopic atomic mass model based on the Hartree-Fock-Bogoliubov method. The Landau quantization of electron motion caused by the strong magnetic field is found to have a significant impact on the composition and the equation of state of crustal matter. It is also shown that the outer crust of magnetars could be much more massive than that of ordinary neutron stars.
We examine four candidate mechanisms that could explain the high surface temperatures of magnetars. (1) Heat flux from the liquid core heated by ambipolar diffusion. It could sustain the observed surface luminosity $L_s\approx 10^{35}$ erg/s if core heating offsets neutrino cooling at a temperature $T_{core}>6\times 10^8$ K. This scenario is viable if the core magnetic field exceeds $10^{16}$ G and the heat-blanketing envelope of the magnetar has a light element composition. We find however that the lifetime of such a hot core should be shorter than the typical observed lifetime of magnetars. …
We revisit in this work a model for repeating Fast Radio Bursts based of the release of energy provoked by the magnetic field dynamics affecting a magnetar's crust. We address the basics of such a model by solving the propagation of the perturbation approximately, and quantify the energetics and the radiation by bunches of charges in the so-called {\it charge starved} region in the magnetosphere. The (almost) simultaneous emission of newly detected X-rays from SGR 1935+2154 is tentatively associated to a reconnection behind the propagation. The strength of $f$-mode gravitational radiation exci…
Fast radio bursts are millisecond-duration radio pulses of extragalactic origin. A recent statistical analysis has found that the burst energetics of the repeating source FRB 121102 follow a power-law, with an exponent that is curiously consistent with the Gutenberg-Richter law for earthquakes. This hints that repeat-bursters may be compact objects undergoing violent tectonic activity. For young magnetars, possessing crustal magnetic fields which are both strong ($B \gtrsim 10^{15}$ G) and highly multipolar, Hall drift can instigate significant field rearrangements even on $\lesssim$ century l…
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）
Current models of magnetars require extremely strong magnetic fields to explain their observed quiescent and bursting emission, implying that the field strength within the star's outer crust is orders of magnitude larger than the dipole component inferred from spin-down measurements. This presents a serious challenge to theories of magnetic field generation in a proto-neutron star. Here, we present detailed modelling of the evolution of the magnetic field in the crust of a neutron star through 3-D simulations. We find that, in the plausible scenario of equipartition of energy between global-sc…
Novae breves from magnetar giant flares: Potential probes of neutron star crusts
Peking University（北京大学）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；Guangxi Key Laboratory for Relativistic Astrophysics, School of Physical Science and Technology, Guangxi University（广西大学物理科学与技术学院相对论天体物理重点实验室）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
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…
The most strongly magnetized neutron stars, the magnetars, have spectacular outbursts of gamma-ray flares powered by decay of the magnetic field. The rapidly changing field is strong enough that it should be able to stress and rupture the star's crust, with potentially interesting seismic consequences. This was confirmed in dramatic fashion a few years ago with the discovery of long-lived seismic vibrations excited by rare giant flares. The starquakes associated with the giant flares are, it seems, so catastrophic that they leave the whole star ringing. These discoveries have opened up the pos…
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…
Neutron tunneling in neutron star crusts can release enormous amounts of energy on a short timescale. We have clarified aspects of this process occurring in the outer crust regions of neutron stars when oscillations or cataclysmic events changes the crustal ambient density. We report a time-dependent Hartree-Fock-Bogoliubov model to determine the rate of neutron diffusion and conclude that a large amount of energy, in the range of 10^40 - 10^44 erg, can be released rapidly. We suggest that this mechanism may be the source of hitherto unknown phenomena such as the Fast Radio Bursts (FRBS).
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…
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…
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 …
Quasi-periodic oscillations inferred during rare magnetar giant flare tails were initially interpreted as torsional oscillations of the neutron star (NS) crust, and have been more recently described as global core+crust perturbations. Similar frequencies are also present in high signal-to-noise magnetar short bursts. In magnetars, disturbances of the field are strongly coupled to the NS crust regardless of the triggering mechanism of short bursts. For low-altitude magnetospheric magnetar models of fast radio bursts (FRBs) associated with magnetar short bursts, such as the low-twist model, crus…
The de-excited energy of electron capture (EC) induced by magnetic field decay may be a new source for heating magnetar crust, so we do a quantitative calculation on the EC process near the outer crust and analyze their influence on persistent X-ray radiation of magnetars, adopting the experimental data or the results of theoretical model (including the large-scale shell model and quasi-particle random phase approximation).
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 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…
Magnetars are neutron stars showing dramatic X-ray and soft $γ$-ray outbursting behaviour that is thought to be powered by intense internal magnetic fields. Like conventional young neutron stars in the form of radio pulsars, magnetars exhibit "glitches" during which angular momentum is believed to be transferred between the solid outer crust and the superfluid component of the inner crust. Hitherto, the several hundred observed glitches in radio pulsars and magnetars have involved a sudden spin-up of the star, due presumably to the interior superfluid rotating faster than the crust. Here we re…
Magnetars have been suggested as the most promising site for the origin of observed soft gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs). In this work we investigate the possibility that SGRs and AXPs might be observational evidence for a magnetic phase separation in magnetars. We study magnetic domain formation as a new mechanism for SGRs and AXPs in which magnetar-matter separates into two phases containing different flux densities. We identify the parameter space in matter density and magnetic field strength at which there is an instability for magnetic domain formation. We co…
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…
Magnetar magnetothermal evolution with Landau-quantized electrons: enhanced Joule heating due to free electron diamagnetism and the magnetar heating problem
Columbia Astrophysics Laboratory, Columbia University（哥伦比亚大学天体物理实验室，哥伦比亚大学）
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…
Hyperactive Magnetar Eruptions: Giant Flares, Baryon Ejections, and Fast Radio Bursts
Princeton University（普林斯顿大学）；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）；Flatiron Institute（平顿研究所）；Monash University（蒙纳士大学）
We have studied the various properties of magnetically deformed atoms, replaced by deformed Wigner-Seitz cells, at the outer crust region of strongly magnetized neutron stars (magnetars) using a relativistic version of Thomas-Fermi model in cylindrical coordinates.
We investigate the density-shear instability in Hall-MHD via numerical simulation of the full non-linear problem, in the context of magnetar activity. We confirm the development of the instability of a plane-parallel magnetic field with an appropriate intensity and electron density profile, in accordance with analytic theory. We find that the instability also appears for a monotonically decreasing electron number density and magnetic field, a plane-parallel analogue of an azimuthal or meridional magnetic field in the crust of a magnetar. The growth rate of the instability depends on the Hall p…
We study the simultaneous effects of the symmetry energy and temperature on the crust-core transition of a magnetar. The dynamical and the thermodynamical spinodals are used to calculate the transition region within a relativistic mean-field approach for the equation of state. Quantizing magnetic fields with intensities in the range of $ 2\times 10^{15}<B<5\times 10 ^{16}$G are considered. Under these strong magnetic fields, the crust extension is very sensitive to the density dependence of the symmetry energy, and the properties that depend on the crust thickness could set a constraint on the…
The iterative method recently proposed for determining the internal constitution of the outer crust of a nonaccreted neutron star is extended to magnetars by taking into account the Landau-Rabi quantization of electron motion induced by the presence of a very high magnetic field. It is shown that in the strongly quantizing regime, the method can be efficiently implemented using new analytical solutions for the transitions between adjacent crustal layers. Detailed numerical computations are performed to assess the performance and precision of the method.
This work looks at some definitive signatures of magnetars, in particular of period closures accompanied by a decline of X-ray radiation in two models. We review some of the previous works which are based on the well known dynamo model in which the star is born with a period of a few milliseconds at high temperatures. In such a convection regime the dynamo mechanism can amplify the the magnetic fields to the magnetar value. This is in contrast to a screened core model which posits that a high density phase transition occurs in the inner core of magnetars that dynamically aligns all the neutron…
