We study torsional Alfvén oscillations of magnetars, i.e., neutron stars with a strong magnetic field. We consider the poloidal and toroidal components of the magnetic field and a wide range of equilibrium stellar models. We use a new coordinate system (X,Y), where $X=\sqrt{a_1} \sin θ$, $Y=\sqrt{a_1}\cos θ$ and $a_1$ is the radial component of the magnetic field. In this coordinate system, the 1+2-dimensional evolution equation describing the quasi-periodic oscillations, QPOs, see Sotani et al. (2007), is reduced to a 1+1-dimensional equation, where the perturbations propagate only along the Y-axis. We solve the 1+1-dimensional equation for different boundary conditions and open magnetic field lines, i.e., magnetic field lines that reach the surface and there match up with the exterior dipole magnetic field, as well as closed magnetic lines, i.e., magnetic lines that never reach the stellar surface. For the open field lines, we find two families of QPOs frequencies; a family of "lower" QPOs frequencies which is located near the X-axis and a family of "upper" frequencies located near the Y-axis. According to Levin (2007), the fundamental frequencies of these two families can be interpreted as the turning points of a continuous spectrum. We find that the upper frequencies are constant multiples of the lower frequencies with a constant equaling 2n+1. For the closed lines, the corresponding factor is n+1 . By these relations, we can explain both the lower and the higher observed frequencies in SGR 1806-20 and SGR 1900+14.
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…
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…
I present recent results studying flare emission in magnetars. Strong quasi-periodic oscillations observed in the tail of giant magnetar flares are frequently interpreted as evidence for global seismic oscillations. I demonstrate that such a global oscillation is not directly observable in the lightcurve. New work suggests the amplitude for the strongest QPO stays nearly constant in the rotation phases where it is observed, which I argue suggests it is produced by an additional emission process from the star.
We study the torsional magneto-elastic oscillations of relativistic superfluid magnetars and explore the effects of a phase transition in the crust-core interface (nuclear pasta) which results in a weaker elastic response. Exploring various models with different extension of nuclear pasta phases, we find that the differences in the oscillation spectrum present in purely elastic modes (weak magnetic field), are smeared out with increasing strength of the magnetic field. For magnetar conditions, the main characteristic and features of models without nuclear pasta are preserved. We find in genera…
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 …
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…
We study coupled axial and polar axisymmetric oscillations of a neutron star endowed with a strong magnetic field, having both poloidal and toroidal components. The toroidal component of the magnetic field is driving the coupling between the polar and axial oscillations. The star is composed of a fluid core as well as a solid crust. Using a two dimensional general relativistic simulation and a magnetic field B = 10^16 G, we study the change in the polar and axial spectrum caused by the coupling. We find that the axial spectrum suffers a dramatic change in its nature, losing its continuum chara…
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…
Magneto-elastic oscillations of neutron stars are believed to explain observed quasi-periodic oscillations (QPOs) in the decaying tail of the giant flares of highly magnetized neutron stars (magnetars). Strong efforts of the theoretical modelling from different groups have increased our understanding of this phenomenon significantly. Here, we discuss some constraints on the matter in neutron stars that arise if the interpretation of the observations in terms of superfluid, magneto-elastic oscillations is correct. To explain the observed modulation of the light curve of the giant flare, we desc…
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…
We study the time-evolution of axisymmetric oscillations of superfluid magnetars with a poloidal magnetic field and an elastic crust, working in Newtonian gravity. Extending earlier models, we study the effects of composition gradients and entrainment on the magneto-elastic wave spectrum and on the potential identification of the observed quasi periodic oscillations (QPOs). We use two-fluid polytropic equations of state to construct our stellar models, which mimic realistic composition gradient configurations. The basic features of the axial axisymmetric spectrum of normal fluid stars are repr…
Magnetic flares and induced oscillations of magnetars (super-magnetized neutron stars) are promising sources of gravitational waves (GWs). We suggest that the GW emission, if any, would last longer than the observed X-ray quasi-periodic oscillations (X-QPOs), calling for the longer-term GW analyses from a day to months than the current searches. Like the pulsar timing, the oscillation frequency would also evolve with time because of the decay or reconfiguration of magnetic field, which is crucial for the GW detection. With the observed GW frequency and its time-derivatives, we can probe the in…
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…
Recent observations of the periodic Fast Radio Burst source 180916.J0158+65 (FRB 180916) find small linear polarization position angle swings during and between bursts, with a burst activity window that becomes both narrower and earlier at higher frequencies. Although the observed chromatic activity window disfavors models of periodicity in FRB 180916 driven by the occultation of a neutron star by the optically-thick wind from a stellar companion, the connection to theories where periodicity arises from the motion of a bursting magnetar remains unclear. In this paper, we show how altitude-depe…
Motivated by stability considerations and observational evidence, we argue that magnetars possess highly-tangled internal magnetic fields. We propose that the quasi-periodic oscillations (QPOs) seen to accompany giant flares can be explained as torsional modes supported by a tangled magnetic field, and we present a simple model that supports this hypothesis for SGR 1900+14. Taking the strength of the tangle as a free parameter, we find that the magnetic energy in the tangle must dominate that in the dipolar component by a factor of $\sim 14$ to accommodate the observed 28 Hz QPO. Our simple mo…
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…
The discovery of quasi-periodic oscillations (QPOs) in magnetar giant flares has opened up prospects for neutron star asteroseismology. However, with only three giant flares ever recorded, and only two with data of sufficient quality to search for QPOs, such analysis is seriously data limited. We set out a procedure for doing QPO searches in the far more numerous, short, less energetic magnetar bursts. The short, transient nature of these bursts requires the implementation of sophisticated statistical techniques to make reliable inferences. Using Bayesian statistics, we model the periodogram a…
Strong quasi-periodic oscillations in the tails of the giant gamma-ray flares seen in SGR 1806-20 and SGR 1900+14 are thought to be produced by starquakes in the flaring magnetar. However, the large fractional amplitudes (up to ~20%) observed are difficult to reconcile with predicted amplitudes of starquakes. Here we demonstrate that the steeply pulsed emission profile in the tail of the giant flare can enhance the observed amplitude of the underlying oscillation, analogously to a beam of light oscillating in and out of the line of sight. This mechanism will also broaden the feature in the pow…
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 …
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…
Ultra-long-duration gamma-ray burst GRB 111209A was found to be associated with a very luminous supernovae (SNe) SN 2011kl. The physics of GRB 111209A/SN 2011kl has been extensively studied in the literures, but does not settle down yet. By investigating in detail the characteristics of the X-ray light curve of GRB 111209A, coupled with the temporal and spectral features observed in SN 2011kl, we argue that a short-living supramassive magnetar can be responsible for the initial shallow X-ray emission. Then the electromagnetic extraction of spin energy from a black hole results in the steeply d…
A newly formed magnetar has been proposed as the central engine of short GRBs to explain on-going energy injection giving observed plateau phases in the X-ray lightcurves. These rapidly spinning magnetars may be capable of emitting pulsed emission comparable to known pulsars and magnetars. In this paper we show that, if present, a periodic signal would be detectable during the plateau phases observed using the Swift X-Ray Telescope recording data in Window Timing mode. We conduct a targeted deceleration search for a periodic signal from a newly formed magnetar in 2 Swift short GRBs and rule ou…
We present an analysis of highly magnetized neutron stars "magnetars", in search for high frequency oscillations in the recurrent emission from the soft gamma repeater SGR 1806-20, and we discuss the physical interpretation of these oscillations and its implications on the neutron star properties and structure. We present evidence for Quasi-Periodic Oscillations (QPOs) in the recurrent outburst activity from SGR 1806-20 using RXTE observations. By searching for timing signals at the frequencies of the QPOs discovered in the 2004 December 27 giant flare from the source, we find three QPOs at 84…
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…
The light curve of many supernovae (SNe) and gamma-ray bursts (GRBs) can be explained by a sustained injection of extra energy from its possible central engine, a rapidly rotating strongly magnetic neutron star (i.e. magnetar). The magnetic dipole radiation power that the magnetar supplies comes at the expense of the star's rotational energy. However, radiation by gravitational waves (GWs) can be more efficient than magnetic dipole radiation because of its stronger dependence on neutron star spin rate Omega, i.e. Omega^6 (for a static 'mountain') or Omega^8 (for a r-mode fluid oscillation) ver…
Quasi-periodic oscillations (QPOs) discovered in the decaying tails of giant flares of magnetars are believed to be torsional oscillations of neutron stars. These QPOs have a high potential to constrain properties of high-density matter. In search for quasi-periodic signals, we study the light curves of the giant flares of SGR 1806-20 and SGR 1900+14, with a non-parametric Bayesian signal inference method called D$^3$PO. The D$^3$PO algorithm models the raw photon counts as a continuous flux and takes the Poissonian shot noise as well as all instrument effects into account. It reconstructs the…
We suggest stellar oscillations are responsible for the strange radio behaviors of Anomalous X-ray pulsars and soft Gamma-ray repeaters (AXP/SGRs), within the framework of both solid quark star model and magnetar model. In solid quark star model, the extra voltage provided by oscillations activates the star from under death line to above death line. In magnetar model, oscillations enlarge the radio beam so that increase the possibility to detect it. Later radio emission decays and vanishes as oscillations damp.
Quasi-periodic oscillations (QPOs) discovered in soft-gamma repeaters (SGRs) are expected to help us to study the properties of matter in neutron stars. In earlier investigations, we identified the QPOs of frequencies below $\sim100$ Hz observed in giant flares of SGR 1806$-$20 and SGR 1900+14 as the crustal torsional oscillations. For this purpose, we calculated the frequencies of the fundamental torsional oscillations with various angular indices $\ell$, by changing the stellar mass and radius. In this work, we try to explain the additional QPO frequencies recently reported by Huppenkothen e…
We report on radio observations of five magnetars and two magnetar candidates carried out at 1950 MHz with the Green Bank Telescope in 2006-2007. The data from these observations were searched for periodic emission and bright single pulses. Also, monitoring observations of magnetar 4U0142+61 following its 2006 X-ray bursts were obtained. No radio emission was detected was detected for any of our targets. The non-detections allow us to place luminosity upper limits (at 1950 MHz) of approximately L < 1.60 mJy kpc^2 for periodic emission and L < 7.6 Jy kpc^2 for single pulse emission. These are t…
We analyze the slow periodicities identified in burst sequences from FRB 121102 and FRB 180916 with periods of about 16 and 160 d, respectively, while also addressing the absence of any fast periodicity that might be associated with the spin of an underlying compact object. Both phenomena can be accounted for by a young, highly magnetized, precessing neutron star that emits beamed radiation with significant imposed phase jitter. Sporadic narrow-beam emission into an overall wide solid angle can account for the necessary phase jitter, but the slow periodicities with 25 to 55 % duty cycles const…
Quasi-periodic oscillations (QPOs) observed in the giant flares of magnetars are of particular interest due to their potential to open up a window into the neutron star interior via neutron star asteroseismology. However, only three giant flares have been observed. We therefore make use of the much larger data set of shorter, less energetic recurrent bursts. Here, we report on a search for QPOs in a large data set of bursts from the two most burst-active magnetars, SGR 1806-20 and SGR 1900+14, observed with the Rossi X-ray Timing Explorer (RXTE). We find a single detection in an averaged perio…
We perform two-dimensional simulations of Alfven oscillations in magnetars, modeled as relativistic stars with a dipolar magnetic field. We use the anelastic approximation to general relativistic magnetohydrodynamics, which allows for an effective suppression of fluid modes and an accurate description of Alfven waves. In addition, we compute Alfven oscillation frequencies along individual magnetic field lines with a semi-analytic approach, employing a short-wavelength approximation. Our main findings are as follows: a) we confirm the existence of two families of quasi-periodic oscillations (QP…
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）
Magnetars are highly magnetized neutron stars that are characterized by recurrent emission of short-duration bursts in soft gamma-rays/hard X-rays. Recently, FRB 200428 were found to be associated with an X-ray burst from a Galactic magnetar. Two fast radio bursts (FRBs) show mysterious periodic activity. However, whether magnetar X-ray bursts are periodic phenomena is unclear. In this paper, we investigate the period of SGR 1806-20 activity. More than 3000 short bursts observed by different telescopes are collected, including the observation of RXTE, HETE-2, ICE and Konus. We consider the obs…
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…
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 origin(s) and mechanism(s) of fast radio bursts (FRBs), which are short radio pulses from cosmological distances, have remained a major puzzle since their discovery. We report a strong Quasi-Periodic Oscillation(QPO) of 40 Hz in the X-ray burst from the magnetar SGR J1935+2154 and associated with FRB 200428, significantly detected with the Hard X-ray Modulation Telescope (Insight-HXMT) and also hinted by the Konus-Wind data. QPOs from magnetar bursts have only been rarely detected; our 3.4 sigma (p-value is 2.9e-4) detection of the QPO reported here reveals the strongest QPO signal observe…
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 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 effect of magnetic fields on the frequencies of toroidal oscillations of neutron stars is derived to lowest order. Interpreting the fine structure in the QPO power spectrum of magnetars following giant flares reported by Strohmayer and Watts (2006) to be "Zeeman splitting" of degenerate toroidal modes, we estimate a crustal magnetic field of order 10^{15} Gauss or more. We suggest that residual m, -m symmetry following such splitting might allow beating of individual frequency components that is slow enough to be observed.
Our numerical simulations show that axisymmetric, torsional, magneto-elastic oscillations of magnetars with a superfluid core can explain the whole range of observed quasi-periodic oscillations (QPOs) in the giant flares of soft gamma-ray repeaters. There exist constant phase, magneto-elastic QPOs at both low (f<150 Hz) and high frequencies (f>500 Hz), in full agreement with observations. The range of magnetic field strengths required to match the observed QPO frequencies agrees with that from spin-down estimates. These results strongly suggest that neutrons in magnetar cores are superfluid.
We investigate the effect of strong magnetic fields on the adiabatic radial oscillations of hadronic stars. We describe magnetized hadronic matter within the framework of the relativistic nonlinear Walecka model and integrate the equations of relativistic radial oscillations to determine the fundamental pulsation mode. We consider that the magnetic field increases, in a density dependent way, from the surface, where it has a typical magnetar value of $10^{15}$ G, to the interior of the star where it can be as large as $3 \times 10^{18}$ G. We show that magnetic fields of the order of $10^{18}$…
In juxtaposition with the standard model of rotation powered pulsar, the model of vibration powered magnetar undergoing quake-induced torsional Alfven vibrations in its own ultra strong magnetic field experiencing decay is considered. The presented line of argument suggests that gradual decrease of frequencies (lengthening of periods) of long-periodic pulsed radiation detected from a set of X-ray sources can be attributed to magnetic-field-decay induced energy conversion from seismic vibrations to magneto-dipole radiation of quaking magnetar.
