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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 magnetars 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 to the continuum of Alfven modes in the core, we construct a fully relativistic dynamical model of the magnetar which allows: i) Fast and long simulations without numerical dissipation. ii) Very fine sampling of the stellar structure. We find that the presence of strong magnetic field in the crust results in localizing of some high-frequency crustal elasto-magnetic modes with the radial number n>1 to the regions of the crust where the field is nearly horizontal. While the hydro-magnetic coupling of these localized modes to the Alfven continuum in the core is reduced, their energy is drained on a time-scale much less than 1 second. Therefore the puzzle of the observed QPOs with frequencies larger than 600 Hz still stands.
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In this letter, we present the first 3D force-free general relativity simulations of the magnetosphere dynamics related to the magnetar outburst/flare phenomenology. Starting from an initial dipole configuration, we adiabatically increase the helicity by twisting the footprints of a spot on the stellar surface and follow the succession of quasi-equilibrium states until a critical twist is reached. Twisting beyond that point triggers instabilities that results in the rapid expansion of magnetic field lines, followed by reconnection, as observed in previous axi-symmetric simulations. If the injection of magnetic helicity goes on, the process is recurrent, periodically releasing a similar amount of energy, of the order of a few % of the total magnetic energy. From our current distribution, we estimate the local temperature assuming that dissipation occurs mainly in the highly resistive outermost layer of the neutron star. We find that the temperature smoothly increases with injected twist, being larger for spots located in the tropical regions than in polar regions, and rather independent of their sizes. After the injection of helicity ceases, the magnetosphere relaxes to a new stable state, in which the persistent currents maintain the footprints area slightly hotter than before the onset of the instability.
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, crustal oscillations may be associated with additional radio bursts in the encompassing short burst event (as recently suggested for SGR 1935+2154). Given the large extragalactic volume probed by wide-field radio transient facilities, this offers the prospect of studying NS crusts leveraging samples far more numerous than galactic high-energy magnetar bursts by studying statistics of sub-burst structure or clustered trains of FRBs. We explore the prospects for distinguishing NS equation of state models with increasingly larger future sets of FRB observations. Lower $l$-number eigenmodes (corresponding to FRB time intervals of $sim5-50$ ms) are likely less susceptible than high-$l$ modes to confusion by systematic effects associated with the NS crust physics, magnetic field, and damping. They may be more promising in their utility, and also may corroborate models where FRBs arise from mature magnetars. Future observational characterization of such signals can also determine whether they can be employed as cosmological standard oscillators to constrain redshift, or can be used to constrain the mass of FRB-producing magnetars when reliable redshifts are available.
Magnetar giant flares may excite vibrational modes of neutron stars. Here we compute an estimate of initial post-flare amplitudes of both the torsional modes in the magnetars crust and of the global f-modes. We show that while the torsional crustal modes can be strongly excited, only a small fraction of the flares energy is converted directly into the lowest-order f-modes. For a conventional model of a magnetar, with the external magnetic field of about 10^{15} Gauss, the gravitational-wave detection of these f-modes with advanced LIGO is unlikely.
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 as a combination of red noise at low frequencies and white noise at high frequencies, which we show is a conservative approach to the problem. We use empirical models to make inferences about the potential signature of periodic and quasi-periodic oscillations at these frequencies. We compare our method with previously used techniques and find that although it is on the whole more conservative, it is also more reliable in ruling out false positives. We illustrate our Bayesian method by applying it to a sample of 27 bursts from the magnetar SGR J0501+4516 observed by the Fermi Gamma-ray Burst Monitor, and we find no evidence for the presence of QPOs in any of the bursts in the unbinned spectra, but do find a candidate detection in the binned spectra of one burst. However, whether this signal is due to a genuine quasi-periodic process, or can be attributed to unmodeled effects in the noise is at this point a matter of interpretation.
The tidal force from a third body near a binary system could introduce long-term oscillations in the binarys eccentricity, known as Kozai-Lidov oscillations. We show that the Kozai-Lidov oscillations of stellar-mass black hole binaries have the potential to be observed by LISA. Detections of such binaries will give insights into binary formation channels and also provide an important benchmark of observing Kozai-Lidov oscillations directly.
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