Magnetar Crusts Research Articles

Magnetic field evolution in magnetar crusts through three-dimensional simulations

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 modeling of the evolution of the magnetic field in the crust of a neutron star through 3D simulations. We find that, in the plausible scenario of equipartition of energy between global-scale poloidal and toroidal magnetic components, magnetic instabilities transfer energy to nonaxisymmetric, kilometer-sized magnetic features, in which the local field strength can greatly exceed that of the global-scale field. These intense small-scale magnetic features can induce high-energy bursts through local crust yielding, and the localized enhancement of Ohmic heating can power the star's persistent emission. Thus, the observed diversity in magnetar behavior can be explained with mixed poloidal-toroidal fields of comparable energies.

Spin-polarized neutron matter: Critical unpairing and BCS-BEC precursor

We obtain the critical magnetic field required for complete destruction of $S$-wave pairing in neutron matter, thereby setting limits on the pairing and superfluidity of neutrons in the crust and outer core of magnetars. We find that for fields $B \ge 10^{17}$ G the neutron fluid is non-superfluid -- if weaker spin-1 superfluidity does not intervene -- a result with profound consequences for the thermal, rotational, and oscillatory behavior of magnetars. Because the dineutron is not bound in vacuum, cold dilute neutron matter cannot exhibit a proper BCS-BEC crossover. Nevertheless, owing to the strongly resonant behavior of the $nn$ interaction at low densities, neutron matter shows a precursor of the BEC state, as manifested in Cooper-pair correlation lengths {being} comparable to the interparticle distance. We make a systematic quantitative study of this type of BCS-BEC crossover in the presence of neutron fluid spin-polarization induced by an ultra-strong magnetic field. We evaluate the Cooper pair wave-function, quasiparticle occupation numbers, and quasiparticle spectra for densities and temperatures spanning the BCS-BEC crossover region. The phase diagram of spin-polarized neutron matter is constructed and explored at different polarizations.

Tunneling of Relativistic Bosons Induced by Magnetic Fields in the Magnetar's Crust

The present work is devoted to the study of bosons evolving in the frozen magnetar's crust endowed with an ultra-strong magnetic field orthogonal to an electric field, both described by periodic functions. We discuss the quantum tunneling process through the one-dimensional potential barrier along Oz. The solutions to the Klein–Gordon equation are expressed in terms of Mathieu's functions which, for computable particle's energy range, are turning from oscillatory to exponentially growing modes along Oz. Within the Jeffreys–Wentzel–Kramers–Brillouin framework, the transmission coefficient is computed for the particle momentum in the middle of the instability range.

Role of Landau quantization on the neutron-drip transition in magnetar crusts

The role of a strong magnetic field on the neutron-drip transition in the crust of a magnetar is studied. The composition of the crust and the neutron-drip threshold are determined numerically for different magnetic field strengths using the experimental atomic mass measurements from the 2012 Atomic Mass Evaluation complemented with theoretical masses calculated from the Brussels-Montreal Hartree-Fock-Bogoliubov nuclear mass model HFB-24. The equilibrium nucleus at the neutron-drip point is found to be independent of the magnetic field strength. As demonstrated analytically, the neutron-drip density and pressure increase almost linearly with the magnetic field strength in the strongly quantizing regime for which electrons lie in the lowest Landau level. For weaker magnetic fields, the neutron-drip density exhibits typical quantum oscillations. In this case, the neutron-drip density can be either increased by about $14%$ or decreased by $25%$ depending on the magnetic field strength. These variations are shown to be almost universal, independently of the nuclear mass model employed. These results may have important implications for the physical interpretation of timing irregularities and quasiperiodic oscillations detected in soft gamma-ray repeaters and anomalous x-ray pulsars, as well as for the cooling of strongly magnetized neutron stars.

Influence of Magnetic Field Decay on Electron Capture in Magnetars

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).

Magnetar giant flare oscillations and the nuclear symmetry energy

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 modes and assign them to observed giant flare quasi-periodic oscillation frequencies from the soft gamma-ray repeater SGR 1806-20. We find magnetar crusts that match observations for various magnetic field strengths, entrainment of the free neutron gas in the inner crust, and crust-core transition densities. We find that observations can be reconciled with smaller values of the symmetry energy slope parameter, L, if there is a significant amount of entrainment of the neutrons by the superfluid or if the crust-core transition density is large. We also find neutron star masses and radii which are in agreement with expectations from what is known about low-density matter from nuclear experiment. Matching observations with a field-free model we obtain the approximate values of M =1.35 Msun and R = 11.9 km. Matching observations using a model with the surface dipole field of SGR 1806-20 (B=2.4x10^15 G) we obtain the approximate values of M = 1.25 Msun and R = 12.4 km.

The effects of ultra-strong magnetic fields on electron capture rates for iron group nuclei in the outer crust of magnetars

Based on the work of Wang et al. (Chin. Phys. Lett. 29:049701, 2012), we re-investigated electron capture on iron group nuclei in the outer crust of magnetars and studied magnetar evolution. Effects of ultra-strong magnetic field on electron capture rates for 57Co have been analyzed in the nuclear shell model and under the Landau-level-quantization approximation, and the electron capture rates and the neutrino energy loss rates on iron group nuclei in the outer crust of magnetar have been calculated. The results show that electron capture rates on 57Co are increase greatly in the ultra-strong magnetic field, and above 3 orders of magnitude generally; and the neutrino energy loss rates by electron capture on iron group nuclei increase above 3 orders of magnitude in the range from B=4.414×1013 G to B=4.414×1015 G. These conclusions play an important role in future studying the evolution of magnetar. Furthermore, we modify the expressions of the electron chemical potential (Fermi energy) and phase space factor by introducing Dirac δ-function, and select appropriate parameters of temperature T, magnetic field B and matter density ρ in the our crust, thus our results will be reliable than those of Wang et al.

Friedel crystals and the outer crust of magnetars

The strong magnetic fields found on the surface of magnetars are known to have profound effects on 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 and compute some of the elastic moduli and lattice phonon dispersion relations in this ``Friedel-crystal'' phase.

Parametric resonant states of charged fermions in the magnetar’s crust

We have presently derived the positive-energy solutions to the Dirac equation minimally coupled to a depth-dependent spatially harmonic tangential magnetostatic field to the magnetar crust, similar to the one proposed by Wareing and Hollerbach. It turns out that, for ultra-relativistic fermions and time-intervals much less the characteristic time (comparable to the average Ohmic timescale in the crust), the corresponding linearly independent modes get their depth-dependent amplitudes expressed in terms of Mathieu’s functions and therefore, non-trivial resonances arise, leading to instabilities in the system, for computable ranges of the model parameters. In order to detail these features, we have also discussed the current density components, pointing out the regions for which the particle density has a double bounded modulation. Finally as the magnetic field induction is increasing, the instability range gets larger triggering the exponential growth of the amplitudes, once the imaginary part of the Mathieu Characteristic Exponent becomes more and more dominant.

Properties of the outer crust of strongly magnetized neutron stars from Hartree-Fock-Bogoliubov atomic mass models

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.

FERMIONS IN MAGNETAR'S CRUST IN TERMS OF HEUN DOUBLE CONFLUENT FUNCTIONS

The present paper is devoted to the study of relativistic fermions evolving in a periodic magnetic field frozen in the magnetar's crust. The Heun's Double Confluent functions being the solutions to the Dirac-type equation, their series expansion allows us to write down the expressions of the current density components. For typical values of the magnetic induction, b0~1015 G , so that the magnetic length is much smaller than the extension of the crust, we get a nontrivial quantization law for the particle momentum along Oz.

TWISTING, RECONNECTING MAGNETOSPHERES AND MAGNETAR SPINDOWN

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 magnetic flux, which may be associated with the observed giant flares. These events are accompanied by a short period of ultra-strong spindown, resulting in an abrupt increase in spin period, such as was observed in the giant flare of SGR 1900+14.

MODELING MAGNETAR OUTBURSTS: FLUX ENHANCEMENTS AND THE CONNECTION WITH SHORT BURSTS AND GLITCHES

The availability of a large amount of observational data recently collected from magnetar outbursts is now calling for a complete theoretical study of outburst characteristics. In this letter (the first of a series dedicated to model magnetar outbursts), we tackle the long-standing open issue of whether or not short bursts and glitches are always connected to long-term radiative outbursts. We show that the recent detection of short bursts and glitches seemingly unconnected to outbursts is only misleading our understanding of these events. We show that, in the framework of the starquake model, neutrino emission processes in the magnetar crust limit the temperature, and therefore the luminosity. This natural limit to the maximum luminosity makes outbursts associated with bright persistent magnetars barely detectable. These events are simply seen as a small luminosity increase over the already bright quiescent state, followed by a fast return to quiescence. In particular, this is the case for 1RXS J1708-4009, 1E 1841-045, SGR 1806-20, and other bright persistent magnetars. On the other hand, a similar event (with the same energetics) in a fainter source will drive a more extreme luminosity variation and longer cooling time, as for sources such as XTE J1810-197, 1E 1547-5408 and SGR 1627-41. We conclude that the non-detection of large radiative outbursts in connection with glitches and bursts from bright persistent magnetars is not surprising per se, nor it needs of any revision on the glitches and burst mechanisms as explained by current theoretical models.

Thermoresistive instability in magnetar crusts

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 {\tau}_{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.

On the excitation of f modes and torsional modes by magnetar giant flares

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 magnetar's 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 flare's 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.

Anisotropic electronic screening and damping in magnetars

We calculate the screening of the ion-ion potential due to electrons, in the presence of a large background magnetic field, at densities of relevance to neutron star crusts. Using the standard approach to incorporate electronic screening through the one-loop polarization function, we show that the magnetic field produces important corrections at both short and long distances. In extreme fields, realized in highly magnetized neutron stars called magnetars, electrons occupy only the lowest Landau levels in the relatively low-density region of the crust. Here our results show that the screening length for Coulomb interactions between ions can be smaller than the inter-ion spacing. More interestingly, we find that the screening is anisotropic, and the screened potential between two static charges exhibits long-range Friedel oscillations parallel to the magnetic field. This long-range oscillatory behavior is likely to affect the lattice structure of ions and can possibly create anisotropic structures in the magnetar crusts. We also calculate the imaginary part of the electron polarization function, which determines the spectrum of electron-hole excitations and plays a role in damping lattice phonon excitations. We demonstrate that even for modest magnetic fields this damping is highly anisotropic and will likely lead to anisotropic phonon heat transport in the outer neutron star crust.

Implications of magnetar non-precession

Abstract The objects known as anomalous X-ray pulsars and soft gamma repeaters are commonly identified with magnetars, neutron stars with ultrastrong magnetic fields. The rotational history of these objects has, so far, revealed no evidence of free precession. At the same time, these objects do not generally appear to have magnetic axes nearly parallel or orthogonal to their spin axes. In this Letter we show that the combination of these two observations, together with simple rigid-body dynamics, leads to non-trivial predictions about the interior properties of magnetars: either (i) elastic stresses in magnetar crusts are close to the theoretical upper limit above which the crustal matter yields or (ii) there is a ‘pinned’ superfluid component in the magnetar interior. As a potentially observable consequence of these ideas we point out that in the case of no pinned superfluidity, magnetars of stronger magnetic field strength than those currently observed would have to be nearly aligned/orthogonal rotators.

MAGNETIC FIELD-DECAY-INDUCED ELECTRON CAPTURES: A STRONG HEAT SOURCE IN MAGNETAR CRUSTS

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 are an important, if not the primary, mechanism powering magnetars' soft X-ray emission.

Coulomb crystals in the magnetic field

The body-centered-cubic Coulomb crystal of ions in the presence of a uniform magnetic field is studied using the rigid electron background approximation. The phonon mode spectra are calculated for a wide range of magnetic-field strengths and for several orientations of the field in the crystal. The phonon spectra are used to calculate the phonon contribution to the crystal energy, entropy, specific heat, Debye-Waller factor of ions, and the rms ion displacements from the lattice nodes for a broad range of densities, temperatures, chemical compositions, and magnetic fields. Strong magnetic field dramatically alters the properties of quantum crystals. The phonon specific heat increases by many orders of magnitude. The ion displacements from their equilibrium positions become strongly anisotropic. The results can be relevant for dusty plasmas, ion plasmas in Penning traps, and especially for the crust of magnetars (neutron stars with superstrong magnetic fields B > or approximately equal 10(14) G ). The effect of the magnetic field on ion displacements in a strongly magnetized neutron star crust can suppress the nuclear reaction rates and make them extremely sensitive to the magnetic-field direction.

Alfvén quasi-periodic oscillations in magnetars

Abstract We investigate torsional Alfvén oscillations of relativistic stars with a global dipole magnetic field, via two-dimensional numerical simulations. We find that (i) there exist two families of quasi-periodic oscillations (QPOs) with harmonics at integer multiples of the fundamental frequency, (ii) the lower-frequency QPO is related to the region of closed field lines, near the equator, while the higher-frequency QPO is generated near the magnetic axis, (iii) the QPOs are long-lived, (iv) for the chosen form of dipolar magnetic field, the frequency ratio of the lower to upper fundamental QPOs is ∼0.6, independent of the equilibrium model or of the strength of the magnetic field, and (v) within a representative sample of equations of state and of various magnetar masses, the Alfvén QPO frequencies are given by accurate empirical relations that depend only on the compactness of the star and on the magnetic field strength. The lower and upper QPOs can be interpreted as corresponding to the edges or turning points of an Alfvén continuum, according to the model proposed by Levin (2007). Several of the low-frequency QPOs observed in the X-ray tail of SGR 1806-20 can readily be identified with the Alfvén QPOs we compute. In particular, one could identify the 18- and 30-Hz observed frequencies with the fundamental lower and upper QPOs, correspondingly, while the observed frequencies of 92 and 150 Hz are then integer multiples of the fundamental upper QPO frequency (three and five times, correspondingly). With this identification, we obtain an upper limit on the strength of the magnetic field of SGR 1806-20 (if is dominated by a dipolar component) between ∼3 and 7 × 1015 G. Furthermore, we show that an identification of the observed frequency of 26 Hz with the frequency of the fundamental torsional ℓ= 2 oscillation of the magnetar's crust is compatible with a magnetar mass of about from 1.4 to 1.6 M⊙ and an equation of state (EOS) that is very stiff (if the magnetic field strength is near its upper limit) or moderately stiff (for lower values of the magnetic field).