High frequency oscillations during magnetar flares

The recent discovery of high frequency oscillations during giant flares from the Soft Gamma Repeaters SGR 1806-20 and SGR 1900+14 may be the first direct detection of vibrations in a neutron star crust. If this interpretation is correct it offers a novel means of testing the neutron star equation of state, crustal breaking strain, and magnetic field configuration. We review the observational data on the magnetar oscillations, including new timing analysis of the SGR 1806-20 giant flare using data from the Ramaty High Energy Solar Spectroscopic Imager and the Rossi X-ray Timing Explorer. We discuss the implications for the study of neutron star structure and crust thickness, and outline areas for future investigation.      

Quasi-periodic oscillations in low-mass X-ray binaries and constraints on the equation of state of neutron star matter

Recently discovered quasi-periodic oscillations in the X-ray brightness of low-mass X-ray binaries are used to derive constraints on the mass of the neutron star component and the equation of state of neutron star matter. The observations are compared with models of rapidly rotating neutron stars which are calculated by means of an exact numerical method in full relativity. For the equations of state we select a broad collection of models representing different assumptions about the many-body structure and the complexity of the composition of superdense matter. The mass constraints differ from their values in the approximate treatment by ∼10 per cent. Under the assumption that the maximum frequency of the quasi-periodic oscillations originates from the innermost stable orbit, the mass of the neutron star is in the range M ∼1.92–2.25 M_⊙. The quasi-periodic oscillation in the Atoll-source 4U 1820−30 in particular is only consistent with equations of state that are rather stiff at high densities, which is explainable, so far, only with pure nucleonic/leptonic composition. This interpretation contradicts the hypothesis that the protoneutron star formed in SN 1987A collapsed to a black hole, since this would demand a maximum neutron star mass below 1.6 M_⊙. The recently suggested identification of quasi-periodic oscillations with frequencies of about 10 Hz with the Lense–Thirring precession of the accretion disc is found to be inconsistent with the models studied in this work, unless it is assumed that the first overtone of the precession is observed.     

Comptonization and QPO origins in accreting neutron star systems

We develop a simple, time-dependent Comptonization model to probe the origins of spectral variability in accreting neutron star systems. In the model, soft 'seed photons' are injected into a corona of hot electrons, where they are Compton upscattered before escaping as hard X-rays. The model describes how the hard X-ray spectrum varies when the properties of either the soft photon source or the Comptonizing medium undergo small oscillations. Observations of the resulting spectral modulations can determine whether the variability is due to (i) oscillations in the injection of seed photons, (ii) oscillations in the coronal electron density, or (iii) oscillations in the coronal energy dissipation rate. Identifying the origin of spectral variability should help clarify how the corona operates and its relation to the accretion disc. It will also help in finding the mechanisms underlying the various quasi-periodic oscillations (QPOs) observed in the X-ray outputs of many accreting neutron star and black hole systems. As a sample application of our model, we analyse a kilohertz QPO observed in the atoll source 4U 1608–52. We find that the QPO is driven predominantly by an oscillation in the electron density of the Comptonizing gas.     

Theory of the radio emission of pulsars

A consistent theory of excitation, stabilization, and propagation of electromagnetic oscillations in a relativistic one-dimensional electron-positron plasma flowing along curved magnetic field lines is presented. It is shown that in such a medium which is typical of the magnetosphere of a neutron star there exist unstable natural modes of oscillations. Nonlinear saturation of the instability leads to an effective energy conversion into transverse oscillations capable of leaving the magnetosphere of a pulsar. The polarization spectrum and the directivity pattern of generated radiation are determined. A comparison with observations has shown that the theory makes it possible to explain practically all the basic characteristics of observed pulsar radio emission.     

中子星X射线双星中kHz QPO现象的理论解释

罗西X射线时变探测器(RXTE)在中子星小质量X射线双星中发现了千赫兹准周期振荡现象(kHzQPO)。kHzQPO的频率一般在几百到上千赫兹,其动力学时标与吸积盘最内部区域物质的运动时标一致,因此普遍认为kHz QPO产生于中子星表面附近区域,携带了来自中心中子星及周围强引力场信息,如质量、自转周期、角动量、半径、磁场等。kHz QpO现象的理解为研究强引力场和致密物质状态开启了一扇新的窗口。着重介绍基于kHz QPO的基本现象和相应的理论模型。     

Impact of neutron star oscillations on the accelerating electric field in the polar cap of pulsar

Pulsar “standard model”, that considers a pulsar as a rotating magnetized conducting sphere surrounded by plasma, is generalized to the case of oscillating star. We developed an algorithm for calculation of the Goldreich-Julian charge density for this case. We consider distortion of the accelerating zone in the polar cap of pulsar by neutron star oscillations. It is shown that for oscillation modes with high harmonic numbers (l,m) changes in the Goldreich-Julian charge density caused by pulsations of neutron star could lead to significant altering of an accelerating electric field in the polar cap of pulsar. In the moderately optimistic scenario, that assumes excitation of the neutron star oscillations by glitches, it could be possible to detect altering of the pulsar radioemission due to modulation of the accelerating field. This work was partially supported by RFBR grant 04-02-16720, and by the grants N.Sh.-5218.2006.2 and RNP-2.1.1.5940.     

Oscillations in radiation-driven outflows

In this paper we investigate the dynamical behaviour of radiation-driven winds, specifically winds that arise when Compton scattering transfers momentum from the radiation field to the gas flow. Such winds occur during strong X-ray bursts from slowly accreting neutron stars, and also may be driven from the inner regions of a black hole or neutron star accretion disc when the mass transfer rate is very high. By linearizing the radiation hydrodynamic equations around steady spherical outflow, we evaluate the time-dependent response of these winds to perturbations introduced at their inner boundaries. We find that although radiation-driven winds are generally stable, they act as mechanical filters that should produce quasi-periodic oscillations or peaked noise in their radiation output when perturbations force them stochastically. This behaviour may underlie the photospheric oscillations observed in some strong Type I X-ray bursts.     

The magnetosphere of oscillating neutron stars in general relativity

Just as a rotating magnetized neutron star has material pulled away from its surface to populate a magnetosphere, a similar process can occur as a result of neutron-star pulsations rather than rotation. This is of interest in connection with the overall study of neutron star oscillation modes but with a particular focus on the situation for magnetars. Following a previous Newtonian analysis of the production of a force-free magnetosphere in this way Timokhin et al., we present here a corresponding general-relativistic analysis. We give a derivation of the general relativistic Maxwell equations for small-amplitude arbitrary oscillations of a non-rotating neutron star with a generic magnetic field and show that these can be solved analytically under the assumption of low current density in the magnetosphere. We apply our formalism to toroidal oscillations of a neutron star with a dipole magnetic field and find that the low current density approximation is valid for at least half of the oscillation modes, similarly to the Newtonian case. Using an improved formula for the determination of the last closed field line, we calculate the energy losses resulting from toroidal stellar oscillations for all of the modes for which the size of the polar cap is small. We find that general relativistic effects lead to shrinking of the size of the polar cap and an increase in the energy density of the outflowing plasma. These effects act in opposite directions but the net result is that the energy loss from the neutron star is significantly smaller than suggested by the Newtonian treatment.     

Seismic signatures of strange stars with crust

We study acoustic oscillations (eigenfrequencies, velocity distributions, damping times) of normal crusts of strange stars. These oscillations are very specific because of huge density jump at the interface between the normal crust and the strange matter core. The oscillation problem is shown to be self-similar. For a low (but non-zero) multipolarity l , the fundamental mode (without radial nodes) has a frequency of ∼300 Hz and mostly horizontal oscillation velocity; other pressure modes have frequencies ≳20 kHz and almost radial oscillation velocities. The latter modes are similar to radial oscillations (having approximately the same frequencies and radial velocity profiles). The oscillation spectrum of strange stars with crust differs from the spectrum of neutron stars. If detected, acoustic oscillations would allow one to discriminate between strange stars with crust and neutron stars and constrain the mass and radius of the star.     

Natural MHD oscillations of a neutron star

Natural, low-frequency, hydromagnetic oscillations of an isolated, nonrotating neutron star, which are localized in the peripheral crust, the structure of which is determined by the electron-nuclear plasma (the Ae phase), are studied. The plasma medium of the outer crust is treated as a homogeneous, infinitely conducting, incompressible continuum, the motions of which are determined by the equations of magnetohydrodynamics. In the approximation of a constant magnetic field inside the crust (the magnetic field outside the star is assumed to have a dipole structure), the spectrum of normal poloidal and toroidal hydromagnetic oscillations, due to presumed residual fluctuations of flow and their associated fluctuations in magnetic field strength, is calculated. Numerical estimates given for the periods of MHD oscillations fall in the range of periods of radio pulsar emission, indicating a close connection between the residual hydromagnetic oscillations and the electromagnetic activity of neutron stars. Translated from Astrofizika, Vol. 40, No. 1, pp. 77–86, January–March, 1997.     

Self-similar pressure oscillations in neutron star envelopes as probes of neutron star structure

We study eigenmodes of acoustic oscillations of high multipolarity l ∼ 100–1000 and high frequency (∼100 kHz), localized in neutron star envelopes. We show that the oscillation problem is self-similar. Once the oscillation spectrum is calculated for a given equation of state (EOS) in the envelope and given stellar mass M and radius R , it can be rescaled to a star with any M and R (but the same EOS in the envelope). For l ≳ 300, the modes can be subdivided into the outer and inner ones. The outer modes are mainly localized in the outer envelope. The inner modes are mostly localized near the neutron drip point, being associated with the softening of the EOS after the neutron drip. We calculate oscillation spectra for the EOSs of cold-catalyzed and accreted matter and show that the spectra of the inner modes are essentially different. A detection and identification of high-frequency pressure modes would allow one to infer M and R and determine also the EOS in the envelope (accreted or ground state) providing a new, potentially powerful method to explore the main parameters and internal structure of neutron stars.     

Superfluid signatures in magnetar seismology

We investigate the role of neutron star superfluidity for magnetar oscillations. Using a plane-wave analysis, we estimate the effects of a neutron superfluid in the elastic crust region. We demonstrate that the superfluid imprint is likely to be more significant than the effects of the crustal magnetic field. We also consider the region immediately beneath the crust, where superfluid neutrons are thought to coexist with a type II proton superconductor. Since the magnetic field in the latter is carried by an array of fluxtubes, the dynamics of this region differ from standard magnetohydrodynamics. We show that the presence of the neutron superfluid (again) leaves a clear imprint on the oscillations of the system. Taken together, our estimates show that the superfluid components cannot be ignored in efforts to carry out 'magnetar seismology'. This increases the level of complexity of the modelling problem, but also points to the possibility of using observations to probe the superfluid nature of supranuclear matter.     

Neutrinooszillationen in Neutronensternmaterie

According to the suggestion of T. J. Mazurek (1979) neutrino oscillations occuring during the dynamic stellar collapse (M ≥ 10M) could be result in a transfer of leptonic zero-point energy to baryons. Then the adiabatic index increases above γ ≥ 4/3, and such an increase is necessary to reverse the collapse. From the theory of neutrino oscillations of B. Pontekorvo (1967) we derive the oszillation length L of neutrinos in vacuum and the characteristic oscillation lengh L^* of neutrinos taking into consideration the refraction index n_e of neutron star matter. The comparison of both oscillation lenghts shows that for electron densities, characteristically of neutron star matter, the oscillation lenght L is considerable larger than the oscillation lenght L^*. Therefore neutrino oscillations cannot influence the scenario for neutrino emission of the neutron star.     

The energy dependence of burst oscillations from the accreting millisecond pulsar XTE J1814−338

The nature of the asymmetry that gives rise to Type I X-ray burst oscillations on accreting neutron stars remains a matter of debate. Of particular interest is whether the burst oscillation mechanism differs between the bursting millisecond pulsars and the non-pulsing systems. One means to diagnose this is to study the energy dependence of the burst oscillations: here we present an analysis of oscillations from 28 bursts observed during the 2003 outburst of the accreting millisecond pulsar XTE J1814−338. We find that the fractional amplitude of the burst oscillations falls with energy, in contrast to the behaviour found by Muno et al. in the burst oscillations from a set of non-pulsing systems. The drop with energy mirrors that seen in the accretion-powered pulsations; in this respect XTE J1814−338 behaves like the other accreting millisecond pulsars. The burst oscillations show no evidence for either hard or soft lags, in contrast to the persistent pulsations, which show soft lags of up to 50 μs. The fall in amplitude with energy is inconsistent with current surface-mode and simple hotspot models of burst oscillations. We discuss improvements to the models and uncertainties in the physics that might resolve these issues.     

Vortex structure of neutron stars with triplet neutron superfluidity

The vortex structure of the “npe” phase of neutron stars with a ³P₂ superfluid neutron condensate of Cooper pairs is discussed. It is shown that, as the star rotates, superfluid neutron vortex filaments described by a unitary ordering parameter develop in the “npe” phase. The entrainment of superconducting protons by the rotating superfluid neutrons is examined. The entrainment effect leads to the appearance of clusters of proton vortices around each neutron vortex and generates a magnetic field on the order of 10¹² G. ³P₂ neutron vortex filaments combine with quark semi-superfluid vortex filaments at the boundary of the “npe” and “CFL” phases. At the boundary of the “Aen” and “npe” phases, they combine with ¹S₀ neutron vortex filaments. In this way, a unified vortex structure is formed. The existence of this structure and its collective elastic oscillations explain the observed oscillations in the angular rotation velocity of pulsars.     

Vortex lattice oscillations in rotating neutron stars with quark “CFL” cores

Collective elastic oscillations of a lattice of nonabelian quark semisuperfluid vortex filaments in the superfluid core of a rotating neutron star are examined. It is shown that in the incompressible fluid approximation, transverse long wavelength oscillations (Tkachenko oscillations) owing to shear deformation of the vortex lattice propagate in a plane perpendicular to the axis of rotation. The periods of these oscillations are consistent with rotational variations on the order of 100-1000 days observed in the pulsars PSR B0531+21 and PSR B1828-11. Translated from Astrofizika, Vol. 52, No. 1, pp. 165–169 (February 2009).     

Radio emission from X-ray sources

The radio emission from some point X-ray sources is suggested to be due to plasma oscillations in the region where the inflowing stream through the inner Lagrange point impinges on the accreting disk around a neutron star in a binary system.     

Astrophysical consequences of neutron-antineutron oscillations

Grand unified theories predict baryon number violating interactions and one of the implications of this is the possible existence of neutron-antineutron oscillations. The neutron-antineutron oscillations have been considered in the neutron rich astrophysical sources such as solar flares, supernovae explosions, neutron stars and the nucleosynthetic phase of the early universe in order to partly account for the antiproton flux of the cosmic rays at low energies and the -ray emission, at GeV energies. Low magnetic fields and high neutron concentrations provide the right environment for the production of antineutrons and hence antiprotons and GeV rays.     

A toy model for global magnetar oscillation

The presence of a magnetic field in a neutron star interior results in a dynamical coupling between the fluid core and the elastic crust. We consider a simple toy-model where this coupling is taken into account and compute the system’s mode oscillations. Our results suggest that the notion of pure torsional crust modes is not useful for the coupled system, instead all modes excite Alfvén waves in the core. However, we also show that among a rich spectrum of global MHD modes the ones most likely to be excited by a fractured crust are those for which the crust and the core oscillate in concert. For our simple model, the frequencies of these modes are similar to the “pure crustal” frequencies. We advocate the significant implications of these results for the attempted theoretical interpretation of QPOs during magnetar flares in terms of neutron star oscillations.      

Quasi-sinusoidal oscillations of the angular velocity of pulsars

We study the oscillations of the angular velocity of pulsars, obtaining an equation for the angular velocity and its derivative taking account of the curvature of vortices. We show that this equation has a quasisinusoidal solution and find the period of these oscillations. We show that the estimates for the value of the periods for various models of neutron stars give quantities of the order of tens of days, which is in agreement with the observations of the quasi-periodic oscillations and fluctuations of the angular velocity of pulsars.Translated fromAstrofizika, Vol. 38, No. 2, 1995.