Sergey Bastrukov

SPHEROIDAL AND TORSIONAL MODES OF QUASISTATIC SHEAR OSCILLATIONS IN THE SOLID GLOBE MODELS OF NUCLEAR PHYSICS AND PULSAR ASTROPHYSICS

The past three decades of investigation on nuclear physics and pulsar astrophysics have seen gradual recognition that elastodynamic approach to the continuum mechanics of nuclear matter provides proper account of macroscopic motions of degenerate Fermi-matter constituting interior of the nuclear material objects, the densest of all known today. This paper focuses on one theoretical issue of this development which is concerned with oscillatory behavior of a viscoelastic solid globe in the regime of quasistatic, force-free, noncompressional oscillations less investigated in the literature compared to oscillations in the regime of standing shear waves. We show that in this case the problem of computing frequency and lifetime of spheroidal and torsional modes of nonradial shear vibrations damped by viscosity can be unambiguously resolved by working from the energy balance equation and taking advantage of the Rayleighs variational method. The efficiency of this method is demonstrated by solid globe models of nuclear physics and pulsar astrophysics dealing with oscillations of a spherical mass of a viscoelastic Fermi-solid with homogeneous and nonhomogeneous profiles of the bulk density, the shear modulus, and the shear viscosity.

On the stability of global non-radial pulsations of neutron stars

A neutron star is the cosmic nuclear object in which the energy of gravitational pull is brought to equilibrium by elastic energy stored in the neutron Fermi-continuum. Evidence for the viscoelastic behaviour of a stellar nuclear matter provides a seismological model of pulsar glitches interpreted as a sudden release of the elastic energy. In laboratory nuclear physics, the signatures of viscoelasticity of nuclear matter are found in the current investigations on the collective nuclear dynamics, in which a heavy nucleus is modelled by a spherical piece of viscoelastic Fermi-continuum compressed to the normal nuclear density. It is plausible to expect, therefore, that the motions of self-gravitating nuclear matter constituting the interior of neutron stars should be governed by the equations of an elastic solid, rather than by hydrodynamic equations describing the behaviour of gaseous plasma inside the main sequence stars. In this paper, we present arguments that elastodynamic equations, originally introduced in the context of nuclear collective dynamics, can provide a proper account of elasticity in the large scale motions of neutron matter under its own gravity. Emphasis is placed on mathematical physics underlying the constructive description of the continuum mechanics and the rheology of macroscopic nuclear matter. The capability of the elastodynamic approach is examined by analysis of oscillatory dynamics of a neutron star in the standard homogenous model, operating with a spherical mass of self-gravitating degenerate neutron matter whose viscoelastic behaviour is described in terms of the spheroidal and torsional gravitational-elastic eigenmodes, inherenly related to viscoelasticy. The energy variational principle is utilized to compute the frequencies of viscoelastic gravitational pulsations and their relaxation time. The method is demonstrated for both the idealized homogeneous model and the neutron star models constructed on realistic equations of state. Finally, we derive analytic conditions for the stability of a neutron star to linear elastic deformations accompanying the non-radial pulsations, and discuss the fingerprints of these pulsations in the electromagnetic activity of radiopulsars.

Electromagnetic activity of a pulsating paramagnetic neutron star

The fact that neutron star matter possesses the capability of maintaining a highly intense magnetic field has been and still is among the most debatable issues in pulsar astrophysics. Over the years, there were several independent suggestions that the dominant source of pulsar magnetism is either the field-induced or the spontaneous magnetic polarization of the baryon material. The Pauli paramagnetism of degenerate neutron matter is one of the plausible and comprehensive mechanisms of the magnetic ordering of neutron magnetic moments, promoted by a seed magnetic field inherited by the neutron star from a massive progenitor and amplified by its implosive contraction due to the magnetic flux conservation. Adhering to this attitude and based on the equations of magnetoelastic dynamics underlying continuum mechanics of single-axis magnetic insulators, we investigate electrodynamics of a paramagnetic neutron star undergoing nonradial pulsations. We show that the suggested approach regains a recent finding of Akhiezer et al. [1] that the spin-polarized neutron matter can transmit perturbations by low-frequency transverse magnetoelastic waves. We found that nonradial torsional magnetoelastic pulsations of a paramagnetic neutron star can serve as a powerful generator of a highly intense electric field producing the magnetospheric polarization charge whose acceleration along the open magnetic field lines leads to the synchrotron and curvature radiation. Analytic and numerical estimates for periods of non-radial torsional magnetoelastic modes are presented and are followed by a discussion of their possible manifestation in currently monitored activity of pulsars and magnetars.

Non-radial vibrations of neutron stars

Non-radial oscillations of a non-rotating neutron star are studied. A neutron star is modelled by a spherically symmetric distribution of nuclear matter possessing the properties of an elastic solid bounded by Newtonian gravity. The analytic formalism describing the spheroidal gravitation-elastic vibrations is developed. Emphasis is placed on calculation of the eigenfrequencies of non-radial vibrations. First numerical estimates are presented and compared with those obtained in earlier calculations on the basis of Kelvins hydrodynamic model.

Signatures of field induced spin polarization of neutron star matter in seismic vibrations of paramagnetic neutron star

A macroscopic model of the dissipative magneto-elastic dynamics of viscous spin polarized nuclear matter is discussed in the context of seismic activity of a paramagnetic neutron star. The source of the magnetic field of such a star is attributed to Pauli paramagnetism of baryon matter promoted by a seed magnetic field frozen into the star in the process of gravitational collapse of a massive progenitor. Particular attention is given to the effect of shear viscosity of incompressible stellar material on the timing of non-radial torsional magneto-elastic pulsations of the star triggered by starquakes. By accentuating the fact that this kind of vibration is unique to the seismology of a paramagnetic neutron star we show that the high-frequency modes decay faster than the low-frequency modes. The obtained analytic expressions for the period and relaxation time of this mode, in which the magnetic susceptibility and viscosity enter as input parameters, are then quantified by numerical estimates for these parameters taken from early and current works on transport coefficients of dense matter. It is found that the effect of viscosity is crucial for the lifetime of magneto-torsion vibrations but it does not appreciably affect the periods of this seismic mode which fall in the realm of periods of pulsed emission of soft gamma-ray repeaters and anomalous x-ray pulsars—young super-magnetized neutron stars, radiating, according to the magnetar model, at the expense of the magnetic energy release. Finally, we present arguments that the long periodic pulsed emission of these stars in a quiescent regime of radiation can be interpreted as a manifestation of weakly damped seismic magneto-torsion vibrations exhibiting the field induced spin polarization of baryon matter.

Elasticity of nuclear medium as a principal macrodynamical promoter of electric pygmy dipole resonance

Abstract Motivated by arguments of the nuclear core-layer model formulated in [S.I. Bastrukov, J.A. Maruhn, Z. Phys. A 335 (1990) 139], the macroscopic excitation mechanism of the electric pygmy dipole resonance (PDR) is considered as owing its origin to perturbation-induced effective decomposition of a nucleus into two spherical domains–undisturbed inner region treated as a static core and dynamical layer undergoing elastic shear vibrations. The elastic restoring force is central to the excitation mechanism under consideration and has the same physical meaning as in macroscopic model of nuclear giant resonances involving distortions of the Fermi-sphere providing unified description of isoscalar giant electric and magnetic resonances of multipole degree l ⩾ 2 in terms of two fundamental vibrational modes in an elastic sphere, to wit, as spheroidal (electric) and torsional (magnetic) modes of shear elastic oscillations of the nodeless field of material displacements excited in the entire nucleus volume. In the present Letter focus is placed on the emergence of dipole overtone in the frequency spectrum of spheroidal elastic vibrations as Goldstone soft mode. To emphasis this feature of dipole resonant excitation imprinted in the core-layer model we regain spectral equation for the frequency of spheroidal elastic vibrations trapped in the finite-depth layer, derived in the above paper, but using canonical equation of an elastic continuous medium. The obtained analytic equations for the frequency of dipole vibrational state in question and its excitation strength lead to the following estimates for the PDR energy centroid E PDR ( E 1 ) = [ 31 ± 1 ] A − 1 / 3 MeV and the total excitation probability B PDR ( E 1 ) = [ 1.85 ± 0.05 ] 10 −3 Z 2 A − 2 / 3 e 2 fm 2 throughout the nuclear chart exhibiting fundamental character of this soft dipole mode of nuclear resonant response.

ON THE SURFACE GYROMAGNETIC PLASMONS IN A METAL SPHERE

It is argued that in the long wavelength limit of electromagnetic, far infrared, field optical response of an ultrafine metal particle threaded by uniform magnetic field can be properly modeled by equations of semiclassical electron theory in terms of the surface inertial-wave-like oscillations of free electrons driven by Lorentz restoring force. The detailed calculation of the frequency of size-independent gyromagnetic plasmon resonances computed as a function of multipole degree of electron cyclotron oscillations is presented. This spectrum is derived in juxtaposition with the canonical Mies spectral formula for the surface plasmon resonances caused by the Coulomb-force-driven plasma oscillations of conduction electrons.

Magnetoelastic pulsations of neutron stars

We discuss non-radial pulsations of a non-rotating neutron star brought to equilibrium in the state of superparamagnetic magnetization of stellar material. High-lighted are equations of magneto-elastodynamics underlying macroscopic description of large-scale motions of magnetically anisotropic neutron matter possessing properties of elastic Fermi-solid. It is shown that incompressible permanently magnetized nuclear matter can transmit perturbations by transverse magnetoelastic waves. The unique feature of oscillatory behavior of superparamagnetic neutron star is its capability of supporting torsional, differentially-rotational magnetoelastic pulsations. Based on the energy variational principle, analytic form is derived for period of non-radial magnetotorsion pulsations triggering Alfvenic hydromagnetic waves in the neutron star magnetosphere. Our order of magnitude estimates for period of this axial, odd parity magnetotorsion mode, referred to as m/t-mode, suggest that magnetoelastic pulsations may affec...

Alfvén mode in the response of a spherical particle of a nonmagnetic semiconductor or a semimetal

Abstract The behavior of a spherical particle of a semimetal or a nonmagnetic semiconductor placed in a permanent magnetic field is studied in the continuum model. The particle is associated with a neutral solid state plasma (carriers of conductivity are electrons and holes with equal particle density) embedded into a spherical volume inside which the penetrating magnetic field is presumed to be uniform. The low-frequency particle response is described in terms of long wavelength magnetoplasma oscillations of the compensated electron-hole plasma. The dependence of the frequency upon the radius is found to be a characteristic feature of the magnetoplasma Alfven mode in the response of a spherical particle of a semimetal and a nonmagnetic semiconductor.

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.