Wave Beams in an Inhomogeneous Plasma in a Transverse Magnetic Field

The propagation of axisymmetric magnetohydrodynamic waves near the equatorial plane of the crust of a neutron star in a transverse magnetic field is considered. The magnetic field is perpendicular to the equatorial plane. The magnetic fields and electric currents excited by this wave beam at the stellar surface are determined.     

Wave beams in the magnetoelastic crust of pulsars

The propagation of axially symmetric magnetoelastic waves near the equatorial plane of the crust of a neutron star embedded in a transverse magnetic field is examined. The crust is treated as a solid-state plasma and waves are excited in it in the form of a transverse magnetic field applied to the inner boundary of the star’s crust. The time dependent equation is solved in a linear approximation assuming that the perturbing magnetic field is small compared to the unperturbed field. A simple, exact solution in the form of linear gaussian beams is obtained without additional conditions being imposed on the dissipation, dispersion, and narrowness of the beam, provided only that the velocity c_n of these waves depends weakly on position. This last condition is satisfied for the plasma in the crust of a neutron star. As it propagates to the star’s surface, the radius of the beam remains constant. The electric currents generated by the wave beam on the star’s surface are also calculated. __________ Translated from Astrofizika, Vol. 50, No. 4, pp. 547–556 (November 2007).     

Linear Wave Beams in the Crust of a Neutron Star

The propagation of axially symmetric wave beams near the equatorial plane of a neutron star is studied. These waves are excited by a spatially bounded perturbation in the form of a transverse magnetic field applied to the inner boundary of the crust of the star. For a small ratio of the perturbed to the unperturbed magnetic field, a linear theory can be employed to solve the evolution equation. This condition is satisfied in the crust plasma of a neutron star for typical radio luminosities of pulsars. The resulting simple, exact solution in the form of linear gaussian beams exists without additional conditions on the dissipation, dispersion, and narrowness of the beams, if the velocity c _n of these waves is constant. The latter requirement is well satisfied for the plasma in neutron star crusts. The width of the gaussian beam also depends weakly on position.     

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.      

强磁场下中子星外壳的组分和状态方程

本文计算和讨论了强磁场下由冷的催化物质组成的中子星外壳的组份和状态方程。文中考虑了晶格能和强磁场下均匀电子气体的交换能的贡献.得出结论:(1)强磁场使低密度区的状态方程变软;(2)强磁场对高密度区的状态方程几乎没有影响;(3)核质量公式对外壳的组份影响较明显.     

The effect of the neutron-star crust on the evolution of a core magnetic field

We consider the expulsion of the magnetic field from the super-conducting core of a neutron star and its subsequent decay in the crust. Particular attention is paid to a strong feedback of the distortion of magnetic field lines in the crust on the expulsion of the flux from the core. This causes a considerable delay in the core flux expulsion if the initial field strength is larger than 10¹¹ G. It is shown that the hypothesis on the magnetic field expulsion induced by the neutron-star spin-down is adequate only for a relatively weak initial magnetic field B ≈10¹¹ G. The expulsion time-scale depends not only on the conductivity of the crust, but also on the initial magnetic field strength itself. Our model of the field evolution naturally explains the existence of the residual magnetic field of neutron stars. Its strength is correlated with the impurity concentration in neutron-star crusts and anticorrelated with the initial field strengths.     

Expulsion of magnetic flux from the core and its dissipation in the crust of a neutron star

We construct a model for the magnetic-field evolution of an isolated neutron star by assuming that its core is a type II superconductor and that the field penetrates the core in the form of magnetic lines (fluxoids). We consider the fluxoid expulsion from the core and the field dissipation in a conducting crust. The magnetic-field evolution is calculated self-consistently by taking into account the inverse effect of crustal magnetic line bending on the fluxoid velocity in the core. We consider the evolution of two magnetic configurations, in which the bulk of the magnetic flux passes through the neutron-star core and crust. The buoyancy of fluxoids and the force from the neutron vortexes are mainly responsible for their expulsion from the core in the former and latter cases, respectively.     

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.     

The evolution of the magnetic fields of neutron stars

Observational evidence, and theoretical models of the magnetic field evolution of neutron stars is discussed. Observational data indicates that the magnetic field of a neutron star decays significantly only if it has been a member of a close interacting binary. Theoretically, the magnetic field evolution has been related to the processing of a neutron star in a binary system through the spin evolution of the neutron star, and also through the accretion of matter on the neutron star surface. I describe two specific models, one in which magnetic flux is expelled from the superconducting core during spin-down, via a copuling between Abrikosov fluxoids and Onsager-Feynman vortices; and another in which the compression and heating of the stellar crust by the accreted mass drastically reduces the ohmic decay time scale of a magnetic field configuration confined entirely to the crust. General remarks about the behaviour of the crustal field under ohmic diffusion are also made.     

Can a slowly rotating neutron star be a radio pulsar?

It is shown that the radius of curvature of magnetic field lines in the polar region of a rotating magnetized neutron star can be significantly less than the usual radius of curvature of the dipole magnetic field. The magnetic field in the polar cap is distorted by toroidal electric currents flowing in the neutron star crust. These currents close up the magnetospheric currents driven by the electron–positron plasma generation process in the pulsar magnetosphere. Owing to the decrease in the radius of curvature, electron–positron plasma generation becomes possible even for slowly rotating neutron stars, with   PB ^−2/3₁₂ < 10 s  , where P is the period of star rotation and   B ₁₂= B /10¹² G  is the magnitude of the magnetic field on the star surface.     

Cooling of neutron stars with strong toroidal magnetic fields

We present models of temperature distribution in the crust of a neutron star in the presence of a strong toroidal component superposed to the poloidal component of the magnetic field. The presence of such a toroidal field hinders heat flow toward the surface in a large part of the crust. As a result, the neutron star surface presents two warm regions surrounded by extended cold regions and has a thermal luminosity much lower than in the case the magnetic field is purely poloidal. We apply these models to calculate the thermal evolution of such neutron stars and show that the lowered photon luminosity naturally extends their life-time as detectable thermal X-ray sources. Work partially supported by UNAM-DGAPA grant #IN119306.     

Hydromagnetic planetary waves in vertically sheared zonal flow and transverse magnetic field

Hydromagnetic planetary waves propagating through a zonal flow and a transverse magnetic field both of which are sheared in the vertical direction are studied. It is found that the effect of the transverse magnetic field is to make planetary waves, which characteristically propagate westwards, propagate eastwards in both westerly and easterly zonal flows. It is also shown that at a critical level the rays are guided by the zonal flow only and that the waves are either attenuated or escalated by an exponential factor as they cross a critical level.     

Dynamical processes in flux tabes and their role in chromospheric heating

We model the dynamical interaction between magnetic flux tubes and granules in the solar photosphere which leads to the excitation of transverse (kink) and longitudinal (sausage) tube waves. The investigation is motivated by the interpretation of network oscillations in terms of flux tube waves. The calculations show that for magnetic field strengths typical of the network, the energy flux in transverse waves is higher than in longitudinal waves by an order of magnitude. But for weaker fields, such as those that might be found in internetwork regions, the energy fluxes in the two modes are comparable. Using observations of footpoint motions, the energy flux in transverse waves is calculated and the implications for chromospheric heating are pointed out.     

Magnetic deformation of magnetars for the giant flares of the soft gamma-ray repeaters

We present one possible mechanism for the giant flares of the soft gamma-ray repeaters (SGRs) within the framework of the magnetar (superstrongly magnetized neutron star) model, motivated by the positive period increase associated with the August 27 event from SGR 1900+14. From second-order perturbation analysis of the equilibrium of the magnetic polytrope, we find that there exist different equilibrium states separated by the energy of the giant flares and the shift in the moment of inertia to cause the period increase. This suggests that, if we assume that global reconfiguration of the internal magnetic field of     suddenly occurs, the positive period increase     as well as the energy ≳10⁴⁴ erg of the giant flares may be explained. The moment of inertia can increase with a release of energy, because the star shape deformed by the magnetic field can be prolate rather than oblate. In this mechanism, since oscillation of the neutron star will be excited, a ∼ ms-period pulsation of the burst profile and an emission of gravitational waves are expected. The gravitational waves could be detected by planned interferometers such as LIGO, VIRGO and LCGT.     

Time signatures of impulsively generated waves in a coronal plasma

Impulsively generated waves in solar coronal loops are numerically simulated in the frame-work of cold magnetohydrodynamics. Coronal inhomogeneities are approximated by gas density slabs embedded in a uniform magnetic field. The simulations show that an initially excited pulse results in the propagation of wave packets which correspond to both trapped and leaky waves. Whereas the leaky waves propagate outside the slab, the trapped waves occur as a result of a total reflection from the slab walls. Time signatures of these waves are made by a detection of the trapped waves at a fixed spatial location. For waves excited within the slab, time signatures exhibit periodic, quasi-periodic and decay phases. The time signatures for waves excited outside the slab, or for a multi-series of variously shaped impulses generated at different places and times, can possess extended quasi-periodic phases. The case of parallel slabs, when the presence of a second slab influences the character of wave propagation in the first slab, exhibits complex time signatures as a result of solitary waves interaction.     

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.     

Resistive relaxation of a magnetically confined mountain on an accreting neutron star

Three-dimensional numerical magnetohydrodynamic (MHD) simulations are performed to investigate how a magnetically confined mountain on an accreting neutron star relaxes resistively. No evidence is found for non-ideal MHD instabilities on a short time-scale, such as the resistive ballooning mode or the tearing mode. Instead, the mountain relaxes gradually as matter is transported across magnetic surfaces on the diffusion time-scale, which evaluates to  τ_I∼ 10⁵–10⁸ yr  (depending on the conductivity of the neutron star crust) for an accreted mass of   M _a= 1.2 × 10⁻⁴ M_⊙  . The magnetic dipole moment simultaneously re-emerges as the screening currents dissipate over  τ_I  . For non-axisymmetric mountains, ohmic dissipation tends to restore axisymmetry by magnetic reconnection at a filamentary neutral sheet in the equatorial plane. Ideal-MHD oscillations on the Alfvén time-scale, which can be excited by external influences, such as variations in the accretion torque, compress the magnetic field and hence decrease  τ_I  by one order of magnitude relative to its standard value (as computed for the static configuration). The implications of long-lived mountains for gravitational wave emission from low-mass X-ray binaries are briefly explored.     

Magnetic and spin evolution of neutron stars in close binaries

The evolution of neutron stars in close binary systems with a low-mass companion is considered, assuming the magnetic field to be confined within the solid crust. We adopt the standard scenario for the evolution in a close binary system, in which the neutron star passes through four evolutionary phases ('isolated pulsar'–'propeller'– accretion from the wind of a companion – accretion resulting from Roche-lobe overflow). Calculations have been performed for a great variety of parameters characterizing the properties of both the neutron star and the low-mass companion. We find that neutron stars with more or less standard magnetic field and spin period that are processed in low-mass binaries can evolve to low-field rapidly rotating pulsars. Even if the main-sequence life of a companion is as long as 10¹⁰ yr, the neutron star can maintain a relatively strong magnetic field to the end of the accretion phase. The model that is considered can account well for the origin of millisecond pulsars.     

The dynamo theory of plasma turbulence wave in rotating celestial bodies

The various modes of plasma turbulence waves (including MHD waves) are easily excited under cosmic circumstances. In this paper, if we consider that the celestial bodies rotate, there is a source term generated for the magnetic induced equation by the excited plasma turbulence waves. If we expand the turbulent field in the Fourier series and include rotation velocity, the dynamo equation for turbulent waves is obtained. We have also obtained the solutions of various wave forms corresponding to different rotation velocities and then we significantly discuss the magnetic fields in the Sun, planets, and other celestial bodies.     

Magnetogasdynamic cylindrical shock wave in an isothermal state of a gas,II

Non-self-similar isothermal flows behind weak cylindrical shock waves are investigated. The shock is assumed to be propagating in a medium at rest with uniform density permeated by a uniform transverse magnetic field. The electrical conductivity of the gas is infinite everywhere. The total energy of the disturbance is not constant but can be made to increase at a slow rate. A comparative study has been made between the results with an without a magnetic field.