Ballooning modes in the inner magnetosphere of the Earth

In this paper the low-frequency ideal MHD (magnetohydrodynamical) perturbations in the inner magnetosphere of the Earth are studied. The set of partial differential equations obtained from the MHD equations in the ballooning approximation and the dipole model of the geomagnetic field is used for this purpose. These equations describe both small-scale and large-scale perturbations in the magnetospheric plasmas. In the “cold” plasma approximation the obtained equations describe poloidal and toroidal standing Alfvén modes. The account of plasma pressure leads to the appearance of an additional type of oscillations—the slow magnetosonic modes. The stability of the magnetospheric plasma with respect to the ballooning perturbations was analyzed. We describe the ballooning perturbations taking into account a coupling between the poloidal Alfvén modes and the slow magnetosonic modes.     

A non-adiabatic analysis for axisymmetric pulsations of magnetic stars

This paper presents the results of a non-adiabatic analysis for axisymmetric non-radial pulsations including the effect of a dipole magnetic field. Convection is assumed to be suppressed in the stellar envelope, and the diffusion approximation is used to radiative transport. As in a previous adiabatic analysis, the eigenfunctions are expanded in a series of spherical harmonics. The analysis is applied to a  1.9-M_⊙  , main-sequence model  (log  T _eff= 3.913)  . The presence of a magnetic field always stabilizes low-order acoustic modes. All the low-order modes of the model that are excited by the κ-mechanism in the He  ii ionization zone in the absence of a magnetic field are found to be stabilized if the polar strength of the dipole magnetic field is larger than about 1 kG. For high-order p modes, on the other hand, distorted dipole and quadrupole modes excited by the κ-mechanism in the H ionization zone remain overstable, even in the presence of a strong magnetic field. It is found, however, that all the distorted radial high-order modes are stabilized by the effect of the magnetic field. Thus, our non-adiabatic analysis suggests that distorted dipole modes and distorted quadrupole modes are most likely excited in rapidly oscillating Ap stars. The latitudinal amplitude dependence is found to be in reasonable agreement with the observationally determined one for HR 3831. Finally, the expected amplitude of magnetic perturbations at the surface is found to be very small.     

Effects of finite resistivity on magnetorotational instabilities in a realistic accretion flow

A local perturbation analysis is performed on a realistic background accretion flow in a global magnetic field. The adopted background model is an analytic solution to the resistive MHD equations and describes magnetically-controlled advection-dominated accretion flows (ADAFs) with an accuracy to the first order in the resistive corrections. The results show that there are three independent wave modes, which may be called the Rayleigh, Balbus–Hawley and resistive modes. Within our resistive-MHD corrections to the ideal-MHD limit, a Balbus–Hawley-like criterion for the instability of axisymmetric perturbations appears as a consequence of the competition between damping due to magnetic diffusion and excitation due to shear flow. As for non-axisymmetric perturbations, the former two modes are likely to be unstable in the presence of shears because the magnetic diffusion acts as a stabilizer only to axisymmetric perturbations within our approximation.     

Long-wavelength MHD instability in the prefront of collisionless shocks with accelerated particles

Collisionless shocks in turbulent space plasmas accelerate particles by the Fermi mechanism to ultrarelativistic energies. The interaction of accelerated particles with the plasma inflow produces extended supersonic MHD flows of multicomponent plasma. We investigate the instabilities of a flow of three-component turbulent plasma with relativistic particles against long-wavelength perturbations with scales larger than the accelerated particle transport mean free path and the initial turbulence scales. The presence of turbulence allows us to formulate the system of single-fluid equations, the equation of motion for the medium as a whole, and the induction equation for the magnetic field with turbulent magnetic and kinematic viscosities. The current of accelerated particles enters into the induction equation with an effective magnetic diffusion coefficient. We have calculated the local growth rates of the perturbations related to the nonresonant long-wavelength instability of the current of accelerated particles for MHD perturbations in the WKB approximation. The amplification of long-wavelength magnetic field perturbations in the flow upstream of the shock front can affect significantly the maximum energies of the particles accelerated by a collisionless shock and can lead to the observed peculiarities of the synchrotron X-ray radiation in supernova remnants.     

Modulation and symmetry changes in stellar dynamos

Stellar dynamos are governed by non-linear partial differential equations (PDEs) which admit solutions with dipole, quadrupole or mixed symmetry (i.e. with different parities). These PDEs possess periodic solutions that describe magnetic cycles, and numerical studies reveal two different types of modulation. For modulations of Type 1 there are parity changes without significant changes of amplitude, while for Type 2 there are amplitude changes without significant changes in parity. In stars like the Sun, cyclic magnetic activity is interrupted by grand minima that correspond to Type 2 modulation. Although the Sun's magnetic field has maintained dipole symmetry for almost 300 yr, there was a significant parity change at the end of the Maunder Minimum. We infer that the solar field may have flipped from dipole to quadrupole polarity (and back) after deep minima in the past and may do so again in the future. Other stars, with different masses or rotation rates, may exhibit cyclic activity with dipole, quadrupole or mixed parity. The origins of such behaviour can be understood by relating the PDE results to solutions of appropriate low-order systems of ordinary differential equations (ODEs). Type 1 modulation is reproduced in a fourth-order system while Type 2 modulation occurs in a third-order system. Here we construct a new sixth-order system that describes both types of modulation and clarifies the interactions between symmetry-breaking and modulation of activity. Solutions of these non-linear ODEs reproduce the qualitative behaviour found for the PDEs, including flipping of polarity after a prolonged grand minimum. Thus we can be confident that these patterns of behaviour are robust, and will apply to stars that are similar to the Sun.     

Density perturbations set up by a rotating galactic dipole

The response of material to a rotating magnetic dipole, considered as primeaval, the axis of which liesin the galactic plane of a model galaxy, is examined. In the three cases of (2.1) gas gradient dominant; (2.2) magnetic pressure and gravity dominant; and (2.3) gas pressure, magnetic pressure and gravity dominant with viscosity neglected, the flow pattern is found to be always characterised by two streamers of high-velocity matter emerging in the plane of the galaxy. The accompanying density distribution suggests a ready analogy with spiral galaxies, especially of SBc and SBb type; the main implication of the hypothesis, however, is that galactic dipoles will inevitably set up density perturbations of a form suitable for the generation of spiral arms via the mechanism of density waves.     

Nonlinear coupling between electromagnetic fields in a strongly magnetized electron-positron plasma

The nonlinear coupling between electromagnetic fields in a strongly magnetized electron-positron plasma is considered. We point out that compressional magnetic field perturbations are excited by the rotational part of the nonlinear current, and derive a new nonlinear system of equations that is basic for studies of modulational instabilities and coherent nonlinear structures in magnetized electron-positron plasmas.     

Adiabatic consideration of the motion of charged particles in superposed dipole and uniform magnetic fields

The motion of a charged particle is studied within a magnetic field. This field consists of two separate fields; a dipole and a uniform magnetic field, parallel to dipole's magnetic moment. The present study is maintained by means of the adiabatic theory. We use a numerical integration of the equations of motion and give comparative results between the adiabatic theory and the numerical integration. The previous results are applied to the case of the Earth's open magnetosphere. Diagrams and tables support this application.     

Torsional Alfvén modes in dipole and toroidal magnetospheres

Propagation of torsional Alfvén waves in the magnetosphere is examined for two models of the Earth's magnetic field, one where the field is toroidal, the other being a dipole field. Both models yield magnetically guided torsional wave modes which are strongly localized in all directions transverse to the steady magnetic field. The transverse structure is determined by a self-consistent solution of the ideal MHD equations. It is shown that the torsional wave is guided even when b is finite, where b is the component of the wave magnetic field in a direction parallel to the steady magnetic field.     

Exact MHD solutions for rotating,magnetic stars

Simple exact solutions of the magnetohydrodynamic equations are found for rotating, magnetic stars. The velocity and magnetic field are axisymmetric and purely toroidal, and the magnetic energy density equals the kinetic energy density. For constant mass density, the solution reduces to that of Chandrasekhar (1956), which is stable even against non-axisymmetric perturbations. For an ideal gas equation of state, the condition for radiative thermal equilibrium is solved to lowest order in the non-spherical perturbation. The velocity, magnetic field and non-spherical pressure and temperature perturbations all vanish within cones centered around the rotation axis, |cos |>x _i a zero of a Legendre polynomial. Low-order, long-period stellar oscillations may be excited by MHD instabilities near the equatorial region which become damped near the axis.     

Uy phoenicis: RR lyrae variable,not dwarf nova

Stellar and atomic systems obey analogous angular momentum/mass relationships and analogous angular momentum/magnetic dipole moment relationships. The dimensional constants in both pairs of angular momentum laws appear to be related by a simple set of self-similar scaling equations, suggesting that atomic and stellar systems may be self-similar.     

Wave processes in nonlinear beams during propagation of waves in pulsar plasmas with different magnetic field orientations

The propagation of nonlinear three-dimensional waves in the form of gaussian beams in pulsars is examined. The defining equations for the wave motion of a plasma with high particle velocities, high electrical conductivity, high wave frequency, and high magnetic fields are the standard equations of magnetogas dynamics. Nonlinear, time-dependent equations are derived for relatively small perturbations of the medium and the orders of magnitude of the parameters of motion such that all the terms in the time-dependent equation are of the same order are written down. Various directions of the unperturbed magnetic field and of the wave propagation which may arise during plasma motion in quasars are considered. In a number of cases a closed analytic solution can be constructed for the propagation of axially symmetric gaussian beams. __________ Translated from Astrofizika, Vol. 49, No. 3, pp. 409–417 (August 2006).     

X射线脉冲星周期的变化与吸积盘边界的K-H不稳定性

本文在中子星磁层与吸积盘之间引入了一个速度、密度、压强和磁场都连续变化的有限厚度的剪切层,以代替Anzer理论中的切向间断面,用磁流体力学方法讨论了中子星磁层与吸积盘交界处等离子体可压缩情况下平面波扰动的K-H不稳定性。结果表明,K-H不稳定性依然存在,径向波矢扰动成为不稳定的主要模式。文中特别讨论了剪切层厚度取值对中子星自转的影响,表明适当调节剪切层厚度就可解释X射线脉冲星周期的变化。将此模型应用到脉冲X射线源Her X-1上,得到较好的结果。     

Meridional (north-south) motions of the solar wind

The steady state hydrodynamic equations which describe the solar wind flow are linearized and used to study the spatial behavior of zonal pressure perturbations. Such perturbations produce meridional (north-south) motions in the solar wind. To simplify the spatial dependence of the zero-order variables and to take advantage of the supersonic regime, the analysis is restricted to heliocentric distances greater than 0.1 AU (astronomical unit). A simplified problem involving a north-south magnetic field asymmetry is also treated. The emphasis of the paper is to determine what pressure perturbations are required at the inner boundary (0.1 AU) to produce at earth north-south deviations from radial flow of 1° to 3°.     

Influence of a dipole magnetic field on the topology of toroidal magnetic configurations around a gravitating body

The topological structure of the toroidal magnetic field, which is affected by a dipole magnetic field, is studied. It is shown, that a dipole magnetic field is able to split the initial toroidal configuration into two toroids and, at a certain critical value of the magnetic dipole, can completely destroy the toroidal configuration. The dependence of the total mass excess on the dipole magnetic field is found.     

The non-axisymmetrical configuration of a large-scale solar and stellar magnetic field

The non-axisymmetric and nonlinear solutions of the magnetostatic equations are given in three-dimensional space of spherical coordinates (r, θ, ?). These solutions are applied to the large-scale solar magnetic field. Their basic features are similar to a dipole field near the polar regions and the polarity reverses near the equator. These features agree with observations for the large-scale solar magnetic field. The solutions can also be applied to investigating the connection between the structure of the magnetic field and the density distribution of the corona. It is shown that the tops of the closed magnetic field associate with density enhancements. Similar results may apply to the large-scale configuration of the stellar field.     

Nonlinear Generation of Fluting Perturbations by Kink Mode

We study the excitation of fluting perturbations in a magnetic tube by an initially imposed kink mode. We use the ideal magnetohydrodynamic (MHD) equations in the cold-plasma approximation. We also use the thin-tube approximation and scale the dependent and independent variables accordingly. Then we assume that the dimensionless amplitude of the kink mode is small and use it as an expansion parameter in the regular perturbation method. We obtain the expression for the tube boundary perturbation in the second-order approximation. This perturbation is a superposition of sausage and fluting perturbations. The amplitude of the fluting perturbation takes its maximum at the middle of the tube, and it monotonically decreases with the distance from the middle of the tube.     

Alfvén polar oscillations of relativistic stars

We study polar Alfvén oscillations of relativistic stars endowed with a strong global poloidal dipole magnetic field. Here, we focus only on the axisymmetric oscillations which are studied by numerically evolving the two-dimensional perturbation equations. Our study shows that the spectrum of the polar Alfvén oscillations is discrete in contrast to the spectrum of axial Alfvén oscillations which is continuous. We also show that the typical fluid modes, such as the f and p modes, are not significantly affected by the presence of the strong magnetic field.     

The secular variation of pulsar magnetic dipole moments

The time dependences of the inertia tensor and of a dissipative torque caused by the nonleptonic weak interaction have been investigated for a certain class of pulsars with no solid core. Early in the life of the pulsar, the angular velocity vector is predicted to move with respect to fixed body axes in such a way that it becomes perpendicular to the magnetic dipole moment. During this motion, the solid outer shell suffers plastic deformation so that the dipole moment becomes approximately collinear with a principal axis. After 10⁴ or 10⁵ yr, the dissipative torque is negligibly small compared with the electromagnetic torque, the Euler equations are those for a simple rigid body, and alignment of spin and dipole moment occurs. If the dipole moment discussed by Lyneet al. (1975) is interpreted as being equal to the component perpendicular to the spin, its secular decay is a natural property of this model and is not a consequence of field decay through electrical resistivity.     

Quasi-Alfvén oscillations of magnetic surfaces

A system of equations has been derived for the modes of free oscillation of the magnetosphere when it is regarded as an adiabatic magnetic dipole trap filled with cold inhomogeneous plasma. The limiting case of infinite longitudinal conductivity corresponding to the assumption that the electric field is orthogonal to the geomagnetic field has been studied. The boundary at the ionosphere is supposed to be perfectly conducting.The eigenmode spectrum has been found to have discrete and continuous components. The eigenmodes of the discrete component correspond to quasi-magnetosonic modes and the eigenmodes of the continuous component to quasi-Alfvén modes.Assuming the magnetosphere to be axisymmetric, a general expression in the form of a Frobenius series has been derived for quasi-Alfvén oscillations of magnetic shells near resonant magnetic surfaces.