Pulsar radio emission. II. Inclined rotator

A new mechanism of production of pulsar radio emission is suggested. An equation for pulsar radio luminosity is derived for the case of an inclined rotator.Translated from Astrofizika, Vol. 39, No. 3, pp. 489–514, July–September, 1996.     

Moment of inertia of a neutron star. II. Relativistic corrections

In part I we suggested an approximate equation to determine the contribution of relativistic effects to the moment of inertia of a superdense star. In the present paper it is tested on model neutron stars with nine different variants of the equation of state of superdense matter. It is established that the approximation error does not exceed 5% for stable configurations. A more accurate version of the Ravenhall—Pethick equation [D. G. Ravenhall and C. J. Pethick, Astrophys. J., 424, 846 (1994)] for the moment of inertia as a function of the mass and radius of a neutron star is derived. Translated from Astrofizika, Vol. 40, No. 4, pp. 507–516, October–December, 1997.     

Radiation transport in a cylinder. I. Resolvent of the fundamental integral equation

A new method is presented for calculating spectral line radiation transport in a homogeneous circular cylinder with infinitely long axis for isotropic scattering with complete frequency redistribution or no change in frequency. In addition to the cylinder, scattering in a layer symmetric about its midpoint and in a sphere are also studied. Equations are derived which are satisfied by the resolvent of the fundamental integral equation describing these cases of scattering. By applying a Hankel transform over a finite interval, the resolvent is expressed in terms of an auxiliary function. An equation is derived for this auxiliary function which is easily soluble by iteration, with the speed of its convergence increasing with growth in the radius of the scattering region.Translated from Astrofizika, Vol. 37, No. 1, pp. 111–127, January–March, 1994.This study was carried out with financial support from the Russian Fund for Fundamental Studies (project 93-02-2957).     

Moment of inertia of a neutron star. I. Relativistic equation for the accumulated moment of inertia

A relativistic, first-order differential equation is derived for the accumulated moment of inertia of a spherically symmetric celestial body. An approximate equation is proposed to describe the contribution of relativistic effects to the moment of inertia of a superdense star. For configurations of an incompressible fluid, this approximation describes the results of the numerical calculations of Chandrasekhar and Miller to within 5% in the entire range of central pressures from 0 to ∞. Translated from Astrofizika, Vol. 40, No. 1, pp. 87–96, January–March, 1997.     

On non-adiabatic oscillations of gaseous systems in hydromagnetics

The general variational principle obtained by Unno for the study of stellar stability is extended to include the effects of magnetic fields in the general case where the perturbations are nonadiabatic. The unperturbed configuration is non-rotating, but internal motions are possible.A general stability equation is derived, using the modified variational principle. In the simplest case, this equation is identical to the one derived by Unno except for the appearance of magnetic terms in one of the coefficients (through the Lorentz force). If dissipation is neglected, the characteristic equation reduces to the one derived by Frieman and Rotenberg in the stationary case and by Kovetz in the static case.The stability of magnetic stars against homologous oscillations is examined and the usual result for the dynamical mode is obtained.     

Virial oscillations of celestial bodies III. The solution of the evolutionary problem in non-newtonian time scale

Generalized Jacobi's equation is derived by introducing the friction force into the equations of motion of mass points constituting the system.The exact solution of the equation of virial oscillations of celestial bodies written for non-conservative systems is obtained using non-linear time scale in the course of the change of variables for a particular friction force law.The nature of the undamped virial oscillations of celestial bodies is though to be related to the system unstability near the state determined by the virial theorem. Thus, the friction force changes its sign near the unstable equilibrium state and due to dissipation of energy during evolution of the system the undamped virial oscillations can be described as self-exited oscillations.     

Clustering of non-point mass system of galaxies in the expanding Universe

We derive the cosmic energy equation for the non-point mass system of galaxies (galaxies with halos) by using the adiabatic approximation for the growth of gravitational clustering of galaxies in the expanding Universe. The cosmic energy equation so derived represents the general form of conservation of energy for the expanding volume. Using the derived form of cosmic energy equation we try to study the evolution of correlation potential energy of the system. We also try to explore the condition under which the approximation of extensivity may be applied to the infinite gravitating non-point mass system of galaxies.     

The Fokker-Planck equation for charged particles moving in random electromagnetic fields

The Fokker-Planck equation which describes the motion of charged particles in a random electromagnetic field is derived from the Liouville equation by a new method. The size of the perturbing magnetic field, for the Fokker-Planck equation to be valid, is calculated in a regime appropriate for cosmic-ray diffusion.     

Exact solution of the equation of radiative transfer for semi-infinite plane-parallel isotropic scattering atmosphere with scattering albedo ω0 ≤ 1 by a method based on Laplace transform and Wiener-Hopf technique

By performing the one-sided Laplace transform on the scalar integro-differential equation for a semi-infinite plane-parallel isotropic scattering atmosphere with a scattering albedo ₀ 1, an integral equation for the emergent intensity has been derived. Application of the Wiener-Hopf technique to this integral equation will give the emergent intensity. The intensity at any optical depth for a positive scattering angle is also derived by inversion. The intensity at any optical depth for a negative scattering angle is also derived in terms of Cauchy's principal value using Plemelj's formulae.     

The comoving-frame equation of radiative transfer in a curvilinear coordinate system

The comoving-frame equation of radiative transfer and moment equations are derived in orthogonal, curvilinear coordinates, inclusive of terms of orderv/c. The equation of radiative transfer, which contains the terms due to the effect of curvature of coordinate lines explicitly as well as those of Doppler shift and aberration, is the generalization of Castor's equation for spherical symmetry and of Buchler's equation for Cartesian coordinates. The moment equations agree with Buchler's.     

Description of Solar Cosmic Ray Propagation in the Interplanetary Medium on the Basis of the Kinetic Equation

The propagation of solar cosmic rays in interplanetary space is considered based on the kinetic equation. The expression for cosmic ray density under instantaneous particle injection by a point-like source is obtained. The set of a differential equation system for harmonics of cosmic ray distribution function is obtained starting from the kinetic equation. The cosmic ray transport equation, taking into account the presence of the second harmonic of particle angular distribution, is derived and the solution of this equation is obtained.     

Long nonlinear waves in a compressible magnetically structured atmosphere

The propagation of nonlinear slow sausage small-amplitude waves in a magnetic slab in a magnetic environment is considered. The equation for surface waves that is allied form of the Benjamin-Ono equation and the equation for body waves that is allied form of the equation for body waves in the slab are derived with the use of the method of stretching variables. The solutions of the equation for surface waves in the form of solitary waves are obtained numerically.     

Compressible,conductive, steady MHD flow in a gravitational field

The magnetohydrodynamics of a compressible fluid with finite electrical conductivity in a gravitational field is treated analytically. For the case of one ignorable coordinate in cylindrical and Cartesian coordinates the problem is reduced to a scalar partial differential equation. The ideal gas equation of state is considered. For simplicity, the new equation is derived for a two-component motion. The application of this result to mass flow in sunspots is discussed.     

The two-body problem with drag and radiation pressure

The Kepler problem including radiation pressure and drag is treated. The equation of the orbit is derived and the scalar and vector integrals of motion are obtained by direct operation on the vector form of the equation of motion.     

Discrete ULF modes in the Earth’s magnetosphere near the Alfven frequency minimum

The equation of small oscillations of ULF waves in the Earth’s magnetosphere is derived accounting for a fast magnetosonic wave. The spectrum of discrete Alfven modes near the Alfven frequency minimum is studied on the basis of this equation.     

The evolution of adiabatic density perturbations

The evolution of adiabatic perturbations has been studied in Friedmann-Lemaître universes containing a mixture of non-interacting matter and radiation. The differential equation governing the growth of infinitely long adiabatic fluctuations has been derived. In the case of the Einstein-de Sitter universe, an exact solution is given to this differential equation.     

Ion acoustic solitons of KdV and modified KdV equations in weakly relativistic plasma containing nonthermal electron,positron and warm ion

In this paper, the ion-acoustic solitons in a weakly relativistic electron-positron-ion plasma have been investigated. Relativistic ions, Maxwell-Boltzmann distributed positrons and nonthermal electrons are considered in collisionless warm plasma. Using a reductive perturbation theory, a Korteweg-de Vries (KdV) equation is derived, and the relativistic effect on the solitons is studied. It is found that the amplitude of solitary waves of the KdV equation diverges at the critical values of plasma parameters. Finally, in this situation, the solitons of a modified KdV (mKdV) equation with finite amplitude is derived.     

视超光速运动的相对论超光速模型

从相对论出发，在视超光速源质心相对于观测者静止的条件下，推导出两个向相反方向运动的视超光速子源之间的视速度方程，这一方程包含了相对论射束模型的表现横向速度公式，且对高、低速不同条件均为适用。     

Dust-acoustic solitary waves and double layers with two temperature ions in a nonextensive dusty plasma

Small amplitude dust-acoustic solitary waves in an unmagnetized dusty plasma consisting of electrons and two temperature ions obeying the q-nonextensive distribution are investigated. Employing reductive perturbation method, the Korteweg-de Vries (KdV) equation is derived. From the solitonic solutions of KdV equation, the influence of nonextensivity of electrons as well as ions and dust concentration on the amplitude and width of dust-acoustic solitary waves has been studied. It is observed that both positive and negative potential dust acoustic solitary waves occur in this case. The modified KdV (mKdV) equation is derived in order to examine the solitonic solutions for the critical plasma parameters for which KdV theory fails. The parametric regimes for the existence of mKdV solitons and double layers (DLs) have also been determined. Positive potential double layers are found to occur in the present study.     

Wave-particle interaction around the lower hybrid resonance

Wave-particle interaction in the ionosphere is studied theoretically for wave frequencies around the lower hybrid resonance (LHR) frequency. An expression is derived for the growth rate of whistler-mode waves propagating in a magneto-active plasma penetrated by a tenuous beam of nonthermal particles. This expression is an extension of that derived in a previous paper by employing the electrostatic dispersion equation; here, the full-wave dispersion equation is used which reduces to the electrostatic one for large values of refractive index.