Effect of Coriolis force on the shapes of rotating stars and stars in binary systems

In this paper an attempt has been made to determine the effect of Coriolis force on the shapes of Roche equipotential surfaces of rotating stars and stars in binary systems. Equations of Roche equipotential surfaces have been obtained for rotating and binary stars which take into account the effects of Coriolis force besides the centrifugal and gravitational forces. Shapes of Roche equipotentials and values of Roche limits are obtained for different values of angular velocity of rotation for rotating stars and for different values of mass ratios for the binary stars. The obtained results have been compared with the corresponding results in which the effect of Coriolis force has not been considered.     

Magnetic Neutron Stars. I. Static Field Configurations

The paper is the first in a series dealing with the structure of magnetic and rotating neutron stars including general relativistic effects. The geometry of fossile magnetic fields frozen in the highly conductive neutron star matter in a non-rotating (or weakly rotating) star is studied. § 2 treats the general poloidal field in a vacuum outside the star. The geometry of magnetic fields within the star — whose matter is governed by a barytropic equation of state — is restricted by the condition that the magnetic force density should be curl-free to maintain equilibrium (§ 3). Numerical results are obtained for a poloidal and a toroidal dipole field (§ 4).     

Hot plasma waves surrounding the Schwarzschild event horizon in a Veselago medium

This paper investigates wave properties of hot plasma in a Veselago medium. For the Schwarzschild black hole, the 3+1 GRMHD equations are re-formulated which are linearly perturbed and then Fourier analyzed for rotating (non-magnetized and magnetized) plasmas. The graphs of wave vector, refractive index and change in refractive are used to discuss the wave properties. The results obtained confirm the presence of Veselago medium for both rotating (non-magnetized and magnetized) plasmas. This work generalized the isothermal plasma waves in the Veselago medium to hot plasma case.     

The structure of the accretion disc boundary layer around a rotating,non-magnetized star

The process of disc accretion onto rotating nonmagnetized stars is considered. Closed system of equations is written for the boundary layer which exists between Keplerian outer part of the disc and more slowly rotating star surface. Under certain simplifying assumptions the system is solved numerically for main physical variables. Energy conservation equation is used for finding the boundary layer radiation intensity. The results are discussed with a special emphasize on their importance as well as on possible shortcomings.     

The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

The classical Poisson equations of rotational motion are used to study the attitude motions of an Earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate Earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the Earth.A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Longterm solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.This paper represents a part of the author's Ph. D. dissertation for the Mathematics Department, Auburn University.     

Corrected Hawking temperature of Warped AdS3 rotating Black Hole by using tunneling method

In this paper, we have calculated the corrected Hawking temperature for the Warped AdS₃ rotating Black Hole by using the tunneling method beyond the semi-classical approximation for the Warped AdS₃ rotating Black Hole. For this purpose, we have isolated the r-t sector of the metric from the angular part throughout a coordinate transformation near the horizon.     

A second-order perturbation theory for differentially rotating gaseous polytropes

The aim of the present investigation has been to specify the structure of a differentially rotating gaseous polytrope, by extending Chandrasekhar's method to include second-order terms in the perturbation parameter. The formal results obtained permit the determination of the polytropic structure for all types of differential rotation of cylindrical symmetry. The formalism developed works efficiently in the limiting case of uniform rotation and the results obtained are compared with those of previous investigations of uniformly rotating polytropes.     

The equilibria and periodic orbits around a dumbbell-shaped body

This paper investigates the equilibria, their stability, and the periodic orbits in the vicinity of a rotating dumbbell-shaped body. First, the geometrical model of dumbbell-shaped body is established. The gravitational potential fields are obtained by the polyhedral method for several dumbbell-shaped bodies with various length–diameter ratios. Subsequently, the equilibrium points of these dumbbell-shaped bodies are computed and their stabilities are analyzed. Periodic orbits around equilibrium points are determined by the differential correction method. Finally, in order to understand further motion characteristic of dumbbell-shaped body, the effect of the rotating angular velocity of the dumbbell-shaped bodies is investigated. This study extends the research work of the orbital dynamics from simple shaped bodies to complex shaped bodies and the results can be applied to the dynamics of orbits around some asteroids.     

Vibrational stability of the rotating Roche model

The aim of the first part of this investigation will be to establish the explicit form of the linearized systems of differential equations governing arbitrary oscillations (of amplitudes small enough for their squares and higher powers to be negligible) of the rotating Roche model in Clairaut's coordinates (in which their radial component is identified with the total potential). By solving these equations in a closed form we shall prove that this model is incapable of performing such oscillations (for any type of symmetry) about equipotential surfaces representing the figures of equilibrium, as soon as the centrifugal force will cause their equilibrium form to depart from a sphere.In the second part of this paper we shall set up the closed forms of the Laplace equation in Clairaut (non-orthogonal) as well as Roche (orthogonal) coordinates associated with the rotating Roche model; and by a construction of their solution establish successively the explicit forms of the respective harmonic functions associated with such figures (as a generalization of Legendre functions which are similarly associated with a sphere.     

The Eulerian equations of differentially rotating gaseous polytropes

In this paper, we present in detail the whole process by which the Eulerian general equation is obtained, holding in case of a differentially rotating gaseous polytrope. The explicit form of this equation is derived on the basis of a model developed in a previous investigation.     

On the stability of triangular libration points of the photogravitational restricted circular three-body problem

This paper considers the restricted circular three-body problem with respect to the radiation repulsion force acting upon a particle on the part of one of the main bodies (the Sun). The characteristic of the family of stationary particular solutions of the problem (libration points) representing the relative equilibrium positions in a rotating Cartesian system is given. On the basis of the KAM theory with the help of a computer a nonlinear analysis of the triangular libration points stability for the planar case is carried out. These libration points are proved to be strictly stable by Liapunov practically in the whole area of fulfilling the necessary stability conditions. Instability is discovered at the resonant curve of the third order and at the greater part of the resonant curve of the fourth order. The plotted results of the investigation allowed us to draw a conclusion about the Liapunov stability of the triangular libration points in a problem with respect to the radiation pressure for all the planets of the Solar system.     

General relativistic spectra of accretion discs around rapidly rotating neutron stars: effect of light bending

We present computed spectra, as seen by a distant observer, from the accretion disc around a rapidly rotating neutron star. Our calculations are carried out in a fully general relativistic framework, with an exact treatment of rotation. We take into account the Doppler shift, gravitational redshift and light-bending effects in order to compute the observed spectrum. We find that light bending significantly modifies the high-energy part of the spectrum. Computed spectra for slowly rotating neutron stars are also presented. These results would be important for modelling the observed X-ray spectra of low-mass X-ray binaries containing fast-spinning neutron stars.     

On inertial drifts in pulsar magnetospheres

It is pointed out that, in a number of papers, Ardavan has obtained incorrect results because of his invalid neglect of inertial drifts in attempting to obtain an integral of the motion for steadily rotating pulsar magnetospheres.     

Effects of plasma rotation on alfvén solitons in pulsar magnetospheres

Nonlinear Alfvén wave in a hot rotating and strongly magnetized electron-positron plasma is considered. Using relativistic two fluid equations, the dispersion relation for Alfvén wave in the rotating plasma is obtained. Large amplitude Alfvén solitons are found to exist in the rotating pulsar plasma. Rotational effects on solitons are discussed.     

Self-consistent electromagnetic field in a nearly co-rotating magnetosphere

An example of the self-consistent solution which belongs to the non-trivial solution, obtained in a previous paper (Kaburaki, 1985), is found in a nearly co-rotating inner magnetosphere. Though the stellar wind is neglected there compared with the co-rotatinal velocity, drift motion around the magnetic axis, which is a manifestation of inertial effects, is determined self-consistently with the electromagnetic field. In this process, explicit expressions for the energy integral in the rotating frame and for the density distribution are also obtained. These expressions contain a fundamental length, which is to be evaluated according to physical conditions of a magnetosphere and determines the asymptotic-kinetic energy of a plasma particle at infinity. The electric current associated with the drift motion is too small to alter the original magnetic field, but the electric field is modified by the inertial effects even in the inner magnetosphere. The integrated Ohm's law is used to describe a force balance in the rotating frame, in the limits of weak and strong magnetic field.     

关于脉冲星非共转模型的研究

本文讨论了共轴、纯转动、force-free的脉冲星系统,在Burman理论基础上建立了一个非共转模型(其中含待定参量,共转情况是它的特例)。利用系统稳定的近似条件——系统能量最小确定特定参量,得到一个与G-J模型类似的共转模型。由于考虑了惯性效应,不存在星风,是稳定态,但没有辐射。在转轴与磁矩有小偏角时,利用非平衡系统更普遍的稳定条件——熵产生最小,确定本模型的参量,得到的辐射能量在量级上与观测值相符合。     

On Pulsar Electrodynamics in Rotating Frames

In this paper we have considered a rotating, perfectly conducting sphere and have calculated the electric and magnetic field distributions measured by the rotating observer using the anholonomic approach. The calculations have been done for the following two cases: (1) rotating charged spherical shell and (2) a uniformely magnetized sphere. We have shown that in the limiting situation (a/c)² 1 and 1, the magnetic field distribution is the same for both observers, inertial and noninertial. The expressions obtained for the electric field components in the rotating frame have been compared with the corresponding expressions in the inertial frame, where the observer is at rest. Some of the results are in agreement with Post's approach to noninertial electrodynamics.     

The multipole expansion of the radiation field from a relativistically rotating oblique magnetic dipole

Using the methods of Haxton and Ruffini the multipole expansion of the radiation field of an arbitrarily fast rotating magnetic dipole, with its axis inclined relative to the rotation axis, is obtained. This result is compared with the Fourier decomposition of the radiation emitted by the rotating dipole, obtained by Belinskyet al.     

The equilibrium and stability of uniformly rotating gaseous systems in hydromagnetics

The theory for investigating the equilibrium and stability of a uniformly rotating gaseous system with a prevalent magnetic field is developed by using the virial tensor approach. Most of the discussion in this paper depends on the assumption that on the surface of the system, the magnetic field is zero. In Appendix A, however, we have considered the case in which the surface magnetic field is non-zero.We have obtained the nine modes of oscillations, grouped into the transverse shear, toroidal and pulsation modes. From this analysis have also found the conditions under which the sequence of a uniformly rotating axially symmetric configuration in the presence of a magnetic field should have a point of bifurcation, that is, a point where objects with genuine triplanar symmetry branch off. This condition is also generalized in the Appendix to include the effects of differential rotation and non-zero surface magnetic field.Applications to the cosmogonic fission problem, the study of the pulsation of rotating magnetic stars and some radio astrophysical problems are briefly discussed.