The equilibrium structure of loaded rotating polytropes

The equilibrium structure of rotating polytropes with a compact core has been studied by means of Chandrasekhar's first-order perturbation theory. Several numerical solutions are given. The results show that the larger the core mass, the smaller the critical central angular velocity will be, and for the same angular velocity, the larger the core mass, the more oblate the rotation ellipsoid will be.     

The equilibrium,stability and evolution of a rotating magnetized gaseous disk

The exact solutions for the equilibrium of rotating gaseous disk with poloidal magnetic field are obtained. The stability of the disk with respect to uniform expansion and contraction is investigated by means of the variational principle. It is shown that if the equilibrium is determined by gravitational and magnetic forces only, the disk is in neutral equilibrium with respect to perturbations of the form r=r. The instability to short-waves perturbations is studied by the quasi-classical method. The analysis shows that if the magnetic field isH>2G, where is the surface density, then these perturbations are stabilized. The configurations of the electrical field induced by the rotation of magnetized disk are found. In conclusion, the questions of the evolution of the disk are discussed in connection with the quasar model when pulsar-like radiation is taken into account.     

Density distortion within a rotating body

This paper ascertains the distortion of the density distribution within a self-gravitating body in hydrostatic equilibrium under the influence of rotation.For this purpose, the Poisson equation has been solved by using the undistorted density profile _o(a) within the Laplacian to obtain the distorted density (a, ). The Laplacian has been expressed in terms of a system of curvilinear coordinates for which the equipotential surfaces constitute a family of fundamental surfaces.In performing the requisite algebraic manipulations, the Clairaut and Radau equations developed in a previous paper (Lanzano, 1974) were utilized to eliminate the derivatives of the elements pertaining to the equipotential surfaces.The density distortion has been obtained up to third-order terms in a small rotational parameter.     

Surface temperature of a rotating charged body

The surface temperature of a rotating, charged body is found separately under the Kerr-Newman metric and the vector graviton metric. Particular reference is made to pulsars. It is found that, 1) under the Kerr-Newman metric, the surface temperature rises from the poles to the equator, when the radius R of the body is greater than a certain critical value, r_n. When R= r_n, the surface temperature is uniform. When R < r_n, the above gradient is reversed. For pulsars, the equatorial temperature is some 3 × 10⁴ K higher than the polar temperature. 2) Under the Vector graviton field metric, a similar temperature differential exists, but it is much smaller in size.     

Post-newtonian equilibrium configurations of rotating polytropes

Post-Newtonian equations are solved numerically for stellar models with a polytropic pressure-density relation for the case of uniform rotation, no meridional currents, and axial symmetry. The solution is obtained by following Stoeckly's numerical technique. Parameters characterizing the critical configuration are determined and compared with the values obtained recently by Fahlman and Anand, who followed Chandrasekhar's series expansion method.     

The multipolar structure of the gravitational radiation from a rotating body

We give the metric coefficients of the retarded field of non-plane gravitational waves from a multipolar source at infinity, and hence the expression for the power of the multipole radiation from a slowly rotating body. When specific calculations are made for the quadrupole radiation, we find that the radiation from a rotating body has a strong directivity. Our calculated results for the total power of two pulsars are in good agreement with previous estimates.     

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.     

Rayleigh-Taylor instability of a Hall plasma with arbitrary density gradient

The Rayleigh-Taylor instability of a plasma layer in the presence of a horizontal magnetic field is investigated, taking into account the effects of Hall-currents and an arbitrarily large density gradient. It is shown for the general case that if the density decreases vertically upward, the system is thoroughly stable.For a plasma layer with exponentially varying density an approximate dispersion relation is obtained using the Galerkin's method. An analysis of the roots of the dispersion relation reveals that the Hall-currents loosen the stabilizing influence of the magnetic field and impart instability to the system. For sufficiently large values of the density gradient and the Hall currents the system is throughly destabilized for all perturbations.     

Orbits and manifolds near the equilibrium points around a rotating asteroid

We study the orbits and manifolds near the equilibrium points of a rotating asteroid. The linearised equations of motion relative to the equilibrium points in the gravitational field of a rotating asteroid, the characteristic equation and the stable conditions of the equilibrium points are derived and discussed. First, a new metric is presented to link the orbit and the geodesic of the smooth manifold. Then, using the eigenvalues of the characteristic equation, the equilibrium points are classified into 8 cases. A theorem is presented and proved to describe the structure of the submanifold as well as the stable and unstable behaviours of a massless test particle near the equilibrium points. The linearly stable, the non-resonant unstable, and the resonant equilibrium points are discussed. There are three families of periodic orbits and four families of quasi-periodic orbits near the linearly stable equilibrium point. For the non-resonant unstable equilibrium points, there are four relevant cases; for the periodic orbit and the quasi-periodic orbit, the structures of the submanifold and the subspace near the equilibrium points are studied for each case. For the resonant equilibrium points, the dimension of the resonant manifold is greater than 4, and we find at least one family of periodic orbits near the resonant equilibrium points. As an application of the theory developed here, we study relevant orbits for the asteroids 216 Kleopatra, 1620 Geographos, 4769 Castalia and 6489 Golevka.     

The equilibrium state of shock-heated rotating atmosphere under the force of gravitation

Equations are developed to describe the flow of a rotating atmosphere under force of gravitation heated by an arbitrary distribution of cylindrical shock waves. Solutions are obtained for the outer solar atmosphere with a steady mass motion in which the heat supplied by shock wave is balanced by the convective heat loss due to this motion. It is found that, for very large range of shock strength and frequencies, the temperature profile is similar to that predicted by the constant shock-strength hypothesis. This hypothesis is used as the basis of a model of the outer solar atmosphere starting near the solar atmosphere.     

The equilibrium configuration of rapid rotating compact stars and some gravitational effects

In this paper, the equilibrium configurations of rapid rotating compact stars and some gravitational effects are studied within the general relativity by use of the Harrison-Wheeler equation of state and by the self-consistent field method. Numerical calculations show that the equilibrium configuration of a rotating star is a spheroid. For large spin velocities, say, ω > 3.0 × 10² sec⁻¹ the eccentricity and mass increase very rapidly as the angular velocity increases, for the critical angular velocity of the rotating star, the eccentricity is about 0.7, the increase in mass is about 10–35%. The difference of the gravitational redshifts at the surface of the star caused by rotation, and the difference of the light bending when the beam moves in the direction of rotation or in the opposite direction are obvious.     

On secular stability of rapidly rotating stars of arbitrary structure

The aim of the present paper will be to utilize Poincaré's criteria to investigate secular stability of self-gravitating configurations, of arbitrary structure, in the state of rapid rotation. The potential energy, a knowledge of which is necessary for application of these criteria, will be determined by an extension of Clairaut's method; and its evaluation in terms of suitably chosen generalized coordinates carried out explicitly to quantities of fourth order in superficial oblateness, for configurations of arbitrary internal structure.The method employed can, moreover, clearly be extended to attain accuracy of any order — at the expense of mere manipulative work which lends itself to machine automation; and the angular velocity of axial rotation can be an arbitrary function of position as well as of the time. An application of our results to homogeneous configurations in rigig-body rotation will be undertaken to demonstrate that our method, when applied to a case for which a closed solution exists, leads to results which are consistent with it.     

Non-stationary motion of a rotating infinitely flattened self-gravitating system near an equilibrium state

An example of a rotating infinitely flattened self-gravitating particle system in steady state is considered. Non-stationary motion of the system in the neighborhood of this equilibrium solution is determined through the sencond-order perturbation. The first order perturbation terms give rise to a configuration of straight bars emanating from the center which become skewed under the influence of the second-order terms. In the case of a single bar, as in a barred spiral, the skewing is in the arms leading or arms trailing sense, according to whether the system is developing away from or approaching the equilibrium state.     

Fission sequence and equilibrium models of rigidity rotating polytropes

Equilibrium sequences of self-gravitating and polytropic stars including binary stars are computed for various polytropic indexes. We find a fission sequence from an ellipsoidal configuration to a binary by way of dumb-bell equilibrium.Paper presented at the Lembang-Bamberg IAU Colloquium No. 80 on Double Stars: Physical Properties and Generic Relations, held at Bandung, Indonesia, 3–7 June, 1983.     

The existence and stability of the equilibrium points of a triaxial rigid body moving around another triaxial rigid body

The motion of two mutually attracting triaxial rigid bodies has been considered. Thirty six particular solutions corresponding to the libration points and analogous to the points Spoke, Arrow and Float (Duboshin, 1959) have been found. The stability of these libration points has been discussed in two categories of cases. In the first category, different shapes of the bodies have been taken and in the second category, the mass and the linear dimensions of one of the bodies have been taken small in comparison to the other.     

Chaotic gravitational zones around a regularly shaped complex rotating body

In preparation for the Rosetta mission, the location and widths of gravitational resonances surrounding a regularly shaped and possibly complex rotating body are mapped following the second fundamental model of resonance. It is found that for uniaxial rotation of the central body, the surrounding resonances are widest for prograde orbits. If the figure axis is tilted with respect to the spin axis of the central body, an additional number of wide resonances appear with a preference for prograde and inclined orbits, and the occurrence of initial conditions which lie in the globally connected chaotic web is significantly increased. For larger rotational excitations, it is seen how these new additional resonances overlap internally at low eccentricity for very large semi-major axes. However, with exceptions for some excited short-axis rotational modes of the central body, it is argued that most resonances vanish for retrograde orbits lying in the plane normal to the body spin, and that resonant or non-resonant stability therefore can be expected for a wide range of mean orbit eccentricities.     

The external field of a rotating and charged body in the vector graviton metric theory

We discuss certain properties of the external field of a rotating and charged body in the frame of the vector graviton metric field theory. We find: 1) a black hole cannot have angular momentum or charge, that is, a rotating body whether charged or not, cannot be a black hole. The Kerr black hole and the Kerr-Newman black hole do not exist. 2) For a rotating and charged axisymmetric body, there exists a latitude-dependent critical distance r_k(θ), such that the radial force acting on a test particle is attractive or repulsive according as the particle is outside or inside the critical distance. The repulsive force means that a massive object cannot collapse indefinitely. Maximum redshift in this case comes from sources on the equator. 3) A test particle also experiences a force along the meridian.     

The change in satellite orbital inclination caused by a rotating atmosphere with day-to-night density variation

The theory specifying the change i in a satellite's orbital inclination due to atmospheric rotation, in terms of the decrease in orbital period T, has been extended to an atmosphere with sinusoidal variation of density between day and night. It is found that with certain special sets of values for the orbital parameters, the day-to-night variation in the Earth's atmosphere can alter the equation for i/T by as much as 25% though only for a few days. Appreciable changes in i/T persisting for several months can only occur for certain resonant orbits: the maximum change is then about 8%. Near-resonance is very unlikely, but the resonance conditions are derived so that orbits can be recognised and avoided.