Angular momentum flux from an isolated system ofN-bodies in higher multipole moments

The present paper contains a systematic study of the generalization of the angular momentum formula in higher multipole moments from aN-body isolated system in the linear approximation of general relativity.     

Astronomical relativistic reference systems with multipolar expansion: the global one

With the rapid development of techniques for astronomical observations,the precision of measurements has been significantly increasing. Theories describing astronomical relativistic reference systems, which are the foundation for processing and interpreting these data now and in the future, may require extensions to satisfy the needs of these trends. Besides building a framework compatible with alternative theories of gravity and the pursuit of higher order post-Newtonian approximation, it will also be necessary to make the first order post-Newtonian multipole moments of celestial bodies be explicitly expressed in the astronomical relativistic reference systems.This will bring some convenience into modeling the observations and experiments and make it easier to distinguish different contributions in measurements. As a first step,the global solar system reference system is expressed as a multipolar expansion and the post-Newtonian mass and spin moments are shown explicitly in the metric which describes the coordinates of the system. The full expression of the global metric is given.     

The neutron-star oscillations model for gamma-ray bursts

Exact analytic expressions for the vacuum electromagnetic fields produced by an oscillating magnetized sphere are obtained. The solutions are analysed for various modes of pulsation and for low-order multipole magnetic moments. Within the context of neutron star oscillations, the possibility of gamma-ray generation is discussed. It is shown that the radial pulsations provide an efficient mechanism for generation of gamma-radiation and electron-positron pairs in some regions around the neutron star. For this, the non-vanishing quadrupole magnetic moment oblique to the dipole moment is required. The model for gamma-ray bursts that we propose is briefly considered.     

A momentum-conserving N-body scheme with individual time steps

We present an N-body code called Taichi for galactic dynamics and controlled numerical experiments. The code includes two high-order hierarchical multipole expansion methods: the Barnes-Hut (BH) tree and the fast multipole method (FMM). For the time integration, the code can use either a conventional adaptive KDK or a Hamiltonian splitting integrator. The combination of FMM and the Hamiltonian splitting integrator leads to a momentum-conserving N-body scheme with individual time steps. We find Taichi performs well in the typical applications in galactic dynamics. In the isolated and interacting galaxies tests, the momentum conserving scheme produces the same result as a conventional BH tree code. But for similar force accuracies, FMM significantly speeds up the simulations compared to the monopole BH tree. In the cold collapse test, we find the inner structure after relaxation can be sensitive to the force accuracies. Taichi is ready to incorporate special treatment of close encounters thanks to the Hamiltonian splitting integrator, suitable for studying dynamics around central massive bodies.     

On the use of STF-tensors in celestial mechanics

The purpose of this article is to emphasize the usefulness of STF-tensors in celestial mechanics. Using STF-mass multipole moments and Cartesian coordinates the derivations of equations of motion, the interaction- and tidal-potentials for an isolated system ofN arbitrarily shaped and composed, purely gravitationally interacting bodies are particularly simple. Using simple relations between STF-tensors and spherical harmonics it is shown how all Cartesian formulas can be converted easily into the usual spherical representations. Some computational aspects of STF-tensors and spherical harmonics are discussed. A list of useful formulas for STF-tensors is provided.     

Die Ausbreitung der skalaren Kugelwellen bis zur 2. Náherungsordnung im Gravitationsfeld mit Quadrupolstruktur

By means of the perturbation expansion scheme with respect to the gravitational constant we give a retarded solution of the covariant wave equation for the potential of a free massless scalar field in an axially symmetric gravitational background field of a point mass with a quadrupole moment. For the zeroth order solution we choose a spherical symmetric wave as an ansatz. Our results show that far from the source the spherical symmetric second order wave tail is effectively generated by the loss of mass, caused by gravitational radiation, and that all the other second order tail terms are compensable by first order multipole moments corresponding to a change of the boundary conditions.     

Measurement of the angular momentum of Jupiter and the Sun by use of the Lense-Thirring effect

We investigate the feasibility of using the Lense-Thirring effect to measure the rotational angular momentum of Jupiter and the Sun. This experiment uses gyroscopes in close Jovian and solar orbits. It is important because it provides direct, unique information. The angular momentum is not derivable from the gravitational moments when non-uniform rotation is present. Analysis shows that this experiment could be done around Jupiter with current technology, but could not be done around the Sun for some years.Supported in part, by a Dissertation Research Assistantship of the Graduate College, Iowa State University.     

Some aspects of rotational and magnetic energies for a hierarchy of celestial objects

Celestial objects, from earth like planets to clusters of galaxies, possess angular momentum and magnetic fields. Here we compare the rotational and magnetic energies of a whole range of these celestial objects together with their gravitational self energies and find a number of interesting relationships. The celestial objects, due to their magnetic fields, also posses magnetic moments. The ratio of magnetic moments of these objects with the nuclear magnetic moments also exhibits interesting trends. We also compare their gyromagnetic ratio which appears to fall in a very narrow range for the entire hierarchy of objects. Here we try to understand the physical aspects implied by these observations and the origin of these properties in such a wide range of celestial objects, spanning some twenty orders in mass, magnetic field and other parameters.     

Computation of Jupiter interior models from gravitational inversion theory

A method for deriving a planetary interior model which exactly satisfies a set of N gravitational constraints is implemented. For Jupiter, recent spacecraft measurements provide the mass, radius at a standard pressure level, rotation law, multipole moments of the internal mass distribution, and constraints on the internal composition and temperature distribution. By appropriate iterations, interior models are found which exactly satisfy these constraints. The models are assumed to have constant chemical composition and constant specific entropy in the hydrogenic envelope. The derived pressure-density relation in the outer envelope depends sensitively on the observational uncertainty in the mass multipole moment J₄. Models are not forced to fit the more indirectly derived constraints, which are instead used as consistency checks. For a helium mass fraction in the envelope (Y) equal to 0.20, the inferred pressure at a mass density ≈ 0.2 g/cm³ is about a factor of 2 higher than would be indicated by experimental hydrogen shock compression data in the relevant pressure range of 10⁵ to 10⁶ bar. The inferred pressure distribution is in much better agreement with the shock data for a nominal Y = 0.30 ± 0.05. This value of Y is interpreted in terms of an enhancement in the envelope, by a factor of order 5 over solar abundance, of species primarily consisting of CH₄, NH₃, and possibly H₂O. The same method is applied to Saturn, but existing uncertainties in Saturn's gravitational parameters are still too large to allow useful conclusions about the composition of its envelope.     

Spin Angular Momentum Imparted by Gravitational Waves

Following the demonstration that gravitational waves impart linear momentum, it is argued that if they are polarised they should impart angular momentum to appropriately placed ‘test rods’ in their path. A general formula for this angular momentum is obtained and used to provide expressions for the angular momentum imparted by plane and cylindrical gravitational waves. This revised version was published online in July 2006 with corrections to the Cover Date.     

Toroidal field instability and eddy viscosity in Taylor‐Couette flows

Toroidal magnetic fields subject to the Tayler instability can transport angular momentum. We show that the Maxwell and Reynolds stress of the nonaxisymmetric field pattern depend linearly on the shear in the cylindrical gap geometry. Resulting angular momentum transport also scales linear with shear. It is directed outwards for astrophysical relevant flows and directed inwards for superrotating flows with dΩ/dR > 0. We define an eddy viscosity based on the linear relation between shear and angular momentum transport and show that its maximum for given Prandtl and Hartmann number depends linear on the magnetic Reynolds number Rm. For Rm ≃ 1000 the eddy viscosity is of the size of 30 in units of the microscopic value. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The distribution of the spin angular momentum of the planets

It is shown that the present day observed linear relationship between the logarithm of the spin angular momentum of the planets and the logarithm of the mass can be explained in terms of mass loss from a set of protoplanets initially identical in mass, chemical composition and spin angular momentum.One leave of absence from Rajshahi University, Bangladesh.     

A revised calculation of the bremsstrahlung cross-section in the high magnetic field of pulsars

It has been postulated that electron bremsstrahlung in a strong external magnetic field is the dominant radiation mechanism within the accretion plasma near the magnetic polar regions of binary X-ray sources. Earlier works on the cross section for such a process proved to be unsatisfactory.The present work uses the simple structure of the propagator obtained in a previous calculation for mildly relativistic electrons occupying no more than the first few Landau levels. Particular emphasis is put on the integration over the possible range of momentum transfer during a single collision with the ion. Typical behaviour for two linear polarization modes is illustrated for forward and backward electron scattering. It is found that the previously predicted behaviour at low frequencies for the two modes is only correct in the limit of weak field and large momentum transfer. At higher frequencies resonances are present irrespective of the polarization of the emitted radiation.     

Large scale magnetic dipole and multipole progressive waves in the photosphere

The physical meaning of the photospheric short-period magnetic variation is interpreted. The motion of progressive waves along the equator with a 4.12 year circulation period may explain the basic feature of the variation. These waves have only one wavelength along the equator. The field distribution of one constituent of these waves is similar to that of a rotating dipole. The subharmonics of this dipole-wave are multipole terms circulating with periods of multiples of 4.12 years and the wave-lengths along the equator contain the same multiplying factor. The interference of the dipole and the multipole waves with a background rotation and with the 27-day Bartels rotation time results in a series of periods recorded by the earlier published analysis. The relevant linear relationship for the angular velocities has also been proved based on the magnetic observation.     

Formation of higher harmonics of the galactic cosmic-ray distribution function

We derive equations for the multipole moments of the distribution function of Galactic cosmic rays with energies 1–20 TeV that experience random scattering by turbulence with a power-law spectrum. We take into account the irregularity of the local interstellar medium (LISM) in the neighborhood of the solar system due to the presence of interstellar clouds, the interstellar wind flow around the heliomagnetosphere, and preceding supernova explosions in the local superbubble. The amplitudes of the second and third harmonics of the cosmic-ray distribution function are expressed in terms of the amplitude of the first harmonic without assuming them to be small compared to the first harmonic. Reconciling their values in magnitude and phase with the observed values requires a significant LISM irregularity, which is consistent with other observational data on the LISM structure. Our model is consistent with the assumption that supernova remnants in the Galactic disk located at distances from the Solar system much larger than the particle transport mean free path are the sources of the particles under consideration.     

天文常数中的相对论问题

现代天文观测技术的日新月异、广义相对论的１ＰＮ近似方法在天体力学和天体测量中的广泛应用,使得有必要在１ＰＮ框架中严格而细致地重新审查天文常数系统。在相对论框架里,太阳系天体的质量应当定义为ＢＤ质量,它们的相对变化不超过１０＾－１９,可视为守恒量;引力势满足的方程不再是Ｐｏｉｓｓｏｎ方程而与坐标规范的选择有关,引力势也不再能用传统的球谐函数展开。应当选定一种规范,并且以ＢＤ多极矩作为天文常数。黄赤交     

Regions of stability in rotational dynamics

We investigate the rotational dynamics of a triaxial planet moving on a Keplerian orbit around its star. The dynamics is ruled by several parameters, like the eccentricity, the obliquity, the non-principal rotation, the angular momentum, etc. We consider two specific cases in which the planet is symmetric or asymmetric, according to whether two moments of inertia coincide or differs from each other. We study the dynamics by constructing maps of dynamical stability based on the computation of the maximum Lyapunov characteristic number versus some typical parameters. The results show that only specific resonances appear in the symmetric case, while the asymmetric case shows a much richer phenomenology.     

Rotational dynamics of celestial bodies: Generalized rotation and considerations of angular momentum

The transformation equations under generalized rotation are obtained for an initially defined reduced velocity tensor governing the motion of a deformable finite material continuum. Then angular momentum considerations lead to relations between flow properties of the continuum and properties of a coordinate system introduced to describe generalized rotation of the continuum. Such relations could define preferable coordinate systems perceiving zero angular momentum for the continuum or referring that it moves according to linear laws.     

Auroral ion velocity distributions using a relaxation model

For application to the auroral ionosphere we have calculated ion velocity distributions for a weakly-ionized plasma subjected to crossed electric and magnetic fields. By replacing the Boltzmann collision integral with a simple relaxation model, we have been able to obtain an exact solution to Boltzmann's equation. This solution has the advantage over a series expansion in that all the higher order velocity moments are inherent in it. The exact solution is particularly advantageous when studying large departures of the distribution from its Maxwellian form because these departures are caused by the higher velocity moments. In general, however, a simple relaxation model can only be used to obtain qualitative information on the distribution function. Consequently, we can determine when the higher order velocity moments affect the ion velocity distribution and the nature of their effect, but we cannot obtain accurate quantitative results. The higher velocity moments have their greatest effect on the distribution function above about 120 km, where the ion-neutral collision frequency is less than the ion cyclotron frequency. As the magnitude of the electric field increases, these higher moments act to decrease the number of ions at the peak of the distribution function. Peak densities are reduced by a few per cent for perpendicular electric fields of about 20 mV m^?1.