On the secular decrease in the semimajor axis of Lageos's orbit

The semimajor axis of the Lageos satellite's orbit is decreasing secularly at the rate of 1.1 mm day^–1. Ten possible mechanisms are investigated to discover which one (s), if any, might be causing the orbit to decay. Six of the mechanisms, resonance with the Earth's gravitational field, gravitational radiation, the Poynting-Robertson effect, transfer of spin angular momentum to the orbital angular momentum, drag from near-earth dust, and atmospheric drag by neutral hydrogen are ruled out because they are too small or require unacceptable assumptions to account for the observed rate of decay. Three other mechanisms, the Yarkovsky effect, the Schach effect, and terrestrial radiation pressure give perturbations whose characteristic signatures do not agree with the observed secular decrease (terrestrial radiation pressure appears to be too small in any case); hence they are also ruled out. Charged particle drag with the ions at Lageos's altitude is probably the principal cause of the orbital decay. An estimate of charged particle drag based upon laboratory experiments and satellite measurements of ion number densities accounts for 60 percent of the observed rate of decrease in the semimajor axis, assuming a satellite potential of –1V. This figure is in good agreement with other estimates based on charge drag theory. A satellite potential of –1.5V will explain the entire decay rate. Atmospheric drag from neutral hydrogen appears to be the next largest effect, explaining about 10 percent of the observed orbital decay rate.     

Particle content and degrees of freedom of a gravitational field in 4th order theories of gravity

In gravitational theories of 4-th order, the influence of certain properties of the field equations (tracelessness, conformal invariance, scale in variance respectively their breaking) for the “particle content” (number of degrees of freedom, mass, spin) is investigated. Using the plane-wave ansatz valid in linearized theory it is possible to determine the mass content of the theory, but one cannot get assertions about the number of degrees of freedom and the spin states corresponding to the field quanta. In the linearized theory, this can be done with a spin projection formalism. Using the Cauchy initial value problem and a counting method first developed by EINSTEIN one can get, however, a useful definition of the concept of the degrees of freedom for the full nonlinear theory. This is due to the fact that this method allows to incorporate the concrete structure of the field equations (and thus their nonlinearities). Analysing different general-relativistic field theories via these approaches the influence of the various structures of nonlinearities is discussed. It is, in particular, shown that those results obtained by the spin projection formalism can be reproduced by “nonlinear methods”.     

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.     

On linear equations of variation in dynamical problems

The linear equations of variation, associated with a motion of a particle moving in a plane under a field of force which admits a first integral of the motion of any form, are drawn up in terms of the tangential and normal displacements. The existence of the first integral implies that the normal displacement satisfies a single second-order differential equation, the tangential displacement being given from the solution of this by a single quadrature. The special cases are examined in which the integral is one of energy, and in which it is one of angular momentum. The extension is made to the motion of two particles moving in a plane under a conservative force-field depending on their positions, which admits also an integral of angular momentum. (The study of the relative motion in the gravitational problem of three bodies in the plane may be put into this form by Jacobi's formulation). An equation is given for finding the non-zero characteristic exponents of a periodic solution of this second problem.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 17–23, 1969.     

Orbital dynamics of the gravitational field in Bardeen space-time

In this paper, the orbital dynamics of the gravitational field in Bardeen space-time are investigated. The equations of the particle’s orbital motion are given by solving the Lagrangian equation, and the stability and types of orbits are studied by means of analysing the effective potential of particles. Also, with the help of phase-plane method, the closed and non-closed orbits of test particle are analysed. We find that the stability and types of orbits in the Bardeen space-time are determined not only by the particles’ energy but also by the angular momentum. And for q=0.5M and b<3.3731M, absorbed by the black hole is the only fate of the test particle. We also find that the position of the innermost stable circular orbit of Bardeen black hole occurs at r _min =5.5722M.     

Formation of solar nebula and mass distribution in the planetary system

The formation of the solar nebula and the distribution of mass in its planetary system is studied. The underlying idea is that the protosun, fragmented out from an interstellar cloud as a result of cluster formation, gathered the planetary material and, hence, spin angular momentum by gravitational accretion during its orbital motion around the centre of the Galaxy. The study gives the initial angular momentum of the solar nebula nearly equal to the present value of the solar system.     

Structure and evolution of low-mass W Ursae Majoris type systems – III. The effects of the spins of the stars

In a previous paper, using Eggleton's stellar evolution code, we have discussed the structure and evolution of low-mass W Ursae Majoris (W UMa) type contact binaries with angular momentum loss owing to gravitational radiation or magnetic braking. We find that gravitational radiation is almost insignificant for cyclic evolution of low-mass W UMa type systems, and it is possible for angular momentum to be lost from W UMa systems in a magnetic stellar wind. The weaker magnetic activity shown by observations in W UMa systems is likely caused by the lower mass of the convective envelopes in these systems than in similar but non-contact binaries. The spin angular momentum cannot be neglected at any time for W UMa type systems, especially for those with extreme mass ratios. The spin angular momenta of both components are included in this paper and they are found to have a significant influence on the cyclic evolution of W UMa systems. We investigate the influence of the energy transfer on the common convective envelopes of both components in detail. We find that the mass of the convective envelope of the primary in contact evolution is slightly more than that in poor thermal contact evolution, and that the mass of the convective envelope of the secondary in contact evolution is much less than that in poor thermal contact evolution. Meanwhile, the rate of angular momentum loss of W UMa type systems is much lower than that of poor thermal contact systems. This is indeed caused by the lower masses of the convective envelopes of the components in W UMa type systems. Although the models with angular momentum loss for W UMa systems exhibit cyclic evolution, they seem to show that a W UMa system cannot continue this type of cyclic evolution indefinitely, and it might coalesce into a fast-rotating star after about 1200 cycles of evolution (about  7.0 × 10⁹ yr  ).     

Production of massive spin — 1/2 particles in Robertson-Walker universes with external electromagnetic fields

In this paper we investigate the combined influence of both cosmological and electromagnetic particle creation mechanisms upon massive particles with spin 1/2 on the basis of general covariant Dirac theory.Curved space-time, a radiation-dominated Friedmann universe, is treated as an unquantized gravitational field and the low-frequency part of the 2.7 K background radiation is approximated by homogeneous, constant, and parallel external electric and magnetic fields. We calculate the number density of spin 1/2 particles with massm which are created under the influence of both these external fields.We find that the electric field and the magnetic field both amplify the genuine, purely gravitational particle production. This influence of the magnetic field, which is in contrast to its reducing effect as far as the creation of spin-zero particles is concerned, can clearly be traced back to its coupling to the spin of the particles.Under certain conditions the electromagnetic fields in the early universe can influence the particle creation process even more than the gravitational field.     

Axially symmetric solution in teleparallel equivalent of general relativity, energy, momentum and angular momentum

We apply the energy-momentum tensor which is coordinate independent, of the gravitational field established in the Hamiltonian structure of the teleparallel equivalent of general relativity (TEGR), to an axially symmetric tetrad field to calculate energy, momentum and angular momentum. Also the definition of the gravitational energy is used to investigate the energy within the external event horizon of this tetrad.     

Black hole spin dependence of general relativistic multi-transonic accretion close to the horizon

We introduce a novel formalism to investigate the role of the spin angular momentum of astrophysical black holes in influencing the behavior of low angular momentum general relativistic accretion. We propose a metric independent analysis of axisymmetric general relativistic flow, and consequently formulate the space and time dependent equations describing the general relativistic hydrodynamic accretion flow in the Kerr metric. The associated stationary critical solutions for such flow equations are provided and the stability of the stationary transonic configuration is examined using an elegant linear perturbation technique. We examine the properties of infalling material for both prograde and retrograde accretion as a function of the Kerr parameter at extremely close proximity to the event horizon. Our formalism can be used to identify a new spectral signature of black hole spin, and has the potential of performing the black hole shadow imaging corresponding to the low angular momentum accretion flow.     

On the nonradiative magnetized accretion flows with convection

In this paper, we explore the radial structure of radiatively inefficient accretion flows (RIAFs) in the presence of an ordered magnetic field and convection. We assume the magnetic field has the toroidal and vertical components. We apply the influences of convection on equations of angular momentum and energy. The convective instability can transport the angular momentum inward or outward. We establish two cases for consideration of the effects of convection parameter on magnetized RIAFs. In the first case, we assume the convection parameter as a free parameter and in the other case we calculate convection parameter through use of mixing length theory. In both cases, the solutions show that a magnetized RIAF is very sensitive to the convection parameter and transport direction of angular momentum due to convection. Moreover, we show that the convection strength strongly depends on magnetic field and viscosity.     

Testing tidal-torque theory – I. Spin amplitude and direction

We evaluate the success of linear tidal-torque theory (TTT) in predicting galactic-halo spin using a cosmological N -body simulation with thousands of well-resolved haloes. The protohaloes are identified by tracing today's haloes back to the initial conditions. The TTT predictions for the protohaloes match, on average, the spin amplitudes of the virialized haloes of today, if linear growth is assumed until ∼ t ₀/3, or  55–70  per cent of the halo effective turn-around time. This makes it a useful qualitative tool for understanding certain average properties of galaxies, such as total spin and angular momentum distribution within haloes, but with a random scatter of the order of the signal itself. Non-linear changes in spin direction cause a mean error of ∼50° in the TTT prediction at t ₀, such that the linear spatial correlations of spins on scales ≥1  h ⁻¹ Mpc are significantly weakened by non-linear effects. This questions the usefulness of TTT for predicting intrinsic alignments in the context of gravitational lensing. We find that the standard approximations made in TTT, including a second-order expansion of the Zel'dovich potential and a smoothing of the tidal field, provide close-to-optimal results.     

Expanding,homogeneous, ellipsoidal density perturbations. III. A simple theory for the acquisition of angular momentum by tidal torques with the effects of the spin growth on the expansion included

The effects of the acquisition of angular momentum on the expansion of homogeneous, ellipsoidal density perturbations is investigated by generalizing the theory of previous papers of this series, where spin grows to the first order in overdensity. A small difference is found to be between the two cases, except for the fact that the body under consideration becomes unbound earlier in the current approach. A comparison is also made with the results of a different theory, where spin grows to the second order in overdensity. Quasi-oblate triaxial configurations turn out to gain less angular momentum in respect to both oblate and more elongated configurations with same minor to major axis ratio. In all cases of physical interest, the spin growth from the beginning to the maximum ellipsoidal volume exceeds the spin growth from the maximum ellipsoidal volume to the turnaround of the major axis, by a factor of at least 3. It is also inferred that the spin growth from the turnaround of the major axis on, probably does not exceed about one third the angular momentum previously gained.     

Gravitational instability in the dust layer of a protoplanetary disk: Interaction of solid particles with turbulent gas in the layer

Gravitational instability of the dust layer formed after the aggregates of dust particles settle toward the midplane of a protoplanetary disk under turbulence is considered. A linearized system of hydrodynamic equations for perturbations of dust (monodisperse) and gas phases in the incompressible gas approximation is solved. Turbulent diffusion and the velocity dispersion of solid particles and the perturbation of gas azimuthal velocity in the layer upon the transfer of angular momentum from the dust phase due to gas drag are taken into account. Such an interaction of the particles and the gas establishes upper and lower bounds on the perturbation wavelength that renders the instability possible. The dispersion equation for the layer in the case when the ratio of surface densities of the dust phase and the gas in the layer is well above unity is obtained and solved. An approximate gravitational instability criterion, which takes the size-dependent stopping time of a particle (aggregate) in the gas into account, is derived. The following parameters of the layer instability are calculated: the wavelength range of its subsistence and the dependence of the perturbation growth rate on the perturbation wavelength in the circumsolar disk at a radial distance of 1 and 10 AU. It is demonstrated that at a distance of 1 AU, the gas–dust disk should be enriched with solids by a factor of 5–10 relative to the initial abundance as well as the particle aggregates should grow to the sizes higher than about 0.3 m in order for the instability to emerge in the layer in the available turbulence models. Such high disk enrichment and aggregate growth is not needed at a distance of 10 AU. The conditions under which this gravitational instability in the layer may be examined with no allowance made for the transfer of angular momentum from the gas in the layer to the gas in a protoplanetary disk outside the layer are discussed.     

The spin evolution of nascent neutron stars

The loss of angular momentum owing to unstable r-modes in hot young neutron stars has been proposed as a mechanism for achieving the spin rates inferred for young pulsars. One factor that could have a significant effect on the action of the r-mode instability is fallback of supernova remnant material. The associated accretion torque could potentially counteract any gravitational-wave-induced spin-down, and accretion heating could affect the viscous damping rates and hence the instability. We discuss the effects of various external agents on the r-mode instability scenario within a simple model of supernova fallback on to a hot young magnetized neutron star. We find that the outcome depends strongly on the strength of the magnetic field of the star. Our model is capable of generating spin rates for young neutron stars that accord well with initial spin rates inferred from pulsar observations. The combined action of r-mode instability and fallback appears to cause the spin rates of neutron stars born with very different spin rates to converge, on a time-scale of approximately 1 year. The results suggest that stars with magnetic fields ≤10¹³ G could emit a detectable gravitational wave signal for perhaps several years after the supernova event. Stars with higher fields (magnetars) are unlikely to emit a detectable gravitational wave signal via the r-mode instability. The model also suggests that the r-mode instability could be extremely effective in preventing young neutron stars from going dynamically unstable to the bar-mode.     

The dynamical stability of W Ursae Majoris-type systems

Theoretical study indicates that a contact binary system would merge into a rapidly rotating single star due to tidal instability when the spin angular momentum of the system is more than a third of its orbital angular momentum. Assuming that W Ursae Majoris (W UMa) contact binary systems rigorously comply with the Roche geometry and the dynamical stability limit is at a contact degree of about 70 per cent, we obtain that W UMa systems might suffer Darwin's instability when their mass ratios are in a region of about 0.076–0.078 and merge into the fast-rotating stars. This suggests that the W UMa systems with mass ratio   q ≤ 0.076  cannot be observed. Meanwhile, we find that the observed W UMa systems with a mass ratio of about 0.077, corresponding to a contact degree of about 86 per cent would suffer tidal instability and merge into the single fast-rotating stars. This suggests that the dynamical stability limit for the observed W UMa systems is higher than the theoretical value, implying that the observed systems have probably suffered the loss of angular momentum due to gravitational wave radiation (GR) or magnetic stellar wind (MSW).     

Some astrophysical consequences of the extended Maxwell-like gravitational field equations

The Maxwell-like gravitational field equations have been generalized and coupled through the gravitational four-potential on the electromagnetic Maxwell's equations. It is shown that this has several astrophysical consequences, of which the main are the following (i) the gravitational instability of a system of mass bodies manifesting itself by a Hubble-like motion on cosmological scales, (ii) the possible change of light intensity propagating through a large distance (and so a possible change of the real energy output of some very distant objects, e.g., quasars), (iii) non-stability of a planetary system on the cosmological time scales, due to the momentum increase of the moving bodies in a generalized gravitational field.     

Theoretical estimates of intrinsic galaxy alignment

It has recently been argued that the observed ellipticities of galaxies may be determined at least in part by the primordial tidal gravitational field in which the galaxy formed. Long-range correlations in the tidal field could thus lead to an ellipticity–ellipticity correlation for widely separated galaxies. We present a new model relating ellipticity to angular momentum, which can be calculated in linear theory. We use this model to calculate the angular power spectrum of intrinsic galaxy shape correlations. We show that, for low-redshift galaxy surveys, our model predicts that intrinsic correlations will dominate correlations induced by weak lensing, in good agreement with previous theoretical work and observations. We find that our model produces ' E -mode' correlations enhanced by a factor of 3.5 over B -modes on small scales, making it harder to disentangle intrinsic correlations from those induced by weak gravitational lensing.