Cosmological mass model in general relativity

Relativistic cosmological field equations are obtained for a non-static stationary Bertotti-Robinson-type space-time for interacting perfect fluid and electromagnetic field. The cosmological solution to the field equations are obtained and the nature of the electromagnetic field as well the perfect fluid are studied. The electromagnetic field generated here corresponds to a special generic case and the perfect fluid distribution degenerates into a barotropic perfect fluid with equation of statep+=0, >0. It is shown here that the interacting barotropic fluid can generate gravitation only when the cosmological constant being a function ofx in a dynamic field.     

Kinetic equations for neutrino spin- and type-oscillations in a medium

Quantum kinetic equations for the distribution function of massive Dirac neutrinos have been obtained. They describe neutrino spin- and type-oscillations in a medium. The processes of elastic and inelastic scattering of neutrinos with medium components as well as -processes have been taken into account. Applications of developed equations for stellar collapse are discussed.     

On the origin of rotation of a celestial body

The differential equations of the self-rotation of a celestial body have been evaluated. From an integral of these equations a formula for angular velocity of the celestial body was obtained. This formula after being applied to the rotation of the Sun and of the Earth gives, respectively, the following angular velocity ranges: 0.588×10^–6<<18, 187×10^–6 and 0.7533×10^–5<<12,4266×10^–5. These are up to three times narrower than those previously obtained by Savi and Kaanin [1].     

Transfer of Polarized Radiation: Nonlinear Integral Equations for I-Matrices in the General Case and for Resonance Scattering in a Weak Magnetic Field

General equations of the Wiener-Hopf type for a matrix source function with nonsymmetrical kernel matrices are considered in the form of continuous superpositions of exponentials. Certain problems in the transfer of polarized radiation reduce to equations of this kind. In general there are two different H-matrices in the theory (which are a generalization of the Ambartsumian-Chandrasekhar scalar H-function), generated by an initial equation of the Wiener-Hopf type and its analog, but with the kernel matrix and the unknown matrix of the source function being transposed. In addition there are two corresponding I-matrices, actually consisting of Laplace transforms of the matrix source functions, through which the Stokes vector of the escaping radiation is directly determined. In the problem of diffuse reflection from a half-space, the I-matrices are expressed in terms of a product of these two H-matrices, and for the latter there is a system of nonlinear equations which is a generalization of the corresponding Ambartsumian-Chandrasekhar scalar equation. In the problem of the emission of partially polarized radiation from a half-space containing uniformly distributed internal sources we have obtained a system of two nonlinear equations for the I-matrices directly. In the special case of a symmetrical kernel matrix, this system of two equations reduces to one equation. It is shown that in the case of resonance scattering in a weak magnetic field (the Hanle effect) in the approximation of complete frequency redistribution, the system of two nonlinear equations for the I-matrices (of dimension 6×6) also reduces to one nonlinear equation, although the kernel matrix for the main integral equation for the matrix source function () is not symmetrical. For this case we have found a matrix generalization of the so-called law, consisting of an equation of the type (0)Â ^T (0) = (where T denotes transposition) at the boundary of a half-space containing uniformly distributed primary sources of partially polarized radiation.     

Numerical stabilization of Keplerian motion

The time transformation dt/ds=r is studied in detail and numerically stablized differential equations are obtained for =1,2, and 3/2. The case =1 corresponds to Baumgarte's results.     

Cyclotron wave instability in the corona and origin of solar radio emission with fine structure

The longitudinal waves (Bernstein modes and plasma waves near the hybrid frequency) in a mixture of equilibrium coronal plasma and a small group of energetic electrons are investigated. The energetic electrons have a nonequilibrium momentum distribution inherent in trapped particles. The frequency dependence of the cyclotron instability increments is studied. Attention is paid to a significant role of the relativistic effects for the cyclotron instability of longitudinal waves. For sufficiently large velocity of nonequilibrium electrons the increments are shown to increase when the hybrid frequency coincides with one of the gyrofrequency harmonics (double plasma resonance). The results obtained are used in Parts II and III to explain tadpoles and zebra-pattern in solar radio bursts.     

A fourth-order solution of the ideal resonance problem

The second-order solution of the Ideal Resonance Problem, obtained by Henrard and Wauthier (1988), is developed further to fourth order applying the same method. The solutions for the critical argument and the momentum are expressed in terms of elementary functions depending on the time variable of the pendulum as independent variable. This variable is related to the original time variable through a Kepler-equation. An explicit solution is given for this equation in terms of elliptic integrals and functions. The fourth-order formal solution is compared with numerical solutions obtained from direct numerical integrations of the equations of motion for two specific Hamiltonians.     

Time-dependent Green's functions of the cosmic ray equation of transport

Two spherically symmetric time-dependent Green's functions of the equation of transport for cosmic rays in the interplanetary region are derived by transform techniques. The solar wind velocity is assumed radial and of constant speedV. In the first model the radial diffusion coefficient =₀ r (₀ constant), and in the second solution =₀= constant. The solutions are for monoenergetic, impulsive release of particles from a fixed heliocentric radius. Integration of the solutions over timet, fromt=0 tot=, gives the steady-state Green's functions obtained previously.     

Investigation of the electrostatic charging of dust particles in a Paul-trap

Dust particles (glass, tungsten, and nickel) with sizes ranging from 0.25 to 3m were levitated in a Paul-trap and charged by ions or electrons. For ions the particle potential is limited at field strength of about 1×10⁹ V m^–1 by a temperature-dependent discharge mechanism. The particles interaction with 2 to 20 keV electrons always leads to positive surface potentials which can be explained in terms of a decreased absorption of electrons by small particles. Micrometer sized agglomerates were used for the investigation of the electrostatic fragmentation. Fragmentation takes place in a twofold manner: small surface flufl can be removed or the parent particle can be disrupted into smaller agglomerates.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Linear and circular polarization by hollow organic grains

Hollow cylindrical organic particles with a mean refractive index 1.15 and radius 0.1 m, coated with a SiO₂-Fe mantle of thickness 0.006 m, are shown to possess wavelength dependences of linear and circular polarization which are in good accord with astronomical data. Such particles endowed with ferromagnetic or superparamagnetic properties may be selectively aligned by the Davis-Greenstein mechanism.     

Orbital Distribution Arbitrarily Close to the Homothetic Equilateral Triple Collision in the Free‐Fall Three‐Body Problem with Equal Masses

The existence of escape and nonescape orbits arbitrarily close to the homothetic equilateral triplecollision orbit is considered analytically in the threebody problem with zero initial velocities and equal masses. It is proved that escape orbits in the initial condition space are distributed around three kinds of isosceles orbits. It is also proved that nonescape orbits are distributed in between the escape orbits where different particles escape. In order to show this, it is proved that the homotheticequilateral orbit is isolated from other triplecollision orbits as far as the collision at the first triple encounter is concerned. Moreover, the escape criterion is formulated in the planarisosceles problem and translated into the words of regularizing variables. The result obtained by us explains the orbital structure numerically.     

The prominence radiation theory

The present work is a review of papers related to the theory of prominence radiation. Special attention is paid to stationary equations and the theory of radiation diffusion in the lines and continua of hydrogen, helium and metals.We conclude that prominences are low-temperature formations T _e 7000 K, of low density 10¹² particles per cm³, n _e 10¹¹ cm^–3, effective thickness 10⁹ cm, and that the chemical composition of prominences and that of the Sun's atmosphere are the same. The prominence radiation in the lines of hydrogen, helium and metals is due mainly to quasiresonance scattering of the photospheric radiation.     

Painlevé Analysis and Nonlinear Periodic Solutions for Isothermal Magnetostatic Atmospheres

The equations of magnetohydrodynamic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential , known as the Grad–Shafranov equation. Specifying the arbitrary functions in the latter equation, one gets a nonlinear elliptic equation. Analytical solutions of the elliptic equation are obtained for the case of a nonlinear isothermal atmosphere in a uniform gravitational field. The solutions are obtained by using the Painlevé analysis, and are adequate for describing parallel filaments of diffuse, magnetized plasma suspended horizontally in equilibrium in a uniform gravitational field.     

Expansions in power series by computer

The paper describes a technique of expanding power series solutions to sets of equations that can be applied formally to a set of equations by a compiler type program. A program suitable for an algebra system is generated that when run will produce the power series expansions by recurrence relations. Examples are given from Celestial mechanics.     

Kelvin-Helmholtz instability of superposed hydromagnetic fluids of different densities with finite-resistivity

The hydromagnetic Kelvin-Helmholtz instability of two superposed fluids of different densities is studied. One of the fluids is assumed to be static with finite-resistivity and another fluid is streaming and nonconducting. The equations of the problem are linearized and the dispersion relation using relevant boundary conditions has been derived. It is found that the ratio of densities of the fluids () modifies the condition of ideal-plasma modes. The influence of on stable and unstable regions as compared to the case when is unity has been investigated and illustrated. Further, the combined effect of small finite-resistivity and different densities of the fluids is analyzed. It has been found that merely changes the constant of proportionality of the growth rate, which is obtained for the fluids of the same densities.     

On the integrability of the Roche coordinates

The aim of the present paper is to prove that the system of partial differential equations, which define a set of curvilinear coordinates , , that are orthogonal to the Roche equipotentials (r, , ) incorporating the effects of both rotationaland tidal distortion, does not admit of any formal integrals; and can be solved only numerically in an asymptotic manner. This fact is related with analytic properties of the problem of three bodies, in which represents the potential.     

H αfiltergram observations of ellerman bombs and its magnetic reconnection model

From theH filtergram observations obtained at Ganyu station, identification and statistic works made for Ellerman bombs, it is found that they often occur in the superpenumbra area of a mature sunspot. We suggest a plasmoid model to account for the basic properties of a typical bomb: lifetime 11 min, diameter 5 × 10⁷ cm, accompanying jet velocity 40 km/s, total energy 10²⁷ erg,Te 10⁴ K. First, a numerical simulation is made to prove that plasmoids can be lifted from the solar convective zone by magnetic buoyancy. Between the plasmoid and its surroundings a strong current sheet builds up in which a peculiar MHD (with plasma ponderamotive force) - resistive instability takes place. After the magnetic reconnection has begun, a local explosive instability ensues whose growth rate is so high that it allows the exhaustion of the high temperature particles from the sheet in a short period. In this way, the temperature of a bomb may be kept unchanged or only rise slightly.     

Exact solution to radiation-filled Brans-Dicke closed space cosmology

Under the assumption of a power law (k·R ⁿ=C,C=const.) between the gravitational constantk and the radius of curvatureR of the Universe and forP=1/3 the exact solution is sought for the cosmological equations of Brans and Dicke. The solution turns out to be valid for closed space and the parameter of the scalar-tensor theory is necessarily negative. The radius of curvature increases linearly with respect to the age of the Universe while the gravitational constant grows with the square of the radius of curvature. It has been shown (Lessner, 1974) that in this case (KR ²) the spatial component of the field equations is independent of the remaining equations. However, our solution satisfies this independent equation. This solution for the radiation-dominated era corresponds to the solution for the matter-dominated era found by Dehnen and one of the authors (Dehnen and Obregón, 1971). Our solution, as is the solution previously obtained for the matter-dominated era, is in contradiction to Dirac's hypothesis in which the gravitational constant should decrease with time in an expanding Universe.     

Acceleration of electrons in absence of detectable optical flares deduced from type III radio bursts,Hα activity and soft X-ray emission

The relationship between H absorption features, type III radio bursts and soft X-ray emission has been examined in order to determine the characteristics of the particle acceleration process operating when a H-flare may not be detectable. It is found that transient H activity observed in the absence of reported flares is associated with production of relatively weak type III radio and soft X-ray emission. Since such optical phenomena are much more frequent than flares themselves, it is concluded that instabilities generating fast particles may be produced in the corona in a quasi-continuous way with coincident perturbations in the lower solar atmosphere.The soft X-ray component, which is similar to the precursor in flares, is not necessarily the direct product of fast particles, but is probably associated with some type of heating since both the soft X-ray emission and the H features exhibit a similar evolution, the type III bursts occurring near the maximum of this perturbation. The observations are consistent with a model in which the electron acceleration region is located at an altitude where the ion density is 10⁹ cm^–3 and most of the accelerated electrons( 20 keV) are confined to coronal altitudes where the ion density is 10¹⁰ cm^–3.     

Monochromatic images in stokes parameters and the structure of magnetic fields in sunspots

Taking into account magneto-optical effects, we have obtained numerical solutions of the transfer equations for the Stokes parameters, calculated the linearly polarized intensity (U) and constructed its monochromatic images of unipolar sunspots. By comparison with the observational material of the vector magnetograph of the Marshall Space Flight Center, Huntsville (Alabama), we have found that the model of radial magnetic fields may give rise to U monochromatic images close to those observed. The same conclusion has been obtained previously by Landi Degl'Innocenti (1979), although his analysis was performed with the Milne-Eddington approximation instead of a detailed sunspot model. Moreover, we have shown that the model of spiral magnetic fields leads to results in contrast with observations.