Evidence for a small,high-Z,iron-like solar core

Radial and nonradial oscillation equations without and with the gravitation perturbation (with and without the Cowling approximation, CA) are solved numerically using the profile from a more accurate high-Z core (HZC) solar model. This more accurate HZC model was generated with the CRAY X-MP/48 supercomputer at the San Diego Supercomputer Center. Frequencies of oscillation in the five-min band (5MB) and frequencies with period near 160 min are presented in tables and plotted in echelle diagrams. The model was generated by integrating the stellar structure equations from the center to he surface, as done in Rouse (1964), using a maximum space step, ;x _m = 5 × 10^–4, decreasing to 10^–6 in the hydrogenionization zone just below the photosphere. Two subsets of space mesh points are used to calculate the oscillation frequencies, viz., one with a maximum space step of 5 × 10^–3, decreasing to 10^–6 with a total of 621 points (mesh 5I) and the other with a maximum space step of 2 × 10^–3, with a total of 867 points (mesh 5J).With the surface boundary condition applied at x = 1.0, the l – 1 degree nonradial frequencies with CA and the l-degree frequencies without CA are in very good agreement with the frequency spacings for observed frequencies of oscillation labeled l = 1 to 5, but with the l – 1 frequencies with CA about 10 Hz or so less than the observations and the l frequencies without CA about 10 Hz or so greater than the observations. And for the Duvall and Harvey (1983) observations labeled l = 10 and l = 20, the l = 9 and l = 19 nonradial solutions with CA agree to about 5 Hz or less with the observations. Considering from the two preceeding papers in this series that increasing the density in the outer envelope and photosphere will increase the 5MB frequencies and applying the outer boundary condition at x > 1.0 will decrease the 5MB frequencies, the net affects of such changes could move one or the other set of frequencies closer to the observations — or require a slightly different model structure to obtain accurate agreements with the values of the observed frequencies throughout the 5MB.In either case, it is concluded that the first-order, radially-symmetric structure of the model outside the HZC is close to the structure of the real Sun. This is of fundamental importance because a real gas adiabatic temperature gradient (Rouse, 1964, 1971) is used in the outer convective region without free parameters.Other aspects of agreements and differences between radial and nonradial solutions, with CA and without CA are discussed. In particular, the l = 4, 6, 8, and 9 g-mode solutions with CA indicate that the observed 160.01 min period may be a common l-mode period of oscillation. More research is proposed.     

Population dynamics in the Ukrainian SSR (1959-1984)

Changes in the spatial distribution of the population of the Ukraine between 1959 and 1984 are analyzed. Attention is given to changes in the rural and urban population composition over time as well as to regional variations in population dynamics.     

Coulomb-trapped particles in the electromagnetic fields of an oblique magnetic rotator

An oblique, rotating magnetized sphere emits electromagnetic waves which, for large magnetization, can quickly accelerate charged particles to very high energies. A central, attractive Coulomb force can trap particles in the region beyond the light cylinder by balancing the accelerating influence of the radiation on the particles. We sample some of the particle orbits possible under these dynamical conditions. A general feature of these orbits is that non-interacting particles started with random initial conditions in the domain of attraction of these orbits will arrange themselves on a curve corotating with the axis of magnetization. Such particle configurations can be a source of pulsed radiation. In the idealized case of no interparticle interactions the spectral index for the radiation emitted by one frequently occurring configuration is found to be –2/3, for emission from radio to -ray frequencies. The dynamical conditions in this simple model closely match those prevalent in outer pulsar magnetospheres, making it possible that part of the radiation from pulsars is emitted by trapped plasma in the region beyond the light cylinder.     

Unsteady hydromagnetic flow through a porous medium between two infinite parallel porous plates with time-varying suction

Unsteady two-dimensional flow of a viscous incompressible and electrical-conducting fluid through a porous medium bounded by two infinite parallel plates under the action of a transverse magnetic field is presented when there is time-varying suction at the plates. The lower plate is at rest while the upper plate is oscillating in its own plane about a constant mean velocity. Expressions for the velocity, fluctuating parts of the velocity, amplitude, and phase of the skin-friction are obtained. The flow phenomenon has been characterized by the parametersK (permeability of the porous medium),N(magnetic parameter) (frequency parameter), andA(variable suction parameter) and the role of these parameters on the flow characteristics has been studied.     

Magnetic reconnection in high-temperature plasma of solar flares

Quasi-steady high-temperature current sheets are an energy source during the main or hot phase of solar flares. Such sheets are shown to be stabilized with respect to the tearing instability by a small transverse component of magnetic field existing in the sheets.     

Implications of liouville's theorem on the apparent brightness temperatures of solar radio bursts

Liouville's theorem for radiation, of which the generalized étendue is a consequence, implies ² d² d² A = constant along the ray path, where is the refractive index and d² and d² A are the ranges, respectively, of solid angle and of area that define a ray (actually a bundle of rays). Implications of this concept on the propagation of radio waves from the actual to the apparent source in the solar corona (i.e., the scatter image of the true source) are discussed. The implications for sources of fundamental plasma radiation include: (1)The observed solid angle (defining the directivity) and apparent area A of the source are compatible with Liouville's theorem only if the apparent source (the scatter image of the true source) corresponds to the envelope of subsources with a small filling factor f. (2) The brightness temperature T _Bof the actual source is greater than that of the apparent source by f ^-1. (3) For sources of fundamental plasma radiation the factor f is very small ( 10^-2). (4) A long-standing discrepancy between the observed low value of T _B at meter/decameter wavelengths for the quiet Sun and the known coronal temperature may be resolved by noting that the implied coronal temperature is given by T _B f and that the factor f must be significantly less than unity.A brief discussion is included of the relation between Liouville's theorem, the generalized étendue, Milne's laws, occupation numbers, extension in phase, and suppression of emission by a medium with refractive index unequal to unity.     

A new approach to the librational solution in the Ideal Resonance Problem

The librational motion of the Ideal Resonance Problem (Garfinkel, 1966, Jupp, 1969) is treated through an initialnon-canonical transformation which, however, leaves the equations of motion in a quasi-canonical form, with Hamiltonian expressed in standard trigonometric functions amenable to traditional averaging techniques. The perturbed solutions, similarly expressed intrigonometric near-identity transformations, and their frequencies can be found to arbitrary order, with the elliptic integrals expected of the system introduced only in a final explicit quadrature for a Kepler-type equation in the angular variable. The specific transformations and resulting equations of motion are introduced, and explicit solutions for the original variables are found to second order, with mean motion accurate to fifth. Limitation of the present solution to the librational region, the extension of that solution to higher order, and observations on the form of the associated Hamiltonian are also discussed.     

Nature of the symbiotic binary V 1329 Cyg

The published photometric and spectroscopic data of the symbiotic binary V 1329 Cyg are interpreted. It is shown, that V 1329 Cyg is an eclipsing binary with an elliptical orbit orbit (e=0.28). The cooler component fills up the Roche-lobe at periastron. A model of moving gaseous structures in the system is proposed and their influence on the radial velocity curve is shown. The following characteristics of the system are derived: the cooler component is an M6 giant with mass 7.9M , radius 339R and luminosityM _bol=–5.42, the hot component is a white dwarf surrounded by an accretion disk. The mean distance between the components is 842R and in periastron it decreases to 605R .     

Cylindrical oscillations of force-free electromagnetic fields

This paper is devoted to Force-Free Electromagnetic Oscillations in a constant magnetic field. A correction is made in the derivation of the basic equation. The paper confirms the predicted spectrum of frequencies, namely _n = _o (n + 1)^1/2;n = 0, 1, 2, .... In addition it is suggested that hybrid frequency _n = ( _n ² + _H ² )^1/2 should be found in observational data.