Collapse of the spherical stellar system

A new numerical method is proposed for solving the problems connected with the evolution of spherical clusters. The method is based upon the solution of the algebraic equations describing the motions of spherical shells.The stage of the collapse of a typical cluster is considered. The initial configuration is taken as a system with a uniform density distribution and with velocities much less than the virial ones. The model close to a stationary one has been obtained. The mass of the stationary cluster comprises about 60% of the initial one. The density distribution of the outer part of the cluster approximately corresponds to a profile of R ^–3.3.     

Structure of the satellitary accretion disk of Saturn

A detailed computation on the equilibrium structure of an accretion disk around Saturn from which the regular satellites presumably originated is reported. Such a disk is the predecessor of the self-dissipating disk that is formed when the mass infall stops (Cassen and Moosman, 1981, Icarus48, 353–376). When determining the disk structure local energy balance was assumed. Convention was taken into account by introducing local energy dissipation and, in an approximate manner, sonic convection. Changes in the disk structure were investigated by varying the free parameters, i.e., the external flux from both the protosun and the protoplanet, the abundance of dust and the strength of turbulence. It has been verified that the external energy flux does not play an important role in the evolution of the disk structure. Models characterized by either longer times (?3 10³ year) or a noticeable depletion of condensable elements (10^?2 times less than the solar value) have a total mass of the order of 0.34?0.1 times the mass of the regular satellites increased by the mass of the light elements. Low turbulence models (Reynolds critical number $\text{Re}{}^1\text{= 150}$) are characterized approximately by a total mass twice as large the mass of the regular satellites. All the studied models present a temperature distribution that allows the condensation of iron, silicate, and, in the outer regions, ice grains. All models but the one with 10^?2 of the solar value of condensable elements are characterized by a wide convective region that contains the formation zone of the regular satellites.     

Decimetric type III radio bursts and associated hard X-ray spikes

A detailed comparison is made between hard X-ray spikes and decimetric type III radio bursts for a relatively weak solar flare on 1981 August 6 at 10: 32 UT. The hard X-ray observations were made at energies above 30 keV with the Hard X-Ray Burst Spectrometer on the Solar Maximum Mission and with a balloon-born coarse-imaging spectrometer from Frascati, Italy. The radio data were obtained in the frequency range from 100 to 1000 MHz with the analog and digital instruments from Zürich, Switzerland. All the data sets have a time resolution of 0.1 s or better. The dynamic radio spectrum shows many fast drift type III radio bursts with both normal and reverse slope, while the X-ray time profile contains many well resolved short spikes with durations of 1 s. Some of the X-ray spikes appear to be associated in time with reverse-slop bursts suggesting either that the electron beams producing the radio bursts contain two or three orders of magnitude more fast electrons than has previously been assumed or that the electron beams can trigger or occur in coincidence with the acceleration of additional electrons. One case is presented in which a normal slope radio burst at 600 MHz occurs in coincidence with the peak of an X-ray spike to within 0.1 s. If the coincidence is not merely accidental and if it is meaningful to compare peak times, then the short delay would indicate that the radio signal was at the harmonic and that the electrons producing the radio burst were accelerated at an altitude of 4 × 10⁹ cm. Such a short delay is inconsistent with models invoking cross-field drifts to produce the electron beams that generate type III bursts but it supports the model incorporating a MASER proposed by Sprangle and Vlahos (1983).     

Thermal effect on the pulses of the rotating Sun

In this paper, a theoretical investigation is undertaken of the group travel-time for the Sun's pulses to travel from the source of the pulse to the solar surface. For mathematical simplicity, we consider a simple ionized model of the Sun that includes the thermal effect and rotation with uniform angular velocity. The expression for the group travel time gives two terms: the term arising from the linear theory which varies inversely to (2-)^1/2 and the term introduced by the thermal effect which is inversely proportional to (2-)^7/2. The thermal effect variation has been shown and an estimation of the temperature of the medium has been made. Furthermore, the velocity distribution and the amplitude of the magnetic field of the wave, arising from the damping of ionized particles, have been calculated.     

Phenomenological theory of gravitational vacuum

An idea is developed that the vacuum in the gravitational field acquires properties of an elastic medium described by a definite tension _ik . The vacuum is stated to also participate in the formation of the space-time metric, together with the usual matter. So, the matter, vacuum and metric form a complex unity determined by the solution of the field equations. The vacuum may prove to play an essential role in the extremely strong fields existing in superdense celestial bodies. The tensor _ik is not to be identified with the pseudo-tensor of the energy-momentum of the gravitational field the idea of which is preserved.The problem of vacuum is investigated in the case of the central symmetry static field. A number of properties of the tensor _ik is found using the symmetry of the field and comparison with the post-Newton limit. The external and internal problems, as well as the procedure of joining the solutions on the surface of a celestial body, have been formulated. The stellar surface is determined in the usual way:P(r) = 0 whereP is the matter pressure. The theory includes three dimensionless parametersa=p/,b=p / (,p, p are the density of the vacuum energy and of its pressures in the radial and transverse directions) and determining the vacuum elastic properties. Generally speaking, they depend on the valueP/c² in the stellar centre where is the mass density. From general physical considerations it is shown that 0 1 + lim _P (l/q). The field equations are solved for the simple version of the theoryb=–a. There are solutions corresponding to superdense celestial bodies with masses considerably exceeding that of the Sun.     

Differential rotation in a solar-driven quasi-axisymmetric circulation

We consider the concept of a quasi-axisymmetric circulation to explore the global scale dynamics of planetary atmospheres. The momentum and energy transport processes in the smaller scales are formulated in terms of anisotropic eddy diffusion. In the early work of Williams and Robinson (1973) these concepts have been introduced to describe the Jovian circulation. Our study differs in that we adopt a spectral model (with vector spherical harmonics) and consider a linear system; we are also examining a different parameter regime. The troposphere of Jupiter is assumed to be weakly convectively unstable, and the circulation is driven by the fundamental component of solar differential heating with a broad maximum at the equator. Mode coupling arising from the Coriolis action is considered in self consistent form, and momentum and energy are allowed to cascade from lower to higher order modes. With a limited number of spherical harmonics, up to order 40, and with homogeneous boundary conditions, the conservation equations are integrated between the 25 and 10^–5 bar pressure levels. In addition, a simplified single layer model is discussed which, even though heuristic in nature, elucidates and complements the numerical results. Our analysis leads to the following conclusions: (a) For a negative stability, S ₀ = T ₀/r + , the energy transports arising from large scale advection by the meridional circulation can amplify the response to the external heating. This crucially depends on the latitudinal structure of the circulation, so that banded wind fields with equatorial zonal jets are preferentially excited. (b) With a negative stability of order S ₀ ~ – 10^–6 K cm^–1, the computed number of positive (and negative) zonal jets is similar to that observed on Jupiter. (c) The observed magnitudes in the zonal wind velocities require that the vertical eddy diffusion coefficient is of the order K _r ~ 3 × 10⁵ cm² s^–1, which in turn is consistent with the observed outward flux of energy from the planetary interior (F K _r S ₀ ); this diffusion rate is also of the right order of magnitude to obey mixing length theory. (d) The ratio between the horizontal and vertical eddy diffusion coefficients (relative mixing factor) is of critical importance. If it is too large ( 10⁵), differential rotation or alternating zonal jets cannot be maintained; if it is too small ( 10⁴), the equator tends to corotate. The intermediate value of order R ~ 5 × 10⁴ is again consistent with mixing length theory. (e) With the above constraints on the transport coefficients, the flow is quasigeostrophic. (f) The meridional circulation is multicellular and of the Ferrel-Thomson type. It is consistent with the observed cloud striations in the Jovian atmosphere. (g) In the stable stratosphere at higher altitudes the fundamental component, directly driven by the Sun, dominates. The circulation degenerates, and broad, positive zonal jets develop at middle latitudes, resembling the observed wind field in the visible cloud cover of the Venus atmosphere.Applied Research Corporation, Landover, Maryland, U.S.A.     

Oscillations of the Hα emission in solar prominences

The time dependence of Doppler shift and line-center intensity is simultaneously observed for the H emission of three solar prominences, each one during about two hours. Doppler oscillations with periods near one hour and amplitudes between 1 and 2 km s^–1 are conspicuously visible in the recordings of all three prominences. Fourier analysis yields periods of 50, 60, and 64 min, as well as slight indications of short periods near 3 and 5 min. No oscillations are found in the line-center brightness.     

Radar observations of asteroid 1580 Betulia

Radar observations of the asteroid 1580 Betulia, made at a wavelength of 12.6 cm, show a mean radar cross section of 2.2 ± 0.8 km² and a total spectral bandwidth of 26.5 ± 1.5 Hz. Combining our bandwidth measurements with the optically determined rotation period sets a lower limit to the asteroid's radius of 2.9 ± 0.2 km.     

On the influence of mass loss and convective overshooting on the evolution of massive stars

Evolution of massive stars losing mass with the rateM H L/V C is computed (for =1,2,7). It is shown that observed mass loss rates correspond to 0.3 and, therefore, mass loss by stellar wind cannot play any significant role in the evolution of normal massive stars. However, for several types of massive stars (WR, OH/IR, X-ray sources) enhanced mass loss explains their peculiar features. Computations of evolutionary sequences of massive stars with convective overshooting taken into account (as a formal increase of the convective core) show that a significant broadening of the hydrogen-burning band in the H-R diagram may be obtained.     

On the infrared observations of stellar flares

In connection with the appearance of the first results of infrared observations of stellar flares, a more elaborate analysis ofnegative infrared flares as a phenomenon, predicted by the fastelectron hypothesis, has been carried out. As a result, the wavelength regions of negative flares are established for the stars of different spectral types as well as the calculated amplitudes of the negative flares (Tables I and II). The analysis of the infrared observations (c.f. Kilyachkoet al., 1978) lead to the following conclusions:

1. The negative infrared flares discovered around 8000 Å is not in agreement with the theory in the case of the flare star UV Cet. Some traces of negative flares have been noted for a number of less powerful flares of EV Lac.
2. The amplitudes of the recorded positive flares of UV Cet and EV Lac on λ8000 Å are in good agreement with the magnitudes predicted by the fast-electron hypothesis (non-thermal bremsstrahlung).
3. In the future the negative flares around 8000 Å should be looked for in early-type flare stars of types M0-K5.
4. For a positive discovery of negative flares, future observations must be carried out in the wavelength region of 1–3 μm.