On symmetrical planetary corotations

Exact corotations are equilibrium points in the phase space of the asteroidal elliptic restricted problem of three bodies averaged over the synodic period, at a mean-motions resonance. If the resonant critical angle is =(p+q) _jup –p–q, exact corotations are double resonant motions defined by the conditionsd/dt=0 andd(– _jup )/dt=0. The first condition is characteristic of the periods resonance(p + q) : p and the second one is a secular resonance equivalent to that usually known as thev ₅-resonance. This paper presents the symmetric solutions =0 (mod ), = _jup (mod ). Corotations have a coherence property which is unique in non-collisional Celestial Mechanics: An elementary calculation shows that, in the neighbourhood of these solutions, the motions cluster aroundp independent longitude values and are, in each cluster, as close together as and are close to the equilibrium values.     

The influence of the sunspot model on the Li-abundance

The dependence of the Li-abundance on the equivalent width of the Li-resonance doublet at 6708 Å is calculated for different umbral models. The choice of the model strongly influences the deduced Li-abundance (up to a factor 8 or log _Li = 0.9) even when using recent umbral models. Detailed discussion of the observations and reduction with the most suitable umbral model (Stellmacher and Wiehr, 1970) leads to an abundance of log _Li = 1.1±0.05 (in the log _H = 12.0 scale).     

Evolution of Migrating Planet Pairs in Resonance

Numerical simulations of the evolution of planets or massive satellites captured in the 2/1 and 3/1 resonances, under the action of an anti-dissipative tidal force. The evolution of resonant trapped bodies show a richness of solutions: librations around stationary symmetric solutions with aligned periapses ( = 0) or anti-aligned periapses ( = ), librations around stationary asymmetric solutions in which the periapses configuration is fixed, but with taking values in a wide range of angles. Many of these solutions exist for large values of the eccentricities and, during the semimajor axes drift, the solutions show turnabouts from one configuration to another. The presented results are valid for other non-conservative anti-dissipative forces leading to adiabatic convergent migration and capture into one of these resonances.     

Stability properties for encounterless self-gravitational stellar gas and plasma

The stability properties of the collisionless plasma and encounterless stellar gas described by the Vlasov equations are studied. The introduction of the multiple Water Bag model allows, for one-dimensional plane geometry, a treatment of the general case and removes some of the difficulties connected with the formulation of the energy variation. From this last result it can be deduced that both plasma and stellar systems steady state described by a monotonically decreasing distributionF() are stable. The demonstration is extended to the spherically symmetric case for self-gravitating gas. Next the constraint of a monotonically decreasingF() is relaxed and it is supposed that the instability appears through the point =0. This is known to be true for some type of plasma instabilities (two streams) but is a simple working hypothesis in the gravitational case. For this marginal mode theN bags equations degenerate into a single wave equation and the stability of the system is given by the sign of the eigenvalues of a Schroedinger type operator. A simple physical picture is obtained for the plasma case where the quantitity (dF/d) dV (the square of the local maximum wavenumber of instability) is introduced. A virtual variation of this quantity indicates if the initial steady state was stable or unstable.     

Dimensional Analysis of the Flare Distribution Problem

Dimensional analysis is used to derive the distribution of solar flare energies,p() = A-^3/2, in accordance with recent observational and numerical results. Several other scalings, notably _fl ² , where _fl is the flare duration, are obtained as well.     

Rigorous estimates for the series expansions of Hamiltonian perturbation theory

In the present paper we prove a theorem giving rigorous estimates in the problem of bringing to normal form a nearly integrable Hamiltonian system, using methods of classical perturbation theory, i.e. series expansions in the small parameter . For any order of normalization, we give a lower bound _* ^r for the convergence radius of the normalized Hamiltonian, and a greater bound for the remainder, i.e. the non normalized part of the Hamiltonian. As an application, we consider the case of weakly coupled harmonic oscillators with highly nonresonant frequencies and show how, by optimizing, for fixed , the orderr of normalization, one gets for the remainder a greater bound of the formAe ^–(*₁/) ^a , with positive constantsA,a and ₁ ^* exponential estimate of Nekhoroshev's type.     

The solar abundance of thorium and lead

Two new Th ii lines have been identified in the spectrum of the solar photosphere. The abundance derived from these lines together with the previously known Th ii line at 4019 Å, is log _Th = 0.85 ± 0.20 in the log _H = 12.00 scale. Analysis of three Pb i lines in the photospheric spectrum resulted in an abundance of log _pb = 1.90 ± 0.10. The solar Th/Pb ratio is: _Th/ _Pb = 0.09 _-0.005 ^0.09 .     

Analysis of spectra of α CMi and α Cen A observed with the orbiting stellar ultraviolet spectrophotometer S59 in ESRO's TD1A satellite

Ultraviolet spectra of CMi and Cen A taken with moderate spectral resolution (approx. 1.8 Å) are used to analyse whether a determination of stellar chemical abundances of Fe and Cr and of the photospheric parameters is possible. For CMi, for which good spectral data are available, we findT _eff=7660±110 K; logg _eff=3.05±0.1. Further, log(Fe)=–0.06±0.09; log (Cr)=–0.01±0.09 with regard to standard (solar) abundances. For Cen A the resulting data — particularly the photospheric ones — are less certain, but it seems that the Fe abundance may be smaller than the standard value.     

Поле излучения в полубесконечной атмосфере, содержащей источники энергии

, , , , . , , . , , - - ( , ..). - .     

On the solution of the radiative transfer equations for polarized radiation

A general formalism is presented to obtain an analytical solution of the radiative transfer equations for polarized radiation when the absorption Mueller matrix for the Stokes parameters is constant along the ray-path. The formalism is then applied to find an analytical approximation of the Stokes parameters profiles for a typical chromospheric line having an optical-depth dependence of the source function of the form S() = ( + )^1/2(1 + )^1/2.     

Implications of a strongly peaked polar magnetic field

Using the flux-transport equation in the absence of sources, we study the relation between a highly peaked polar magnetic field and the poleward meridional flow that concentrates it. If the maximum flow speed _m greatly exceeds the effective diffusion speed /R, then the field has a quasi-equilibrium configuration in which the poleward convection of flux via meridional flow approximately balances the equatorward spreading via supergranular diffusion. In this case, the flow speed () and the magnetic field B() are related by the steady-state approximation () (/R)B()/B() over a wide range of colatitudes from the poles to midlatitudes. In particular, a general flow profile of the form sin ^p cos ^q which peaks near the equator (q p) will correspond to a cos ⁿ magnetic field at high latitudes only if p = 1 and _m = n /R. Recent measurements of n 8 and 600 km² s^–1 would then give _m 7 m s^–1.     

Exact solutions in Jordan-Brans-Dicke homogeneous universes I

Spatially homogeneous, anisotropic Bianchi types I-II-III-V-VI_o-VI_h and Kantowski-Sachs (KS) are shown to have perfect fluid solutions in Jordan-Brans-Dicke (JDB) cosmological theory. All the solutions obey the relation =a²+b+c, where and are the re-scaled energy density and the re-scaled scalar field, respectively, and is a time parameter. This relation is derived in Bianchi type-I and gives rise to the general solution for this model universe. In the remaining Bianchi types this same relation is shown to hold as well; and new solution, some of which do not possess locally rotational symmetry, are obtained.     

The eclipsing system of epsilon Aurigae and its possible relevance to the formation of a planetary system

Recent observations of the eclipsing system of Aurigae converge to a conclusion that its secondary (invisible) component constitutes a flat disc, some 40 AU across, which is semitransparent, of constant optical depth, and dims light non-selecting without a trace of polarization. Its constituent particles must, therefore, be large in comparison with the wavelength of observation — probably greater, on the average, than 10 ; with no upper limit imposed by the observations. The mass of this disc appears to be no less than 20 ; and its mean temperature, approximately 500K.The primary component of Aurigae is an F2 Ia supergiant, probably less than one million years old; while its less massive (and, consequently, less evolved) companion has not yet reached a stellar stage. The external characteristics of this disc-like companion appear to approximate the properties that have frequently been postulated as pre-requisites for the formation of a planetary system. A hypothesis is put forward that, in the secondary component of Aurigae, we witness at present, an evolutionary process that may result in the formation of a planetary system very much more massive than our own in the astronomically near future.With a possible exception of S Doradus, which according to Gaposchkin (1943) is an eclipsing variable with a period of 40.2 y.     

Перенос поляризации излучения В магнитоактивной космической плазме

u , . , .. (1.10), (1.2) ( (1.2)) . (1964) . (1.10), , , , (1.13). , , S _iq ,R _iglm ,K _iqlm (1.10) . , . . , (1.3), (2.3); (2.8)–(2.10). , , , , z (2.20), .. , , (. (2.15)). (K _{e, 0} ) . ^S , ( (2.24)). (2.24a) ^S ±/4. , , (K _{e, o}<0). L, — , , ; , . .     

О механззме оптического, рентгеновского и гамма-излучения пульсара в краБе

, , . , . ( , , ), - qqi . - ; , - . , , .     

О влиянии флукаций электронной концентрации на меру дисперсии и мету вращения

, (DM) (RM). , DM RM N _e = n _e ds. M _e = n _e H cos ds ; . Lerche (1970a, b) , DM RM N _e M _e . .     

A nonlinear tensor field and the second metric tensor

In our preceding paper {see [L. Sh. Grigorian and S. Gottlöber, Astrofizika (in press)]} we investigated a self-gravitating system consisting of a scalar field and a linear tensor field _ik= _ki with minimal coupling and with allowance for the action of vacuum polarization effects. In the present paper we investigate the case of a nonlinear tensor field _ik. The action S ⁽⁾ of the field _ik is determined by the difference R_ik — _ik, where R_ik is the space-time Ricci tensor and Rik is the analogous quantity constructed using the metric _ik=g_ik+_ik induced by _ik ( is a free parameter). Here S ⁽⁾ coincides with the previously known expression for the action of a linear field _ik. Equations of motion are derived for _ik in curved space-time. The energy-momentum metric tensor, determining the contribution of _ik to the gravitational field equations, is calculated.Translated from Astrofizika, Vol. 39, No. 1, pp. 135–144, January-March, 1996.     

The distribution of the angular momenta of galaxies

Since the average relation between the angular momentaP and the massesM of galaxies can be represented by a power lawPM , we can define a relative angular momentum =P/M (or a constant timeP/M ). For a random motion picture within protogalaxies, should follow a Maxwellian distribution and consequently the dispersion of log should be 0.210.For the reasonable range of ( to 2), the limited sample of galaxies with known dynamical parameters gives between and 1 times the Maxwellian value. For the plausible special case =2 the reciprocal of the maximum rotational velocityv _m is already a measure of and the larger sample ofv _m-values not only yields the Maxwellian but, moreover, shows the shape of the distribution.

---

PM , =constP/M . , (lg )=0.210. 7/42, . =2 v _m- .

     

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.     

Solar isotopic composition and abundance of europium

High resolution spectra of six photospheric Eu ii lines have been studied using the method of spectrum synthesizing. The isotope ratio is found to be Eu₁₅₃/Eu₁₅₁ = (48 ± 6)/(52 6) and the solar abundance of europium equals log _Eu = 0.7 ± 0.2 in the log _H = 12.00 scale.