Об устойчивости лагранжевых решений пространственной эллиптической задачи трех тел

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Stability of the librational triangular points of the three-dimensional elliptic restricted three-body problem is studied. The problem is solved in the non-linear statement at the small values of eccentricity.For all values ofe, , besides ones which correspond to the resonances of the third and the fourth order the librational points are stable taking into account the terms up to the fourth order in the normal form of the Hamiltonian function of the perturbed motion.At sufficiently smalle and the non-stability in sense of Liapunov has been proved. The approximate equations of the boundary of the stability area in the planee, has been obtained. The cause of the non-stability is an equality of the rotational period of the principal attracting masses in the elliptic orbit and the period of oscillation of indefinitely small mass along the direction perpendicular to the plane of their motion.

     

Particle lifetimes in strong diffusion

The mean lifetime of a particle distribution, driven to isotropy by intense pitch-angle diffusion, is calculated by analytical means for conditions applicable to the Earth's magnetosphere. The resulting algebraic expressions reduce to [64La/35v _c ² (1–)] in the limit of a small equatorial loss cone (half-angle _c ), wherev is the particle speed,L is the magnetic shell parameter,a is the radius of the Earth, and is the particle albedo from the atmosphere at either foot of the field line. Distinction is made in the full expressions for between complete isotropy (caused by strong pitch-angle diffusion all along the field line) and incomplete isotropy (caused by strong diffusion that is localized at the magnetic equator) over the upward hemisphere in velocity space.     

Возможный механизм радиоизлучения пульсаров

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Pitch angle scattering of solar particles: Comparison of ‘particle’ and ‘field’ approach

In the quasi-linear theory of pitch angle scattering the power spectrum of magnetic field fluctuations is related to the shape of the pitch angle diffusion coefficient D(), the absolute value of the mean free path , and the rigidity dependence of the mean free path (R). We discuss these relations in detail during the solar particle event of 11 April, 1978 which was observed on HELIOS-2 at a distance of 0.49 AU from the Sun. Magnetic field measurements obtained during the time of the event are used as a basis for the layer model in which the method of particle trajectories in an actually measured field is used to simulate pitch angle diffusion. The values of D() and based on the trajectory simulation for 100 MeV protons (field approach) are compared with results obtained from solar proton data (particle approach) and with predictions from quasi-linear theory based on the additional assumption of the slab model for magnetic field fluctuations (QLT approach). The time of the event is characterized by a high level of field fluctuations, the observed mean free path of about 0.03 AU for 100 MeV protons is smaller than the average value near 1 AU. Results from the field and particle approaches agree surprisingly well. The remaining difference in the mean free path of about a factor of 2 could be due to tangential discontinuities which are measured by the magnetometer, but not seen by the real particles traveling along the average field. The results from the field and QLT approaches based on the same set of magnetic field measurements differ by about a factor of 4. One of the reasons for this discrepancy is that the conditions for resonance scattering are only marginally valid. In addition, the wave vectors representing Alfvén-type fluctuations may not be totally field aligned. This deviation from the slab model would cause an increase of the theoretically predicted mean free path and lead to better agreement with the other two approaches.     

General-relativistic hierarchical cosmology: An exact model

An exact solution of Einstein's equation is stated in which the density (), pressure (p), scale factorS and metric coefficients are functions of only one dimensionless self-similar variable,ct/R, wheret is cosmic time andR is a co-moving radial coordinate. The solution represents a cosmology that begins as a static sphere having R ^–2 and evolves into an expanding model which is pressure-free and has a hierarchical type of density law ( R ^–, approximately, with =a number, 02). It is suggested that this model should supersede the previous models of Wesson and other workers, since it appears to be the simplest cosmology for a hierarchy.     

Non-restricted double-averaged three body problem in Hill's case

A limiting case of the problem of three bodies (m ₀,m ₁,m ₂) is considered. The distance between the bodiesm ₀ andm ₁ is assumed to be much less than that between their barycenter and the bodym ₂ so that one may use Hill's approximation for the potential of interaction between the bodiesm ₁ andm ₂. In the absence of resonant relations the potential, double-averaged by the mean longitudes ofm ₁ andm ₂, describes the secular evolution of the orbits in the first approximation of the perturbation theory.As Harrington has shown, this problem is integrable. In the present paper a qualitative investigation of the evolution of the orbits and comparison with the analogous case in the restricted problem are carried out.The set of initial data is found, for which a collision between the bodiesm ₀ andm ₁ takes place.The region of the parameters of the problem is determined, for which plane retrograde motion is unstable.In a special example the results of approximate analysis are compared with those of numerical integration of the exact equations of the three body problem.

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m ₀,m ₁,m ₂. , m ₀ m ₁. m ₂, m ₁ m ₂ m ₁ m ₂ . , . . , m ₀ m ₁. , . .

     

A coronal loop model for the production of X-ray and radio flares in the RS CVn binary HR 1099

The RS CVn binary stellar system HR 1099 is a source of both X-ray and radio flares. We present here a model of the system in which the two types of flare are produced by the same population of mildly-relativistic ( 10) electrons, injected into a coronal loop. After reviewing possible radiation mechanisms we conclude that, given the probable conditions in the flaring region, the radio emission is gyrosynchrotron radiation and the X-ray emission is thermal bremsstrahlung. The thermal X-ray source must lie in the stellar chromosphere, but the apparent absence of plasma absorption at radio frequencies indicates that the radio source is located high in the coronal loop. Using the relationships given by Dulk and Marsh (1982) for the radio emission from a power-law electron energy spectrum,N() ( - 1)^–, we conclude that 3 7, with 30% of the electron population trapped in the radio source. Some implications of these results for one particular version of the model are discussed.     

О колебаниях хвоста магнитосферы в приБлижении квазигидро динамики

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Solar particle propagation from 1 to 5 AU

A statistical analysis of solar particle events, observed by the GSFC-UNH charged particle detector on board Pioneer 10 and Pioneer 11 from March 1972 to December 1974 (from 1 to 5 AU for each spacecraft), is carried out with the goal of experimentally determining the statistical average interplanetary propagation conditions from 3 to 30 MeV. A numerical propagation model is developed that includes diffusion with a diffusion coefficient of the form k _r =k _o r , convection, adiabatic deceleration, and a variable coronal injection profile. The statistical analysis is carried out by individually analyzing each of five parameters (t _max, (t_max), t ₅, ) that are uniquely defined in a solar particle event. Each of the five parameter data sets were analyzed in terms of both a spacecraft-solar flare connection longitude 50°, and a numerical model that employed a variable exponential decaying coronal injection profile.The five individual parameter analyses are combined with the results that the statistical average radial interplanetary diffusion coefficient from 1 to 5 AU is given by k _r = (1.2 ± 0.4) × 10²¹ cm² s^-1 with = 0.0± 0.3 for 3.4 to 5.2 MeV protons and k _r = (2.6 ± 0.6) × 10²¹ cm² s^-1 with () = 0.0± 0.3 for 24 to 30 MeV protons. Using the classical relationship for the radial scattering mean free path _r, i.e. k _r = _r/3, we obtain _r = 0.09 ± 0.03 AU and 0.075 ± 0.020 AU for the low and high energy data, respectively. These results show, from 1 to 5 AU and from 3 to 30 MeV, that _r is both independent of radial distance and approximately independent of rigidity (for _r~P , where P = rigidity, = -0.15 ± 0.20).The above diffusion coefficients are inconsistent With both the predictions of the diffusion coefficient from present theoretical transport models and with the diffusion coefficient used in modulation studies at low energies.     

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.

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

     

The configuration of a thin,rotating self-similar disk in general relativity

Einstein's equations for a rotating pressure-free space-time are reduced to a system of four first-order non-linear ordinary differential equations in one self-similar dimensionless variable. Numerical results are given for the vacuum solution. A compatible thin disk can be specified by a surface density and an angular velocity . Self-similarity as a statement of the absence of scales implies that and can be written as=c ²/4Gr, =c/r, and demands that and be pure numbers.     

The scattering of light by dielectric particles

We consider homogeneous particles with a frequency-dependent index of refractionn =n +in = 1 +(), ()1, in an outer electromagnetic field. From general considerations we derive an expression for the total scattering cross-section of these particles. We calculate the efficiency factor for the sphere, the infinite circular cylinder, and for an ellipsoidal particle with the main axesa=1,b=2,c=1. In contrast with the ray approximation, the present method can be used to calculate the polarization of the scattered light from ellipsoids.     

Пульсар в краБе: замагниченные трещины в коре как ключ к механизмам истечения вещества, радио- и высокочастотного излучений

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Взаимодействие вещества и излучения В Горячей модели вселенной

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In this paper we continue the work of Weymann, investigating the causes of distortion of the spectrum of the residual radiation from the Planck curve. We discuss the distortion to the spectrum, resulting from recombination of primeval plasma.We then derive an analytic expression for the distortion to the equilibrium spectrum due to Compton scattering by hot electrons. On the basis of the observational data we conclude that a period of the existence of neutral hydrogen is inescapable in the hot model of the universe. It is concluded that any injection of energy att>10¹⁰ sec (red shiftz<10⁵) give the distortions of the equilibrium spectrum.

     

Photoelectrons and solar wind/lunar limb interaction

It is suggested that boundary conditions for solar wind/lunar limb interactions are active. The whole-Moon limb does not evoke a shock cone because warm (13 eV/electron) solar wind electrons are replaced by cool (2 eV/electron) photoelectrons that are ejected from the generally smooth areas of the lunar terminator illuminated at glazing angles by the Sun. A localized volume of low thermal pressure is created in the solar wind by these cool photoelectrons. The solar wind expands into this turbulence-suppressive volume without shock production. Conversely, directly illuminated highland areas exchange hot photoelectrons (> 20 eV/electron) for warm solar wind electrons. The hot electrons generate a localized pressure increase (p) in the adjacent solar wind flow which evokes a shock streamer in the solar wind. Shock streamers are identifiable by a coincident increase in the magnitude (B p) of the solar wind magnetic field immediately external to the lunar wake. Shock occurrence is controlled by lunar topography, solar activity in the hard ultraviolet (> 20 eV), solar wind electron density and thermal velocity, and the intensity of the solar wind magnetic field.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.     

The effect of chemical abundance oscillations on the pulsational properties of A 5M ⊙ hydrogen-helium star

A model of a first generation intermediate star of 5M , with Z=0 has been considered. The model is at an advanced stage of its evolution and has a double shell burning. It burns helium in the inner shell, and hydrogen, via CNO cycle, in the outer shell. =(log/log) _T and _T =(log/logT) were computed allowing for the oscillations of the relative mass abundance of the reagents in nuclear reactions. Including =(log/log) _T and =(log/logT) of mean molecular weight and the effect of the oscillations of abundances due to nuclear reactions, stability was studied. Contrary to the results of the static calculations, we found that instability due to the excitation mechanism provided by the high temperature sensitivity of energy generation rate propagates up to the surface. Thus the model in question was found to be unstable against radial adiabatic pulsations, in its fundamental mode.     

Cold plus hot dark matter and structure formation of the universe

Cold plus hot (neutrino) dark matter models are studied and compared with the tilted cold dark matter models (which have a non-Zel'dovich initial density perturbation spectrum). For the hybrid dark matter models, a simpler treatment for the relativistic neutrinos is presented. The numerical results of this treatment are shown to be in good agreement with those given by other authors. Comparing the theoretical and the observational results of the quadrupole fluctuations of the cosmic background radiation and the large-scale velocity field of galaxies, the hybrid dark matter models require a fraction of neutrino density 0.3, a fraction of cold dark matter _c 0.7 and a number of massive neutrino speciesN = 1 for the case of Hubble's constantH ₀ = 50 km s^–1 Mpc^–1. The distribution of comoving number density of quasars at high redshifts is studied using the Press-Schechter theory. The calculations show that the hybrid dark matter model ( _c 0.7, 0.3) and the tilted CDM model withn = 0.7 0.8 both account for the observed quasar abundance at high redshift.     

Determination of the total amount of hydrogen atoms in a quiescent prominence

A brief quantitative review of the determination of the chemical composition of the Sun and stars is given. The method of estimation of the total amount of hydrogen atoms in a prominence is considered.The values of relative abundances of some infrequent elements in the solar atmosphere are refined using metal emission lines in the spectrum of a quiescent prominence. The most probable values of relative abundances for itrium _Y1×10^–9, zirconium _Zr2×10^–9, and scandium _Sc3.8×10^–9 are derived.     

The proton-proton reaction and related reactions in an intense magnetic field

The reaction rates for the proton-proton reaction and the related electron capture reaction in a strongly magnetized relativistic electron gas of arbitrary degree of degeneracy are computed. The proton-proton reaction rates are unaffected by the presence of the magnetic field for field strengths up to the critical valueH _q =m ² c ³/e=4.414×10¹³G. For fields greater thanH _q , the proton-proton reaction rates are enhanced linearly with (=H/H _q ).The PeP reaction is investigated in detail for a wide range of temperatures, densities and magnetic field strengths that are of interest. The main results are as follows: In the non-degenerate regime the reaction rates are significantly reduced for high temperatures (T ₉5) and low fields (1). For instance, _pep(H)=0.04 _pep(O) at =10^–3,T ₉=10. For relatively high fields (>1) and low temperatures (T ₉2), the reaction rates are enhanced approximately linearly with . In the complete degenerate regime the reaction rates are reduced up to one-third of the field-free value for moderate densities (₆/_e10). At high densities (₆/_e10) the reaction rates are unaffected by the magnetic field.     

A study of the young open cluster NGC 6611

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