On the influence of gradients in the angular velocity on the solar meridional motions

If fluctuations in the density are neglected, the large-scale, axisymmetric azimuthal momentum equation for the solar convection zone (SCZ) contains only the velocity correlations and where u are the turbulent convective velocities and the brackets denote a large-scale average. The angular velocity, , and meridional motions are expanded in Legendre polynomials and in these expansions only the two leading terms are retained (for example, where is the polar angle). Per hemisphere, the meridional circulation is, in consequence, the superposition of two flows, characterized by one, and two cells in latitude respectively. Two equations can be derived from the azimuthal momentum equation. The first one expresses the conservation of angular momentum and essentially determines the stream function of the one-cell flow in terms of : the convective motions feed angular momentum to the inner regions of the SCZ and in the steady state a meridional flow must be present to remove this angular momentum. The second equation contains also the integral indicative of a transport of angular momentum towards the equator.With the help of a formalism developed earlier we evaluate, for solid body rotation, the velocity correlations and for several values of an arbitrary parameter, D, left unspecified by the theory. The most striking result of these calculations is the increase of with D. Next we calculate the turbulent viscosity coefficients defined by whereC _ro ⁰ and C _o ⁰ are the velocity correlations for solid body rotation. In these calculations it was assumed that ₂ was a linear function of r. The arbitrary parameter D was chosen so that the meridional flow vanishes at the surface for the rotation laws specified below. The coefficients v _ro ⁱ and v _0o ⁱ that allow for the calculation of C _ro and C _0o for any specified rotation law (with the proviso that ₂ be linear) are the turbulent viscosity coefficients. These coefficients comply well with intuitive expectations: v _ro ¹ and –v _0o ³ are the largest in each group, and v _0o ³ is negative.The equations for the meridional flow were first solved with ₀ and ₂ two linear functions of r ( ₀ ¹ = – 2 × 10 ^–12 cm ^–1) and ( ₂ ¹ = – 6 × 10 ¹² cm ^–1). The corresponding angular velocity increases slightly inwards at the poles and decreases at the equator in broad agreement with heliosismic observations. The computed meridional motions are far too large ( 150m s^–1). Reasonable values for the meridional motions can only be obtained if _o (and in consequence ), increase sharply with depth below the surface. The calculated meridional motion at the surface consists of a weak equatorward flow for gq < 29° and of a stronger poleward flow for > 29°.In the Sun, the Taylor-Proudman balance (the Coriolis force is balanced by the pressure gradient), must be altered to include the buoyancy force. The consequences of this modification are far reaching: is not required, now, to be constant along cylinders. Instead, the latitudinal dependence of the superadiabatic gradient is determined by the rotation law. For the above rotation laws, the corresponding latitudinal variations of the convective flux are of the order of 7% in the lower SCZ.     

The dependence of the frequency spectra of the interplanetary magnetic-field fluctuations on the direction of the mean field

The frequency spectra of the interplanetary magnetic field fluctuations are the projection of their wavenumber spectra onto one dimension. Only the frequency spectra can be measured by spacecrafts. It is studied how their measured size depends on the direction of the mean fieldB ₀, which structures the symmetry of the fluctuations relative to the solar wind system. It is specialized for the slab model, Alfvén waves, magneto-acoustic waves and the isotropic case. For the slab model the frequency spectra are proportional to , whereq is the spectral index and the angle betweenB ₀ and the radial direction. For the diffusion coefficientK _TT the relation holds.     

Synchronization features of the magnetic nova V1500 Cyg

An analysis of an eleven-year photometric study of the first magnetic nova V1500 Cyg from observations made at the Crimean Observatory is presented. The data indicate the existence of a beat period caused by rotational-orbital asynchronization as well as its increase with time. The current rotational period of the primary component — a magnetic white dwarf — was calculated for each year by using the current values of the beat period and a constant value for the orbital period. It is shown that rapid synchronization of the components has not occurred uniformly with time: the rate of increase of the rotational period of the white dwarf was during 1977–1979 and over the next ten years. This would lead to synchronization of the rotational and orbital periods over about 230 year if remains constant at 2.7 · 10^–8.Translated fromAstrofizika, Vol. 39, No. 2, pp. 193–199, April–June, 1996.     

Epstein weight functions for non-radial oscillations of polytropes

Weight functions for the determination of the periods of linear adiabatic non-radial oscillations have been calculated in the same manner as Epstein's classic treatment of purely radial oscillations. Quadrupole (l=2) oscillations for thef and lower orderp andg-modes were considered. One group of static models were polytropes in the range 1.0n4.0 with ; thus included were configurations that were convectively stable, unstable and neutrally stable throughout. Another group consisted ofn=3.0 polytropes with convective shells or convective cores; ₁ was set at different values in each region in order to produce stability ( ) or instability ( ). The weight function provides a pictorial means for assessing the relative importance of each region of a given static model with respect to generating a given non-radial mode.     

The light curved in the CM field

In this paper we introduce the CM field in Sections 2 and 3 based on the paper by Wang and Peng (1985), and calculate the light curved in the CM field in Section 4. The result shows thatP makes _CM larger than _C at , and smaller at . Under a special circumstance which source, CM lens, and observer are in the same line, if we get | ₀₌₀ , and | _=/2 , we can determine theP(M) andQ(M) of the CM lens,M is the mass of the CM lens.     

The critical and the saturation content of magnetic monopoles in rotating relativistic objects

Both the critical content _c ( N _m /N _B , whereN _m ,N _B are the total numbers of monopoles and nucleons, respectively, contained in the object), and the saturation content _s of monopoles in a rotating relativistic object are found in this paper. The results are:

Charged particle diffusion in the presence of Alfvén waves: The perpendicular particle flux

The diffusion of charged particles through a weak stochastic electro-magnetic field which is superimposed on a constant background magnetic field is considered. The stochastic electromagnetic fields are assumed to consist of unpolarized Alfvén waves propagating at arbitrary angles to the direction . When the Alfvén waves are propagating in directions other than and the particle gyro-radius,r _g, is sufficiently large (but may be smaller than the correlation length of the stochastic fields) it is shown that the particle flux perpendicular to the direction is , wherev is the particle speed andf the particle density. The expression forK differs from those calculated by previous authors. For small particle gyro-radii the flux S has a different functional form and is identical to that found by Urch (1977) to describe particle diffusion when the Alfvén waves only propagate in the direction .     

Possible semi-annual variation of the Newtonian constant of gravitation

A possible semi-annual variation of the Newtonian constant of gravitationG is established. For the aphelion and perihelion points of the Earth's orbit we find, respectively,

Fourier analysis of the light curves of eclipsing variable stars

The aim of the present paper is to find the eclipse perturbations, in the frequency-domain, of close eclipsing systems exhibiting partial eclipses.After a brief introduction, in Section 2 we shall deal with the evaluation of thea _n ^(l) integrals for partial eclipses and give them in terms ofa ₀ ⁰ ,a ₀ ⁰ (of the associated -functions) and integrals; while Section 3 gives the eclipse perturbations arising from the tidal and rotational distortion of the two components. The are given for uniformly bright discs (h=1) as well as for linear and quadratic limb-darkening (h=2 and 3, respectively).Finally, Section 4 gives a brief discussion of the results and the way in which they can be applied to practical cases.     

Simulations of cosmic-ray particle diffusion

The diffusion of charged particles in a stochastic magnetic field (strengthB) which is superimposed on a uniform magnetic fieldB ₀ k is studied. A slab model of the stochastic magnetic field is used. Many particles were released into different realizations of the magnetic field and their subsequent displacements z in the direction of the uniform magnetic field numerically computed. The particle trajectories were calculated over periods of many particle scattering times. The ensemble average was then used to find the parallel diffusion coefficient . The simulations were performed for several types of stochastic magnetic fields and for a wide range of particle gyro-radius and the parameterB/B ₀. The calculations have shown that the theory of charged particle diffusion is a good approximation even when the stochastic magnetic field is of the same strength as the uniform magnetic field.     

Der offene sternhaufen NGC 2362

The very young open star cluster NGC 2362 was investigated by the strip method on charts of two photographs taken with the 1-m Schmidt telescope of the European Southern Observatory. Up to the limiting magnitudeM _v ^* =5 _. ^m 8 the cluster contains 100 stars and can be described by the Gaussian density law (6). Further results are: Mass = 246 , central mass density ₀ = 43.1 = 246 pc^-3 , radiusR2.6 pc, mean velocity of the stars = 0.64 km s^–1.

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Mitteilungen Serie A.     

3He enrichments by magnetosonic waves in current-driven instabilities

A theoretical model for³He enrichments in solar energetic particles is developed. First, current-driven, electrostatic instabilities that have frequencies ( is the cyclotron frequency of³He) are investigated for a plasma consisting of H,⁴He,³He, and electrons with the density of³He much lower than those of H and⁴He. It is found that in many cases the oblique ion-acoustic waves can have positive growth rates at frequencies and, at the same time, negative growth rates at and at _H. This can occur near the marginal state of the instability. The wave damping at these frequencies is caused by the cyclotron resonances of⁴He and H. The cyclotron damping at is negligible, however, because the abundance of³He is very small. The H cyclotron waves can be unstable at for a wide region of plasma parameters; the electron-to-ion temperature ratio must beT _e /T _H 1.5. To destabilize the₄He cyclotron waves with , high⁴He density and high electron temperature are both required. Then,³He enrichments are studied on the basis of the theory of nonlinear magnetosonic waves, which can promptly accelerate ions. The current-driven electrostatic waves with can enhance fluctuation velocities of³He. Thus, in the presence of these waves, magnetosonic waves can selectively accelerate³He particles to high energies. Finally, cyclotron resonances of heavy ions with the waves or are briefly discussed.     

Linear waves in a radiating and scattering grey medium

The problem on linear waves in a radiating and scattering grey medium is studied using Whitham's method. Analysis of the basic equations distinguishes two limiting cases: the one is theequilibrium case in which the energy exchange between the gas and radiation plays an essential role, and the other is theScattering case in which the effect of energy exchange is negligible. A new type ofradiation acoustic wave with the speed is found in the scattering case. The governing equations for linearized one-dimensional flow are reduced to one equation of radiative acoustics valid to order 1/c, and the criterion for the two limiting cases is derived from studying this equation. The harmonic solution is analytically studied to show that theeffective optical depth corresponding to the wavelength of perturbation gives the measure of the interaction between the gas and radiation. When _eff1, the sound speeda _g ² =P _g / and the propagating speed of radiative disturbancea _f ² =fc ² appear as the modified classical and radiation-induced modes respectively, wheref is the Eddington factor. When _eff1, the isentropic sound speeda _s ² =(P _g +P _r / appears in the equilibrium case, and the radiation acoustic speeda _A ² appears in the scattering case. The dispersion relation of the harmonic solution is numerically calculated. The result shows that the wave pattern depends critically on the ratio=P _g /(P _g +P _r ). When , the speeda _S anda _A arise from the modified classical mode, and when , they originate from the radiation-induced mode.     

The large-number hypothesis and the Earth's expansion

The equation of state of the terrestrial material obtained from seismic data is adopted to construct three zone earth models under hypothesis of variable constant of gravityG as proposed by Dirac. Three hypotheses are investigated: variableG without creation, creation such thatm (mass) G ^–1, and multiplicative creation,mG ^–2. It is shown that, with the currently accepted value of the Hubble constant, , and for each hypothesis. On the multiplicative creation, the Earth radius would have been 5100 km, which is in agreement with estimate by some geophysicists.     

K emission-line widths and the solar chromosphere

Closely spaced microphotometer tracings parallel to the dispersion of one excellent frame of a K-line time sequence have been utilized for a study of the nature of the K_2v , K_2R intensities in the case of the solar chromosphere. The frequency of occurrence of the categories of intensity ratio are as follows: per cent; per cent; per cent; per cent; per cent. Two types of absorbing components are postulated to explain the pattern of observed K_2v , k_2R intensity ratios. One component with minor Doppler displacements acting on the normal K₂₃₂ profile, where K_2V >K_2R , produces the cases K_2v K_2R , K_2v = K_2R , K_2v <K_2R . The other component arises from dark condensations which are of size 3500 kms as seen in K_2R . They have principally large down flowing velocities in the range 5–8 km/sec and are seen on K₃ spectroheliograms with sizes of about 5000 kms, within the coarse network of emission. These dark condensations give rise to the situation K_2R = 0.K₂-line widths are measured for all tracings where K_2v , K_2R are measurable simultaneously. The distribution curve of these widths is extremely sharp. The K₂ emission source is identified with the bright fine mottles visible on the surface. Evidence for this interpretation comes from the study of auto-correlation functions of K₂ intensity variations and the spacing between the bright fine mottles from both spectrograms and spectroheliograms. The life time of the fine mottling is 200 sec.The supergranular boundaries which constitute the coarse network come in two intensity classes. A low intensity network has the fine mottles as its principal contributor to the K emission. When the network is bright, the enhancement is caused by increased K emission due to the accumulation of magnetic fields at the supergranule boundary. The K₂ widths of the low intensity supergranular boundary agree with the value found for the bright mottles. Those for the brighter network are lower than this value, similar to the K₂ widths as seen in the active regions.It is concluded that bright fine mottling is responsible for the relation, found by Wilson and Bappu, between K emission line widths and absolute magnitudes of the stars.The paper discusses the solar cycle equivalents that stellar chromospheres can demonstrate and indicates a possible line of approach for successful detection of cyclic activity in stellar chromospheres.     

On the stability of ultrarelativistic stars

This paper present two new theorems on the theory of the stability of highly relativistic stars. Thefirst theorem states that a highly relativistic, spherical star is stable if and only if its adiabatic index (assumed to be constant in the interior regions) is greater than a certain critical value, _crit which depends in a specified way on the high-density equation of state. This critical value is analogous to the Newtonian value , but because of relativistic effects it is typically somewhat larger than . Thesecond theorem shows that at high central densities, the curves of —(binding energy) vs. radius, —E _B (R) for certain hot, isentropic sequences of stellar models must exhibit damped clockwise spirals. This spiraling reflects the onset of instability in one radial mode of pulsation after another as the central density increases along the sequence.     

Coherent Emission Mechanisms in Radio Pulsars

A theory of pulsar radio emission generation, in which the observed waves are produced directly by the maser-type plasma instabilities on the anomalous cyclotron-Cherenkov resonance and the Cherenkov-drift resonance , is capable of explaining the main observational characteristics of pulsar radio emission. The instabilities are due to the interaction of the fast particles of the primary beam and from the tail of the distribution with the normal modes of a strongly magnetized one-dimensional electron-positron plasma. The waves emitted at these resonances are vacuum-like electromagnetic waves that may leave the magnetosphere directly. The cyclotron-Cherenkov instability is responsible for core emission pattern and the Cherenkov-drift instability produces conal emission. The conditions for the development of the cyclotron-Cherenkov instability are satisfied for the both typical and millisecond pulsars provided that the streaming energy of the bulk plasma is not very high γ _p = 5 ÷ 10. In a typical pulsar the cyclotron-Cherenkov and Cherenkov-drift resonances occur in the outer parts of magnetosphere at r _res ≈ 10⁹cm. This theory can account for various aspects of pulsar phenomenology including the morphology of the pulses, their polarization properties and spectral behavior. This revised version was published online in July 2006 with corrections to the Cover Date.     

Non-singular de Sitter universe inR+R 2−2Λ gravity

For the theory described by the action and taking the FRW flat space metric we find an exact non-singular de Sitter model universe exp(t ²), with . It is also proved that the standard general relativity de Sitter cosmology , >0 is also a model of this higher derivative theory of gravity. If the metric is conformally flatS could describe a consistent quantum theory and its classical solutions would correspond to cosmological models in this theory.This work was supported in part by CONACYT grand P228CCOX891723, and DGICSA SEP grant C90-03-0347.     

Radio frequency emission in electron beam-plasma and beam-beam interaction

A linear excitation of electromagnetic modes at frequencies , in a plasma through which two electron beams are contra-streaming along the magnetic field is investigated. This may be a source of the observed emissions at auroral latitudes.     

The spherically-symmetrical trajectories of spin particles in the Schwarzschild field

The motion of spin particles in the Schwarzschild field is examined in this paper. It is shown that Mathisson-Papapetrou equations under additional conditions , where is the Lie derivative of the Killing vector _j , permit only radial motion, motion in the equatorial plane and in the equilibrium points. All these types of motion are considered more in detail.