The symmetric tensor field in the relativistic theory of gravitation

The system of a self-gravitating scalar field is frequently used in inflationary cosmological models. In the present paper we study a more complicated system containing an extra linear tensor field _ik=_ki with minimal coupling. We determine five of the six free parameters that occur in the most general expression for the actionS of this field. In doing so we assume that in flat space-time the field _ik must be invariant under gauge transformations. In a special case theS found becomes a known expression for the action of a massless tensor field _ik. We compute the metric energy-momentum tensor that determines the contribution of _ik to the Einstein equations. We also exhibit the equations of motion of _ik in curved space-time.Translated fromAstrofizika, Vol. 38, No. 3, 1995.     

An integrable case of a rotational motion analogous to that of Lagrange and Poisson for a gyrostat in a Newtonian force field

The scope of the present paper is to provide analytic solutions to the problem of the attitude evolution of a symmetric gyrostat about a fixed point in a central Newtonian force field when the potential function isV ⁽²⁾.We assume that the center of mass and the gyrostatic moment are on the axis of symmetry and that the initial conditions are the following: (t ₀)=₀, (t ₀)=₀, (t ₀)=(t ₀)=₀, ₁(t ₀)=0, ₂(t ₀)=0 and ₃(t ₀)= ₃ ⁰ .The problem is integrated when the third component of the total angular momentum is different from zero (B ₁ 0). There now appear equilibrium solutions that did not exist in the caseB ₁=0, which can be determined in function of the value ofl ₃ ^r (the third component of the gyrostatic momentum).The possible types of solutions (elliptic, trigonometric, stationary) depend upon the nature of the roots of the functiong(u). The solutions for Euler angles are given in terms of functions of the timet. If we cancel the third component of the gyrostatic momentum (l ₃ ^r =0), the obtained solutions are valid for rigid bodies.     

Period distributions in pulsating and binary stars

We analyze the hypothesis of quantization in bands for the angular momenta of binary systems and for the maount of actionA _c in stable and pulsating stars. This parameter isA _c=Mv _eff R _eff, where the effective velocity corresponds to the kinetic energy in the stellar interior and the effective radius corresponds to the potential energyGM ²/R _eff. Analogous parameters can be defined for a pulsating star withm=M where is the rate of the massm participating in the oscillation to the total massM andv _osc,R _osc the effective velocity and oscillation radius.From an elementary dimensional analysis one has thetA _c (energy x time) (period)^1/3 independently ifA _c corresponds to the angular momentum in a binary system, or to the oscillation in a pulsating star or the inner energy and its time-scaleP _eff in a stable star.From evolving stellar models one has that P _effP _eff(solar)1.22 hr a near-invariant for the Main Sequence and for the range of masses 0.6M <M<1.6M .With this one can give scalesn _k=kn ₁ withk integers andn ₁=(P/P ₁)^1/3 withP ₁=P _eff1.22 hr. In these scales proportional toA _c, one sees that the periods in binary and pulsating stars are clustered in discrete unitsn ₁,n ₂,n ₃, etc.This can be seen in pulsating Scuti, Cephei, RR Lyrae, W Virginis, Cephei, semi-regular variables, and Miras and in binary stars as cataclysmic binaries, W Ursa Majoris, Algols, and Lyrae with the corresponding subgroups in all these materials. Phase functions (n _k) in RR Lyrae and Cephei are also associated with discrete levelsn _k.the suggested scenario is that the potential energies and the amounts of actionE _p(t), A_c(t) are indeed time-dependent, but the stars remain more time in determinated most proble states. The Main Sequence itself is an example of this. These most probable states in binary systems, or pulsating or stable stars, must be associated with velocities sub-multiplesc/ _F , given by the velocity of light and the fine structure constant.Additional tests for such a hypothesis are suggested when the sufficient amount of observational data are available. They can made with oscillation velocities in pulsating stars and velocity differences of pairs of galaxies.     

Cosmological parameters and redshift periodicity

This work is the continuation of the search for such a cosmological model using which the observed redshift distribution of galaxies in the sample of Broadhurstet al. (1990) turns out to be maximally periodic in the calculated spatial distance. In a previous work, Paálet al. (1992) have demonstrated that among theflat models with non-negative cosmological constant (e.e., vacuum density) the one with a vacuum: dust ratio 2:1 provides the optimum. Now we extend that study to the case of arbitrary space curvature and find equally good periodicity in a surprisingly wide range of models. By use of the dimensionless parameters ₀= ₀/ _crit and ₀=/3H ₀ ² acceptable periodicity is obtained forall points of the parameter plane within the strip between the parallel lines 0.83₀–0.30< ₀(₀)<0.83₀+0.85(₀<1.8), whilst the best periodicities appear along the line ₀=0.83₀+0.39 fitting to the previous optimum at ₀=1/3, ₀=2/3. Any nonpositive value of ₀ gives bad periodicity unless the space curvature is strongly negative and ₀<0.4. Fairly good periodicity is observed only in the range of the deceleration parameter –1.2q ₀<0.2, corresponding to a small or even negative total gravitational attraction and an expansion time-scale longer than usually expected.     

Existence of the continuations in theN-body problem

The method of obtaining the estimates of the maximalt-interval ( _–, ₊) on which the solution of theN-body problem exists and which is such that some fixed mutual distance (e. g. ₁₂) exceeds some fixed non-negative lower bound, for allt contained in ( _–, ₊), is considered. For given masses and initial data, the increasing sequences of the numbers _k , each of which provides the estimate ₊ > _k , are constructed. It appears that if ₊ = +, then .     

Estimation of the clear sky and the ground emissivity in Bahrain

The clear sky emissivity ₀ and the ground emissivity _g in Bahrain is studied. The study reveals that the annual value of ₀ is 0.88 ± 0.039 relating to the maximum and the minimum values in August and February, respectively. Meanwhile, the annual value of _g is 0.338 ± 0.228, where the maximum and the minimum values are in July and January, respectively. These two parameters are related to the transmittance factor .     

Effect of perturbations in Coriolis and centrifugal forces on the stability of libration points in the restricted problem

The location and the stability of the libration points in the restricted problem have been studied when small perturbation and are given to the Coriolis and the centrifugal forces respectively. It is seen that the pointsL ₄ andL ₅ form nearly equilateral triangles with the primaries and the pointsL ₁,L ₂,L ₃ remain collinear. It is further observed that for the pointsL ₄ andL ₅, the range of stability increases or decreases depending upon whether the point (, ) lies in one or the other of the two parts in which the (, ) plane is divided by the line 36-19=0 and the stability of the collinear points is not influenced by the perturbations and they remain unstable.     

Effects of the Sector Structure of the Interplanetary Magnetic Field on Galactic Cosmic Ray Anisotropy

We study the effects of the sector structure of the interplanetary magnetic field (IMF) on the Galactic cosmic ray (GCR) anisotropy at solar minimum by using Global Network neutron monitor data. The hourly neutron monitor data for 1976 were averaged for the positive (+) and negative (–) IMF sectors (+ and – correspond to the antisolar and solar directions of magnetic field lines, respectively) and then processed by the global survey method. We found that the magnitude of the GCR anisotropy vector is larger in the positive IMF sector and that the phase shifts toward early hours. The derived GCR components A _r, A , and A for the different + and – sectors are then used to calculate the angle ( 46°) between the IMF lines and the Sun–Earth line, the solar wind velocity U ( 420 km/s), the ratio of the perpendicular (K ) and parallel (K _||) diffusion coefficients K /K _|| = ( 0.33), and other parameters that characterize the GCR modulation in interplanetary space.     

Cyclotron waves in the solar wind

Cyclotron waves in the solar wind near 1 AU with frequencies well below the electron cyclotron frequency and wavelengths much larger than the electron cyclotron radius but less than the proton cyclotron radius are considered. The cyclotron radii are defined from parallel thermal velocity of electron component and proton component with respect to the interplanetary magnetic field. No LH cyclotron waves are found to propagate for _p < 0, where _p 1 –T _p/T _p is the temperature anisotropy of the proton component with respect to the interplanetary magnetic field. The damping or growth of RH cyclotron waves is found to depend on the frequency range and the temperature anisotropy of the proton component. The RH cyclotron waves are damped in the frequency range _r | _p | _p for _p < 0, where _p is the proton cyclotron frequency. RH cyclotron instabilities occur in the frequency range | _p | _p > _r > | _p | _p /(1– _r ) for _p < 0. The marginal state is at _r =| _p | _p .Abstract presented at theInternational Symposium on Solar-Terrestrial, São Paulo, Brazil, 17–22 June, 1974     

On the value of 'αAR' from Vector Magnetograph data

This investigation is the second of two centering on the parameter =(×B_h)_z/B_z=₀J_z/B_zand its derivation from photospheric vector magnetogram data. While can be evaluated at every spatial position where the vector B is measured, for many reasons it is useful to determine a single value of to parameterize the magnetic complexity of an entire active region, here called _AR(see Leka and Skumanich, 1999). As such, the limitations in today's vector magnetograph data, e.g., finite spatial resolution and limited field of view, may influence any final '_AR' value. We apply three methods of calculating '_AR' to degraded high-spatial-resolution data and find that in general the discrepancies worsen for decreasing resolution compared to the original. We apply the three methods to sub-regions centered on the constituent sunspots for AR 7815. Two of the sub-regions are shown to have magnetic twist with significant magnitude but opposite sign. We show by mosaicing or otherwise combining separate sunspot observations that a measure of _ARcan be calculated which is consistent with a single large field-of-view observation. Still, the _AR0 assigned for the entire active region is an average, and does not accurately represent the magnetic morphology of this flux system. To measure the validity of the _ARparameterization, we demonstrate that, from each method, a relevant quantity can be calculated which describes the 'goodness of fit' of the resulting _AR. Given the spatial variation of (x,y) over an active region, it is suggested that such a second parameter be used either to indicate uncertainty in _ARor as a criterion for data selection, as appropriate.     

Carbon suboxide and the genetic code

Carbon suboxide (C₃O₂) polymers formed in the primitive atmosphere would have produced an organic compound soup of high concentration on the Earth. Various vestiges of C₃O₂ are found in the present genetic scheme, which might suggest that the living system had formed from the polymer soup.     

Detection of CH3D on Titan

We report the detection of ¹³CH₃D in Titan's stratosphere from Cassini/CIRS infrared spectra near 8.7 μm. Fitting simultaneously the ν₆ bands of both ¹³CH₃D and ¹²CH₃D and the ν₄ band of CH₄, we derive a D/H ratio equal to and a ¹²C/¹³C ratio in deuterated methane of , consistent with that measured in normal methane.     

Charged particle transport in turbulent magnetic fields: The perpendicular diffusion coefficient

The diffusion of charged particles in a static turbulent magnetic field, which is superimposed on a constant magnetic fieldB ₀ k, is considered. Previous calculations of the particle flux in a direction perpendicular tok have related the fluxS to the particle number densityf byS = – (f) where is found from the power spectrum of the turbulent magnetic field. It is shown that this formula is inconsistent with the notion, developed by Jokipii and Parker (1969), that the perpendicular particle flux primarily arises because of random-walking of magnetic field lines across the directionk. For a simple example of a turbulent magnetic field it is shown that the above expression forS is incorrect; the particle fluxS is recalculated and a new relationship betweenS andf is found. This new expression forS is shown to be consistent with particle diffusion across the directionk being due to random-walking of the magnetic field lines.     

Determination of mass-loss rates from the first order momentW 1 of unsaturated P Cygni line profiles

The escape probability method introduced by Sobolev to treat the transfer of line photons is used in order to derive the expressions of thenth order momentW _n (E()/E _c –1)(–₁₂) ⁿ ·d of a P Cygni profile formed in rapidly expanding envelopes around a central point-like source under various physical and geometrical conditions.With the only assumption that there is mass-conservation of the species in the flow, we state for the case of optically thin lines that the relation between the first order momentW ₁ and the quantityM _n (level), first established by Castoret al. (1981) under more restrictive conditions, is in fact independent of the type of velocity fieldv(r) and a fortiori of the distribution adopted for the radial opacity ₁₂ ^r (X). These results also remain unchanged when including collisions (0) and/or an additional rotational velocity fieldv (r) in the expanding atmosphere. We investigate the presence of an underlying photospheric absorption line and conclude that for realistic cases, neglecting this boundary condition to the radiative transfer leads to an underestimate of the mass-loss rate by a factor of about 20%. By means of a three-level atom model, we demonstrate that all results derived for a single line transition equally apply for an unresolved doublet profile providedW ₁ andM _n (level) are calculated with the weighted wavelength _D and total oscillator strengthf _D of the doublet.Considering the occultation and inclination effects caused by the finite size of the central core, we refine the value of the multiplicative constant fixing the ratio ofW ₁ toM _n (level). We show that this relation allows a determination of the mass-loss rate with an uncertainly less than 30%, irrespective of the sizeL _max of the atmosphere and of the limb-darkening affecting the stellar core. Reviewing all possible sources of error, we finally conclude that this method of deriving a mass-loss rate from the analysis of an unsaturated P Cygni profile is very powerful. The total uncertainty affecting the determination ofM _n (level) from the measurement ofW ₁ should be smaller than 60%.     

The bimetric theory of gravitation with a dynamic background metric

We study the bimetric theory of gravitation with background metric _ik. In contrast to the accepted point of view, in which _ik, is a metric given a priori, we assume that _ik is a dynamic variable determined from the condition that the total action of the gravitating system must be an extremum. As a result it turns out that (1) _ik can be described by the Einstein equation in space-time with the metric _ik and (2) the energy-momentum tensor of the graviational field _ik, is the source of _ik. In this sense _ik can be considered a secondary field in relation to g_ik. We determine the conditions for existence of integral covariant conservation laws. Two of the latter have no analogs in the theory with the background metric given a priori.Translated fromAstrofizika, Vol. 37, No. 3, 1994.The author is grateful to the participants in the seminar of the Department of Theoretical Physics at Erevan State University, and also to W. Bleier, K. A. Bronnikov, V. N. Mel'nikov, and G. Yu. Treder for discussions and valuable remarks. The investigations presented in this paper were partly financed by the International Scientific Fund, grant Ph1-262-0902.     

A case of commensurability induced by oblateness

In the three-dimensional restricted three-body problem, it is known that there exists a near one-to-one commensurability ratio between the planar angular frequencies (s _{1, 2, 3}) and the corresponding angular frequency (S ₂) in thez-direction at the three collinear equilibria (L _{1, 2, 3}), which is significant for small and practically important values of the mass parameter (). When the more massive primary is treated as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries, it is established that oblateness induces a one-to-one commensurability at the exterior pointL ₃ (to the right of the more massive primary) and at the interior pointL ₂ for 01/2 and that atL ₁ no such commensurability exists. However, the values of the oblateness coefficient (A ₁) involved atL ₂ are too high to have any practical significance, while those atL ₃ being small for small values of may be useful for generating periodic orbits of the third kind.     

Hydrodynamic models for population-II cepheids

The nonlinear self-excited pulsations of population-II stars with mass 0.6M and luminosities from 128 to 1280L are studied. The pulsation periods are found to be in the range of 1.3 to 19 days. An increase of the stellar luminosity is shown to be accompanied by an increasing nonadiabaticity and decreasing efficiency of the radiative damping region. This leads to both an increase of the growth rate while pulsations are exciting and an increase of the oscillation amplitude of the limit cycle. In the models withL800L the efficiency of the radiative damping region becomes so small that amplitude growth ceases due to a dissipation of the mechanical energy by shocks in the stellar atmosphere. The models with periods of from 1.3 to 3 days show the bump on their light curves. The bump is connected with a travelling pulse generated at the antinode of the second overtone at maximum compression. The time delays estimated for the pulses reflected of the stellar core are in a good agreement with the pulse resonance condition proposed by Aikawa and Whitney (1983). The model with the period of 2.1 days revealed double resonance ₀ = 2₂, 2₀ = 3₁ causing alternating oscillations with slightly different periods and amplitudes. The models with period of 10 days and longer reveal the resonance ₀ = 2₁. This resonance causes the flat top on the light curve at a period of about 10 days and appearance of a shallow alternating minimum at longer periods, as is observed in RV Tau variables. The theoretical period-luminosity relation proposed for population-II cepheids is in good agreement with that obtained from observations.     

Genericity of the non-periodic solutions of the central force problem

We study the classical problem of two-dimensional motion of a particle in the field of a central force proportional to a real power of the distancer. for negative energy and (0, 2), each energy levelI _h is foliated by the invariant toriI _hc of constant angular momentumc and, by Liouville-Arnold's theorem, the flow on eachI _hc is conjugated to a linear flow of rotation number _h (c).A well-known result asserts that if we require _h (c) to be rational for every value ofh andc, the, must be equal to one (Kepler's problem). In this paper we prove that for almost every (0, 2) _h (c) is a non-constant continuous function ofc, for everyh<0. In particular, we deduce that motion under central potentials is generically non-periodic.Partially supported by CIRIT under grant No. EE88/2.