The cosmological model of Brans-Dicke theory

We use the generalized Brans-Dicke theory, in which the Pauli metric is identified to be the physical space-time metric, to study the Universe in different epochs. Exact analytical expressions for dilaton field , cosmological radiusR and density parameter are obtained fork=+1,0,–1 Universe in the radiation-dominated epoch. For matter dominated Epoch, exact analytical expressions for Hubble parameterH, cosmological radius, dilaton field, deceleration factorq, density parameter and the gravitational coupling of the ordinary matter are obtained for the flat Universe. Other important results are: (1) the density parameter is always less than unity for the flat Universe because the dilaton field plays a role as an effective dark matter, and (2) the new Brans-Dicke parameter must be larger than 31.75 in order to consistent with the observed data.     

Accelerating universe with time variation of G and Λ

We study a gravitational model in which scale transformations play the key role in obtaining dynamical G and Λ. We take a non-scale invariant gravitational action with a cosmological constant and a gravitational coupling constant. Then, by a scale transformation, through a dilaton field, we obtain a new action containing cosmological and gravitational coupling terms which are dynamically dependent on the dilaton field with Higgs type potential. The vacuum expectation value of this dilaton field, through spontaneous symmetry breaking on the basis of anthropic principle, determines the time variations of G and Λ. The relevance of these time variations to the current acceleration of the universe, coincidence problem, Mach’s cosmological coincidence and those problems of standard cosmology addressed by inflationary models, are discussed. The current acceleration of the universe is shown to be a result of phase transition from radiation toward matter dominated eras. No real coincidence problem between matter and vacuum energy densities exists in this model and this apparent coincidence together with Mach’s cosmological coincidence are shown to be simple consequences of a new kind of scale factor dependence of the energy momentum density as ρ∼a ⁻⁴. This model also provides the possibility for a super fast expansion of the scale factor at very early universe by introducing exotic type matter like cosmic strings.     

The photospheric velocity field of Procyon

BUSS observations of the profiles of two well observed spectral lines in the ultraviolet spectrum of CMi (Procyon; F5 IV–V) are analysed with a Fourier transform method in order to determine values of various parameters of the velocity field of the upper photosphere. We find a microturbulent line-of-sight velocity componentL = 0.9 ± 0.4 km s^–1, a macroturbulent velocity componentL _M = 5.3 ± 0.2 km s^–1, and a rotational velocity componentv _R sini=10.0±1.2 km s^–1. In these calculations a single-moded sinusoidal isotropic macroturbulent velocity function was assumed. The result appears to be sensitive to the assumed shape of the macroturbulence function: for an assumed Gaussian shape the observations can be described withv _R sini=4 km s^–1 andL _M = 11.6 ± 2.7 km s^–1. A comparison is made with other results and theoretical predictions.     

Gravitation und weitreichende schwache Wechselwirkungen bei Neutrino-Feldern Gedanken zu einer Theorie der solaren Neutrinos

The strange non-evidence of the solar-neutrino current by the experiments of DAVIS et al. postulates a fundamental revision of the theory of weak interactions and of its relations to gravitation theory. (We assume that the astrophysical stellar models are not completely wrong.) – Our paper is based on PAULI 's grand hypothesis about the connection between weak and gravitational interactions. According to PAULI and BLACKETT the (dimensionless) gravitation constant is the square of the (dimensionless) FERMI -interaction constant and according to the hypotheses of PAULI, DE BROGLIE , and JORDAN the RIEMANN -EINSTEIN gravitational metric g_ik is fusioned by the four independent WEYL ian neutrino fields (β-neutrinos and β-antineutrinos, μ-neutrinos and μ-antineutrinos). This fusion gives four reference tetrads h_i^A(x^l) as neutrino-current vectors, firstly. Then, the metric g_ik is defined by the equation g_ik = η_AB h_i^Ah_η^B according to EINSTEIN 's theory of tele-parallelism in RIEMANN ian space-times. The relation of the gravitation field theory to FERMI 's theory of weak interactions becomes evident in our reference-tetrads theory of gravitation (TREDER 1967, 1971). – According to this theory the coupling of the gravitation potential h_i^A with the matter T_ιⁱ is given by a potential-like (FERMI -like) interaction term. In this interaction term two WEYL spinor-fields are operating on the matter-tensor, simultanously. Therefore, the gravitation coupling constant is PAULI 's square of the FERMI -constant. Besides of the fusion of the RIEMANN -EINSTEIN metric g_ik by four WEYL spinors we are able to construct a conformal flat metric ĝ_ik = ϕ²η_ik by fusion from each two WEYL spinors. (This hypothesis is in connection with our interpretation of EINSTEIN 's hermitian field theory as a unified field-theory of the gravitational metric g_ik and a WEYL spinor field [TREDER 1972].) Moreover, from the reference-tetrads theory is resulting that the WEYL spinors in the “new metric” ĝ_ik are interacting with the DIRAC matter current by a FERMI -like interaction term and that these WEYL spinors fulfil a wave equation in the vacuum. Therefore, we have a long-range interaction with the radiced gravitational constant \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {\frac{{tm^2 }}{{hc}}} $\end{document} as a coupling constant. That means, we have a long-range interaction which is 10¹⁸ times stronger than the gravitation interaction. – However, according to the algebraic structure of the conform-flat this long-range interaction is effective for the neutrino currents, only. And for these neutrinos the interaction is giving an EINSTEIN -like redshift of its frequences. The characteristic quantity of this “EINSTEIN shift” is a second gravitation radius â of each body: N = number of baryons, m = mass of a baryon.) This radius â is 10¹⁸ times larger than the EINSTEIN -SCHWARZSCHILD gravitation radius a = fM/c²: But, this big “weak radius” â has a meaning for the neutrinos, only.–The determination of the exterior and of the interior “metrics” ĝ_ik is given by an “ansatz” which is analogous to the ansatz for determination of strong gravitational fields in our tetrads theory. That is by an ansatz which includes the “self-absorption” of the field by the matter. For all celestial bodies the “weak radius” â is much greater than its geometrical dimension. Therefore, a total EINSTEIN redshift of the neutrino frequences v is resulting according to the geometrical meaning of our long-range weak interaction potential ĝ_ik = ϕ²η_ik. That means, the cosmic neutrino radiation becomes very weak and unable for nuclear reactions. Theoretically, our hypothesis means an ansatz for unitary theory of gravitation and of weak interaction. This unitary field theory is firstly based on EINSTEIN 's hermitian field theory and secondly based on our reference-tetrads theory of gravitation.     

Generalized de Sitter solution in multi-dimensional cosmology with static internal spaces

A multi-dimensional cosmological model with space-time consisting of n(n ≥ 2) Einstein spaces M_i is investigated in the presence of a cosmological constant λ and a homogeneous minimally coupled free scalar field. A generalized de Sitter solution was found for λ > 0 and a Ricci-flat external space for the case of static internal spaces with fine tuning of parameters.     

The S3–4 ionospheric irregularities satellite experiment: Probe detection of multi-ion component plasmas and associated effects on instability processes

The pulsed plasma probe technique has been expanded to include simultaneous determinations of absolute electron density, density fluctuations, electron temperature, and mean-ion-mass with resolution limited only by probe geometry, sheath size, and telemetry. The technique has been designed to test for coupling of electron density variations and ion composition irregularities in multi-component plasmas by the comparison of electron density fluctuation power spectraP _N(k) and a newly-developed diagnostic parameter, the mean-ion-mass fluctuation spectraM _i/M _iP _M(k). In addition, the experiment extends satellite-borne irregularity spectral analyses down to the 5–20 m range while attempting to identify F-region plasma instability processes on the basis of characteristics inN _e,T _e, N _e,P _N,M _i, andP _M. Initial results demonstrate the expanded diagnostic capability for high spatial resolution measurements of mean-ion-mass and provide experimental evidence for the role of ion composition in multi-stepped plasma instability processes. Specific results include a spectral indexX _n inP _N=A _nf^–X _n of 1.6–2.9 over the wavelength range from 1 km to 6 m under conditions identified with an unstable equatorial nighttime ionosphere. Simultaneous measurements ofM _i/M _i(P _M=A _M f ^–X _m) andN _e/N _e(P _N=A _n f ^–X _n) have shown a general behavior tending to lower power (A _m<A _n) and softer spectra (X _m<X _n) in ion mass fluctuations when compared with fluctuations in total plasma density. Limited analyses of the two power spectral elements raise hopes for the differentiation between plasma mechanisms that can lead to similar indices inP _N.Paper originally submitted to the journalSpace Science Instrumentation.     

Some remarks about cosmology in brans and Dicke's theory

It is established that, in contrast to Einstein's theory, in the cosmological equations of the theory by Brans and Dicke the spatial component of the field equations follows from the remaining equations and the conservation lawT ^ik _jk=0 only if one excludes the power law R ^–2. Some consequences are discussed.     

The product of the globular cluster collapse

In this paper we calculate the number of close binaries formed during the evolution process of a globular cluster core. The globular cluster core is assumed to contain a massive black hole at its center. We show that the central black hole can drive binaries formation in the core and the rate of binaries formation depends on the mass of the black hole at its center. When the massM of the black hole is between 10² M and 3×10³ M , there will be a few binaries formed. When the mass of the black hole is 4×10³ M M6×10³ M , the number of binary star formation will suddenly increase with a jump to the maximum value 58. When the mass of the black hole is 7×10³ M M9×10³ M , the number of binary star will immediately decrease. Whether cluster X-ray is produced mainly by the central black hole or by binaries in the core depends on the mass of the central black hole. Therefore, two cases arise: namely, black hole accretion domination and binaries radiation domination. We do think that we cannot exclude the possibility of the existence of a central black hole even when binary radiation characteristics have been observed in globular cluster X-ray sources.     

Grain formation in the expanding gas flow around cool luminous stars

We studied grain formation process and flow structure around cool luminous mass-loss stars. The nucleation and growth theory of Yamamoto and Hasegawa was extended to the case of expanding gas flow.The envelope was assumed to be steady, spherically symmetric, in thermal and radiative equilibrium, optically thin, and driven by radiation pressure on grains. For oxygen rich stars, Mg-silicate was found to be the first condensate which can drive the gas effectively. The following stellar parameters were chosen; stellar massM _*=1M , effective temperatureT _*=3000K, stellar luminosityL _* from 7.5×10³ to 2.0×10⁴ L , and mass-loss rate |M| from 1.0×10^–6 to 1.0×10^–4 M yr^–1.Main results of calculations are as follows; (1) grain condensation temperatureT _c9801080 K; (2) total gas pressure at the condensation pointP _t6×10^–116×10^–9 atm; (3) scale parameterA _c10³6×10⁴; and (4) final grain sizer _f=400Å1m. For the smaller |M| or the largerL _*, these values are the smaller. We recognized two types of flow solutions (1) Dust driven flow for large |M|, which reaches the sonic point near the condensation point; and (2) Modified Parker flow for small |M| for which grain sizer _f is almost independent of |M|.A comparison with observational results ofL _* and gas terminal velocityV suggests that Mg-silicate grains are of submicron size, which are effective for interstellar extinction in visible and infrared. Fe-grains condense in the rarefied outflow with a size probably smaller than 100Å, which may contribute for interstellar ultraviolet extinction. The envelope has three-layer structure inner dense region with small outflow velocity, grain formation layer and outer rarefied region with fast outflow velocity.No flow solutions exist forM _* greater than a critical stellar massM _*cr for a given stellar luminosityL _* and mass-loss rate |M|.For example, critical stellar massM _*cr=1.8M forL _*=10⁴ L ,T _*=3000 K, and |M|=10^-5 M yr^-1.     

Steady mass-loss from supermassive stars

Structures of Newtonian super-massive stars are calculated with the opacity for Comptor effectK ₀/(1 + T), whereK ₀=0.21(1 +X and =2.2×10^–9K^–1. The track of the Main-Sequence is turned right in the upper part of the HR diagram. Mass loss will occur in a Main-Sequence stage for a star with mass larger than a critical mass. The cause of mass loss and the expansion of the radius is continuum radiation pressure. The critical mass for mass loss is 1.02×10⁶ M for a Population I star, and 1.23×10⁵ M for Population III star. Mass loss rates expected in these stars are 3.3×10^–3 and 4.0×10^–3 M yr^–1, respectively.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

Brightness distribution of diffuse soft X-rays

The brightness distribution of diffuse soft X-rays in the pulse height range 0.15–0.3 keV (L-band) and 0.5–0.8 keV (M-band) are obtained over a quarter of the sky centered at the galactic anticenter with 1.5 m polypropylene window proportional counters on board a sounding rocket. In theL-band three enhanced regions are noticed on the map. They coincide with the northern and southern Hi holes and the inner part of the galactic radio Loop II.In the northern Hi hole theN _H dependence of theL-band flux and the hardness ratioM/L can be fitted with a local hot plasma model with the absorption by a low velocity neutral hydrogen gas (|V|<25 km s^–1) along the line of sight. The X-ray feature of Loop II is similar to that of Loop I. In the lowN _H region (<3×10²⁰ H atoms cm^–2) theM/L value is lower than 0.3, whereas it varies in the range 0.1–0.4 at low latitudes (|b|<30⁰). This fact seems to be interpreted in terms of a model that a number of hot plasma clouds contribute to X-ray emission.     

Mass accretion onto massive white dwarfs

We have studied the thermonuclear runaways which develop on white dwarfs of 1.205M and 1.358M accreting hydrogen rich material at 10^–10 M yr^–1. It is found that ignition of this material occurs at densities in excess of about 10⁴ gm cm^–3 and that the critical accumulated mass required to initiate the runaway is 0.7(1.5)×10^–4 M for a 1.358(1.205)M white dwarf.     

On the mass and distance of the Quasi-Stellar Object 3C 273

For the QSO 3C 273 we derive, on the basis of two different theoretical models, expressions for a lower limit to the mass of the QSO, as a function of its distance. We conclude that an appreciable gravitational redshift component is consistent with the observational data only if the QSO mass is at least Galactic in magnitude. The setting of an independent upper limit to the QSO massM10¹⁰ M could indicate that the QSO redshift is predominantly cosmological in nature.     

Conformal analogs of the Jordan-Brans-Dicke theory. I.

Recent cosmological observations of large-scale structures (red shift of type Ia supernovae) confirm that the universe is currently expanding at an accelerating rate and its dominant component is dark energy. This has stimulated the development of the theory of gravity and led to many alternative variants, including tensor-scalar ones. This paper deals with the role of conformal transformations in the Jordan-Brans-Dicke theory. Variants of intrinsic, conformally coupled, and Einstein representations are examined. In the Einstein representation an exact analytic solution for the standard cosmological model is obtained. It is expressed in terms of the relative energy contributions of ordinary matter Ω _m , the scalar field Ω _CK , and a term Ω_Λ related to the cosmological constant Λ . Information on the evolution of the universe for the case with a minimally coupled scalar field is given in the form of graphs.     

Ages and masses of delta scuti stars in the praesepe cluster

Physical parameters and radial pulsation modes are determined for three Delta Scuti stars in the Praesepe cluster: HD 73345, HD 73712, and HD 73746. Their agest and evolutionary massesM _eare interpolated in the track systems of Iben (1967) and Paczyski (1970). By combining these age estimates with our previous results for nine other Delta Scuti-stars in the Praesepe cluster (Tsvetkov, 1989), the following weighted mean age estimates of this cluster are obtained: (14.2 ± 1.3) × 10⁸ yr (Iben) and (5.4 ± 0.4) × 10⁸ yr (Paczyski). Age and evolutionary mass estimates of the twelve cluster variables are also obtained in the modern track system of Maeder and Meynet (1988), in which the weighted mean cluster age is (15.3 ± 1.0) × 10⁸ yr.Pulsation massesM _Qcalculated from the fitting formulae of Faulkner (1977) and Fitch (1981) as well as massesM _g=gR ² / G were evaluated for the twelve cluster variables by Tsvetkov (1990) or in the present paper. In most cases there is a satisfactory agreement between our estimates of massesM _e,M _g, andM _Q.Due to a large disagreement between the long period and low luminosity of the star HD 73746, its radial pulsation mode and pulsation massM _Qcannot be evaluated.     

Expanding and shearing magneto-viscous fluid cosmological model in general relativity

The object of this paper is to investigate the behavior of a magnetic field in a viscous fluid cosmological model. It has been assumed that the expansion () is proportional to the eigenvalue ₁ of the shear tensor _i ^j and the coefficient of shearing viscosity is proportional to the scalar of expansion. The paper also discusses the behavior of the model when the magnetic field tends to zero and comments on some other physical properties.     

The proper motion VS redshift relation for superluminal radio sources

Two models for superluminal radio sources predict sharp lower bounds for the apparent velocities of separation. The light echo model predicts a minimum velocityv _min=2c, and the dipole field model predictsv _min=4.446c. Yahil (1979) has suggested that, if either of these models is correct, thenv _min provides a standard velocity which can be used to determine the cosmological parametersH andq ₀. This is accomplished by estimating a lower envelope for the proper motion vs redshift relation. Yahil also argued that the procedure could easily be generalized to include a nonzero cosmical constant . We derive the formulas relating the proper motion to the redshiftz in a Friedmann universe with a nonzero . We show that the determination of a lower envelope for a given sample of measured points yields an estimate of the angle of inclination _i for each source in the sample. We formulate the estimation of the lower envelope as a constrained maximum likelihood problem with the constraints specified by the expected value of the largest order statistic for the estimated _i . We solve this problem numerically using an off-the-shelf nonlinearly constrained nonlinear optimization program from the NAg library. Assuming =0, we apply the estimation procedure to a sample of 27 sources with measured values , using both the light echo and the dipole field models. The fits giveH=103 km s^–1 Mpc^–1 for the light echo model andH=46 km s^–1 Mpc^–1 for the dipole field model. In both cases the fits giveq ₀=0.4, but the uncertainty in this result is too large to rule out the possibility thatq ₀>0.5. When is allowed to be a free parameter, we obtainH=105 km s^–1 Mpc^–1 for the light echo model andH=47 km s^–1 Mpc^–1 for the dipole field model. In both cases the fits giveq ₀=–1 and /H ₀ ² =6.7, but no significance can be attached to these results because of the paucity of measured data at hight redshifts. For all of the fits, we compute the corresponding estimates of the _i and compare the cumulative distribution of these values with that expected from a sample of randomly oriented sources. In all cases we find a large excess of sources at low-inclination angles (high apparent velocities). The expected selection effect would produce such an excess, but the excess is large enough to suggest a strong contamination of the sample by relativistic beam sources which would only be seen at low inclination angles.Applied Research Corporation     

Bianchi Type I string dust cosmological model with magnetic field in general relativity

Bianchi Type I string dust cosmological models in presence and absence of magnetic field following the techniques used by Letelier and Stachel, are investigated. To get the deterministic solution, we have assumed that σ ₁¹ is proportional to the expansion (θ) where σ ₁¹ is the eigen value of shear tensor (σ _i ^j ) and which leads to A=N(BC)⁻ⁿ , n>0 where A,B,C are metric potentials and , N and ℓ are constants. The behaviour of the models in presence and absence of magnetic field are discussed. The other physical and geometrical aspects of the model are also discussed.     

The angular momentum loss of low-mass close binary systems

The detailed evolution of low-mass main-sequence stars (M < 1M ) with a compact companion is studied. For angular momentum loss associated with magnetic braking it is found that about 10^–11–10^–12 M yr^–1 in stellar wind loss would be required. This wind is 10²–10³ times stronger than the solar wind, so we believe here magnetic stellar wind is insufficient. It is well known that there is mass outflow in low-mass close binary systems. We believe here that these outflows are centrifugal driven winds from the outer parts of the accretion disks. The winds extract angular momentum from these systems and therefore drive secular evolution. Disk winds are preferred to winds from the secondary, because of the lower disk surface gravity.     

Theorie litterale du neuvieme satellite de Saturne,Phoebe

We study a theory for the ninth satellite of Saturn, Phoebe, based on the literal solution we have obtained in the main problem of the lunar theory.These series were computed by solving, by successive approximations, the Lagrange's equations expressed in variables, functions of the elliptic elements.We may consider the case of Phoebe simpler than a lunar case because we seek less precision (1/10 geocentric) than in the Lunar case, although the eccentricity of Phoebe is stronger.Main problem: our series are computed to the complete seventh order and a great part of the perturbations of the eighth and ninth order, where we have attributed to the small lunar parameters the order 1 tom ₀=n/n ₀,e ₀,e, sin (i ₀/2), the order 2 to ₀=(a ₀/a)((M ₁–)/(M ₁+M)) and the order 4 toµ ₀(a ₀/a)M ₁ M/M ₁ ² –M ².In the case of Phoebe,µ ₀ equal zero and ±₀ is the ratioa ₀/a.We study the further development of these series by using, instead of parameterm ₀, the quantity m ₀=n/n ₀–m ₁ wherem ₁ is an approached value ofm ₀, in order to accelerate the convergence of the series with respect tom ₀.Comparison with a numerical integration we are adjusting a numerical integration to the observations. We have already more than 100 observations, for the period 1900–1957.At first, we compare the series of the main problem to a numerical integration of the Keplerian problem.

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Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix. Namur, Belgium, 28–31 July, 1980.