Dark energy and flatness from observational H(z)+WMAP constraint

We analyse the dark energy problem using observational H(z) data plus the curvature constraint given by WMAP. After a non-parametric statistical study covering the most probable range of Ω _m0 and H ₀ from different combination of data, we investigate the possibility of having the dark energy EoS parameter ω _x ≠−1. In order to keep strict flatness (1% of deviation from Ω=1), our results point out this is the case for 0.20≲Ω _m0≲0.23 and H ₀≈67 km/s/Mpc, with ω _x ≈−0.55. However, if we admit a 10% deviation from the flatness condition, ω _x may have any value in the range [−1.2,−0.5] for 0.20≲Ω _m0≲0.35 and 67≲H ₀≲74 km/s/Mpc.     

A diffraction limit on the gravitational lens effect

The focussing of gravitational radiation by the interior and exterior gravitational field of a Newtonian gravitational lens is considered. A graphical method for determining the caustic structure of a Newtonian gravitational lens is presented and the caustic structure of a solar type gravitational lens is discussed. Estimates of the amplitude magnification in the caustic region indicate that waves with frequencies less than a critical cutoff frequency ω _c are not amplified significantly. For a lens of massM this cutoff frequency is ω _c ≈(10^-1πM)^-1; for the Sun ω _c ≈10⁴s^-1. Work supported in part by National Science Foundation Grant PHY78-05368.     

Born–Infeld type phantom model in the ω–ω′ plane

In this paper, we investigate the dynamics of Born–Infeld (B–I) phantom model in the ω–ω′ plane, which is defined by the equation of state parameter for the dark energy and its derivative with respect to N (the logarithm of the scale factor a). We find the scalar field equation of motion in ω–ω′ plane, and show mathematically the property of attractor solutions which correspond to ω _φ ∼−1, Ω _φ =1, which avoid the “Big rip” problem and meets the current observations well.      

Parameters of the local warp of the stellar-gaseous galactic disk from the kinematics of Tycho-2 nearby red giant clump stars

We analyze the three-dimensional kinematics of about 82 000 Tycho-2 stars belonging to the red giant clump (RGC). First, based on all of the currently available data, we have determined new, most probable components of the residual rotation vector of the optical realization of the ICRS/HIPPARCOS system relative to an inertial frame of reference, (ω _x , ω _y , ω _z ) = (−0.11, 0.24, −0.52) ± (0.14, 0.10, 0.16) mas yr⁻¹. The stellar proper motions in the form μ_α cos δ have then be corrected by applying the correction ω _z = −0.52 mas yr⁻¹. We show that, apart from their involvement in the general Galactic rotation described by the Oort constants A = 15.82 ± 0.21 km s⁻¹ kpc⁻¹ and B = −10.87 ± 0.15 km s⁻¹ kpc⁻¹, the RGC stars have kinematic peculiarities in the Galactic yz plane related to the kinematics of the warped stellar-gaseous Galactic disk. We show that the parameters of the linear Ogorodnikov-Milne model that describe the kinematics of RGC stars in the zx plane do not differ significantly from zero. The situation in the yz plane is different. For example, the component of the solid-body rotation vector of the local solar neighborhood around the Galactic x axis is M ₃₂⁻ = −2.6 ± 0.2 km s⁻¹ kpc⁻¹. Two parameters of the deformation tensor in this plane, namely M ₂₃⁺ = 1.0 ± 0.2 km s⁻¹ kpc⁻¹ and M ₃₃ − M ₂₂ = −1.3 ± 0.4 km s⁻¹ kpc⁻¹, also differ significantly from zero. On the whole, the kinematics of the warped stellar-gaseous Galactic disk in the local solar neighborhood can be described as a rotation around the Galactic x axis (close to the line of nodes of this structure) with an angular velocity −3.1 ± 0.5 km s⁻¹ kpc⁻¹ ≤ Ω_W ≤ −4.4 ± 0.5 km s⁻¹ kpc⁻¹.     

Static electrically charged fluids in terms of pressure: general property

A most general exact solution to the Einstein-Maxwell equations for static charged perfect fluid is sought in terms of pressure. Subsequently, metrics (e ^λ and e ^υ ), matter density and electric intensity are expressible in terms of pressure. Consequently, Pressure is found to be an invertible arbitrary function of ω(=c ₁+c ₂ r ²), where c ₁ and c ₂(≠0) are arbitrary constants, and r is the radius of star, i.e. p=p(ω). We present a general solution for charged pressure fluid in terms for ω. We list and discuss some old and new solutions which fall in this category.     

Galactic kinematics from OB3 stars with distances determined from interstellar Ca II lines

Based on data for 102 OB3 stars with known proper motions and radial velocities, we have tested the distances derived by Megier et al. from interstellar Ca II spectral lines. The internal reconciliation of the distance scales using the first derivative of the angular velocity of Galactic rotation Ω′₀ and the external reconciliation with Humphreys’s distance scale for OB associations refined by Mel’nik and Dambis show that the initial distances should be reduced by ≈20%. Given this correction, the heliocentric distances of these stars lie within the range 0.6–2.6 kpc. A kinematic analysis of these stars at a fixed Galactocentric distance of the Sun, R ₀ = 8 kpc, has allowed the following parameters to be determined: (1) the solar peculiar velocity components (u _⊙, v _⊙, ω _⊙) = (8.9, 10.3, 6.8) ± (0.6, 1.0, 0.4) km s⁻¹; (2) the Galactic rotation parameters Ω₀ = −31.5 ± 0.9 km s⁻¹ kpc⁻¹, Ω′₀ = +4.49 ± 0.12 km s⁻¹ kpc⁻², Ω″₀ = −1.05 ± 0.38 km s⁻¹ kpc⁻³ (the corresponding Oort constants are A = 17.9 ± 0.5 km s⁻¹ kpc⁻¹, B = −13.6 ± 1.0 km s⁻¹ kpc⁻¹ and the circular rotation velocity of the solar neighborhood is |V ₀| = 252 ± 14 km s⁻¹); (3) the spiral density wave parameters, namely: the perturbation amplitudes for the radial and azimuthal velocity components, respectively, f _R = −12.5±1.1 km s⁻¹ and f _ϑ = 2.0 ± 1.6 km s⁻¹; the pitch angle for the two-armed spiral pattern i = −5.3° ± 0.3°, with the wavelength of the spiral density wave at the solar distance being λ = 2.3 ± 0.2 kpc; the Sun’s phase in the spiral wave x _⊙ = −91° ± 4°.     

Continuity and stability of families of figure eight orbits with finite angular momentum

Numerical solutions are presented for a family of three dimensional periodic orbits with three equal masses which connects the classical circular orbit of Lagrange with the figure eight orbit discovered by C. Moore [Moore, C.: Phys. Rev. Lett. 70, 3675–3679 (1993); Chenciner, A., Montgomery, R.: Ann. Math. 152, 881–901 (2000)]. Each member of this family is an orbit with finite angular momentum that is periodic in a frame which rotates with frequency Ω around the horizontal symmetry axis of the figure eight orbit. Numerical solutions for figure eight shaped orbits with finite angular momentum were first reported in [Nauenberg, M.: Phys. Lett. 292, 93–99 (2001)], and mathematical proofs for the existence of such orbits were given in [Marchal, C.: Celest. Mech. Dyn. Astron. 78, 279–298 (2001)], and more recently in [Chenciner, A. et al.: Nonlinearity 18, 1407–1424 (2005)] where also some numerical solutions have been presented. Numerical evidence is given here that the family of such orbits is a continuous function of the rotation frequency Ω which varies between Ω = 0, for the planar figure eight orbit with intrinsic frequency ω, and Ω = ω for the circular Lagrange orbit. Similar numerical solutions are also found for n > 3 equal masses, where n is an odd integer, and an illustration is given for n = 21. Finite angular momentum orbits were also obtained numerically for rotations along the two other symmetry axis of the figure eight orbit [Nauenberg, M.: Phys. Lett. 292, 93–99 (2001)], and some new results are given here. A preliminary non-linear stability analysis of these orbits is given numerically, and some examples are given of nearby stable orbits which bifurcate from these families.     

Some rotating perfect fluid universes coupled with electromagnetic field interacting with gravitation

Some new interesting solutions, the dynamics, behaviour and phenomena of rotating charged perfect fluid models are investigated, and their physical and geometrical properties are studied in order to substantiate the possibility of the existence of such astrophysical bodies in this Universe. The nature and role of the metric rotation Ω(r,t) as well as that of the matter rotation ω(r,t) are studied for uniform and non-uniform motions. The reactions of the gravitational and charged fields with respect to the rotational motion are studied and possible results are explored for real astrophysical situations, and in some solutions we find the spatial restrictions on the models for realistic conditions. Rotating models which are expanding are obtained in which the rotational motions are decaying with time.     

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.     

The Restricted Three-Body Problem: Comments on the Rotational Effect

The synchronization between the orbital motion and axial rotation of the two component stars of a binary system is reviewed. Some previous published papers are mentioned and the general conclusion is outlined: If we shall use a rotating coordinate system synchronous with one of the two stellar axial rotations, it is not possible to obtain a Jacobi integral and the Roche geometry cannot be further analyzed. In addition, a theoretical approach is summarized in order to use the axial rotations of the two component stars, even if the constants of the stellar structure (k₂)₁, (k₂)₂must be taken into consideration. So it is found that if the stellar angular velocities are higher than the corresponding Keplerian angular velocity (ω_i≫ ω_k, i= ), the problem of the rotational effect could be of practical consideration. Finally, a theoretical relationship between the two constants (k₂)₁and (k₂)₂of the stellar structure is established.     

Toroidal magnetic field in pulsars

The differential rotation of plasma in the core of pulsars (Ω_s ≠ Ω_e) generates convective currents increasing with time which in turn generates the toroidal magnetic field. To avoid difficulties of physical interpretation inherent to the theory of general relativity we have adopted the tetrad approach to discuss the generation of the magnetic field in the core of the neutron stars. The results which we have obtained are in agreement with those obtained earlier. Published in Astrofizika, Vol. 49, No. 4, pp. 613–620 (August 2006).     

Solar quadrupole moment and purely relativistic gravitation contributions to Mercury's perihelion advance

The perihelion advance of the orbit of Mercury has long been one of the observational cornerstones for testing General Relativity (G.R.).The main goal of this paper is to discuss how, presently, observational and theoretical constraints may challenge Einstein's theory of gravitation characterized by β=γ=1. To achieve this purpose, we will first recall the experimental constraints upon the Eddington-Robertson parameters γ,β and the observational bounds for the perihelion advance of Mercury, Δω_obs. A second point will address the values given, up to now, to the solar quadrupole moment by several authors. Then, we will briefly comment why we use a recent theoretical determination of the solar quadrupole moment, J ₂=(2.0 ± 0.4) 10^-7, which takes into account both surfacic and internal differential rotation, in order to compute the solar contribution to Mercury's perihelion advance. Further on, combining bounds on γ and J ₂ contributions, and taking into account the observational data range for Δω_obs,we will be able to give a range of values for β. Alternatively, taking into account the observed value of Δω_obs, one can deduce a dynamical estimation of J ₂ in the setting of G.R. This point is important as it provides a solar model independent estimation that can be confronted with other determinations of J ₂ based upon solar theory and solar observations (oscillation data, oblateness...). Finally, a glimpse at future satellite experiments will help us to understand how stronger constraints upon the parameter space (γω J ₂) as well as a separation of the two contributions (from the quadrupole moment, J ₂, or purely relativistic, 2α²+2αγ–β) might be expected in the future. This revised version was published online in July 2006 with corrections to the Cover Date.     

Entropy-corrected new agegraphic dark energy in Hořava-Lifshitz cosmology

We study the entropy-corrected version of the new agegraphic dark energy (NADE) model and dark matter in a spatially non-flat Universe and in the framework of Hořava-Lifshitz cosmology. For the two cases containing noninteracting and interacting entropy-corrected NADE (ECNADE) models, we derive the exact differential equation that determines the evolution of the ECNADE density parameter. Also the deceleration parameter is obtained. Furthermore, using a parametrization of the equation of state parameter of the ECNADE model as ω _Λ(z)=ω ₀+ω ₁ z, we obtain both ω ₀ and ω ₁. We find that in the presence of interaction, the equation of state parameter ω ₀ of this model can cross the phantom divide line which is compatible with the observation.     

Absolute parameters of the close binary BW Boo with a superasynchronous A2m primary component

Based on two high-dispersion spectra of the close binary BW Boo, we have detected lines of the secondary component whose contribution to the combined spectrum does not exceed 2%. We have determined the rotation velocities of the components and spectroscopic orbital elements. Numerous lines of neutral and ionized iron have been used to determine the effective temperature and surface gravity for the primary component. The photometric light curves for this binary have been solved for the first time. Its primary component is an A2Vm star with a mass of 2 ± 0.1M _⊙ and a radius of 1.9 ± 0.4R _⊙. Its rotation velocity is 2 km s⁻¹, which is a factor of 18 lower than the pseudo-synchronous velocity for this component. The G6 secondary component, a T Tau star, has a rotation velocity of 17 km s⁻¹, amass of 1.1M _⊙, and a radius of 1 R _⊙. The age of the binary has been estimated to be 10⁷ yr.     

Dynamical Behaviour of Compressible Homogeneous Uniformly Rotating Ellipsoids with Nonparallel Angular Velocity and Vorticity

The study of nonequilibrium, self-gravitating, compressible, homogeneous and uniformly rotating gaseous ellipsoidal models is extended from parallel to nonparallel angular velocity and vorticity. The differential equations of motion governing these models are numerically integrated over ranges of initial values of angular velocity and vorticity. The dynamical behaviour of the ellipsoid is found to be almost unchanged when the initial values of Ω₃/Ω_3,e and λ₃/λ_3,e are interchanged, where λ is a function of the vorticity, Ω₃ is the angular velocity along the x₃ axis, and Ω_3,e and λ_3,e are equilibrium values. Models with the same initial value of | Ω₃/Ω_3,e - λ₃/λ_3,e | have similar dynamical behaviour. When this value becomes larger, the oscillations of the semi-axes are larger and are more nonperiodic. For all models, the ellipsoidal configuration is maintained at all times. The magnitude of Ω_l depends on the difference between the values of the semi-axes a_m and a_n, where l, m, and n are cyclic. The smaller this difference is, the larger the angular velocity along the third axis. Thus whenever the model approaches a spheroidal configuration, there may be a large and rapid increase in the angular velocity along the axis of ‘symmetry’. The last two properties, namely the maintenance of the ellipsoidal configuration and the large increase in angular velocity of the model, configuration also hold in the model (T.T.Chia and S.Y.Pung, 1995, Astrophys.\ Space Sci., 229, 215.) with parallel angular velocity and vorticity. However, unlike the earlier model, Ω₂ and Ω₃ are observed to reverse their directions at certain instants during the oscillations; this may have interesting astrophysical implications. This revised version was published online in July 2006 with corrections to the Cover Date.     

Equilibrium Structures of Differentially Rotating Primary Components of Binary Stars

In this paper a method is proposed for computing the equilibrium structures and various other observable physical parameters of the primary components of stars in binary systems assuming that the primary is more massive than the secondary and is rotating differentially about its axis. Kippenhahn and Thomas averaging approach (1970) is used in a manner earlier used by Mohan, Saxena and Agarwal (1990) to incorporate the rotational and tidal effects in the equations of stellar structure. Explicit expressions for the distortional terms appearing in the stellar structure equations have been obtained by assuming a general law of differential rotation of the typeω² = b ₀+b ₁ s ²+b ₂ s ⁴, where ω is the angular velocity of rotation of a fluid element in the star at a distance s from the axis of rotation, and b ₀, b ₁, b ₂ are suitably chosen numerical constants. The expressions incorporate the effects of differential rotation and tidal distortions up to second order terms. The use of the proposed method has been illustrated by applying it to obtain the structures and observable parameters of certain differentially rotating primary components of the binary stars assuming the primary components to have polytropic structures. This revised version was published online in July 2006 with corrections to the Cover Date.     

Star Formation Histories From Faint Galaxy Counts

Multispectral faint galaxy counts, including the deepest Hubble DeepField, are interpreted with the help of our evolution model PEGASE(Fioc and Rocca-Volmerange, 1997). The best fits correspond to galaxyformations at high redshifts, a pure luminosity evolution andclassical luminosity functions. The adopted cosmology is a flatuniverse with the matter density parameter Ω_M =0.3 and acosmological constant Ω_Λ =0.7. A solution with Ω_M=0.01 (open universe) is also acceptable. But a flat universe withΩ_M =1 is clearly excluded. The star formation histories for galaxytypes are derived from scenarios of evolution. The comparison with resultsalready published in the litterature, arises puzzling problems needinga further analysis of star formation tracers, specifically for bright galaxies. This revised version was published online in July 2006 with corrections to the Cover Date.     

Differential Rotation of Strong Magnetic Flux During Solar Cycles 21 – 23

In the present investigation we measure the differential rotation of strong magnetic flux during solar cycles 21 – 23 with the method of wavelet transforms. We find that the cycle-averaged synodic rotation rate of strong magnetic flux can be written as ω=13.47−2.58sin ² θ or ω=13.45−2.06sin ² θ−1.37sin ⁴ θ, where θ is the latitude. They agree well with the results derived from sunspots. A north–south asymmetry of the rotation rate is found at high latitudes (28°<θ<40°). The strong flux in the southern hemisphere rotates faster than that in the northern hemisphere by 0.2 deg day⁻¹. The asymmetry continued for cycles 21 – 23 and may be a secular property.     

Evaluation of disturbances from solar radiation in orbital elements of geosynchronous satellites based on harmonics

Using specialized codes for the search of periodic and linear components we show that direct solar radiation leads to short-period variations of all the orbital elements of geosynchronous satellites. The variation period of the semimajor axis a, orbit inclination i and the longitude of the ascending node Ω is 1 day. Eccentricity e, the argument of perigee ω and the mean anomaly M vary with a period of 0.5 days. Direct solar radiation also leads to long-period variations in e, ω and M with a period of 1 year. The elements a, i and Ω undergo variations only in the amplitude of diurnal variations with a period of 1 or 0.5 years. Secular variability (linear components) are not detected. To obtain the initial value array of the orbital elements we used the Lagrange equations of perturbed motion in the form of a Gaussian with their subsequent integration via a special method of harmonics: the values of the derived orbital elements, obtained from the Lagrange equations, were presented through the periodic functions that are easy to integrate.     

Dark energy models with anisotropic fluid in Bianchi Type-VI 0 space-time with time dependent deceleration parameter

We present two dark energy (DE) models with an anisotropic fluid in Bianchi type-VI ₀ space-time by considering time dependent deceleration parameter (DP). The equation of state (EoS) for dark energy ω is found to be time dependent and its existing range for derived models is in good agreement with the recent observations. Under the suitable condition, the anisotropic models approach to isotropic scenario. We also find that during the evolution of the universe, the EoS parameter for DE changes from ω>−1 to ω=−1 in first model whereas from ω>−1 to ω<−1 in second model which is consistent with recent observations. The cosmological constant Λ is found to be a positive decreasing function of time and it approaches a small positive value at late time (i.e. the present epoch) which is corroborated by results from recent type Ia supernovae observations. The cosmic jerk parameter in our derived models is also found to be in good agreement with the recent data of astrophysical observations. The physical and geometric aspects of both the models are also discussed in detail.