The theory of relativity and super-luminal speeds

According to the different properties between the ds ² and the ds ⁴, it is discussed that the space-time will have the catastrophe nature on the Finsler metric ds ⁴ (see Cao, 1990, Paper II). The space-time transformations and the physical quantities will suddenly change at the catastrophe theory of the space-time. It will be supposed that only the dual velocity of the super-luminal-speed could be observed (see Cao, 1988). If so, a particle with the super-luminal-speedv>c, could be regarded as its anti-particle with the dual velocityv ₁=c ²/v<c.The project was supported by National Natural Science Foundation of China.     

Identification of forbidden coronal lines of Fe x and Ni xii

The transitions 3s ²3p ⁴3d ⁴ D, ⁴ F–3s3p ⁵3d ⁴ F have been studied in the Cl i isoelectronic sequence from Ca iv to Fe x. The determination of the 3s ²3p ⁴3d quartet intervals in Fe x has led to the identification of eleven coronal lines in the region from 1463 Å to 5539 Å as forbidden transitions within this configuration. By extrapolation, an additional coronal line is identified with a similar transition in Ni xii.     

Theorie de Weyl et principe de moindre action: Application a l'etude des mouvements

Sommaire Les lois du mouvement dans une variété riemannienneV ₄ peuvent être déduites d'un principe de moindre action. Nous établissons dans cet article l'équivalence des relations ds=0 et dL=-L _k d^k, où ds ²=L ² est une métrique riemannienne et d _k /dt une fonction homogène de degré 1 des variables dx ⁱ/dt qui définit un espace de Weyl. Ce théorème permet de ramener une théorie de jaugen à un principe de moindre action. Il peut être utilisé dans la théorie de la double métrique de Dirac, obtenue en choissant la théorie des grands nombres comme condition de jauge. Une fibration de l'espace physiqueV ₃ basée sur le théorème de Huyghens permet de déduire les propriétés dynamiques des particules des propriétés des photons dansV ₃, et constitue en ce sens une unification des propriétés dynamiques des particules.

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The laws of motion in a RiemannianV ₄ manifold can be deduced from the principle of least action. We state in this work the equivalence between the equations ds=0 and dL=-L _k d^k, where ds ² =L ² is the Riemannian metric and d _k /dt the homogeneous functions of first degree of the dx ⁱ/dt which define a Weylian space. This theorem can then reduce a gauge theory to a principle of least action. It can be used in the double metric theory of Dirac, obtained by means of the Large Number Hypothesis as a gauging condition. A fibration of the physical spaceV ₃ based on Huyghens' theorem allows the deduction of the dynamical properties of particles by means of the properties of photons inV ₃, and constitutes in this way an unification of the dynamical properties of particles.

     

Theoretical intensities of Fexiv in the solar EUV spectrum

Equilibrium population of Fexiv levels in coronal conditions was calculated including configurations 3s ²3p, 3s3p ², 3s ²3d, 3p ³, 3s3p3d, 3s ²4s, 3s ²4p, 3s ²4d, 3s ²4f. Relative populations of selected levels are given in Table VII. Figure 1 shows the dependence of relative intensities of the strongest lines on electron density. Certain line ratios can be used for the determination of N _e .E.g., at T=2 × 10⁶ K and with a dilution factor 0.4, the intensity ratio of λ211.3 and λ219.0 changes by a factor of 65 if N _e increases from 10⁷ to 10¹¹ (Table VIII). Cascades from the 3s3p3d and 3p ³ configurations are important in the population of some levels of 3s3p ² (Table VI). A possibility of identification of additional lines in the solar spectrum is indicated. NAS-NRC Resident Research Associate.     

The forbidden transitions within 3s 2 3p 5 3d of Fe ix and Ni xi and 3s 2 3p 4 3d of Fe x and Ni xii

Improved level values for 3s ² 3p ⁵ 3d and 3s ² 3p ⁴ 3d of Fe ix and Fe x are derived from the observed forbidden lines with special regard to recent accurate measurements in the vacuum-ultraviolet part of the coronal spectrum. A procedure for estimating expected relative intensities is proposed and used for an additional check on the consistency of the identifications, which now comprise 12 lines of Fe IX and 11 lines of Fe x. Finally, by use of a suitable extrapolation technique the wavelengths of corresponding lines in nickel are predicted, which leads to some new identifications and a total of 6 identified lines of Ni xi and 4 of Ni xii.     

The solution of radiation transfer problem for a slab with space-dependent albedo and anisotropic scattering

The transport of thermal radiation has been considered within a finite slab which absorb and scatter anisotropically. The problem involves the space-dependent single-scattering albedow(x). Two approximations are taken forw(x). In the first it is represented in exponential form asw(x)=w ₀ exp(–x/s), wherew ₀ ands are given constants andx is the optical variable. The second approximation assumes the formw(x) = _r=0 ^R d _r ^* p _r (x/a), whered _r ^* are known expansion coefficients anda is the half optical thickness of the slab. Analytic expressions for the forward, backward radiation intensities and fluxes are given in each approximation. The solution of the linear transport equation is performed on the basis of integral Fourier transforms.     

The identification of Feix and Nixi in the solar corona

The levels of the configuration 3s ²3 _p ⁵3d of Fe ix have been experimentally determined from their combinations with 3s3 _p ⁶3d ³ D in the region 300–400 Å. Wavelengths can now be accurately predicted for all transitions within 3s ²3 _p 53^d, and eight of these can be identified with coronal lines from 2042 to 4585 Å. Also, identifications of solar lines from 171 to 245 Å with electric-dipole and magnetic-quadrupole transitions to the ground state, 3s ²3p ^{6 1} S, are confirmed and extended. Solar identifications with corresponding transitions in Ni xi, both within 3s ²3 _p ⁵3d and to the ground state, are proposed on the basis of a short extrapolation.     

An upper limit on the X-ray luminosity of the microlensing black hole OGLE-1999-BUL-32

Having analyzed the 1999 scanning observations of the Galactic-center region with the PCA spectrometer onboard the RXTE observatory, we obtained upper limits on the flux from the microlensing black hole OGLE-1999-BUL-32 in 1999–2000. We show that the X-ray luminosity of this black hole did not exceed L _x ? 3 × 10³³(d/1kpc)² erg s^?1. Near the maximum amplification of the background star (on June 6, 1999), the upper limit was L _x ? 7 × 10³³(d/1kpc)² erg s^?1.     

General time elements for the two body problem

When integrating a perturbed two-body problem, very often the propagation of the numerical error is reduced by using a new time variables defined by dt/ds=|q| ⁿ , (|q| is the radial distance,t the time). This paper introduces a time element for such transformations, i.e., a new variablet _n is defined so that dt _n/ds=1+ (perturbing terms) andt=F _n(t_n), whereF _n is a known function. The time element equation should be useful in reducing the error in the determination of the timet.F _n is given explicitly forn=1, 3/2, 2, 5/2 and 3, and a general expression is given for other values.The work was performed while the author was an NRC Senior Research Associate, Goddard Space Flight Center, Greenbelt, Md., U.S.A.     

Rosat X-ray observations of the WR stars HD 50896 (WN5) andγ velorum (WC8+O9I)

We present a preliminary analysis of multiple X-ray (0.1–2.5 keV) observations of HD 50896 andγ Velorum obtained with theROSAT satellite. For HD 50896, our 8 observations show variability at the 30% level on timescales of ～ 1 day, together with larger (× 1.7) epoch-changes, but no evidence for rapid variability. No phase-dependent modulation is apparent on the 3^d.766 optical period. The mean PSPC spectrum gives kT = 0.28 keV, log N(H) = 20.6, and L_x = 3.8 × 10³² erg s^?1, and implies that the observed X-rays have undergone little absorption in the WN5 wind. Forγ Velorum, we have 13 observations secured over several cycles in the 78^d.5 binary period. At most binary phases, the X-ray emission is relatively constant, with kT ? 0.19 keV, log N(H) = 20.2, and L_x = 2.5 × 10³¹ erg s^?1. Near orbital phase 0.5, the X-ray emission is enhanced by a factor of 4, due almost entirely to an additional harder component with kT ≥ 2 keV. We believe this is due to X-ray emission produced in the collision of the two stellar winds.     

On the identification of Ar x and Ar xiv in the solar corona and the origin of the unidentified coronal lines

A study of theZ-dependence of the² P intervals of 2s ²2p and 2s ²2p ⁵, aided by recent observational results, confirms the identification in the coronal spectrum of λ 4412 with Arxiv, and of λ 5533.4 with Arx. It is further shown that transitions from metastable levels in the configurations 3s ²3p ^k 3d, withk=3, 4 and 5, of Fexi,x, ix, and Nixiii, xiii, xi can well account for the remaining unidentified coronal lines.     

V792 Her=HD 155638: A totally eclipsing RS CVn binary

Photometry of HD 155638=V792 Her has been analyzed to determine the elements of this totally eclipsing RS CVn binary. The light variation outside eclipse was found to have a period of 27^d.07±0^d.07, which is slightly different from the 27^d.5384±0^d.0045 orbital period. Analysis of the eclipses was achieved by a modification of the Russell-Merrill technique. With the aid of radial velocity measures, absolute elements were obtained for the hot and cool stars, respectively;R _h=2.58R ,R _c=12.28R ,M _h=1.40M ,M _c=1.46M ,i=80^o.61 and velocity semi-amplitudesK _c=48.36 km s^–1±0.79 km s^–1, andK _h=50.50 km s^–1±0.33 km s^–1. The apparent magnitudes areV _h=9 ^m .73 andV _c=8 ^m .48. The distance to HD 155638 was estimated to be 310 parsecs.     

The X-ray source SLX 1732-304 in the globular cluster Terzan 1: The spectral states and an X-ray burst

ART-P/Granat observations of the X-ray burster SLX 1732-304 in the globular cluster Terzan 1 are presented. The X-ray (3–20 keV) fluxes from the source differed by more than a factor of 4 during the observing sessions on September 8 (F _x ? 6.95 × 10^?10 erg cm^?2 s^?1) and October 6, 1990 (F _x ? 1.64 × 10^?10 erg cm^?2 s^?1). The intensity variations of SLX 1732-304 were apparently accompanied by variations in its hardness: whereas the source in its high state had the spectrum with a distinct exponential cutoff typical of bright low-mass X-ray binaries, its low-state spectrum could be satisfactorily described by a simple power law with a photon index α?1.7. During the ART-P observation on September 8, a type I X-ray burst was detected from SLX 1732-304.     

Forbidden transition probabilities of astrophysical interest among low-lying states of V III

Electric and magnetic multipole transitions among low-lying states of doubly ionized vanadium were computed using the multi-configuration Hartree-Fock (MCHF) method with Breit-Pauli (BP) corrections to a non-relativistic Hamiltonian. Energy levels were determined up to and including 3d ²(¹ G)4s b ² G _7/2 and computed energies were found to be in good agreement with experiment and other theories. In addition to Einstein A _ki coefficients for some E2 and M1 transitions, lifetime data and selected weighted oscillator strengths are also reported.     

Subsurface deformation in hypervelocity cratering experiments into high‐porosity tuffs

Hypervelocity impact experiments on porous tuff targets were carried out to determine the effect of porosity on deformation mechanisms in the crater's subsurface. Blocks of Weibern Tuff with about 43% porosity were impacted by 2.5 mm and 12.0 mm diameter steel spheres with velocities between 4.8 km s^?1 and 5.6 km s^?1. The postimpact subsurface damage was quantified with computer tomography as well as with meso‐ and microscale analyses of the bisected crater subsurface. The intensity and style of deformation in mineral clasts and the tuff matrix were mapped and their decay with subsurface depth was determined. Subsurface deformation styles include pore space compaction, clast rotation, as well as microfracture formation. Evaluation of the deformation indicates near‐surface energy coupling at a calculated depth of burial of ~2 projectile diameters (d_p), which is in conflict with the crater shape, which displays a deep, central penetration tube. Subsurface damage extends to ~2 d_p beneath the crater floor in the experiments with 2.5 mm projectiles and increases to ~3 d_p for 12 mm projectiles. Based on overprinting relationships and the geometrical orientation of deformation features, a sequence of subsurface deformation events was derived (1) matrix compaction, (2) intragranular crack formation in clasts, (3) deformation band formation in the compacted matrix, (4) tensile fracturing.     

Structure of X-ray irradiated stellar wind

The effect of X-ray irradiation on the line-driven stellar wind in X-ray binary systems is studied. The product of the X-ray luminosityL _x and the densityn in the wind is a measure to distinguish between the optically thin and thick wind regimes. For an X-ray source of the radiation temperature of 10 keV, the critical value(L _x n) _c , is of the order of 10³⁷ erg s^–1 cm^–3; hence, most of wind-fed X-ray sources lie in the optically thick wind regime because ofL _x n>(L _x n) _c . Then the wind structure is determined not only by the parameter =(L _x /nR ²),R the distance from the X-ray source, but also by the optical thickness due to helium. The formation of fully ionized helium region depends onL _x andn in a way different from that of the Strömgren sphere. In such an optically thick wind, the region behind the He II ionization boundary is little affected by X-ray irradiation and the trace elements remain to be responsible for wind acceleration. Thus, its location is important for the structure of the wind and the interpretation of various phenomena in objects such as wind-fed X-ray pulsars.     

Note on aTheorem of Relativistic Hydrodynamics

A well known theorem of relativistic hydrodynamics states that the streamlines of an isentropic perfect fluid are the future-pointing timelike (FPT) curves extremizing the integral J = ∫ _S1 ^S2 fds, where f is the so-called index function and s the proper time on the world line of the fluid particle. The integral is taken over all possible FPT curves with regular representations xⁱ = xⁱ (s) joining the fixed end events E₁, E₂. The purpose of this note is to show that the streamlines of an adiabatic perfect fluid can likewise be regarded as extremizing curves of the functional J provided the class of admissible curves consists of those FPT curves satisfying the side condition uⁱ∂_iS = 0, uⁱ unit 4-velocity and S the specific proper entropy of the fluid, with the first end point fixed and the second being the end point variable. __________ Published in Astrofizika, Vol. 48, No. 4, pp. 641–647 (October–December, 2005).     

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.     

Principe cosmologique,principe variationnel et theorie des groupes

The Friedmann universes are built on the cosmological principle only. The Robertson-Walker metric is common to all the theories based on a homogeneous, isotropic and irrotational universe. In the present work we examine ways of constructing a metric conformal with that of Robertson and Walker, by means of a variational principle which takes into account the cosmological principle as stated by Weinberg (1972), and based on the existence of orbits generated by a one-parameter group of diffeomorphisms of physical space. The application of the cosmological principle to variational methods allows the determination of first integrals which can characterize the physical properties of the Universe. To this end, we show that the Lagrangian of the Universe, considered as a mechanical system, can be chosen from the germs of functions, and that the form variations δq ⁱ are tangent vectors of the group orbits in a Riemannian manifold. Thus the variation of the action vanishes automatically. There appears a first integral of the Euler equations, which is δq ⁱ (?L/?q1 ⁱ ) = C ^te , and also the condition ?L/?t=0, which means the uniformity of time in a Lagrangian conservative system, and which is a direct application of the cosmological principle. These conditions allow the effective determination of a form invariant Lagrangian in the case of isometries. These conditions can be generalized to the case in which the group trajectories are a partition of physical space. Thus, it is possible to define a time from the group trajectories inV ₃: a second of the group time is a lengthm measured along any orbit θ _p of the group. Any pointp of the manifold can then be considered as the starting point of a bundle of orbits, along which the tangent vectors δq ⁱ could be calculated. From this group time, we can build a metric ds ² conformal to the initial ds ² and for which the orbits, which are geodesic, are orthogonal to the transitivity surfaces of the group in the manifold. This implies new statements of the cosmological principle:

1. At any point of space-time it is possible to construct a metric ds ² from the trajectories generated by a one-parameter group of diffeomorphisms ofV ₄.
2. Any two points of space-time can always be joined by means of trajectories of group.

The variational implications of these two principles are the appearance of spectral line shifts such as 1+z=F(p, t _p)/F(q, t_q), wherep andq are arbitrary points of the manifold, andF the transformation function which allows passage from one metric to another. The identification of group trajectories with physical trajectories depends on these two principles. The photon trajectories inV ₃ is an example of this identification. The trajectories of charged particles inV ₄ are another. Principle (b) stated an entropy condition; its application allows a new expression of action variation, this one leading to a general formulation of the shift of spectral lines by a variational method. If we choose the parabolic Friedmann universe as a realistic model, it is the expansion itself which is the generator of the diffeomorphisms allowing the establishment of a group structure in the manifold. The photons are carried away by expansion and do not resist it. The massive particles moderate this expansion locally, and their trajectories inV ₃ are the result of the reaction. In this scheme there is no theoretical difference between the treatment of particles of vanishing proper mass and massive particles. The Robertson-Walker metric fork=0 corresponds to a picture of the Universe which can be drawn by study of the movement of photons in physical space. Only the study of particles can allow the generalization of this scheme and, from this, make a real Universe which is not just a reflection of the physical properties of the photons alone.     

Exact solution of perfect fluid massive string cosmology in Bianchi type?III space-time with decaying vacuum energy density?Λ

Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using the technique given by Letelier (Phys. Rev. D 20:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations the expansion θ in the model is considered as proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. The vacuum energy density Λ is found to be positive and a decreasing function of time which is supported by the results from recent supernovae Ia observations. It is also observed that in early stage of the evolution of the universe string dominates over the particle whereas the universe is dominated by massive string at the late time. Some physical and geometric properties of the model are also discussed.