Estimation of potential energy curves, dissociation energies, franck-condon factors and r-centroids of comet interesting molecules

The experimental potential energy curves for the different electronic states of molecules like CN, CO and CS observed in comets are constructed by using the Rydberg-Klein-Rees method as modified by Vanderslice et al. The ground state dissociation energies are determined by curve fitting technique using the five parameter Hulburt-Hirschfelder (H-H)function. The estimated dissociation energies are 7.63 ± 0.187, 10.95 ±0.224 and 7.27 ± 0.152 eV for CN, CO and CS respectively. These values are in good agreement with the literature values. Estimated dissociation energies of CN, CO and CS are used in the relation given by Gaydon and ionization potentials are evaluated for CO and CS molecules. The estimated ionization potentials are 13.92and 12.15 eV for CO and CS molecules respectively. The r-centroids and Franck-Condon factors (FC Factors) for the band system of a ³Π_r – X¹Σ⁺ (a – X) and A¹Π – X ¹Σ⁺ (A -X) of CN, A ²Π_i – X²Σ⁺ (A – X) and B²Σ⁺-X²Σ⁺ (B – X) of CO and a ³Π_r – X¹Σ⁺ (a – X) of CS molecules have been calculated employing an approximate analytical methods of Jarmain and Fraser and Nicholls and Jarmain. The absence of the bands in these systems are explained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Franck-Condon factors and <Emphasis Type="Italic">r</Emphasis>-centroids for certain band systems of astrophysical molecules SrF and ScF

The Franck-Condon factors and r-centroids, which are very closely related to vibrational transition probabilities, have been evaluated by the more reliable numerical integration procedure for the bands of B ²∑⁺ − X ²∑⁺, F ²∑⁺ − X ²∑⁺ systems of SrF and C ¹∑⁺ − X ¹∑⁺, G ¹Π − X ¹∑⁺ systems of ScF molecules of astrophysical interest, using a suitable potential.     

Astrophysically useful radiative transition parameters for?the?e1Π–X1Σ+ and 1Σ+–X1Σ+ systems of zirconium oxide

The zirconium oxide (ZrO) is well known for its astrophysical importance. The radiative transition parameters that include Franck-Condon (FC) factor, r-centroid, electronic transition moments, Einstein coefficient, band oscillator strengths, radiative life time and effective vibrational temperature have been estimated for e ¹Π–X ¹Σ⁺ and ¹Σ⁺–X ¹Σ⁺ band systems of ⁹⁰ZrO molecule for the experimentally known vibrational levels using RKR potential energy curves. A reliable numerical integration method has been used to solve the radial Schr?dinger equation for the vibrational wave functions of upper and lower electronic states based on the latest available spectroscopic data and known wavelengths. The estimated radiative transition parameters are tabulated. The effective vibrational temperatures of these band systems of ⁹⁰ZrO molecule are found to be below 4200 K. Hence, the radiative transition parameters help us to ascertain the presence of ⁹⁰ZrO molecule in the interstellar medium, S stars and sunspots.     

Searches for proton decay and superheavy Magnetic Monopoles

Conclusion In conclusion, as of 1984 January, it may be stated that the existence of super-heavy monopoles and the phenomenon of nucleon decay, both of which are extremely important from the point of view of grand unification theories, are still very open questions. While there has been just one magnetic monopole candidate so far, there have been several as far as nucleon decay is concerned. The first candidates for nucleon decay came from the fine-grain calorimeters of KGF, and NUSEX; recently there have been candidates from the water Cerenkov experiments as well. The experimental situation regarding the other important phenomena of relevance to grand unification which we have not discussed in this article — like the finite mass of neutrinos, neutrino oscillations, and neutron oscillations — continues to be indefinite though many dedicated experiments are in progress. With the continued operation of the nucleon decay experiments already collecting data and the commissioning of the new generation of experiments over the next few years, the stage is set for a resolution of this problem in a time scale of 5–10 years. The present indication that the dominant decay mode for the proton (even if it decays) is notp → e⁺π⁰ and that the lower limit to the lifetime of the nucleon is 10³¹ yr, does not favour the simple SU(5) type models. The remarkable discoveries of W^± and Z⁰ with mass values exactly as predicted, have given a boost to the unification based on the gauge theoretical approaches. Whether grand unification can be extended to super-unification, experiment alone can tell. This will be the challenge for the remaining years of this century.     

‘Similar’ coordinate systems and the Roche geometry: application

A new equivalence relation, named relation of ‘similarity’ is defined and applied in the restricted three-body problem. Using this relation, a new class of trajectories (named ‘similar’ trajectories) are obtained; they have the theoretical role to give us new details in the restricted three-body problem. The ‘similar’ coordinate systems allow us in addition to obtain a unitary and an elegant demonstration of some analytical relations in the Roche geometry. As an example, some analytical relations published by Seidov (in Astrophys. J. 603:283, 2004) are demonstrated.     

The determination of gravitational potential differences from satellite-to-satellite tracking

A new, rigorous model is developed for the difference of gravitational potential between two close earth-orbiting satellites in terms of measured range-rates, velocities and velocity differences, and specific forces. It is particularly suited to regional geopotential determination from a satellite-to-satellite tracking mission. Based on energy considerations, the model specifically accounts for the time variability of the potential in inertial space, principally due to earth’s rotation. Analysis shows the latter to be a significant (±1 m²/s²) effect that overshadows by many orders of magnitude other time dependencies caused by solar and lunar tidal potentials. Also, variations in earth rotation with respect to terrestrial and celestial coordinate frames are inconsequential. Results of simulations contrast the new model to the simplified linear model (relating potential difference to range-rate) and delineate accuracy requirements in velocity vector measurements needed to supplement the range-rate measurements. The numerical analysis is oriented toward the scheduled Gravity Recovery and Climate Experiment (GRACE) mission and shows that an accuracy in the velocity difference vector of 2×10⁻⁵ m/s would be commensurate within the model to the anticipated accuracy of 10⁻⁶ m/s in range-rate. This revised version was published online in July 2006 with corrections to the Cover Date.     

Field-Dependent Adaptive Optics Correction Derived with the Spectral Ratio Technique

In this empirical study, we compare high-resolution observations obtained with the 65-cm vacuum reflector at Big Bear Solar Observatory (BBSO) in 2005 and with the Dunn Solar Telescope (DST) at the National Solar Observatory/Sacramento Peak (NSO/SP) in 2006. We measure the correction of the high-order adaptive optics (AO) systems across the field of view (FOV) using the spectral ratio technique, which is commonly employed in speckle masking imaging, and differential image motion measurements. The AO correction is typically much larger (10^′′ to 25^′′) than the isoplanatic angle and can be described by a radially symmetric function with a central core and extended wings. The full-width at half-maximum (FWHM) of the core represents a measure of the AO correction. The average FWHM values for BBSO and NSO/SP are 23.5^′′ and 18.2^′′, respectively. The extended wings of the function show that the AO systems still contribute to an improved speckle reconstruction at the periphery of the 80^′′×80^′′ FOV. The major differences in the level of AO correction between BBSO and NSO/SP can be explained by different contributions of ground-layer- and free-atmosphere-dominated seeing, as well as different FOVs of the wavefront sensors. In addition, we find an anisotropic spectral ratio in sunspot penumbrae caused by the quasi-one-dimensional nature of penumbral filaments, which introduces a significant error in the estimation of the Fourier amplitudes during the image restoration process.     

Regularization of the circular restricted three-body problem using ‘similar’ coordinate systems

The regularization of a new problem, namely the three-body problem, using ‘similar’ coordinate system is proposed. For this purpose we use the relation of ‘similarity’, which has been introduced as an equivalence relation in a previous paper (see Roman in Astrophys. Space Sci. doi:, 2011). First we write the Hamiltonian function, the equations of motion in canonical form, and then using a generating function, we obtain the transformed equations of motion. After the coordinates transformations, we introduce the fictitious time, to regularize the equations of motion. Explicit formulas are given for the regularization in the coordinate systems centered in the more massive and the less massive star of the binary system. The ‘similar’ polar angle’s definition is introduced, in order to analyze the regularization’s geometrical transformation. The effect of Levi-Civita’s transformation is described in a geometrical manner. Using the resulted regularized equations, we analyze and compare these canonical equations numerically, for the Earth-Moon binary system.     

Precision of selenodetic frames of reference

The number of reference points for the fixing of a selenodetic reference frame in the Moon’s body is estimated. It is shown that, for this purpose, from 40 to 100 reference points are sufficient. Precision of the selenodetic coordinate transformations from one system to another is also analysed.     

Spectroscopic Studies on Astrophysically Interesting TaO TaS, ZrS and SiO+ Molecules

The true experimental potential energy curves for the electronic ground states of astrophysically important TaO, TaS, ZrS and SiO⁺molecules are constructed by using the Rydberg–Klein–Rees method as modified by Vanderslice et al. The ground state dissociation energies are determined by curve fitting techniques using the five parameters Hulburt-Hirschfelder (H-H) function. The estimated dissociation energies are 8.19 ± 0.17, 6.9 ±0.14, 5.89 ± 0.12 and 5.75 ± 0.12 eVfor TaO, TaS, ZrS and SiO⁺ respectively. These values are in good agreement with the literature values. The r-centriods and Franck–Condon factors (FC Factors) for the bands of K ² φ _5/2 - X ² Δ _3/2 (K-X) system of TaO, A-X ² Δ (A-X) and B-X ² Δ (B-X)systems of TaS, B ¹ Π - X¹ Σ⁺ (B-X) system of ZrS and B ²Σ⁺ - X² Σ⁺ (B-X) and A ² Π - X² Σ⁺ (A-X)systems of SiO⁺ molecules have been calculated. The Franck–Condon factors (FC factors) are evaluated by the approximate analytical methods of Jarmain and Fraser. The absence of the bands of these systems is explained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Large-scale periodicity in the distribution of QSO absorption-line systems

The spatial-temporal distribution of absorption-line systems (ALSs) observed in QSO spectra within the cosmological redshift interval z=0.0–4.3 is investigated on the base of our updated catalog of absorption systems. We consider so-called metallic systems including basically lines of heavy elements. The sample of the data displays regular variations (with amplitudes ∼15–20%) in the z-distribution of ALSs as well as in the η-distribution, where η is a dimensionless line-of-sight comoving distance, relatively to smoother dependences. The η-distribution reveals the periodicity with period Δη=0.036±0.002, which corresponds to a spatial characteristic scale (108±6)h ⁻¹ Mpc or (alternatively) a temporal interval (350±20)h ⁻¹ Myr for the ΛCDM cosmological model. We discuss the possibility of a spatial interpretation of the results, treating the pattern obtained as a trace of an order imprinted on the galaxy clustering in the early Universe.     

Varying Constants, Nuclear Physics and Unification

Precision measurements of gauge couplings at particle accelerators strongly suggest that the standard model fields are unified at about 10¹⁶ GeV. This talk will consist of a brief review of this evidence and also how in such a setting variations in α _em lead to much larger variations in Λ _QCD . I will then describe how variations in the strong force will impact upon nuclear astrophysics, considering in particular the stability of di-nucleons and stellar and primordial nucleosynthesis. (Based upon collaborations with T. Dent and with A. Csoto, H. Oberhummer and H. Schlattl.) This revised version was published online in July 2006 with corrections to the Cover Date.     

Scenarios for the formation of binary and millisecond pulsars – A critical assessment

The evolution of high-and low-mass X-ray binaries (HMXB and LMXB) into different types of binary radio pulsars, the ‘high-mass binary pulsars’(HMBP) and ‘low-mass binary pulsars’ (LMBP) is discussed. The HMXB evolve either into Thorne-Zytkow objects or into short-period binaries consisting of a helium star plus a neutron star (or a black hole), resembling Cygnus X-3. The latter systems evolve (with or without a second common-envelope phase) into close binary pulsars, in which the companion of the pulsar may be a massive white dwarf, a neutron star or a black hole ( some final systems may also consist of two black holes). A considerable fraction of the systems may also be disrupted in the second supernova explosion. We discuss the possible reasons why the observed numbers of double neutron stars and of systems like Cyg X-3 are several orders of magnitude lower than theoretically predicted. It is argued that the observed systems form the tip of an iceberg of much larger populations of unobserved systems, some of which may become observable in the future. As to the LMBP, we consider in some detail the origins of systems with orbital periods in the range 1–20 days. We show that to explain their existence, losses of orbital angular momentum (e.g., by magnetic braking) and in a number of cases: also of mass, have to be taken into account. The masses of the low-mass white dwarf companions in these systems can be predicted accurately. We notice a clear correlation between spin period and orbital period for these systems, as well as a clear correlation between pulsar magnetic field strength and orbital period. These relations strongly suggest that increased amounts of mass accreted by the neutron stars lead to increased decay of their magnetic fields: we suggest a simple way to understand the observed value of the ‘bottom’ field strengths of a few times 10⁸ G. Furthermore, we find that the LMBP-systems in which the pulsar has a strong magnetic field (> 10¹¹ G) have an about two orders of magnitude larger birth rate (i.e., about 4 × 10^-4 yr^-1 in the Galaxy) than the systems with millisecond pulsars (which have B < 10⁹ G). Using the observational fact that neutron stars receive a velocity kick of ∼450 km/s at birth, we find that some 90% of the potential progenitor systems of the strong-field LMBP must have been disrupted in the Supernovae in which their neutron stars were formed. Hence, the formation rate of the progenitors of the strong-field LMBP is of the same order as the galactic supernova rate (4 × 10^-3 yr^-1). This implies that a large fraction of all Supernovae take place in binaries with a close low-mass (< 2.3 M⊙) companion.     

Determining the orientation parameters of the ICRS/UCAC2 system using the Kharkov catalog of absolute stellar proper motions

The absolute proper motions of about 275 million stars from the Kharkov XPM catalog have been obtained by comparing their positions in the 2MASS and USNO-A2.0 catalogs with an epoch difference of about 45 yr for northern-hemisphere stars and about 17 yr for southern-hemisphere stars. The zero point of the system of absolute proper motions has been determined using 1.45 million galaxies. The equatorial components of the residual rotation vector of the ICRS/UCAC2 coordinate system relative to the system of extragalactic sources have been determined by comparing the XPM and UCAC2 stellar proper motions: ω _x,y,z = (−0.06, 0.17, −0.84) ± (0.15, 0.14, 0.14) mas yr⁻¹. These parameters have been calculated using about 1 million faintest UCAC2 stars with magnitudes R _UCAC2 > 16 ^m and J > 14 ^m . 7, for which the color and magnitude equation effects are negligible.     

Structure and stability of rotating fluid disks around massive objects. I. Newtonian formulation

In this paper we have presented a very general class of solutions for rotating fluid disks around massive objects (neglecting the self gravitation of the disk) with density as a function of the radial coordinate only and pressure being nonzero. Having considered a number of cases with different density and velocity distributions, we have analysed the stability of such disks under both radial and axisymmetric perturbations. For a perfect gas disk with γ= 5/3 the disk is stable with frequency (MG/r³)^1/2 for purely radial pulsation with expanding and contracting boundary. In the case of axisymmetric perturbation the critical γ_c for neutral stability is found to be much less than 4/3 indicating that such disks are mostly stable under such perturbations. On leave of absence from Government College, Jagdalpur 494005.     

Tidal dwarf galaxies in the Stephan's Quintet?

We present kinematics and photometric evidence for the presence of seven candidate tidal dwarf galaxies in Stephan's Quintet. The central regions of the two most probable parent galaxies, NGC 7319 and NGC 7318B, contain little or no gas whereas the intragroup medium and, in particular, the optical tails that seem to be associated with NGC 7318B are rich in cold and ionized gas. Two tidal dwarf candidates may be located at the edge of a tidal tail, another located within a tail, and for the four others there is no obvious stellar/gaseous bridge between them and the parent galaxy. Two of the candidates are associated with H I clouds, one of which is, in addition, associated with a CO cloud. All seven regions have low continuum fluxes and high Hα luminosity densities [F(Hα) = (1-60) × 10-14 ergs s^-1 cm^-2]. Their magnitudes (M_B = –16.1 to –12.6), sizes (∼ 3.5 h₇₅ ^-1 kpc), colors (typically B – R = 0.7), and gas velocity gradients (∼ 8 –26 h₇₅ km s^-1 kpc^-1) are typical for tidal dwarf galaxies. In addition, the ratios between their star formation rates determined from Hα and from the B-band luminosity are typical of other tidal dwarf galaxies. The masses of the tidal dwarf galaxies in Stephan's Quintet range from ∼ 2 × 10⁸ to 10¹⁰ M_⊙, and the median value for their inferred mass-to-light ratios is 7 (M/L)_⊙. At least two of the systems may survive possible ‘fallbacks’ or disruption by the parent galaxies and may already be, or turn into, self-gravitating dwarf galaxies, new members of the group. This revised version was published online in September 2006 with corrections to the Cover Date.     

Colliding Blast Waves Driven by the Interaction of a Short-Pulse Laser with a Gas of Atomic Clusters

Collisions between shocks are commonly found in many astrophysical objects, however robust numerical models or laboratory analogues of these complex systems remain challenging to implement. We report on the development of scaled laboratory experiments which employ new techniques for launching and diagnosing colliding shocks and high Mach number blast waves, scalable to a limited subset of astrophysically-relevant regimes. Use of an extended medium of atomic clusters enables efficient (>80%) coupling of 700 fs, 1 J, 1054 nm laser pulses to a “cluster” gas with an average density of ≈10¹⁹ particles cm⁻³, producing an initial energy density >10⁵ J cm⁻³, equivalent to ≈5×10⁹ J/g. Multiple laser foci are used to tailor the spatial profile of energy deposition, or to launch pairs of counter-propagating cylindrical shocks which then collide. By probing the collision interferometrically at multiple view angles in 5^{^} increments and applying an inverse Radon transform to the resulting phase projections we have been able to tomographicall reconstruct the full three-dimensional, time-framed electron density profile of the system.     

The kinematics of Trapezium-type systems

Summary In this paper the results of the research of the stars proper motions Trapezium components are reported. They are: the galactic coordinates of the solar aprx and the Sun velocity (L _⊙=43±18°,B _⊙=+28±13°,V _⊙=13±4 km s⁻¹), the dispersion of peculiar velocities in the direction of the galactic coordinates for the above mentioned stars (σ _l =±11 km s⁻¹, σ _b =±7 km s⁻¹).The attained accuracy of the proper motions (±0.005″ yr⁻¹) is shown to be insufficient to the study of internal space motions in these systems. At present the work to increase the relative proper motions accuracy for multiple system components and to improve reductions from the relative to absolute proper motions, is being carried out in the Main Astronomical Observatory (Academy of Sciences of the Ukrainian SSR). The new catalogue of the AGK3 stars is composed now in the vicinity of the galactic equator in order to improve reductions from the relative to absolute proper motions. The r.m.s. errors of the proper motions, obtained in the AGK3 system, are ±0.005″ yr⁻¹.     

Vortex structure of neutron stars with CFL quark cores

The Ginzburg-Landau equations are derived for the magnetic and gluomagnetic gauge fields of nonabelian semi-superfluid vortex filaments in color superconducting cores of neutron stars containing a diquark CFL condensate. The interaction of the diquark CFL condensate with the magnetic and gluomagnetic gauge fields is taken into account. The asymptotic values of the energies of these filaments are determined from the quantization conditions. It is shown that a lattice of semi-superfluid vortex filaments with a minimal quantum of circulation develops in the quark superconducting core during rotation of the star. The magnetic field in the core of this vortex is on the order of 10¹⁸ G. A cluster of proton vortices, which develops in the hadron phase surrounding every superfluid neutron vortex owing to an entrainment effect, creates new semi-superfluid vortex filaments with a minimal quantum of circulation in the quark superconducting core. Translated from Astrofizika, Vol. 51, No. 4, pp. 633–646 (November 2008).     

Molecular systems in a strong magnetic field

Brief overview of one-two electron molecular systems made out of protons and/or α-particles in a strong magnetic field B≤4.414×10¹³ G is presented. A particular emphasis is given to the one-electron exotic ions H₃⁺⁺(pppe), He₂³⁺(α α e) and to two-electron ionsH₃⁺(pppee), He₂⁺⁺(α α ee). Quantitative studies in a strong magnetic field are very complicated technically. Novel approach to the few-electron Coulomb systems in magnetic field, which provides accurate results, based on variational calculus with physically relevant trial functions is briefly described.