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.     

Franck-condon factors and -centroids for certain band systems of astrophysical molecular ions CN+ and N+2

The Franck-Condon factors and r-centroids, which are very closelyrelated to relative vibrational transition probabilities, have beenevaluated by the more reliable numerical integration procedure forthe bands of c ¹ - a ¹ and f ¹ - a ¹ systems of CN ⁺ and C ^{2 +} _u- X ^{2 +} _g and D ² _g- A ² _u systems of N ⁺ ₂ molecular ions of astrophysical interest,using a suitable potential.     

Transition probability parameters for the band systems G, H and I-B of astrophysical molecule PO

The transition probability parameters, Franck – Condon factors and r-centroids, have been evaluated by the more reliable numerical integration procedure for the bands of G, H and I-B systems of astrophysical molecule PO, using a suitable potential. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spectroscopic parameters for certain band systems of astrophysically important molecule: Yttrium oxide

The Franck–Condon (FC) factors and r-centroids are defined through elementary integrals that involve vibrational wave functions on which they depend in a sensitive manner. The FC factors and r-centroids have been evaluated by a reliable numerical integration procedure on the basis of RKR potential energy model, for the A²Π_3/2 ? X²Σ⁺, A²Π_1/2 ? X²Σ⁺ and B²Σ⁺ ? X²Σ⁺ band systems of the astrophysically important yttrium oxide molecule. RKR and Morse potential values have been generated for all the four electronic states of YO molecule. All of these three systems of YO show significant rotational independence.     

On Franck-Condon factors and intensity distributions in some band systems of I2, NS and PS molecules

Potential curves for theB andX states of I₂, NS and PS have been obtained by Rydberg-Klein-Rees (RKR) method. From these RKR potentials, Franck-Condon factors (FCFs) lot the above band systems have been calculated using the best available molecular constants, tested for accuracy on the electronic transition moment (ETM)-r-centroid curve in the case of I₂ and used in the study of observed abnormal intensity distribution in some bands of NS. A brief outline of the method used in the calculations of the FCFs is given.     

Gravitational instability for some astrophysical systems

The gravitational instability of an infinite homogeneous self-gravitating mixture through porous medium in the presence of a variable horizontal magnetic field varying in vertical directions has been considered to include, separately, the effects due to suspended particles and collisions between ionized and neutral components. The dispersion relations in both cases have been obtained. It has been found that Jeans's criterion of instability holds good even if the effects due to suspended particles, collisions, porosity, and variable magnetic field are considered.     

Transition probabilities and dissociation energy of astrophysical molecule CrH

The Franck-Condon (FC) factors (transition probabilities) andr-centroids have been evaluated by the reliable numerical integration procedure for the bands of the A⁶⁺ X ⁶⁺ system of astrophysical molecule CrH, using a suitable potential. The dissociation energyD ₀ ⁰ = 2.3 eV for the electronic ground state of CrH has been estimated by fitting the Hulburt-Hirschfelder function to the experimental potential energy curve, using the correlation coefficient.     

Transition probabilities and dissociation energy of astrophysical molecule CoH

The Franck-Condon (FC) factors (transition probabilities) and r-centroids have been evaluated by the reliable numerical integration procedure for the bands of the A ³ φ₄ →X ³ φ₄ system of astrophysical molecule CoH, using a suitable potential. The dissociation energy D ⁰ ₀ = 2.5 ± 0.05 eV for the electronic ground state of CoH has been estimated by fitting Hulburt-Hirschfelder function to the experimental potential energy curve, using the correlation coefficient. This revised version was published online in July 2006 with corrections to the Cover Date.     

Transition probabilities and dissociation energy of astrophysical molecule GeH

The Franck-Condon factors andr-centroids, which are very closely related to vibrational transition probabilities, have been evaluated by the more reliable numerical integration procedure for the bands of A ² Δ - X² π_r system of astrophysical molecule GeH, using a suitable potential. The dissociation energy for the electronic ground state of astrophysical molecule GeH has been estimated precisely as D ⁰ ₀ = 2.69 ± 0.05 eV by fitting the empirical potential function to the experimental potential energy curve using correlation coefficient. This revised version was published online in July 2006 with corrections to the Cover Date.     

A multiphysics and multiscale software environment for modeling astrophysical systems

We present MUSE, a software framework for combining existing computational tools for different astrophysical domains into a single multiphysics, multiscale application. MUSE facilitates the coupling of existing codes written in different languages by providing inter-language tools and by specifying an interface between each module and the framework that represents a balance between generality and computational efficiency. This approach allows scientists to use combinations of codes to solve highly coupled problems without the need to write new codes for other domains or significantly alter their existing codes. MUSE currently incorporates the domains of stellar dynamics, stellar evolution and stellar hydrodynamics for studying generalized stellar systems. We have now reached a “Noah’s Ark” milestone, with (at least) two available numerical solvers for each domain. MUSE can treat multiscale and multiphysics systems in which the time- and size-scales are well separated, like simulating the evolution of planetary systems, small stellar associations, dense stellar clusters, galaxies and galactic nuclei. In this paper we describe three examples calculated using MUSE: the merger of two galaxies, the merger of two evolving stars, and a hybrid N-body simulation. In addition, we demonstrate an implementation of MUSE on a distributed computer which may also include special-purpose hardware, such as GRAPEs or GPUs, to accelerate computations. The current MUSE code base is publicly available as open source at http://muse.li.     

Accurate free–free Gaunt factors for astrophysical plasmas

New calculations of free–free transition matrix element integrals are performed using modern symbolic computing techniques to evaluate the hypergeometric functions with complex arguments. The results are presented in both graphical and tabular form including accurate extrapolation methods. The results are accurate to the level of ∼ 10⁻⁴, beyond which relativistic corrections would be needed, which are not included. The results are also computed over a very wide range of scaled ionic temperature (γ²) and wavelength, extending earlier results to new regimes encountered in highly photoionized and non-equilibrium ionization plasmas. These results will be useful in the spectral range from submillimetre to hard X-ray wavelengths and temperatures from 10 to 10⁹ K.     

Power distributions for self-gravitating astrophysical systems based on nonextensive Tsallis kinetics

The long-time development of self-gravitating gaseous astrophysical systems (in particular, the evolution of the protoplanet accretion disk) is mainly determined by relatively fast processes of the collision relaxation of particles. However, slower dynamical processes related to force (Newton or Coulomb) interactions between particles should be included (as q-collisions) in the nonextensive kinetic theory as well. In the present paper, we propose a procedure to include the Newton self-gravity potential and the centrifugal potential in the near-equilibrium power-like q-distribution in the phase space, obtained (in the framework of nonextensive statistics) by means of the modified Boltzmann equation averaged with respect to an unnormalized distribution. We show that if the power distribution satisfies the stationary q-kinetic equation, then the said equation imposes clear restrictions on the character of the long-term force field and on the possible dependence of hydrodynamic parameters of the coordinates: it determines those parameters uniquely. We provide a thermodynamic stability criterion for the equilibrium of the nonextensive system. The results allow us to simulate the evolution of gaseous astrophysical systems (in particular, the gravitational stability of rotating protoplanet accretion disks) more adequately.     

Molecular parameters for D, E, F, and G-A band systems of the astrophysically significant molecule AlF

Franck-Condon factors and r-centroids, which are a measure of transition probabilities, have been evaluated by a numerical integration procedure for the bands of D¹Δ,E¹Π, F¹Π and G¹Σ⁺– A¹Π systems of AlF molecule.The species has been observed in circumstellar envelopes around AGB stars and spectral studies report its presence in sunspots. The molecular parameters evaluated are necessary for studying the physical and dynamical properties of these sources.     

Expanding and superdense astrophysical systems in general relativistic hierarchical cosmology

A semi-continuous hierarchy, (i.e., one in which there are galaxies outside clusters, clusters outside superclusters etc.), is examined using an expression of the field equations of general relativity in a form due to Podurets, Misner and Sharp. It is shown (a) that for a sufficiently populous hierarchy, the thinning factor( _i+1/ _i [r _i /r _i+1] is approximately equal to the exponentN in a continuous density law (=aR ^–N) provided (r _i /r _i+1)^3-1; (b) that a hierarchical Universe will not look decidedly asymmetric to an observer like a human being because such salient observers live close to the densest elements of the hierarchy (viz stars), the probability of the Universe looking spherically symmetric (dipole anisotropy0.1 to such an observer being of order unity; (c) the existence of a semi-continuous or continuous hierarchy (Peebles) requires that 2 if galaxies, not presently bound to clusters were once members of such systems; (d) there are now in existence no less than ten arguments for believing 2, though recent number counts by Sandageet al. seem to be in contradiction to such a value; (e) Hubble's law, withH independent of distance, can be proved approximately in a relativistic hierarchy provided (i)N=2, (ii)2GM(R)/c ² R1; (iii)Rc (iv)M0 in a system of massM, sizeR (f) Hubble's law holds also in a hierarchy with density jumps; (g)H100 km s^–1 Mpc^–1; (h) objects forming the stellar level of the hierarchy (in a cosmology of the Wilson type) must once have had 2GM/c ² R1; (i) there is a finite pressurep=2Ga in all astrophysical systems (a=R ^N ,N2); (j) for the Galaxy, theory predictsp _G7×10^–12 dyn cm^–2, observation givesp _G5×10^–12 dyn cm^–2; (k) if the mass-defect (or excess binding energy) hypothesis is taken as a postulate, all non-collapsed astrophysical systems must be non-static, and any non-static, p0 systems must in any case be losing mass; (1) the predicted mass-loss rate from the Sun is 10¹² g s^–1, compared to 10¹¹ g s^–1 in the observed solar wind; (m) the mass-loss rates known by observation imply timescales of 5×10⁹ years for the Sun and 10¹⁰ years for other astrophysical systems; (n) degenerate superdense objects composed of fermions must haveN-2 if they were ever at their Schwarzschild radii and comprised a finite numberN _B of baryons; (o)N _B10⁵⁷N for degenerate fermion and boson systems; (p)285-4; (q) the metric coefficients for superdense bodies give equations of motion that imply equal maximum luminosities for all evolving superdense bodies (L _max10⁵⁹ erg s^–1); (r) larger bodies have longer time-scales of energy radiation atL _max (10^–5 s for stars,1 h for QSO's) (s) expansion velocities are c soon after the initial loss of equilibrium in a superdense object; (t) if the density parametera(t) in aR ^–N isa=a (non-atomic constants of physicsc, G, A), andA, thenN=2; (u) N2 is necessary to giveMM at the stellar level of the hierarchy;(v) systems larger than, and including, galaxies must have formed by clumping of smaller systems and not (as advocated by Wertz and others) in a multiple big bang.     

Vibrational transition probabilities,\bar r-centroids and morse PE-curves for SiS

Vibrational transition probabilities-namely, Franck-Condon factors and -centroids-have been evaluated using an approximate analytical method for theD-X system of SiS. Morse potential energy curves forD ¹ andX ¹⁺ states of SiS have been constructed using the latest spectroscopic data. The value of -centroids for the band have been found to decrease linearly with the corresponding wavelength.     

r-Centroids and Franck-Condon factors of the CP,SiC, and CO+ molecules

Ther-centroids and Franck-Condon factors for the bands of theA ² –X ²⁺ of CP,C ³ –X ³ of SiC, andB ²⁺ –X ²⁺ of CO⁺ molecules have been determined. The Franck-Condon factors are evaluated by the approximate analytical method of Jarmain and Fraser. The absence of the bands in these systems is explained.     

Vibrational transition probabilities,\bar r-centroids and PE-curves for OH and PN

Vibrational transition probabilities namely Franck-Condon factors and -centroids have been evaluated using an approximate analytical method for theA-X systems of OH and PN. KKRV potential energy curves forX ² _i ,X ¹⁺,A ²⁺, andA ¹ states of OH and PN have been constructed using the latest spectroscopic data. The value of -centroids for the band have been found to increase linearly with the corresponding wavelengths. We show results for six new bands and OH and eight new bands of PN in the spectra of astronomical objects.     

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.     

The gravitational instability of flow through porous medium for some systems of astrophysical interest

The gravitational instability of flow through porous medium for some hydrodynamical and hydromagnetical systems of astrophysical interest is investigated. The effects of rotation, magnetic field, viscosity and finite electrical conductivity are studied for the gravitational instability through porous medium. The effect of suspended particles on the instability is also considered. It is found that Jean's criterion remains unchanged in the presence of porosity, viscosity, finite conductivity, rotation, magnetic field and suspended particles in the medium.     

Some further reduction formulas for certain classes of-generalized multiple hyper geometric series arising in physical,astrophysical, and quantum chemical applications

The multivariable hypergeometric function $$F_{q_0 :q_1 ;...;q_n }^{P_0 :P_1 ;...;P_n } \left( {\begin{array}{*{20}c} {x_1 } \\ \vdots \\ {x_n } \\ \end{array} } \right),$$ considered recently by A. W. Niukkanen and H.M. Srivastava, is known to provide an interesting unification of the generalized hypergeometric function_p F _q of one variable, Appell and Kampé de Fériet functions of two variables, and Lauricella functions ofn variables, as also of many other hypergeometric series which arise naturally in various physical, astrophysical, and quantum chemical applications. Indeed, as already pointed out by Srivastava, this multivariable hypergeometric function is an obvious special case of the generalized Lauricella function ofn variables, which was first introduced and studied by Srivastava and M. C. Daoust. By employing such fruitful connections of this multivariable hypergeometric function with much more general multiple hypergeometric functions studied in the literature rather systematically and widely, Srivastava presented several interesting and useful properties of this function, most of which did not appear in the work of Niukkanen. The object of this sequel to Srivastava's work is to derive a further reduction formula for the multivariable hypergeometric function from substantially more general identities involving multiple series with essentially arbitrary terms. Some interesting connections of the results considered here with those given in the literature, and some indication of their applicability, are also provided.