The ellipsoidal variables

We perform a Monte Carlo analysis of the eclipse probabilities of short-period binary systems in an attempt to estimate the distribution of ellipsoidal variable system with Main-Sequence components. Our results suggest that possibly as many as one in four of the non-eclipsing, spectroscopic binaries withP(d)10, and Main-Sequence components withM _v 10 could be ellipsoidal variable systems. This result, while an upper limit, would seem to hold irrespective of primary spectral type (B5 to G5).     

Population I pulsating stars

Evolutionary masses corresponding to various evolutionary phases of Population I pulsating stars (89 Delta Scuti variables and 155 classical cepheids) are interpolated in the systems of tracks of Iben (1967) and Paczyski (1970). The evolutionary masses are larger in the latter system than in the former one. The uncertainty of the evolutionary mass of a star is estimated, when various evolutionary phases are possible for this star (a smaller evolutionary mass corresponds to a later phase). Semi-empirical period-evolutionary mass-colour (P-M _e -C) and period-evolutionary mass (P-M _e ) relations are derived for various modes, groups of stars, colour indices (and effective temperature), and evolutionary phases. For Delta Scuti stars, the uncertainty of evolutionary masses calculated from theP-M _e relations for different modes, is estimated. The improvement of the evolutionary mass accuracy is estimated, when aP-M _e -C relation is used instead of the correspondingP-M _e relation. The theoretical and semi-empirical period ratios of radial pulsations derived from theP-M _e relations for Delta Scuti stars, are compared. There is a relatively good agreement between theP-M _e relations for the two types of Population I pulsating stars, but a gap exists between them. The evolutionary masses of these stars are closer in the two systems of tracks and are derived with a relatively higher accuracy in comparison with their ages.     

Age determination of the open cluster NGC 2287 (M41)

We have estimated the age of the open cluster NGC 2287 (M41) by taking into account the rotation of the member stars.TheUBV photoelectric measurement values were taken from Eggen (1974). Besides the Main-Sequence stars this cluster has seven red giants, all of them above the turn-off point.Having obtained the theoretical Hertzsprung-Russell diagram from observed colour-magnitude diagram, we have discussed two methods, given in the literature, to estimate the age of the cluster under consideration. The first method we have followed is to determine the turn-off point on the cluster Main-Sequence. The other is fitting the position of the red giants with the evolutionary tracks of rotating stars with different masses on the Hertzsprung-Russell diagram.We have estimated the cluster age based on the turn-off point as 3.10×10⁷ yr. From the fitting of the evolutionary tracks of rotating stars to the cluster Hertzsprung-Russell diagram, we infer that the age of the cluster is about 8.00×10⁷ yr.     

Main sequence for rotating stars of intermediate mass

We have investigated the evolutionary behaviour of intermediate mass (2, 3, 4, 5, and 7M ) Population I stars, assuming two different rates of rotation at the threshold of stability.In the first part of the study, stars are assumed to start with a critical rotation (fast rotation model) and to progress to the point of rotational instability. The stars evolve by losing mass and become rotationally unstable before they reach the zero-age Main Sequence. It is argued that multiple star systems might be formed through the evolution of rapidly rotating stars. An expression for the rotational mass loss rate is derived as a function of the physical parameters of stars.In the second part of the study, stars are assumed to rotate at a rate below the critical value (slow rotation model). The evolution of slowly rotating stars is followed as far as zero-age Main Sequence on the theoretical Hertzsprung-Russell diagram and compared with that of normal stars. The evolutionary paths are found to be more or less similar to those of normal stars; but their positions on the Main Sequence are characterized by effective temperatures and luminosities lower than those of normal stars. The zero-age Main-Sequence times of these stars are longer than those of normal stars. The rotational rates obtained for the zero-age Main Sequence are in good agreement with observed values.     

Galactic nuclei luminosity: A model of steady spherically-symmetric accretion of optically-thick gas on to Kerr black holes

The eclipsing binary system Epsilon Aurigae, containing an unseen component, is discussed on the basis of its orbital elements. The masses of the components can be approximately 4M and 1M , respectively. It is shown that there is no reason to reject a low-mass model. An opaque elongated eclipsing body is briefly discussed as one of the components which is an accretion disc surrounding a central Main-Sequence star.     

Radii of some Ap,Am and A stars

Based on the observed energy curves of nine Ap stars, three Am stars, four normal A stars and one F0 V magnetic star, their radii have been estimated.Thence, the bolometric magnitudesM _bo1 have been obtained and a plot between logT _e andM _bo1 of these stars shows that a majority of Ap and Am stars are a little above the zero-age Main-Sequence, suggesting that they are slightly more evolved as compared to the normal A stars.The bolometric corrections derived from the aboveM _bo1 are much closer to those computed by Mihalas than to the ones given by Davis and Webb, the latter being about O ^m 1 more negative than the former.     

Photometric elements of the eclipsing binary DN UMa=HR 4560

A total of 704 previously published photoelectricB colour observations of the multiple system HR 4560 are analyzed by means of the light curve models NDE (Popper and Etzel, 1981) and WINK (Wood, 1972) in an iterative procedure. As a result, we have found that componentC of the multiplpe system ADS 8347 is the most probable origin of the observed eclipses. Some relevant astrophysical parameters of the component stars which indicate a normal Main-Sequence binary star have also been estimated.     

Effect of tidal evolution in determining the ages of eclipsing-variable early main sequence close binary systems

New Claret evolutionary model-tracks, constructed for the first time for studying close binary systems (CBS) including tidal evolution constants, are used to determine the age of 112 eclipsing-variable stars in the Svechnikov-Perevozkina catalog by the method of isochrones. There is some interest in comparing the calculated ages with previous estimates obtained for these same close binary systems using evolutionary modeltracks for individual stars taking their mass loss into account. A correlation of the ages of the principal and secondary components is noted, which is most marked for massive close binaries with principal components having masses M₁ ≥ 3 M_⊙. A rejuvenating effect is found to occur for the systems studied here as calculated on the new tracks; it is most distinct for low-mass close binaries with a total mass M₁ + M₂ ≤ 3.5 M_⊙ and is predicted theoretically in terms of magnetic braking. The calculated broadband grid of isochrones, from zero-age main-sequence (ZAMS) to the age of the galaxy, can be used for estimating the ages of close binaries from other catalogs. Ages are given for the 112 eclipsing-variable close binaries with detached components lying within the main sequence. __________ Translated from Astrofizika, Vol. 50, No. 2, pp. 299–312 (May 2007).     

Non-adiabatic interactions in excitedC 2 H molecules and their relationship toC 2 formation in comets

A unified picture of the photodissociation of theC ₂ H radical has been developed using the results from the latest experimental and theoretical work. This picture shows that a variety of electronic states ofC ₂ are formed during the photodissociation of theC ₂ H radical even if photoexcitation accesses only one excited state. This is because the excited states have many avoided corssings and near intersections where two electronic states come very close to one another. At these avoided crossings and near intersections, the excited radical can hop from one electronic state to another and access new final electronic states of theC ₂ radical. The complexity of the excited state surfaces also explains the bimodal rotational distributions that are observed in all of the electronic states studied. The excited states that dissociate through a direct path are limited by dynamics to produceC ₂ fragments with a modest amount of rotational energy, whereas those that dissociate by a more complex path have a greater chance to access all of phase space and produce fragments with higher rotational excitation. Finally, the theoretical transition moments and potential energy curves have been used to provide a better estimate of the photochemical lifetimes in comets of the different excited states of theC ₂ H radical. The photochemically active states are the 2²₊, 2²II, 3²II, and 3²₊, with photodissociation rate constants of 1.0×10^–6, 4.0×10^–6, 0.7×10^–6, and 1.3×10^–6s^–1, respectively. These rate constants lead to a total photochemical lifetime of 1.4×10⁵ s.     

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.     

BVRI photometry and light curve analysis of VW CEP

Synthetic light curve solutions for the W UMa-system VW Cep have been determined by applying the most new version of Wilson (1998)approach to B-observations of 1996 and VRI-observations of 1999. From a consideration of the possible evolution of this system, it is found that the system is a partial eclipsing contact one, and its primary to be a nearly Main-Sequence F5 star of mass 0.85 M _⊙ and the secondary to be a dwarf of spectral type G0 of mass 0.34 M _⊙. This revised version was published online in July 2006 with corrections to the Cover Date.     

Particle motion in models of close binaries

The characteristic features of particle motion in close binaries have been studied for sequences of evolutionary models with small or intermediate masses. The possible behaviour of the particle streams has been determined with regard to the change of systems with time as a result of mass-exchange between the two stellar components. A grid of values for the velocity and direction of ejection from the first Lagrangian point has been investigated. Among the various possibilities, impact of particles with one, or the other component, or orbits encircling the Main-Sequence star have been detailed. This latter possibility seems to lead to the formation of a disk-like structure around the Main-Sequence component. From the results obtained for semi-detached systems of both cases A and B of evolution it is found that the formation of disks is difficult in cases A, and in the early stages of the slow mass exchange in cases B.

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Sommario Sono state studiate le caratteristiche principali delle traiettorie in sequenze di modelli evolutivi di sistemi binari stretti di massa totale piccola e intermedia. E' stato messo in evidenza l'andamento generale delle traiettorie in connessione con la variazione temporale delle proprietà dei sistemi binari dovuta allo scambio di massa tra le componenti. La velocità e la direzione iniziali di eiezione dal primo punto lagrangiano sono state variate con sistematicità in un ampio intervallo di valori. Tra le varie possibilità sono state messe in luce sia l'impatto con l'una o l'altra delle componenti sia la formazione di orbite attorno alla componente di sequenza principale. Quest'ultima eventualità potrebbe condurre alla formazione di una struttura di disco. Dai risultati ottenuti con modelli evolutivi di sistemi semistaccati di casi A e B è emerso che la formazione di una struttura di disco sembra difficile nei casi A e nelle prime fasi dello scambio lento di massa nei casi B.

     

Evolutionary state of W UMa-type systems

The evolutionary status of a sample of 31 W UMa-type systems (20 of W, 9 of A, and 2 of A/W sub-class) is examined and discussed on the basis of their positions in the H-R, mass-radius and mass-luminosity diagrams. The absolute elements of these systems have been evaluated by use of their spectroscopic and photometric data as they were found in the literature. Since different analysis methods have been used by the various investigators this gives the opportunity to make different H-R, mass-radius and mass-luminosity diagrams, according to the method used, and compare the results.Moreover, from the spectral type-period diagram of those systems that have spectral types from O to G2 it was found that all of them lie in the evolved region. Finally, the log (L _l/L _s) log (M _l/M _s) diagrams are presented and discussed.     

The abundance of 3He in the solar wind - A constraint for models of solar evolution

³He is an intermediate product in the proton-proton chain, and standard models of the Sun predict a large bulge of enhanced ³He abundance near M _r /M ₀ = 0.6 in the contemporary Sun. The relatively low abundance of ³He at the solar surface, which is derived from solar wind observations, poses severe constraints to non-standard solar models.Direct measurements of the ³He abundance in the solar atmosphere are extremely difficult, whereas indirect measurements, e.g., in the solar wind, have been performed with considerable precision. The interpretation of solar wind observations with respect to solar surface abundances has been greatly improved in recent years. Abundance measurements have been performed under a large variety of solar wind conditions and refined models have been developed for the transport processes in the chromosphere and the transition region and for the processes occurring in the solar corona. From these measurements we estimate the present isotopic number ratio ³He/⁴He to be (4.1 ± 1.0) × 10^–4 at the solar surface, corresponding to the weight abundance X ₃ = (9.0 ± 2.4) × 10^–5. The zero-age Main-Sequence abundance of ³He (after burning of D) might have been slightly lower (by about 10 to 20%) than the present-day value.Non-standard solar models involving mild turbulent diffusion (Lebreton and Maeder, 1987) could account for a slow secular increase of the ³He/⁴He ratio in the solar atmosphere. On the other hand it is difficult to reconcile models with severe mass loss as proposed by Guzik, Willson, and Brunish (1987) with this constraint. The slowing down of the solar rotation during the early Main-Sequence evolution was accompanied by stronger differential rotation probably implying a more effective mixing of the inner parts. Again, the surface abundance of ³He imposes severe limits on the evolution of the distribution of momentum within the early Sun.     

Evolution of massive close binaries and formation of neutron stars and black holes

Main results of computations of evolution for massive close binaries (10M +9.4M , 16M +15M , 32M +30M , 64M +60M ) up to oxygen exhaustion in the core are described. Mass exchange starting in core hydrogen, shell hydrogen and core helium burning stages was studied. Computations were performed assuming both the Ledoux and Schwarzschild stability criteria for semiconvection. The influence of UFI-neutrino emission on evolution of close binaries was investigated. The results obtained allow to outline the following evolutionary chain: two detached Main-Sequence stars — mass exchange — Wolf-Rayet star or blue supergiant plus main sequence star — explosion of the initially more massive star appearing as a supernova event — collapsed or neutron star plus Main-Sequence star, that may be observed as a runaway star — mass exchange leading to X-rays emission — collapsed or neutron star plus WR-star or blue supergiant — second explosion of supernova that preferentially disrupts the system and gives birth to two single high spatial velocity pulsars.Numerical estimates concerning the number and properties of WR-stars, pulsars and X-ray sources are presented. The results are in favour of the existence of UFI-neutrino and of the Ledoux criterion for describing semiconvection. Properties of several well-known X-ray sources and the binary pulsar are discussed on base of evolutionary chain of close binaries.     

Possible third body effects in the period changes of four Algol binaries: RY Aqr,SZ Her,RV Lyr and V913 Oph

An investigation of the orbital period changes of the neglected eclipsing binaries, RY Aqr, SZ Her, RV Lyr and V913 Oph, is presented based on all published minima times. Although the explanation of magnetic activity on the surface of the secondaries of the studied Algols is still open, the preferred light‐time effect due to the unseen components around the systems seems more plausible in explaining the tilted sinusoidal variations with relatively high‐amplitudes. The minimal mass values of possible tertiary components have been estimated to be about 1.06, 0.25, 0.78 and 2.85 M_⊙ for RY Aqr, SZ Her, RV Lyr and V913 Oph, respectively and the results indicate that their contributions to the total light of the eclipsing pairs are measurable with high accuracy photometric and spectroscopic data, if they exist. Applegate's (1992) model has been discussed as an alternative mechanism assuming that the cooler components have magnetic cycles. It is found that the model parameters of RY Aqr and V913 Oph are consistent with the required values in Applegate's model. In addition to the first detailed orbital study on these systems, a statistical survey on the character of the O – C variations of classical Algols has revealed that about 50 percent of the systems show cyclic behavior. This means that the presence of possible third bodies around classical Algols should be tested with careful analysis using new data. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evolution of low-mass close binaries and the problem of orbital period gap in cataclysmic variables

Evolution of close binary composed of a white dwarf primary and a Main-Sequence secondary has been calculated. Angular-momentum loss via gravitational radiation and magnetic stellar wind have been taken into account. We have found that magnetic stellar wind with a rate greater than (10^–10–10^–9)M yr^–1 is able to drive the evolution with mass exchange. If the time-scale of switch-off of wind when the primary becomes fully convective is not longer than 10⁶ yr, mass exchange interrupts due to a contraction of the secondary and the system becomes unobservable. Mass exchange resumes when components approach one another due to loss of momentum via gravitational radiation. The location and width of the thus-arising gap in the orbital periods are comparable to those observed.     

The evolutionary behaviour of population III intermediate mass stars

Assuming the Big-Bang nucleosynthesis was responsible for the formation of helium, the evolution of first-generation intermediate-mass stars of 5, 7, and 9M with no metals have been studied from the threshold of stability through the stage of helium exhaustion in the cores of the stars. Hydrogen Main-Sequence positions are marked at effective temperatures higher than those of normal stars. The evolutionary tracks during the hydrogen burning phase start to be similar to those of normal stars when the CN-cycle reactions, which are controlled by the triple-alpha reactions, become operative for hydrogen depletion. Helium Main Sequence of Population III stars of intermediate mass occurs at the high effective temperature region of the H-R diagram and stars stay as blue stars until the end of the core helium exhaustion phase. The total time elapsed is in the range of 3×10⁷ and 10⁸yr. The stars with the initial masses of 5, 7, and 9M developed a moderately electron degenerate complete hydrogen-exhausted region with masses of 0.77, 1.06, and 1.42M , respectively, in which the most abundant element is carbon.     

Tidal circularization in massive binaries

We consider the time-scale of orbital circularization for those massive binary systems that produce WR+C systems. Using the observation that such systems have acquired circular orbits on a time-scale of the order of the Main-Sequence lifetime of the initial secondary, we estimate the intrinsic time-scale of the tidal interaction ₀. We find that the tidal dissipation in such systems is very efficient and that, on the average, ₀ ~ 10³ yr.     

CaseA evolution of massive close binary systems

The caseA evolution of close binary systems with total mass of 20.4M is investigated by following the evolution of both components simultaneously. The evolution is followed up to the stage at which a system overflows the outer critical surface or evolves into the phase of modeBr mass-transfer. It is found that the evolution of the systems can be classified into six types. The ranges of initial parameters which lead systems to each type of evolution are shown on the initial-parameter plane. The evolutionary features of each evolution type are described in detail.