An analysis of close binaries (CB) based on photometric measurements

The subject of the paper is the problem of stellar differntial rotation in close binaries (CB) ofRS CV n type. The differential-rotation parameters we find on the basis of the migration of the depression in the light curves caused by the spot effect over the orbital phase. For that purpose, a simple model (Bussoet al., 1985) and inverse-problem procedure, based on the Marquardt (1963) algorithm, are used. To verify the obtained solutions, the SIMPLEX algorithm (Torczon, 1991) is applied, suitable for the nonlinear parameter optimisation. This algorithm enables a correct solution of the nonlinear equation system describing the differential rotation. The procedure is applied in the determination of the parameters of differential rotation forCV Cam, VV Mon andSS Boo binaries.     

An analysis of active close binaries (CB) based on photometric measurements

In order to enable a successful application of the realised CB models (presented in the two former articles of the series) in the analysis of the observed light curves, an efficient method unifying the best properties of the gradient method and of the differential-corrections one into a single algorithm (Djuraevi, 1991) is proposed. This method is realised by modifying the Marquardt (1963) algorithm. The inverse problem is solved in an iterative cycle of corrections to the model elements based on a nonlinear least-square method.The interpretation of photometric observations is based on the choice of optimal model parameters yielding the best agreement between an observed light curve and the corresponding synthetic one. Some of these parameters can be determineda priori in an independent way, while the others are found by solving the inverse problem.The programmes for analysing light curves find the optimal system parameters rapidly, reliably and correctly. The corresponding programme support enables an evident graphic presentation of the results.     

An analysis of active close binaries (CB) based on photometric measurements

For the purpose of analysing light curves of active CB with an accretion disc being at the evolutional phase of an intensive matter exchange between the components a model for light-curve synthesis has been realized where the attention is given to systems like W Ser not sufficiently examined yet with regard that in them the accretion disc is formed around an ordinary star. In the paper one uses the elements presented in the first paper of this series. The model can successfully describe the essential characteristics of the observed light curves due to existence of an accretion disc and a hot spot, as well as those originated in the temperature distribution along the disc radius. The system components are considered in the framework of the nonsynchronous Roche model and the accretion disc of a constant thickness lies in the orbital plane around the star capturing the matter of the neighbouring component.The primary surrounded by the disc is situated relatively well within the Roche oval and its rotation can be significantly nonsynchronous. Near the Lagrange equilibrium pointL ₁ flows from the secondary (which fills the Roche limit) the gas stream nourishing the disc. In the zone where the stream touches the lateral side of the disc a hot spot is formed.The proposed model enables estimating of the basic orbital and physical parameters of active type W Ser CB (Djuraevi, 1991) on the basis of photometric measurements by applying the inverse-problem method.     

An analysis of active close binaries (CB) based on photometric measurements

This is the first in a series of papers devoted to the actual problematics in the determination of orbital and physical parameters of active CB on the basis of the interpretation of photometric observations. One solves the problem in two stages: by obtaining a synthetic light curve in the case when the parameters of the corresponding CB model are givena priori (direct problem) and by determining the parameters of the given model for which the best fit between the synthetic light curve and the observations is achieved (inverse problem (see Djura?evi?, 1991). In the first article of the series one presents the basis of the model developed for the synthesis of asymmetric, deformed, light curves of active CB with spots on their components. The modelling of the CB systems is based on the principles orginated in the Wilson and Devinney (1971; hereafter referred to as WD) model for the synthesis of a light curve generalised to include also the case of a nonsynchronous rotation of the components. The shapes of the components correspond to the equipotentials in the Roche model so that the critical Roche limits can be filled up to an arbitrary degree. In a spherical-coordinate system the surfaces of the components are divided into a large number of elementary cells whose intensity and angular radiation distribution are determined by the star temperature. limb darkening, gravitational darkening, and by the effect of reflection in the system. The active regions are approximated with circular spots. The presence of spots (dark or hot) enables to explain the asymmetry and depressions on the light curves of active CB. The model enables to be also interpreted the light curves of classic CB (without spots).     

An analysis of close binaries (CB) based on photometric measurements (IV)

The paper is devoted to the actual problematics in the determination of orbital and physical parameters of active CB on the basis of the interpretation of photometric observations. One solves the problem in two stages: by obtaining a synthetic light curve in the case when the parameters of the corresponding CB model are given a priori (direct problem) and by determining the parameters of the given model for which the best fit between the synthetic light curve and the observations is achieved (inverse problem). In this paper, the above procedure is applied to a particular case of CB AG Vir.     

An analysis of close binaries (CB) based on photometric measurements (VII)

The paper is devoted to the actual problematics in the determination of orbital and physical parameters of active CB on the basis of the interpretation of photometric observations. One solves the problem in two stages: by obtaining a synthetic light curve in the case when the parameters of the corresponding CB model (Djuraevi, 1992a) are given a priori (direct problem) and by determining the parameters of the given model for which the best fit between the synthetic light curve and the observations is achieved (inverse problem) (Djuraevi, 1992b). In this paper, the above procedure is applied to a particular case of an interpretation of CB light curves AU Ser and RV Corvi.     

An analysis of close binaries (CB) based on photometric measurements (V)

The author considers the current problematics in the determination of the orbital and physical parameters for active close binaries (CB) of W Ser type based on the interpretation of photometric observations. In the particular case one analyses the light curves of CB RX Cas in the framework of the accretion-disc model explained in the second paper of this series (Djuraevi, 1992a). The change of the light curves with that of the system's physical-activity phase is analysed and the orbital and physical parameters of the system are determined for the maximum, minimum and the transition regime of the physical activity by applying the inverse-problem method described in the third paper of the series (Djuraevi, 1992b). In the paper a graphical illustration of the solutions obtained is also given.     

An analysis of close binaries (CB) based on photometric measurements (VI)

The paper is devoted to the actual problematics in the determination of orbital and physical parameters of active CB on the basis of the interpretation of photometric observations. One solves the problem in two stages: by obtaining a synthetic light curve in the case when the parameters of the corresponding CB model (Djuraevi, 1992a) are given a priori (direct problem) and by determining the parameters of the given model for which the best fit between the synthetic light curve and the observations is achieved (inverse problem) (Djuraevi, 1992b). In this paper, the above procedure is applied to a particular case of an interpretation of CB light curves WZ Cep and FT Lupi.     

The photometric reflection effect in close binaries

Some earlier statistical investigations of the reflection effect are repeated using a more precise theory. The conclusions of earlier workers are reversed: it is found that the albedos of earlytype binaries are broadly in agreement with the theory, but that those of cooler systems are substantially less than unity.Various hypotheses to account for this phenomenon are investigated. It is concluded that the observations verify a prediction by Rucinski: cool secondary components possess deep convective envelopes whose structure is altered by the incident radiation in such a way as to depress the radiation from the far interior of the reflecting star.     

The photometric reflection effect in close binaries

A method for evaluating the photometric consequences of the reflection effect in close binaries is described. There is no restriction on the extent of the penumbra and the conversion to monochromatic radiation avoids the ambiguity of the approach based on application of a luminous efficiency factor. The reflected radiation is taken to have a phase law of the form (1–u _r+u _rcos) where represents the angle between the local normal and the observer's line of sight.An estimate of the accuracy of the method is made; it is found that it is suitable for the reduction of light curves of high precision for all systems except those where the components are in contact or almost so.     

Structure of close binaries

Internal models have been obtained for uniformly rotating synchronous close binary systems using a modified double approximation scheme. We have considered primaries of 10M , 5M , and 2M with mass ratios of 0.0 to 1.0 in steps of 0.1, and some results are given for a 1M primary with a mass ratio of 1.0. A maximum luminosity reduction of 2.3% was found for a 10M primary with a mass ratio of 1.0 and 7.7% for a mass ratio of 0.0. The corresponding values for 5M are 2.0% and 7.0%, and for 2M they are 1.6% and 5.3%, respectively. These values were not found to be sensitive to small changes in composition. The maximum equatorial velocity varies from 399 km s^–1 for 2M to 567 km s^–1 for 10M when the mass ratio is zero, but these velocities decrease by 200–300 km s^–1 if the mass ratio is unity. The effect of gravity darkening on the apparent position of the primary in the theoretical H-R diagram was investigated. It was determined that an unresolved close binary of unit mass ratio can lie up to 0.9 magnitudes (depending on inclination) above the main sequence, whereas if the effects of distortion are ignored this number is at most 0.75 magnitudes. There seems to be some observational support for the larger value. Two models of the secondaries are given and their dimensions are compared with their critical Roche lobes.     

Evolution of massive close binaries

The further evolution of a massive X-ray binary consisting of a compact object and an OB supergiant is outlined. The supergiant exceeds its critical Roche lobe and a second stage of mass transfer starts. The remnant of the mass losing star — a pure helium star — develops a collapsing iron core and finally undergoes a supernova explosion. If the compact companion is a black hole the system remains bound; if the compact companion is a neutron star the system is disrupted unless an extra kick allowing an asymmetric explosion is given. Computations were performed for the massive binary 22.5M _⊙+2M _⊙. The possible final evolutionary products are: (1) a black hole and a compact object, in a binary system, (2) two run-away pulsars, (3) a binary pulsar. As final parameters for the described system the eccentricity and period for the recently discovered binary pulsar 1913+16 may be found. An orbital inclination ofi=40° may be derived. The probability for the generation of binary pulsars is very low; in most cases the system is disrupted during the supernova explosion.     

Evolution of massive close binaries

X-ray binaries such as Cen X-3, Cyg X-1, Vela X-1, 2U1700-37, SMC X-1, Cir X-1, with periods ranging from 2^d.087 to 12^d.28, are probably evolution products of massive binary systems. The massive primary starts losing mass after core hydrogen burning and undergoes a supernova explosion. The evolution of binary systems consisting of a 20M⊙ primary and secondaries of respectively 14, 10, 8 and 6M⊙ was computed from Main Sequence stage through the X-ray phase, until the second mass transfer phase. Estimates were performed for the evolution of a secondary of 4M⊙. It may be seen that some of these systems during their X-ray phase match the observed mass ratios and periods.     

The structure of close binaries

A method for calculating the structure of a close binary component is presented. It is seen that the effect of binary distortion is to shift the zero age main sequence to the right. Attempts to construct contact systems with these models confirm the results of earlier workers that this is not possible.     

Evolution of massive close binaries

The evolution of a binary system with components of 10M and 8M is computed through a case B of mass exchange. It is found that after the end of core helium burning, a second stage of mass transfer from the primary occurs. Carbon ignition is prohibited by the large neutrino losses in the degenerated core. The primary remnant, a 1.12M star, ends as a white dwarf. A comparison with the 10M single evolution is made.This research is supported by the National Foundation of Collective Fundamental Research of Belgium (F.K.F.O.) under No. 10303.     

An analysis of v sin (i) correlations in early-type binaries

We use information on the   v sin ( i )  values of early-type binaries in order to search for correlations which may constrain the relative orientation of the stellar spin axes in binary systems. We find correlations in the case of close binaries which suggest that tidal synchronization is effective for binaries whose separation exceeds the stellar radius by more than an order of magnitude, in line with the theoretical predictions of Goldreich & Nicholson and the previous observational analysis of Giuricin et al. In the case of wide binaries, the   v sin ( i )  values are not well correlated, which requires that the magnitude of the spin speeds is not tightly correlated. Under this assumption, we then find that the data provide no significant constraints on the degree of alignment of spin axes. The data are therefore compatible with scenarios (such as disc fragmentation or capture) which differ widely in the expected degree of spin alignment.     

The evolution of massive close binaries

The final state of the primaries of binary systems with initial massesM _1i=10M to 15M is derived from the mass of their C/O-cores. The possibility of a second stage of mass transfer towards the secondary is considered. It turns out that the critical mass for the bifurcation is about 14M : stars with larger masses in this range are the progenitors of neutron stars, while the lower mass stars are the ancestors of white dwarfs.Research supported by the National Foundation of Collective Fundamental Research of Belgium (F.K.F.O.) under No. 10303.     

The evolution of massive close binaries

The influence of tidal, interaction on the periods of massive X-ray binaries during the postsupernova evolution is investigated. It is assumed that after a certain time the orbit has become circular and synchronous. The tidal effects of subsequent evolutionary changes in the moment of inertia of the massive component are calculated. It is shown that, as is already suggested by Sparks and Stecher (1974), for small mass ratios and short binary periods a tidal instability may occur resulting in an accelerating inward spiral motion. Before the onset of the instability the tidal forces maintain a nearly synchronous orbit. Possibly the orbits of Cen X-3 and 3 U 1700-37 are already unstable at present.     

The evolution of massive close binaries

The results of evolutionary computations for massive binary systems (initial masses of the primary 10M ) with mass ratios between 0.3 and 0.8 are summarized and compared with observations in order to verify how far one can go with the conservative assumption of mass exchange. It is found that conservative mass exchange leads to acceptable first-order models of W-R and massive X-ray binaries. However, the comparison between this theory and observation reveals that for the observed systems (W-R and X-ray binaries) a preference exists for low intial mass ratios; moreover, the X-ray luminosities of the theoretical models are systematically too low, though this may be due to the adopted wind model. In addition, the influences of several parameters (distance between the components, chemical composition, primary mass, mass ratio and atmosphere) are examined. These parameters influence the remnant mass and any further evolution only marginally. Attention is also given to the effect on the system parameters of a supernova explosion of the remnant of the mass-losing component. For a large range of systems a disruption probability smaller than 25% is found.     

First photometric analyses of five contact ASAS binaries

We present the first light curve solutions of five binary systems selected from All Sky Automated Survey (ASAS) Catalog of Variable Stars. The light curves of the systems are analyzed and the light parameters are derived. The estimated absolute parameters of the components and the degree of contact values for all targets are also calculated. We compared our results to other known contact binaries by emphasizing the locations of the components on the mass–radius and the H–R diagram. The evolutionary statuses of the systems are also discussed. Results of our analyses confirm that the systems are contact binaries.