Critical equipotential surfaces in close binary systems

The well-known problem of reckoning the critical surfaces (equipotential zero-velocity surfaces) in the close binary systems is approached by an independent method. The formulation of the problem is based on the assumptions of the binary's matter consisting of ionized hydrogen, the system possessing black-body radiation, a potential magnetic field, being in adiabatic equilibrium. Total pressure and total internal energy are examined. The model, implying synchronous rotation of the components, is described by hydromagnetic equations. For a statical case, however, it is representable by the equation of motion alone. Next, the temperature field is reproduced whereby the ratioP _r/P_g= is playing part of a free parameter. The resulting potential functions, applied to particular binaries, furnish the Lagrangian collinear points, critical surfaces and potentials over them in terms of . The families of surfaces thus obtained, compared with those springing from the Roche model, differ qualitatively in their geometry, position of the collinear equilibrium points, number of possible equilibrium states and the values of critical potentials. At identifying the allowed and forbidden regions of the gas motion new areas have been disclosed across which the gas outflow can take place and more possibilities of shell forming both around the individual components and the system as a whole. As the gas enthalpy and radiation are increased, the surfaces' geometry is undergoing changes. The method enables the intensity of gas velocity to be ascertained at any point in the system.The results of the method outlined here complement the picture of possible equilibrium states in the close binary systems in the presence of radiation and magnetic field.     

The influence of radiation pressure on equipotential surfaces in high-temperature binary systems

In this paper we considered the effect of the radiation pressure from both components of the high-temperature binary systems in terms of a modified Roche potential. Usually, the parameters of radiation pressures ₁, ₂ can be written as a function of radiiR, effective temperatureT _eff , and massM of components. The simulation calculation shows that the positions of saddle pointsL ₁ ,L ₂ ,L ₃ and shape of critical surface are changed with radiation pressure factors ₁, ₂. Consequently, use of the conventional critical Roche model to estimate value of radii and mass ratios may be completely unwarranted if effective temperature of both componentsT _eff 30 000 K.These conclusions are applied to Wolf-Rayet binary systems V444 Cygni,v ₂ Velorum, and O-type binary system Y Cygni. The modified critical potentials are calculated and discussed.     

On the orbital eccentricity on an eclipsing binary system

A new method is presented to precisely deduce the orbital eccentricity of an eclipsing binary from observed epochs of its light minima. Application to the system V526 Sagittarii givese=0.2220±0.0016.     

Radius of the Roche equipotential surfaces

In literature, there is no exact analytical solution available for determining the radius of Roche equipotential surfaces of distorted close binary systems in synchronous rotation. However, Kopal (Roche Model and Its Application to Close Binary Systems, Advances in Astronomy and Astrophysics, Academic Press, New York 1972) and Morris (Publ. Astron. Soc. Pac. 106:154, 1994) have provided the approximate analytical solutions in the form of infinite mathematical series. These series expressions have been commonly used by various authors to determine the radius of the Roche equipotential surfaces, and hence the equilibrium structures of rotating stars and stars in the binary systems. However, numerical results obtained from these approximating series expressions are not very accurate. In the present paper, we have expanded these series expressions to higher orders so as to improve their accuracy. The objective of this paper is to check, whether, there is any effect on the accuracy of these series expressions when the terms of higher orders are considered. Our results show that in most of the cases these expanded series give better results than the earlier series. We have further used these expanded series to find numerically the volume radius of the Roche equipotential surfaces. The obtained results are in good agreement with the results available in literature. We have also presented simple and accurate approximating formulas to calculate the radius of the primary component in a close binary system. These formulas give very accurate results in a specified range of mass ratio.     

Determination of orbital eccentricity

A method is proposed for determining orbital eccentricity as a function of the ratio of the moduli of the Oort constants. This method is applicable to the motion of stars belonging to the thin disk, since that their motion in the galactic plane is almost independent of their motion perpendicular to it. The dependence of the orbital eccentricity on the ratio of the moduli of the Oort constants is approximately linear, so that it is possible to determine the eccentricity as a function of the ratio of the moduli of the Oort constants from samples containing many stars from the neighborhood of the sun with high quality data.     

Rotationally-perturbed orbital elements of close binary systems

The aim of this investigation is to present the secular and periodic perturbations of the six orbital elements of a close binary system due to rotational distortion. In our study we consider very small inclinationst of the orbital plane of the system, whereas the eccentricity of the orbit may assume any value between 0<e<1. The final formulae for the various elements have been expressed by means of the unperturbed true anomaly measured from the ascending node.     

Fast and accurate computational tools for gravitational waveforms from binary stars with any orbital eccentricity

The relevance of orbital eccentricity in the detection of gravitational radiation from (steady state) binary stars is emphasized. Computationally effective (fast and accurate) tools for constructing gravitational wave templates from binary stars with any orbital eccentricity are introduced including tight estimation criteria of the pertinent truncation and approximation errors.     

On the orbital eccentricity of V477 Cygni

Recent photoelectric times of minima support the valuee=0.3 obtained by O'Connell (1970). The lower value obtained by Budding (1974) is ruled out.     

Equipotential surfaces in close binary systems: Remarks on the time-dependent potential function

By use of the mass-point model, the equations of the equipotential surfaces are reviewed. A difference between the time-dependent potential function and zero relative velocity surfaces is put in evidence. A drawback in the time-dependent transformation between (, , ) and (x, y, z) coordinate systems is underlined.     

Internal stellar rotation and orbital period modulation in close binary systems

The orbital period modulation, observed in close binary systems with late-type secondary stars, is considered in the framework of a general model that allows us to test the hypothesis proposed by Applegate. It relates the orbital period variation to the modulation of the gravitational quadrupole moment of their magnetically active secondary stars produced by angular momentum exchanges within their convective envelopes. By considering the case of RS CVn binary systems, it is found that the surface angular velocity variation of the secondary component required by Applegate's hypothesis is between 4 and 12 per cent, i.e. too large to be compatible with the observations and that the kinetic energy dissipated in its convection zone ranges from 4 to 43 times that supplied by the stellar luminosity along one cycle of the orbital period modulation. Similar results are obtained for other classes of close binary systems by applying a scaling relationship based on a simplified internal structure model. The effect of rapid rotation is briefly discussed finding that it is unlikely that the rotational quenching of the turbulent viscosity may solve the discrepancy. Therefore, the hypothesis proposed by Applegate is not adequate to explain the orbital period modulation of close binary systems with a late-type secondary.     

The influence of the radiation pressure force on possible critical surfaces in binary systems

Using a spherically symmetric approximation for the radiation pressure force to compute a possible critical surface for binary systems, previous authors found that the surface opens up at the far side of the companion. It is shown that this effect may be unreal, and could be a consequence of the simple approximation for the radiation pressure force. Due to the influence of the radiation force, mass will be lost over the whole surface of the star. In that way much mass could leave the system in massive binary systems. On the basis of evolutionary models, including mass loss by stellar wind, our results were applied on the X-ray binaries 3U 1700-37 and HD 77581.     

Loss of orbital angular momentum in close binary systems during their evolution

A total 91 binary systems of systemic mass less than 6.5M have been studied. It is found that binary systems obey the relation: logH=C–1.8 logM whereC is constant having values –1.18, –2.12 and –2.27 respectively for detached, semi-detached and contact binary systems. It is inferred that during evolution, the systemic orbital angular momentum decreases.     

The connection between the pulsational and orbital periods for eclipsing binary systems

Considering a sample of 20 eclipsing binary systems with δ Scuti type primaries, we discovered that there is a possible relation among the pulsation periods of the primaries and the orbital periods of the systems. According to this empirical relation, the longer the orbital period of a binary, the longer the pulsation period of its pulsating primary. Among the sample, the masses of the secondaries and the separations between the components are known for eight systems for which a  log  P _puls  versus log  F (the gravitational pull exerted per gram of the matter on the surface of the primaries by the secondaries) diagram also verifies such an interrelation between the periods. So, as the gravitational force applied by the secondary component onto the pulsating primary increases, its pulsation period decreases. The detailed physics underlying this empirical relation between the periods needs further confirmation, especially theoretically. However, one must also consider the fact that the present sample does not contain a sufficiently large sample of longer period  ( P > 5 d)  binaries.     

The influence of the orbital eccentricity of a primary on the chaotic region

Applying the resonance overlap theory to the elliptic three-body model, it is shown that the effect of the eccentricity is to increase the size of the chaotic region.     

On synchronism between axial rotation and orbital motion in close binary systems

In this paper we examine the possible outcome of the tidal evolution of a close binary system using a method from which the outline has already been given by Counselman (1973). If the value of the total angular momentum of the system is sufficiently large, two equilibrium states corresponding to synchronism between stellar rotation and orbital motion are possible. In one of these states the total energy attains no extreme value. The considered evolution can be visualized geometrically by the motion of a point along a hyperbolic cylinder in three-dimensional space. A comparison with some observational data reveals that most of the synchronously rotating detached systems have attained a stable equilibrium state of minimum total energy for the given value of total angular momentum.     

The evolution of eccentricity in the eclipsing binary system AS Camelopardalis

In 2002,2004 and 2017 we conducted high precision CCD photometry observations of the eclipsing binary system AS Cam.By analysis of the light curves from 1967 to 2017(our data + data from the literature) we obtained photometric elements of the system and found a change in the system's orbital eccentricity of ?e = 0.03 ± 0.01.This change can indicate that there is a third companion in the system in a highly inclined orbit with respect to the orbital plane of the central binary,and its gravitational influence may cause the discrepancy between observed and theoretical apsidal motion rates of AS Cam.     

Perturbed orbital elements of close binary systems due to tidal lag in longitude

This paper deals with the perturbations which tidal lag in longitude can produce to the orbital elements of a close binary system. The expressions obtained for the six elements of the orbit have been presented as functions of the unperturbed true anomaly, measured from the periastron. Our study includes the effects produced by the second, third, and fourth tidal harmonic distortions. In order to save space these extremely lengthy equations are given in the compact form of summations, by means of Hansen coefficients. Various recurrence relations, which hold good for Hansen coefficients, are also presented. Finally, this paper includes a second-order approximation only for the secular terms of first-order approximation.     

The effect of orbital eccentricity and nodal regression on spin-stabilized satellites

The gyroscopic motion of a spin-stabilized satellite due to gravity gradient torques in a circular orbit has been analyzed to varying degrees in numerous publications. This paper shows that the restriction to a circular orbit is, in fact, not essential and with a slight increase in complexity, noncircular orbits may be treated. More importantly, a uniform regression of the orbital node can also be accounted for. The general results are expressed in closed form using Jacobian elliptic functions. Finally, and this is perhaps most important, certain algebraic integrals of the precession are given which can be used to place limits on the excursions of the spin axis without actually solving for the motion. This allows one to design orientations such that the maximum angle between the orbit normal and spin axis never exceeds a specific amount even though the orbit normal is in precession.