Dynamical effects of mass exchange in close binary systems

The problem of mass exchange in a close binary system is studied from the point of view of the evolution of the orbital elements. It is assumed that the original orbit is nearly circular and one of the components has expanded and fills the area inside the equipotential surface passing through the inner Lagrangian pointL ₁, losing mass to the other component. The mass is assumed to be ejected along the tangent to the equipotential surface passing throughL ₁ in retrograde orbits.It is proved that the eccentricity remains very small. The semimajor axis increases in almost all cases where the mass is being transferred from the less massive to the more massive component, and decreases when the mass is being transferred from the more massive to the less massive component. It is also shown that if the more massive star evolves first and loses mass to its companion, the process of mass exchange continues automatically until the originally more massive component becomes the less massive one and the binary system remains in an almost static condition for long intervals of time, the less massive component occupying the area inside the equipotential surface passing throughL ₁ and surrounding the star.     

Evolution through mass exchange in close binary systems of total mass 2.5M ⊙

Calculations show that the observed semi-detached binary systems of massM ₁+M ₂2.5M can be explained in terms of a mass exchange which starts after the central hydrogen in the original primary has been exhausted.Presented at the Trieste Colloquium on Mass Loss from Stars, September 12–16, 1968.     

Re-analysis of close binary systems

Line-forming regions around close binaries with strong winds ( /4r _* v 10^–4 g cm^–2) are large in extent compared with the stars, large enough to screen them. Their orbitally-modulated Doppler shifts can overestimate the mass function, because of a larger rotational lever arm. In particular, most of the black-hole candidates need not involve companions more massive than a neutron star.The solar-wind problem is reconsidered. An extrapolation to Wolf-Rayet stars suggests that their winds are centrifugally driven. Their mass-loss rates tend to have been overestimated.Seemingly single (massive) stars can hide a (compact) companion.     

Roundchrom emissivity in close binary systems

Roundchrom is a common chromosphere enveloping both components of close binary system. In present article, the problem of the construction of outward boundary of the roundchrom is examined, particularly, identifying this boundary with zero-velocity equipotential Lagrangian surface corresponding to a definite value of Jacoby constantC. The roundchroms for seven RS CVn type close binary systems as well for an interacting binary HD 207739 are constructed. The main parameters of these roundchroms are obtained, particularly, the electron concentrations are of the order of 10¹⁰ cm^–3.     

Dynamical tides in close binary systems

Differential equations governing the dynamical tides in close binary systems consisting of centrally condensed components of viscous gas are split up (Section 2) in their real and imaginary parts, the ratio of which defines the tidal lag. In Sections 3 and 4 these equations will be particularized to a case in which the central mass-point of each star is surrounded by an evanescent envelope the density of which decreases as the inverse square of the central distance. It is shown that self-gravitating configurations built up in accordance with this model are incapable of performing free nonradial oscillations with a frequency comprised between 0 ² ; but explicit expressions for forced oscillations representing dynamical tides are given for an arbitrary form of the external field of force. Equations for the imaginary components of the displacement, constructed for the same model in Section 4, disclose that if the viscosity of stellar material is identified with that of hydrogen plasma, the tidal lag due to a viscous dissipation of kinetic energy may produce dynamical effects, the cumulative outcome of which becomes appreciable on the Kelvin time-scale, but over short intervals of time their stationary photometric effects should be negligible. The latter can become observationally significant only for stars in which turbulent viscosity under near-adiabatic conditions becomes and important factor.     

Tidal evolution in close binary systems

The aim of the present paper will be to give a mathematical outline of the theory of tidal evolution in close binary systems of secularly constant total momentum — an evolution activated by viscous friction of dynamical tides raised by the two components on each other. The first section contains a general outline of the problem; and in Section 2 we shall establish the basic expressions for the energy and momenta of close binaries consisting of components of arbitrary internal structure. In Section 3 we shall investigate the maximum and minimum values of the energy (kinetic and potential) which such systems can attain for given amount of total momentum; while in Section 4 we shall compare these results with the actual facts encountered in binaries with components whose internal structure (and, therefore, rotational momenta) are known to us from evidence furnished by the observed rates of apsidal advance.The results show that all such systems — be these of detached or semi-detached type — disclose that more than 99% of their total momenta are stored in the orbital momentum. The sum of the rotational momenta of the constituent components amounts to less than a percent of the total — a situation characteristic of a state close to the minimum energy for given total momentum. This appears, moreover, to be true not only of the systems with both components on the Main Sequence, but also of those possessing evolved components in contact with their Roche limits.Under such conditions, a synchronism between rotation and revolution (characteristic of both extreme states of maximum and minimum energy) is not only possible, but appears to have been actually approached — if not attained — in the majority of cases. In other words, it would appear that — in at least a large majority of known cases — the existing close binaries have already attained orbits of maximum distension consistent with their momenta; and tidal evolution alone can no longer increase the present separations of the components to any appreciable extent.The virtual absence, in the sky, of binary systems intermediate between the stages of maximum and minimum energy for given momentum leads us to conjecture that the process of dynamical evolution activated by viscous tides may enroll on a time-scale which is relatively short in comparison with their total age — even for systems like Y Cygni or AG Persei, whose total age can scarcely exceed 10⁷ yr. A secular increase of the semi-major axes of relative orbits is dynamically coupled with a corresponding variation in the velocity of axial rotation of both components through the tidal lag arising from the viscosity of stellar material. The differential equations of so coupled a system are given in Section 5; but their solution still constitutes a task for the future.The Lunar Science Institute Contribution No. 90. The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.     

Dynamical tides in close binary systems

The aim of the present paper will be to investigate the circumstances under which an irreversible dissipation of the kinetic energy into heat is generated by the dynamical tides in close binary systems if (a) their orbit is eccentric; (b) the axial rotation of the components is not synchronized with the revolution; or (c) the equatorial planes are inclined to that of the orbit.In Section 2 the explicit form of the viscous dissipation function will be set up in terms of the velocity-components of spheroidal deformation arising from the tides; in Section 3, the principal partial tides contributing to the dissipation will be detailed; Section 4 will be devoted to a determination of the extent of stellar viscosity — both gas and radiative; while in the concluding Section 5 quantitative estimates will be given of the actual rate at which the kinetic energy of dynamical tides gets dissipated into heat by viscous friction in stellar plasma.The results disclose that the amount of heat produced per unit time by tidal interaction between components of actual close binaries equals only about 10^–10th part of their nuclear energy production; and cannot, therefore, affect the internal structure of evolution of the constituent stars to any appreciable extent. Moreover, it is shown that the kinetic energy of their axial rotation can be influenced by tidal friction only on a nuclear, rather than gravitational (Kelvin) time-scale — as long as plasma or radiative viscosity constitute the sole sources of dissipation. However, the emergence of turbulent viscosity in secondary components of late spectral types, which have evolved away from the Main Sequence, can accelerate the dissipation 10⁵–10⁶ times, and thus give rise to appreciable changes in the elements of the system (particularly, in the orbital periods) over time intervals of the order of 10⁵–10⁶ years. Lastly, it is pointed out that, in close binary systems consisting of a pair of white dwarfs, a dissipation of the kinetic energy through viscous tides in degenerate fermion-gas could produce enough heat to account, by itself, for the observed luminosity of such objects.     

Dynamical tides in close binary systems

The aim of the present paper will be to deduce the explicit form of differential equations which govern dynamical tides in close binary systems, with simplifications which are permissible for the mass-point model (Section 2), as well as for one exhibiting finite but high internal density concentration (Section 3). It is pointed out that, whereas the exact formulation of the problem leads to a simultaneous system of equations of sixth order (fourth in the inviscid case), this order reduces to four (or two for inviscid fluids) for the mass-point model; and to five (three for inviscid case) if the density concentration is high but finite.In the last section of this paper the coefficientsC _i,j which specify the amplitudes of the individual partial tides are explicitly formulated as functions of the time.     

Tidal evolution of close binary asteroid systems

We provide a generalized discussion of tidal evolution to arbitrary order in the expansion of the gravitational potential between two spherical bodies of any mass ratio. To accurately reproduce the tidal evolution of a system at separations less than 5 times the radius of the larger primary component, the tidal potential due to the presence of a smaller secondary component is expanded in terms of Legendre polynomials to arbitrary order rather than truncated at leading order as is typically done in studies of well-separated system like the Earth and Moon. The equations of tidal evolution including tidal torques, the changes in spin rates of the components, and the change in semimajor axis (orbital separation) are then derived for binary asteroid systems with circular and equatorial mutual orbits. Accounting for higher-order terms in the tidal potential serves to speed up the tidal evolution of the system leading to underestimates in the time rates of change of the spin rates, semimajor axis, and mean motion in the mutual orbit if such corrections are ignored. Special attention is given to the effect of close orbits on the calculation of material properties of the components, in terms of the rigidity and tidal dissipation function, based on the tidal evolution of the system. It is found that accurate determinations of the physical parameters of the system, e.g., densities, sizes, and current separation, are typically more important than accounting for higher-order terms in the potential when calculating material properties. In the scope of the long-term tidal evolution of the semimajor axis and the component spin rates, correcting for close orbits is a small effect, but for an instantaneous rate of change in spin rate, semimajor axis, or mean motion, the close-orbit correction can be on the order of tens of percent. This work has possible implications for the determination of the Roche limit and for spin-state alteration during close flybys.     

A review of early-type close binary systems

This is a review of close binary systems with very early spectral types (B, O, Of, and WR stars). We limit our selection to systems with Roche model photometric solution only. There are 10 contact systems known at present. Three of them (V701 Sco, BH Cen, and RZ Pyx) are located in the vicinity of the zero-age contact (ZC) according to a Spectral Type — Period diagram. Only the first two systems have absolute dimensions available. Both of these fall into the ZC zone in the logP-logm diagram and the logm-logR diagram. The system TU Mus was thought to be a ZC system is located in the evolved contact zone (EC) in the above diagrams. Both V701 Sco and BH Cen were thought to be having mass ratios about unity. With the much improved light curves of BH Cen and new analysis the mass ratio has been revised to 0.84! This result may favor Shu's model for early-type zero-age contact systems. The evolved systems might be undergone Case A mass exchange except for two systems (V729 Cyg and RY Sct) which might be from Case B. The systems V367 Cyg was classified by Plavec as a W Ser system may be a evolved contact system.It is interesting to note that V729 Cyg (O7f+OfIa), UW CMa(O7f+O) and CQ Cep(WN7+O) are all highly evolved contact systems. The Max II of UW CMa and CQ Cep are displaced to 0.78 and 0.80 phase, respectively. The displacement for V729 Cyg is not known due to poor coverage at this phase. The most distinct feature going from Of to Wolf-Rayet stars is the increasing domination of emission lines. It is suspected that this phaseshifts reflect the increasing activity of mass-flow in the common envelope.There are 8 semidetached systems with reliable absolute dimensions. It is believed that 6 of them are derived from Case A while the remaining 2 are from Case B mass exchange.Paper presented at the Lembang-Bamberg IAU Colloquium No. 80, on Double Stars: Physical Properties and Generic Relations, held at Bandung, Indonesia, 3–7 June, 1983.     

Absolute dimensions of 140 close binary systems

The absolute dimensions of 140 close binaries have been computed. These systems have been extracted from recent catalogues of photometric and spectroscopic elements.     

Analysis of 11 late-type close binary systems

This is a preliminary report on the joint research project between 3 observatories: Beijing, Yunnan, and Behlen Observatories from China and the United States. The systems we have been dealing with are primary of late spectral types and with short periods. Most of the observations were secured from the observatories in China. The computational analysis is carried out in University of Nebraska, Lincoln. The photometric solutions are based on the Wilson and Devinney method. Out of 11 systems analyzed 6 of them: AO Cam, ER Ori. BX Peg, BB Peg, U Peg, and SW Lac are found to be contact systems. All of them are having their primary eclipses at occultation. Therefore they can be classified as W-type W U Ma systems. They also show other W-type characteristics.Three systems: ZZ Aur, RZ Dra, and AX Vir are found to be semi-detached systems, with low mass components filling their Roche surfaces. The massive components are having their radii fairly close to Roche surfaces and are larger than their contact companions.The last two systems: AT Cam and AZ Cam are found to be detached systems, but with their low mass components almost filling their Roche surfaces. This type of configuration is of great interest to our understanding of close binary evolution. We believe that these systems are at phase immediately after the normal Algol phase, where the mass lossing components detached from the Roche surfaces at the conclusion active mass lost phase.Paper presented at the Lembang-Bamberg IAU Colloquium No. 80 on Double Stars: Physical Properties and Generic Relations, held at Bandung, Indonesia, 3–7 June, 1983.     

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.     

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.     

Figures of equilibrium in close binary systems

The equilibrium configurations of close binary systems are analyzed. The autogravitational, centrifugal and tidal potentials are expanded in Clairaut's coordinates. From the set of the total potential angular terms an integral equations system is derived. The reduction of them to ordinary differential equations and the determination of the boundary conditions allow a formulation of the problem in terms of a single variable.     

Accuracy of close binary mass determinations from parallaxes

Absolute masses for W Ursae Majoris and Algol-type close binaries can be determined from their parallax, if observed, and the relative sizes of the stars and their mass ratio, obtained from a light curve solution. An error propagation study compares the typical order of magnitude of the various terms involved, and shows how accurate parallaxes have to be in order to make the procedure work, i.e., making the parallax term not larger than the combined non-parallax terms, and producing reasonably low mass errors. Some comments are made on the possibilities with respect to the HIPPARCOS program.Communication presented at the International Conference on Astrometric Binaries, held on 13–15 June, 1984, at the Remeis-Sternwarte Bamberg, Germany, to commemorate the 200th anniversary of the birth of Friedrich Wilhelm Bessel (1784–1846).     

Infrared photometry for five close binary systems

We present the JHKLM photometry for five close (W Ser) binary systems obtained in the period 1996–2004. Positive phase shifts (with respect of the adopted ephemerides) have been found in the orbital infrared light curves for three binaries, RX Cas, KX And, and β Lyr; the rates of increase in their periods are ～3.5 × 10^?4, ～1.6 × 10^?3, and ～1.4 × 10^?4 days yr^?1, respectively. We have performed the spectral classification of the components of the binaries under study and estimated their parameters.