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.     

On the angular momentum transfer on to compact stars in binary systems

Results of three-dimensional numerical simulations of the gas transfer in close binary systems show that, in addition to the formation of a tidally induced spiral shock wave, it is also possible for accretion streams to be produced, having low specific angular momentum in a region close to the accreting star. These streams are mainly placed above the orbital disc but are also unevenly present in the equatorial plane. The relevance of such flows is related to formation of hot coronae or bulges in regions very close to the accretor centre. The eventual formation of such bulges and shock-heated flows is interesting in the context of advection-dominated solutions and for the explanation of spectral properties of the black hole candidates in binary systems.     

RT sculptoris: An important star for low-mass close binary research

TheUBV light curves of Duerbeck and Karimie (1979) for the southern eclipsing binary RT Sculptoris were analysed using information limit optimizing computer programs. We decide in favour of the transit primary minimum hypothesis. The system is found to be semi-detached, but in the rare primary contact configuration. This implies a fast mass transfer process. Our derived picture of the system broadly corroborates that of Hilditch and King (1986), but our analysis includes a detailed treatment of the hot spot. We also report on recent spectroscopic radial velocity data obtained at Mt. Stromlo, Canberra. The system provides an important case study for low mass close binary research.     

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.     

The solution parameters of very close binary systems

The problems encountered in the derivation of elements from the light curves of very close binary systems are discussed. It is shown that the rectification procedure is critically dependent on the underlying model. The assumption of a contact configuration leads to better coincidence of theoretical and observed light curves. The Fourier analysis method is used to derive the solution parameters of the examples YY Eri and AM Leo. Veröffentlichungen der Dr. Remeis Sternwarte Bamberg, Astronomisches Institut der Universität Erlangen-Nürnberg, volume 10, Nr. 112.     

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.     

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.     

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 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.     

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.     

Tides and angular momentum redistribution inside low-mass stars hosting planets: a first dynamical model

We introduce a general mathematical framework to model the internal transport of angular momentum in a star hosting a close-in planetary/stellar companion. By assuming that the tidal and rotational distortions are small and that the deposit/extraction of angular momentum induced by stellar winds and tidal torques are redistributed solely by an effective eddy-viscosity that depends on the radial coordinate, we can formulate the model in a completely analytic way. It allows us to compute simultaneously the evolution of the orbit of the companion and of the spin and the radial differential rotation of the star. An illustrative application to the case of an F-type main-sequence star hosting a hot Jupiter is presented. The general relevance of our model to test more sophisticated numerical dynamical models and to study the internal rotation profile of exoplanet hosts, submitted to the combined effects of tides and stellar winds, by means of asteroseismology are discussed.     

Accretion activity of young binary systems with low-mass secondary components

The accretion activity of young binaries with low-mass (q = M ₂/M ₁ ≤ 0.1) secondary components is studied. The source of accreted matter is a common disk surrounding the binary system and coplanar with its orbit. Gas dynamic models of these systems are used to calculate the rates of accretion to the components and their dependence on the phase of the orbital period is studied. It is shown that, despite its low mass, the secondary accretes matter at a relatively higher rate than the primary. This result can be regarded as an extension of the work of Artymowicz and Lubow for young binaries with components that have unequal masses. Possible astrophysical applications of the theory are discussed.     

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.     

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.