Tabular mass solutions for close binaries

The solutions for the mass of single-line close binaries with Main-Sequence primaries are given in a tabular form as a result of the application of the mass-luminosity relation. Linear interpolation in a compact bi-variate table suffices to give the values of mass of the two components for a wide range of masses and to a very good approximation. The indeterminacy of the solutions depending on the formulation of the mass-luminosity relation for the primaries is discussed, as well as the condition of filling up their Roche lobes by the secondaries.     

Evolution of close binaries of shorter period and moderate mass

Evolution of close binaries is investigated in which the more massive component has a mass of 5m and reaches the Roche limit when hydrogen is burning in its convective core. It is shown that a large-scale mass transfer occurs, during which the initial primary develops into a contact subgiant or giant, and the mass ratio is reversed or more than reversed.Although the process and its outcome depend on the initial conditions, in particular on the degree of chemical inhomogeneity in the interior of the primary component, the picture of evolution is essentially the same. We can distinguish and describe quantitatively the following phases: (1) Premain-sequence contraction, when the less massive component is an undersize subgiant. (2) Both components are on the main sequence. (3) Rapid mass exchange, when the roles of the components are interchanged. (4) Slow mass transfer, when the system is semi-detached; this phase is typical for the Algol-like binaries. Further evolution depends on the rate of evolution of the components: either we get another phase with an undersize subgiant, or a complicated system in which both stars lose mass. Probabilities of discovery are calculated for the various phases of evolution.The paper is based on the calculations of stellar models with decreasing mass by means of Henyey's method.     

Supernovae in close binaries

The impact of a supernova shell onto 2.82M _⊙ and 20.0M _⊙ main-sequence stars is investigated for various initial orbital separations, and various supernova shell masses and velocities. The inelastic collision between the star and the supernova shell, the shock propagation into the companion star, and other forms of momentum transfer such as the rocket effect are considered. The total momentum transfer due to the supernova is insufficient to eject the companion from the binary as long as the companion retains most of its mass, regardless of the initial orbital separation. Ejection of the companion may occur if the companion is nearly destroyed. Even in contact binaries destruction does not necessarily occur, and if the orbital separation exceeds 10¹² cm, destruction of the companion becomes quite unlikely.     

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.     

Ten new very low‐mass close binaries resolved in the visible

We present preliminary results from the first part of the LuckyCam late M‐dwarf binarity survey. We survey a sample of 48 nearby (< 40 pc) and red (M5–M9) stars with the novel high angular resolution visible light imaging technique Lucky Imaging, in only 8 hours of 2.5m telescope time. We discover 10 new binaries; although the survey is sensitive to brown dwarf companions none are detected. The orbital radius distribution of the newly discovered binaries broadly matches that of previous detections by other groups, although we do discover one wide binary at ∼40 AU. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Accretion and evolution in close binaries

The discovery of X-ray binary systems in the 1960's opened up stellar evolution theory by revealing further endpoints in addition to white dwarfs. This review summarises recent progress in studies of stellar-evolutionary processes that lead to X-ray binaries themselves, the mass transfer rates that power them, and the accretion processes which convert this into electromagnetic radiation. Particular attention is paid to the topics of mass transfer fluctuations and of the accretion by magnetic compact stars.     

Changes of the profiles of spectral lines due to mass transfer in close binaries

In this paper, the model of the ring envelope round the primary component and the stream of the gaseous mass flowing from the secondary component to the primary is constructed on the basis of theoretical computations concerning the exchange of the mass between the components of the binary. The paper studies the influence of the gaseous mass on the profiles of spectral lines before and after occultation; the influence of the stream on the profile in case the secondary is near elongation, is also investigated. The line profiles obtained by numerical computations show that their changes caused by outflowing mass should be well detectable from spectrograms taken at particular phase of the binary. Changes in the lines may influence the measurement of radial velocities. The method for distinguishing the influence of the stream from the influence of the ring is described.     

Very low mass stars in binaries: a theoretical look

We have undertaken a series of hydrodynamic + N ‐body simulations in order to explore the binary properties of young stars. We find that multiple stars are a natural outcome of collapsing turbulent flows, with a high incidence of N > 2 multiples, specially among the higher mass objects. We find a positive correlation of multiplicity with primary mass and a companion frequency that decreases with age, during the first few Myr after formation. Binary brown dwarfs are rarely formed, in conflict with observations. Brown dwarfs as companions are predominantly found orbiting binaries or triples at large separations. The paucity of ultra low mass and low mass ratio binaries has been investigated further, and we tentatively conclude that their formation is intricately related to an appropriate selection of initial conditions and an accurate modelling of disc accretion and evolution. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.

     

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.     

The Hill stability of low mass binaries in hierarchical triple systems

The Hill stability of the low mass binary system in the presence of a massive third body moving on a wider inclined orbit is investigated analytically. It is found that, in the case of the third body being on a nearly circular orbit, the region of Hill stability expands as the binary/third body mass ratio increases and the inclination (i) decreases. This i-dependence decreases very quickly with increasing eccentricity (e ₂) of the third body relative to the binary barycentre. In fact, if e ₂ is not extremely small, the Hill stable region can be approximately expressed in a closed form by setting i = 90°, and it contracts with increasing e ₂ as ${e_2^2}$ for sufficiently low mass binary. Our analytic results are then applied to the observed triple star systems and the Kuiper belt binaries.