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.     

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.     

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 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 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.     

Evolution of massive close binaries and formation of neutron stars and black holes

Main results of computations of evolution for massive close binaries (10M +9.4M , 16M +15M , 32M +30M , 64M +60M ) up to oxygen exhaustion in the core are described. Mass exchange starting in core hydrogen, shell hydrogen and core helium burning stages was studied. Computations were performed assuming both the Ledoux and Schwarzschild stability criteria for semiconvection. The influence of UFI-neutrino emission on evolution of close binaries was investigated. The results obtained allow to outline the following evolutionary chain: two detached Main-Sequence stars — mass exchange — Wolf-Rayet star or blue supergiant plus main sequence star — explosion of the initially more massive star appearing as a supernova event — collapsed or neutron star plus Main-Sequence star, that may be observed as a runaway star — mass exchange leading to X-rays emission — collapsed or neutron star plus WR-star or blue supergiant — second explosion of supernova that preferentially disrupts the system and gives birth to two single high spatial velocity pulsars.Numerical estimates concerning the number and properties of WR-stars, pulsars and X-ray sources are presented. The results are in favour of the existence of UFI-neutrino and of the Ledoux criterion for describing semiconvection. Properties of several well-known X-ray sources and the binary pulsar are discussed on base of evolutionary chain of close binaries.     

Evolution of close binaries and origin of Algol-type systems

The evolution of close binary systems was followed for ten systems with the initial mass of the primary in the range 1–4M and with different initial mass ratios and initial separations. A brief discussion of the evolution of the contact component is presented for two separate cases: when the primary reaches its Roche lobe during central hydrogen burning (case A) and after the exhaustion of hydrogen in the center (case B).The models obtained are compared with observed semi-detached systems separately for massive (with total mass greater than 5M ) and low mass (with total mass below 4M ) binaries. It is shown that the contact components of the observed massive binaries are probably burning hydrogen in the core. On the contrary, the majority of contact components of the observed low-mass binaries are burning hydrogen in the shell. The observed distribution of such binaries as a function of different luminosity excesses of contact components seems to indicate that their origin is connected with case A rather than with case B.     

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.     

On the evolutionary time scale of the accreting component in massive close binaries

The remaining core hydrogen burning lifetime after mass exchange is computed for the mass gaining component in massive close binary systems. Results are obtained for various modes of mass accretion, for a wide range of initial masses and mass ratios, and for different values of mass loss from the system. The effect of mass loss by stellar wind is included. By use of general properties of massive close binary evolution, the position in time of four events is determined: the end of core hydrogen burning of the primary and the secondary, and the occurrence of the supernova of the primary and the secondary. It is found that the two supernova event occur rather close in time, compared to the Main Sequence time scales of the components.This research is supported by the National Foundation of Collective Fundamental Research of Belgium (FKFO) under No. 2.9009.79.     

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.     

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.     

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.     

Very massive close binaries and the puzzling temporal evolution of 14N in the Solar Neighbourhood

Low metallicity very massive stars with an initial mass between 140M_⊙ and 260M_⊙ can be subdivided into two groups: those between 140M_⊙ and 200M_⊙ which produce a relatively small amount of Fe, and those with a mass between 200M_⊙ and 260M_⊙ where the Fe-yield ejected during the supernova explosion is enormous. We first demonstrate that the inclusion of the second group into a chemical evolutionary model for the Solar Neighbourhood predicts an early temporal evolution of Fe, which is at variance with observations whereas it cannot be excluded that the first group could have been present. We then show that a low metallicity binary with very massive components (with a mass corresponding to the first group) can be an efficient site of primary ¹⁴N production through the explosion of a binary component that has been polluted by the pair instability supernova ejecta of its companion. When we implement these massive binary ¹⁴N yields in a chemical evolution model, we conclude that very massive close binaries may be important sites of ¹⁴N enrichment during the early evolution of the Galaxy.     

Tidal circularization in massive binaries

We consider the time-scale of orbital circularization for those massive binary systems that produce WR+C systems. Using the observation that such systems have acquired circular orbits on a time-scale of the order of the Main-Sequence lifetime of the initial secondary, we estimate the intrinsic time-scale of the tidal interaction ₀. We find that the tidal dissipation in such systems is very efficient and that, on the average, ₀ ~ 10³ yr.     

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.     

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.     

Fission candidates among detached close binaries

A comparison between results of model calculations and observed properties of close, but detached low mass binaries with Main Sequence primaries shows statistical trends, which seem to support fission origin for some of these objects: the mass-momentum relation, the relation between mass ratio and separation and the relation between mass ratio and synchronisation speak in favour of close initial separations and small mass ratios of the components.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.     

A slow-down treatment for close binaries

We present a new method for fast numerical integration of close binaries inN-body systems. The basic idea is to slow down the motion of the binary artificially, which makes a faster numerical integration possible but still maintains correct treatment of secular and long-period effects on the motion. We discuss the general principle, with application to close binaries inN-body codes and in the chain regularization.