Properties of Wolf-Rayet stars in eclipsing binary systems

The results of investigations of a number of eclipsing Wolf-Rayet binaries are presented. The ‘core’ radiuses, the ‘core’ temperatures and masses of WR stars in the eclipsing WR+OB binary systems V 444 Cyg, CX Cep, CQ Cep, and CV Ser are obtained (see Table I). The results obtained from the light curves analysis of the V 444 Cyg in the range λλ2460 Å-3.5μ give strong evidence for the Beals (1944) model of WR phenomenon. The chromospheric-coronal effects in the WN5 extended atmosphere are not observed up to a distance ofr?20R _⊙. In the Hertzsprung—Russell diagram all the WR stars lie on the left side from the main sequence between the main sequence and the sequence of uniform helium stars (see Figure 9). Their locations are close to those of the helium remnants formed as a result of mass exchange in massive close binary systems. The period variations in the systems V 444 Cyg and CQ Cep have been discovered and a reliable value of the mass loss rateM=10^?5 M _⊙yr^?1 is obtained, for the two WR stars. The results of the photometric and spectroscopic investigations of the WR stars with low mass companions (post X-ray binary stage?) are presented too (see Table II). The masses of the companions are (1–2)M _⊙, their optical luminosity is ～10³⁶, erg s^?1 which implies that these companions cannot be the normal stars. It is possible that these companions are neutron stars accreting from the stellar wind of the WR stars. Low values of the X-ray luminosities of such WR stars with low mass companions imply that the accretion of matter in such systems is distinct from the accretion process in classical X-ray binary systems. It is noted also that the parameters of low massive companions coupled with WR stars are close to those of helium stars.     

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.     

Bifurcation points in close binary evolution: Medium-mass binaries

The remaining core hydrogen burning lifetime after case B of mass transfer of the secondary (mass gaining) component in a medium mass close binary star is estimated, for mediummass binaries with primaries in the mass range 5M to 9M . From the comparison of this quantity with the helium burning time-scale of the remnant primary a critical mass ratioq _c is derived such that for larger values ofq, mass transfer from the secondary towards the primary starts before the latter has evolved into a white dwarf. Consequences for the advanced stages of medium mass binaries are discussed.     

On steady-state nuclear burning in accreting neutron stars

The properties of the hydrogen burning shell in the envelope of an accreting neutron star have been studied for a range of mass accretion rates, neutron star radii, and metal abundances of the accreted matter. It is found that the hydrogen burning shells lie at densities ranging from 10⁵–6×10⁶ gm cm^–3. For mass accretion rates in excess ofM _c2 hydrogen and helium burn together. ForM _c1MM _c2, the hydrogen burning shell is stabilized by the limited CNO cycle. Implications of these results to the X-ray burst phenomena are briefly 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.     

Late stages of the evolution of close binaries

Close binaries can evolve through various ways of interaction into compact objects (white dwarfs, neutron stars, black holes). Massive binary systems (mass of the primaryM ₁ larger than 14 to 15M ₀) are expected to leave, after the first stage of mass transfer a compact component orbiting a massive star. These systems evolve during subsequent stages into massive X-ray binaries. Systems with initial large periode evolve into Be X-ray binaries.Low mass X-ray sources are probably descendants of lower mass stars, and various channels for their production are indicated. The evolution of massive close binaries is examined in detail and different X-ray stages are discussed. It is argued that a first X-ray stage is followed by a reverse extensive mass transfer, leading to systems like SS 433, Cir X1. During further evolution these systems would become Wolf-Rayet runaways. Due to spiral in these system would then further evolve into ultra short X-ray binaries like Cyg X-3.Finally the explosion of the secondary will in most cases disrupt the system. In an exceptional case the system remains bound, leading to binary pulsars like PSR 1913+16. In such systems the orbit will shrink due to gravitational radiation and finally the two neutron stars will coalesce. It is argued that the millisecond pulsar PSR 1937+214 could be formed in this way.A complete scheme starting from two massive ZAMS stars, ending with a millisecond pulsar is presented.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.     

The product of the globular cluster collapse

In this paper we calculate the number of close binaries formed during the evolution process of a globular cluster core. The globular cluster core is assumed to contain a massive black hole at its center. We show that the central black hole can drive binaries formation in the core and the rate of binaries formation depends on the mass of the black hole at its center. When the massM of the black hole is between 10² M and 3×10³ M , there will be a few binaries formed. When the mass of the black hole is 4×10³ M M6×10³ M , the number of binary star formation will suddenly increase with a jump to the maximum value 58. When the mass of the black hole is 7×10³ M M9×10³ M , the number of binary star will immediately decrease. Whether cluster X-ray is produced mainly by the central black hole or by binaries in the core depends on the mass of the central black hole. Therefore, two cases arise: namely, black hole accretion domination and binaries radiation domination. We do think that we cannot exclude the possibility of the existence of a central black hole even when binary radiation characteristics have been observed in globular cluster X-ray sources.     

Stellar dynamics in young clusters: the formation of massive runaways and very massive runaway mergers

In the present paper we combine an N-body code that simulates the dynamics of young dense stellar systems with a massive star evolution handler that accounts in a realistic way for the effects of stellar wind mass loss. We discuss two topics.

1. The formation and the evolution of very massive stars (with masses >120 M_⊙) is followed in detail. These very massive stars are formed in the cluster core as a consequence of the successive (physical) collisions of the 10–20 most massive stars in the cluster (this process is known as ‘runaway merging’). The further evolution is governed by stellar wind mass loss during core hydrogen and core helium burning (the WR phase of very massive stars). Our simulations reveal that, as a consequence of runaway merging in clusters with solar and supersolar values, massive black holes can be formed, but with a maximum mass ≈70 M_⊙. In low-metallicity clusters, however, it cannot be excluded that the runaway-merging process is responsible for pair-instability supernovae or for the formation of intermediate-mass black holes with a mass of several 100 M_⊙.
2. Massive runaways can be formed via the supernova explosion of one of the components in a binary system (the Blaauw scenario), or via dynamical interaction of a single star and a binary or between two binaries in a star cluster. We explore the possibility that the most massive runaways (e.g. ζ Pup, λ Cep, BD+43°3654) are the product of the collision and merger of two or three massive stars.

     

Close binary systems before and after mass transfer: A comparison of observations and theory

From a search through the literature 174 close binaries with known absolute dimensions have been sampled. Distinction is made between systems before and after mass exchange. Mass, period and mass ratio distributions and relations of the group of unevolved binaries (i.e., prior to mass exchange) are transformed into corresponding distributions and relations of evolved binaries. The transformations are based upon theM _1f=g(M _1f) relation derived from an extended set of published theoretical computations of the evolution of close binaries. From this relation the following characteristics of the system after mass exchange are computed:M _1f,M _2f (andq _f),P _f. Five different modes of mass transfer were applied for the computation of the values ofP _f andM _2f. The variation of the period was calculated using the formalism given by Vanbeverenet al. (1979). The results are compared to the observations of binary systems after mass exchange, and are discussed together with an analysis of the effect of several selection effects present in the distributions. The main conclusion is that, during mass exchange in close binaries, more than 50% of the mass is lost to the system in the process of transfer, removing a large amount of angular momentum.This research is supported by the National Foundation of Collective Fundamental Research of Belgium (F.K.F.O.) under No. 2.9009.79.     

UBV photometry of the WR binary CQ Cephei

Photoelectric observations of the WR binary CQ Cephei (WN6+O9) are presented. the depths of the eclipses in the light curves are best represented by an inclination of the orbit i = (68°.8±0.6) and the width of the very asymmetric eclipse curves can be represented by only an overcontact configuration (Ω₁ = Ω₂ = 3.65 ± 0.05, and f = 27%). Simultaneous solution of the light and radial velocity curves strongly supports CQ Cep's membership of the Cep OB1 association. By considering this membership we obtained absolute dimensions of the system, which lead to a consistent physical model for CQ Cephei. The more luminous WR primary turns out to be the hotter but slightly less massive component: M_WR = 20.8 M⊙, R_WR = 8.2R⊙, T_eff(WR) = 43600 K, and M_o = 21.4 M⊙, R_o = 8.3 R⊙, T_eff(O) = 37000 K.     

Gravitational collapse of cosmic gas clouds and formation of star clusters

In this paper the gravitational collapse of cosmic gas clouds and formation of star clusters has been considered. Hoyle's view of successive fragmentation has been taken as the basic mechanim in the present work. The initial masses of protostars have been estimated as the function of their distances from the centre of the cluster and the intensity of the magnetic field of the medium. It has been shown that the fragmentation process is greatly inhibited by the presence of a strong magnetic field. A model has been constructed showing how a protostar grows in mass by accretion from the surrounding medium, on the basis of the assumption that as the star moves at random in the cluster it picks up a fraction of the material through which it passes. It has been estimated that a protostar of initial mass of about 0.1M grows to one of 1.0M in a time period which ranges from a few multiples of 10⁵ to a few multiples of 10⁷ yr, depending on the parameters involved in the accretion process. The number of stars per unit mass range has also been estimated; it is found to be proportional tom ^–3.3,m being the mass of the star.     

Study of physical properties of spectroscopic binary stars

The main results of a study of a catalogue of physical parameters of 1041 spectroscopic binaries are presented. The distribution of spectroscopic binaries over all main parametersM ₁, a, e, M₁/M₂, P, and certain dependencies between some of them have been found.

1. It appears that among bright (m _v?3 ^m –5 ^m ) stars withM?1M _⊙, about 40% are apparently spectroscopic binaries with comparable masses of components.
2. The majority of spectroscopic binaries with the ratio of the large semiaxis of the orbit to the radius of the primarya/R ₁?20, have eccentricities close to zero. This is probably a consequence of the tidal circularization of orbits of close binaries by viscous friction.
3. The discovery of duplicity of double-line spectroscopic binaries is possible only if the semiamplitude of radial velocityK ₁ is almost 10 times higher than the semiamplitude of the radial velocity of a single-line spectroscopic binary of the same mass.
4. Double-line spectroscopic binaries witha/R _⊙?6(M ₁/M _⊙)^1/3,M ₁≈M ₂?1.5M _⊙ are almost almost absent, and the number of stars witha/R _⊙?6(M ₁/M _⊙)^1/3,M ₁≈1.5M _⊙ is relatively low.
5. The distribution of unevolved SB stars over the large semiaxis may be described by the expression d(N _d/N_t)≈0.2 d loga for 6(M ₁/M _⊙)^1/3?a/R _⊙?100.
6. The intial mass-function for primaries of spectroscopic binaries is the same Salpeter function dN _d≈M ₁ ^?2.35 dM ₁ for 1?M ₁/M _⊙?30.
7. It is possible to explain the observed ratio of the number of single-line spectroscopic binaries to the number of double-line binaries if one assumes that the average initial mass ratio is close to 1 and that the mass of the postmass-exchange remnant of the primary exceeds the theoretical one and/or that half of the angular momentum of the system is lost during mass-exchange.
8. The above-mentioned distributions ofM ₁ anda and assumptions on the mass of remnant and/or momentum loss also allow us to explain the observed shapes of dN/dM, dN/dq, and dN/da distributions after some selection effects are taken into account.

     

Mass loss and shell masses of close binary stars

From the values of period changes for 6 close binary stars the mass transfer rate was calculated. Comparing these values M_t with the values of shell masses M_sh, the expression $$lg \dot M_t = \begin{array}{*{20}c} {4.24} \\ { \pm 24} \\ \end{array} + \begin{array}{*{20}c} {0.63} \\ { \pm 6} \\ \end{array} lg M_{sh} $$ Was derived. The analysis of this expression points out the initial character of the outflow of matter, and one may determine the time interval of the substitution of the shell matter. So one may conclude that for a certain mass transfer rate, a certain amount of matter accumulates in the nearby regions of the system. The study of orbital period changes of close binary stellar systems led to the idea that these secular and irregular changes are due to the mass loss and to the redistribution of masses in a close binary. Secular changes of orbital periods are known for approximately 400 eclipsing binary stars. For many stars, including cataclysmic binaries, irregular period changes are known. Thus, the mass loss and the matter redistribution in close binaries are often observed phenomena.     

The angular momentum-vs-mass relation and the distribution of mass ratios for visual binary systems

The investigation of the angular momentum vs mass relation for binary stars is completed with a study of the 847 systems contained in theFourth Catalog of Orbits of Visual Binary Stars. Because bothJ andM of a visual binary depend steeply on the distance to the system (5th and 3rd powers, respectively), and many of the distances are not well known, the study makes use of an auxiliary parameterR which is independent of distance and proportional toJM ^–5/3.R appears to be uncorrelated withM for the 789 systems for which both can be determined. The non-correlation implies thatJ M ^5/3, expected from Kepler's third law, provides a better fit to the visual binaries than doesJ M ², predicted by some more complex considerations.The distribution functionf(q=M ₂/M₁) of mass ratios for the visual binaries results as a byproduct of the investigation. It peaks extremely sharply towardq=1.0 (much more so than for spectroscopic binaries). Because most visual binaries are wide enough to consist of stars that condensed independently (and so that can be thought of as chosen at random from an initial mass function), one expects the realf(q) to rise toward low ratios. Observational selection against the discovery and study of systems with large magnitude differences between the components must be very large indeed to account for the discrepancy between expectation and observation. The alternative is a mechanism for formation of wide binaries that favours equal components. The distribution of mass ratios for eclipsing binaries is given in an appendix. It peaks strongly atq=0.6–0.75 and largely reflects processes of angular momentum, mass, and energy exchange between the stars in contact systems.     

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.     

Planetary nebulae in planetary and binary systems

The problem of the survival of a low-mass secondary orbiting a primary that becomes a planetary nebula is studied. The values of the mass of the primary are 1.0, 1.5, and 2.0M ; the values of the mass of the secondary 0.001M , 0.01M and 0.1M . The orbital decay and mass of the secondary due to accretion and gravitational drag in the common envelope are presented. The possible application of the results to V471 Tau, UU Sge, WZ Sge and the Sun-Jupiter system are discussed.     

A quantitative analysis of the prototype [WCL] star CPD-56° 8032

We present a detailed, quantitative study of the standard [WC10] Wolf-Rayet central star CPD-56^o 8032 based on new high resolution AAT UCLES observations and the Hillier (1990) WR standard model. Our analysis of CPD-56^o 8032 gives the wind properties (T _*=34500K, lg (L/L )=3.8, lg (M/M a^–1)=–5.4,v =225 km s^–1) and chemistry (C/He=0.5, O/He=0.1, by number), the latter suggesting an intimate relationship with the Ovi PN central stars and the PG 1159-035 objects. A comparison between the wind properties of CPD-56^o 8032 and Sk-66^o 40 (WN 10) indicates that low excitation, low wind velocity WR winds are common to both low mass PN central stars (WC sequence) and high mass post-LBV's (WN sequence).     

Evolution of massive binary stars in the LMC and its implications for radio pulsar population

The Hertzsprung-Russell diagram of the Large Magellanic Cloud compiled recently by Fitzpatrick & Garmany (1990) shows that there are a number of supergiant stars immediately redward of the main sequence although theoretical models of massive stars with normal hydrogen abundance predict that the region 4.5 ≤ logT _eff ≤ 4.3 should be un-populated (“gap”). Supergiants having surface enrichment of helium acquired for example from a previous phase of accretion from a binary companion, however, evolve in a way so that the evolved models and observed data are consistent — an observation first made by Tuchman & Wheeler (1990). We compare the available optical data on OB supergiants with computed evolutionary tracks of massive stars of metallicity relevant to the LMC with and without helium-enriched envelopes and conclude that a large fraction (≈ 60 per cent) of supergiant stars may occur in binaries. As these less evolved binaries will later evolve into massive X-ray binaries, the observed number and orbital period distribution of the latter can constrain the evolutionary scenarios of the supergiant binaries. The distributions of post main sequence binaries and closely related systems like WR + O stars are bimodal-consisting of close and wide binaries in which the latter type is numerically dominating. When the primary star explodes as a supernova leaving behind a neutron star, the system receives a kick and in some cases can lead to runaway O-stars. We calculate the expected space velocity distribution for these systems. After the second supernova explosion, the binaries in most cases, will be disrupted leading to two runaway neutron stars. In between the two explosions, the first born neutron star’s spin evolution will be affected by accretion of mass from the companion star. We determine the steady-state spin and radio luminosity distributions of single pulsars born from the massive stars under some simple assumptions. Due to their great distance, only the brightest radio pulsars may be detected in a flux-limited survey of the LMC. A small but significant number of observable single radio pulsars arising out of the disrupted massive binaries may appear in the short spin period range. Most pulsars will have a low velocity of ejection and therefore may cluster around the OB associations in the LMC.     

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.     

Mass effects in the problem of three bodies

This is a study of the dynamical behavior of three point masses moving under their mutual gravitational attraction in a plane. The initial positions and velocities are identical for all cases studied and only the masses of the participating bodies change in the series of numerical experiments. In this way the effect of the coupling terms in the differential equations of motion are investigated. The motion in all 125 cases begins with an interplay between the three bodies, followed by temporary ejections or by an eventual escape. The total mass of the system is kept constant while the massratios change from 1 to 5. The initial velocities being zero, the total energy is negative in all cases.Approximately 74% of the cases disintegrated (i.e. two bodies formed a binary and the third body escaped) in less than 140 time units, 47% in less than 50 time units and 10% ended in escape in less than 10 time units. Considering three stars with total mass 12M , initially placed at 3, 4 and 5 parsec distances (or three galaxies with mass 2.4×10¹² M , initially placed 30, 40 and 50 kpc apart), the unit of time (approximately the crossing time) becomes 1.5×10⁷ y (3.2×10⁷ y). The average time of disintegration was found to be of the order of 10⁹ y. The average semi-major axis of the binaries left behind after disintegration was 0.7 parsec and the average value of the eccentricity was 0.76. The effect of the masses on the escapes was established and it was found that the bodynot with the smallest mass escaped in 13% of the disintegrated cases. The cases which did not disintegrate in 150 time units were analyzed in detail and the time of their eventual escape was estimated.The numerical results are tabulated regarding escape time, ejection period, total energy, escape energy, terminal velocity, semi-major axis, and eccentricity.The evolution of triple systems is followed from interplays through ejections to escapes and the orbital parameters for the separation of these classes are estimated.