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.     

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.     

Studies of a sample of CPM stars

Summary A sample of CPM stars selected from the AGK2/3 is used to investigate the following points: (a) What is the distribution of mass ratios of binaries with wide separations?, and (b) what is the proportion of wide binaries among stars. The distribution previously derived from the visual binaries of theBright Star Catalogue seem to be an acceptable solution to question (a). On the basis of this, the proportion of stars that have a companion with a separation between 300 and 10000 AU is found to be about 13%. Another possibility is that the distribution of mass ratios is similar to the initial mass function derived by Miller and Scalo (1979) for stars lighter than the Sun. The proportion of wide binaries with mass ratios greater than 0.16 should then be around 17%.     

Liminosity distribution function for visual binary stars

The cosmic scatter of 147 of the best known visual binary stars on the Main Sequence is discussed and a new estimation of the luminosity distribution function for multiple star systems is presented. As long as the mass ratioq of a close binary is not smaller than 0.5, the distribution of close binary components is identical to the van Rhijn liminosity-function. For smaller mass ratios (q<0.5) the number of close companions decreases rapidly. It appears that less than 13% of visual binaries in our sample are simple binary systems.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).     

The pulse-period distribution of binary X-ray pulsars

The pulse-period distribution of binary X-ray pulsars has been considered. A gap in this distribution, in the period rangeP10 s toP100s has been explained in terms of the character of mass transfer in the X-ray binary systems. It is shown that this gap arises because the rotating magnetised neutron stars in these systems are slowed down by accretion torques, either toP10 s when the mass transfer is by means of Roche-lobe overflow in low mass binaries, or toP100 s by stellar winds in massive binaries. The gap is maintained as the slow pulsars (P>100 s) in their spin-up phase cross the gap in a time short compared to their life-time, because of the increase in mass transfer with the evolution of the normal star.     

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.     

BV Dra and BW Dra: Two contact systems in one visual binary

UBV light curves obtained in 1975 for both components of ADS 9537 are presented. These light curves and the light curve of BV Dra by Yamasaki have been solved for geometrical parameters using the synthesis method under two hypotheses explaining theW-subclass light curves: (1) temperature excess of the less massive components; (2) spots on the more massive components; the results are very similar. Because of the poor determinacy of the solutions, mass-ratios have been assumed:q=0.8 for BV Dra and a range inq for BW Dra; our solutions suggest preference for smallerq in the latter system. We compare both variables and conclude that they follow the Main Sequence dependences. We give also a bried discussion of the existing information on other contact binaries in multiple (visual) systems: the contact binaries seem to follow the same statistical distributions for occurrence in multiples as found for detached binaries but severe selection effects limit detectability for multiple systems with wide orbits having semi-axes below 100 a.u.On leave from the Warsaw University Observatory.Visiting Astronomer, Kitt Peak National Observatory which is operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Binary star statistics: the mass ratio distribution for very wide systems

The distribution of mass ratios for a sample of common proper motion (CPM) binaries is determined and compared with that of 798 visual binaries (VB's) studied earlier, in hopes of answering the question: Can the member stars of these systems have been drawn at random from the normal initial mass function for single stars? The observed distributions peak strongly toward q = 1·0 for both kinds of systems, but less strongly for the CPM's than for the VB's. Due allowance having been made for assorted observational selection effects, it seems quite probable that the CPM's represent the observed part of a population drawn at random from the normal IMF, while the VB's are much more difficult to interpret that way and could, perhaps, result from a formation mechanism that somewhat favors systems with roughly equal components.     

Statistical study of Am stars in spectroscopic binary systems

Using the Am components in spectroscopic binaries, the region of metallicism in the (logm, logR) diagram is statistically discussed. The metallic-line characteristics appear in a slightly evolved stage near the Main Sequence within a belt characterized by logg=3.8–4.2, for which the radiiR/R =1.5–2.7. The distribution in the diagram indicates that appreciable differences should exist in the abundances as well as in the mixing lengths of the atmospheres of the Am components.Synchronism between rotation and revolution for the Am components is discussed, and it is clearly found that the synchronism holds accurately for the Am binaries with periods less than about six days, but for those with periods between six and ten days some Am components corotate and some do not, perhaps depending upon their ages.Using the Am spectroscopic binaries with periods less than twelve days, we find that the excess of metallicity is statistically correlated with the rotational velocity; and it is confirmed that the metallicity grossly decreases with increasing rotational velocity. If the effect of a non-Am secondary component is eliminated from a [m ₁]-value for the combined light, the correlation between metallicity excess and rotational velocity for the Am components only should approach [m ₁]/V (km s^–1)=–0.00077.     

Determination of stray light and sunspot intensities based on the observation during the solar eclipse of 30 June, 1973

A program has been developed to evaluated the gravitational binding energy of a clumpy cluster composed ofN particles with a given mass dispersion, a given abundance of binaries and a given massive binary system at the centre. In application to clusters of galaxies nucleated by massivecD binaries, it is found that the gravitational binding energy is typically greater than the equivalent smooth distribution by a factor in the range 2–12. This suggests that the missing mass problem in clusters of galaxies can be reduced by an order of magnitude if the correct binding energy is used in the virial theorem.     

Binary statistics and star formation

Binary statistics, in particular the distributions of mass ratios and orbital periods, are reviewed in an attempt to obtain clues to possible star formation and cloud fragmentation processes. Various observational selection effects which hamper the establishment of the true distributions are discussed. Four different theories of binary formation are compared (fission, fragmentation, capture, and the disintegration of small star clusters), none of which can be ruled out. We conclude that there may be many ways to form binary systems. The dominant mode of binary formation could be ring fragmentation or disc fragmentation depending upon whether the distribution of mass ratios is found to decrease or to increase towards small mass ratios. Future speckle interferometric measurements of a sufficiently large sample of close visual binaries are suggested to settle this important observational question. The present paper is special in that it brings together a wealth of useful information, both observational and theoretical, in one place.Atoms form molecules, stars form binaries.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.We quote Su-Shu Huang in IAU-Colloquium No. 33=Revista Mexicana, Vol. 3 (1977). Many papers related to the present problem can be found there.     

Observations of binaries and evolutionary implications

Comparison of the characteristics of groups of stars in various evolutionary phases and the study of individual systems allow to make estimates of the parameters governing mass loss and mass transfer. Observations enable us in a few cases to determine geometric models for binaries during or after the mass transfer phase (disks, rings, common envelopes, symbiotics, interacting binaries, compact components).From spectra taken at different phases, radial velocity curves can be derived and masses and radii can be determined. In special cases spectra in different spectral ranges (visual, UV, X-ray) are required for the determination of the radial velocities of the two components (for X-ray binaries, for systems with hot and cool components). Information on parameters related to the mass transfer process enables us to consider non conservative evolution — i.e. the computation of evolutionary sequences with the assumption that mass and angular momentum not only are transferred from one of the components towards the other one, but that also mass and angular momentum can leave the system. Careful and detailed analysis of the observations allows in certain cases to determine the parameters governing this mass and angular momentum loss, and for contact phases, to determine the degree of contact.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.     

Statistical properties of spectroscopic binary stars

As part of a study of the mass-ratio distribution of spectroscopic binary stars, the statistical properties of the systems in theEighth Catalogue of the Orbital Elements of Spectroscopic Binary Stars, compiled by Battenet al. (1989), are investigated.Histograms are presented of the distributions of various parameters of the systems in the catalogue as a whole, and compared to those of the previous edition.Histograms of binaries of various spectral types are presented. It is noted that the early-type binaries in the catalogue have on average higher radial-velocity amplitudes, shorter periods, and smaller semi-major axes than late-type binaries. Late-type binaries have relatively more eccentric orbits. Whether the differences noticed between the early- and late-type binaries have any significance with respect to the population of binary stars in the Galaxy is not clear, because it is very hard to assess the extent to which the catalogue is a statistically representative and complete sample.The distribution of semi-major axesa ₁ sini varies considerably among different subsamples.The mass-ratio distribution of single-lined spectroscopic binaries is, for all (sub-)samples, characterized by a decrease in the number of systems according to a power law asq1, forq=M _sec/M _prim>0.25.The mass-ratio distribution of double-lined spectroscopic binaries (SBII) is, for all (sub-)samples but one, characterized by an increase in numbers according to a power law, asq1. The exception to this general behaviour is the sample of SBII systems with magnitudesm5 ^m , which has its maximum atq0.65.The distributions are presented as they are, without corrections for selection effects.     

Wolf-Rayet binaries: Evolutionary causes for their distribution in the Galaxy

On the basis of the most recent data, the fraction of known Wolf-Rayet binaries is 0.22. In the solar neighbourhood (d<2.5 kpc) this fraction is 0.34In order to assess the relative importance of massive binary evolution as one of the ways to produce WR stars, the galactic distribution of WR binaries is compared with that of single WR stars using improved intrinsic parameters and new data for the fainter WR stars.In the galactic plane the increase of the binary frequency with galactocentric distance is confirmed.In a direction perpendicular to the galactic plane it is demonstrated at all distances from the Sun that the single-line spectroscopic WR binaries with small mass functions have definitely larger -distances than the single WR stars and the WR binaries with massive companions. This is consistent with the evolutionary scenario for massive binaries summarized by van den Heuvel (1976). Among the single WR stars the fraction of those with large |z|-distances is increasing with galactocentric distance, like the fraction of the known binaries. This implies that among the high-|z| single WR stars as well as among the WR stars with lower |z|-values many binaries are still to be discovered.The total WR binary frequency in the Galaxy could be well above 50%.Contribution from the Bosscha Observatory No. 79.Invited 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.     

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.     

The ellipsoidal variables

We perform a Monte Carlo analysis of the eclipse probabilities of short-period binary systems in an attempt to estimate the distribution of ellipsoidal variable system with Main-Sequence components. Our results suggest that possibly as many as one in four of the non-eclipsing, spectroscopic binaries withP(d)10, and Main-Sequence components withM _v 10 could be ellipsoidal variable systems. This result, while an upper limit, would seem to hold irrespective of primary spectral type (B5 to G5).     

Statistical study of visual binaries

In this paper, some statistical distributions of wide pairs included in the Washington Double Star Catalog are investigated. Frequency distributions and testing hypothesis are derived for some basic parameters of visual binaries. It was found that the magnitude difference is distributed exponentially, which means that the majority of the components of the selected systems are of the same spectral type. The distribution of mass ratios is concentrated at about 0.7 which agrees with Salpeter mass function. The distribution of the linear separation appears to be exponential which contradicts previous studies for close binaries.     

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.     

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.