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.     

The mass-ratio distribution of spectroscopic binary stars

In order to determine the mass-ratio distribution of spectroscopic binary stars, the selection effects that govern the observations of this class of binary systems are investigated. The selection effects are modelled numerically and analytically. The results of the models are compared to the data inThe Eighth Catalogue of the Orbital Elements of Spectroscopic Binary Stars (DAO8) compiled by Battenet al. (1989). The investigations involve binary systems with Main-Sequence primary components only, in order to avoid confusion of evolutionary and selection effects.For single-lined spectroscopic binaries (SBI) it is found that the mass ratios (q=M _sec/M _prim) in general adhere to a distribution _q q ^-2 forq>q ₀, withq ₀=0.3. The observations are consistent with a distribution that is flat forq<q ₀. The turn-over value varies fromq ₀=0.3 for systems with B-type primaries, toq ₀=0.55 for systems with K-type primaries. The semi-major axesa ₁ are distributed according to _a (a ₁)a ₁ ^-a with an average value of _a =1.3. The power varies from _a =1.7 for systems with B-type primaries to _a =0 for systems with K-type primaries. The eccentricitiese of the orbits of SBI systems are distributed according to _e (e)e ^-1.For double-lined spectroscopic binary stars (SBII) it is found that the shape of theq-distribution, as derived from observations, is almost entirely determined by selection effects. It is shown that the distribution is compatible with theq-distribution found for SBI systems. A sub-sample, consisting of the SBII systems from DAO8 with magnitudesm _V 5 ^m , is less hampered by selection effects, and shows the same shape of theq-distribution as the SBI systems, at theq-interval (0.67, 1).It is estimated that 19–45% of the stars in the solar neighbourhood are spectroscopic binary systems.     

On the surface distribution of chemical anomalies of Ap stars in spectroscopic binary systems

By estimating the orbital inclinations of non-eclipsing Ap spectroscopic binaries with periods less than 13 days, we can obtain a marked statistical result on the frequency distribution of the inclinations which strongly suggests that the abundance anomalies of Ap components tend to concentrate towards the stellar polar region. This would provide a critical test for models of Ap stars.     

Contribution to the search for binaries among Am stars – VIII. New spectroscopic orbits of eight systems and statistical study of a sample of 91 Am stars

Red clump giant (RCG) stars can be used as distance indicators to trace the mass distribution of the Galactic bar. We use RCG stars from 44 bulge fields from the OGLE-II microlensing collaboration data base to constrain analytic triaxial models for the Galactic bar. We find the bar major-axis is oriented at an angle of 24°–27° to the Sun–Galactic Centre line-of-sight. The ratio of semimajor and semiminor bar axis scalelengths in the Galactic plane   x ₀, y ₀  , and vertical bar scalelength z ₀, is   x ₀ :  y ₀ :  z ₀= 10 : 3.5 : 2.6  , suggesting a slightly more prolate bar structure than the working model of Gerhard which gives the scalelength ratios as   x ₀ :  y ₀ :  z ₀= 10 : 4 : 3  .     

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.

     

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.     

Spin evolution of neutron stars in binary systems

I review our understanding of the evolution of the spin periods of neutron stars in binary stellar systems, from their birth as fast, spin-powered pulsars, through their middle life as accretion-powered pulsars, upto their recycling or “rebirth” as spin-powered pulsars with relatively low magnetic fields and fast rotation. I discuss how the new-born neutron star is spun down by electromagnetic and “propeller” torques, until accretion of matter from the companion star begins, and the neutron star becomes an accretion-powered X-ray pulsar. Detailed observations of massive radio pulsar binaries like PSR 1259-63 will yield valuable information about this phase of initial spindown. I indicate how the spin of the neutron star then evolves under accretion torques during the subsequent phase as an accretion-powered pulsar. Finally, I describe how the neutron star is spun up to short periods again during the subsequent phase of recycling, with the accompanying reduction in the stellar magnetic field, the origins of which are still not completely understood.     

Observational study of interacting binary stars

We present a progress report on the results obtained from photometric and spectroscopic observations of the interacting binary stars SW Cyg, RR Dra, Y Leo, and SW Lyn in our Galaxy. Analogous studies could be eventually carried out for interacting binaries in the Local Group galaxies. From this study we note the significant Hα line profile variations in spectra of SW Cyg taken at two different orbital phases.     

Determination of the mass-ratio distribution,I: Single-lined spectroscopic binary stars

For single-lined spectroscopic binary stars (SBI), the mass ratioq=M _sec/M _prim is calculated from the mass functionf(m), which is determined from observations. For statistical investigations of the mass-ratio distribution, the term sin³ i, that remains in the cubic equation from whichq is solved, has to be dealt with.This paper compares the common practise of taking an average value for sin³ i to a deconvolution scheme that takes into account the precise (expected) behaviour ofP (sin³ i) d sin³ i. The behaviour ofP(sin³ i) d sin³ i depends on how orbital planes of binary stars are oriented in space. For a random orientation of orbital planes,P _i(i) di=sini di. For the average value method, it is generally assumed thatP _i(i) di=(4/) sin² i di.For verification purposes, the deconvolution scheme is applied to an observed sample of double-lined spectroscopic binary stars (SBII), and to a synthetic sample of SBI systems, produced by a numerical model. In both cases, the scheme produces better results with the assumption thatP _i(i) di=(4/gp) sin² i di, rather than a purely random orientation of orbital planes. In the case of the synthetic sample of SBI systems, the deconvolution scheme does not produce better results than the method that assumes an average value for sin³ i.Application of the deconvolution method to the double-lined spectroscopic binary systems in theEighth Catalogue of the Orbital Elements of Spectroscopic Binary Stars, provides results which are compatible with the assumption that the orbital planes of these systems are oriented randomly in space.     

Determination of the mass-ratio distribution,II: Double-lined spectroscopic binary stars

The application of the Richardson-Lucy iterative technique for the rectification of measurement errors, to the mass-ratio distribution of the double-lined spectroscopic binary stars (SBII) in theSixth Catalogue of the Orbital Elements of Spectroscopic Binary Stars, is evaluated for the SBII systems in the Eighth version of the Catalogue.The estimates of the real distribution, produced by the Richardson-Lucy method after successive iterations, do not converge in a trivial way. The stop criterion, suggested in the original paper on the method, is used in the application of the method to both real and simulated distributions. It is shown that, in the application to the mass-ratio distribution of the SBII systems, the iterations should stop considerably earlier than was previously assumed.The enhanced peak at mass-ratios near unity, that was found to exist in the real mass-ratio distribution, based on the earlier application of the iterative technique to the SBII systems, is likely to be due to an overshoot effect that occurs when the iterations are carried too far. When the stop criterion is used in the application of the method to the SBII systems in the Eighth version of the Catalogue, the resulting estimate of the real mass-ratio distribution does not shown evidence for anenhanced number of binary stars with mass ratios near unity.     

The gravity-darkening of highly distorted stars in close binary systems

From a quantitative analysis of the photometric ellipticity effect, values of the exponent of gravity-darkening have been empirically deduced for the components of sixteen W UMa systems with accurate cross-correlation spectroscopic mass ratios. In the analysis, the exponents for both components of a W UMa system are assumed to be the same. In view of the generally unstable nature of their light curves and the consequent difficulty to find an unique set of the fractional radii of both components, -values have been derived for various equipotential surfaces with boundary cases set at the inner and outer Roche lobes.The results indicate that if the fill-out factors are less than 0.5 (as is so for most of the actual cases), the deduced -values are all greater than Lucy's conventional value of 0.32. The empirical -values as a whole are found to increase with the mean effective temperature of the components and, furthermore, they show a tendency to decrease with increasing mass ratio, particularly for A-type systems. Thus, a W UMa system consisting of two components of quite different masses has a large empirical -value. These observational evidences indicate that the structure of the photosphere of contact components of W UMa systems is significantly different from that of normal Main-Sequence stars of similar spectral type and may provide a clue to solve puzzles of W UMa stars.     

Close binary systems in multiple stars: II. Eclipsing variables in visual binary and multiple systems

Eclipsing variables in visual binary and multiple stars are searched using data from GCVS, WDS, and CCDM catalogs. The list of 421 eclipsing variables is obtained. The masses of components of multiple systems from the list are estimated using the mass-luminosity relation for the main sequence stars. It is shown that, for 85% multiple systems from the list, the mass of visual components is smaller by a factor of 2 than the total mass of close binary systems. The distributions of orbital elements of visual binary systems are constructed and used for calculation of orbit semi-major axes for star from the list. The distributions of orbit semi-major axes and periods obtained from observations are approximated by Gaussian curves. The maxima of the curves correspond to a = 800 a.u. and P = 7600 years, respectively. The distribution of orbit semi-major axes larger than 800 a.u. is better described by Opik’s law; it is expected that this law describes the real a distribution in the region of small values as well. The frequency of eclipsing variables in multiple stars makes 12% of the total number of stars of this type in GCVS.     

Spectrophotometric studies of Am stars

The relationships among the various physical parameters-namely, the effective temperatures, radii and bolometric magnitudes, determined on the basis of the energy distribution curves of 25 Am stars — have been studied. Their effective temperatures are in the range of 7200 K to 9700 K; the radii, 1.5R to 2.5R ; the bolometric magnitudes, 0.75 mag. to 2.25 mag.; and the masses, 1.5M to 2.25M . The Am stars in general, appear redder than their normal counterparts, the blanketing in the blue andUV regions being the major cause. For the relatively cooler stars, the (B-V) colours are found to be less affected by blanketing. They are located in the neighbourhood of the upper edge of the zero-age Main Sequence band and show a fairly wide range in the evolutionary status among themselves. The bolometric corrections which are independent of the uncertainties in the parallax measurements, follow the same trend as that of the Ap stars, with reference to the temperature.     

Masses and ages of delta scuti stars in eclipsing binary systems

By using data mainly from Frolovet al. (1982) for four Delta Scuti stars in eclipsing binary systems, AB Cas, Y Cam, RS Cha, and AI Hya, their physical parameters, distances, and radial pulsation modes are determined. The evolutionary track systems of Iben (1967), Paczyski (1970), and Maeder and Meynet (1988) are interpolated, in order to estimate evolutionary massesM _eand agest of these variables. Their pulsation massesM _Qare estimated from the fitting formulae of Faulkner (1977) and Fitch (1981). Our estimates of evolutionary massesM _eand pulsation massesM _Qare close to the massesM determined by Frolovet al. (1982) from the star binarity. The only exception is AB Cas, for which there is no agreement between certain star parameters.Another, independent approach is also applied to the stars RS Cha and AI Hya: by using their photometric indicesb — y andc ₁ from the catalogue of López de Cocaet al. (1990) and appropriate photometric calibrations, other sets of physical parameters, distances, modes, ages, evolutionary and pulsation masses of both variables are obtained.     

Effect of Coriolis force on the equilibrium structures of rotating stars and stars in binary systems

Kopal (Adv. Astron. Astrophys. 9:1–65, 1972) introduced the concept of Roche equipotentials to incorporate the effects of rotation and tidal distortions on the equilibrium structure and periods of small oscillations of rotating stars and stars in binary systems. However his expression for the Roche equipotential accounts for only the effects of centrifugal and gravitational forces and does not take into account the effect of Coriolis force. In this paper we have suitably modified Kopal’s expression for Roche equipotentials to incorporate into it the effect of Coriolis force as well. The modified expression for the Roche equipotential has then been used to compute the equilibrium structures and shapes of polytropic models of rotating stars and stars in binary systems.     

Velocity curve analysis of the spectroscopic binary stars by the non-linear least squares

We introduce a new method to derive the orbital parameters of spectroscopic binary stars by a non-linear least squares analysis of residuals. Using measured radial velocity data of four double lined spectroscopic binary systems RZ Cas, CC Cas, V1130 Tau and Y Cygni, we find corresponding orbital and spectroscopic elements. Our numerical results are in good agreement with those obtained by others using more traditional methods.     

MK morphological study of Am stars at 66 Å/mm

The pseudo-luminosity effect in the metallic line A-type stars found by Abt & Morgan (1976) is confirmed in a random sample of 27 Am stars. From a morphological study of their spectra in the wavelength interval 3850-4400 Å at a reciprocal dispersion of 66 Å/mm, revised spectral types are given on the MK system for their K-line and metallic-line spectra. This shows that: (a) our segregation of weak Am from the Am stars largely agrees with that by Cowleyet al. (1969); (b) all the stars in the sample are dwarfs according to their K-line classification; (c) more than 80 per cent exhibit the pseudo-luminosity effect significantly, with their metallic-line spectra resembling a giant or even a supergiant in the violet (3850-4100 Å), and a giant rather than a dwarf in the blue region (4260-4400 Å); (d) in two-thirds of the stars under (c), the Sr n 4077 Å line is found to have a markedly brighter luminosity class compared to any region, and in more than one-third of the sample it is comparable to that in Ap stars; (e) at least five stars exhibit characteristics which might suggest a spectrum variability: among these, the most striking example is 41 Sex A which was found to show a phase-modulated spectrum variation hitherto unknown in Am stars; (f) the metallic-line spectra of another five stars appear to be similar to A-shell type in differing degrees; (g) less than 20 per cent of the sample comprises stars which do not show any significant differential luminosity effect; these stars might have been misclassified or perhaps they are in a quiescent state. We also confirm the conclusion arrived at by Böhm-Vitense & Johnson (1978) that all Am stars may vary and our observations suggest that groups may exist among them.