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.     

A statistical method of estimating the rotation of Be stars

We give a statistical method which will estimate the true rotational velocity V of a Be star from its observed apparent velocity U = Vsini. We show that Be stars do not rotate with the critical velocity and that the ratio between their real velocity and the critical velocity is about 0.7.     

The Restricted Three-Body Problem: Comments on the Rotational Effect

The synchronization between the orbital motion and axial rotation of the two component stars of a binary system is reviewed. Some previous published papers are mentioned and the general conclusion is outlined: If we shall use a rotating coordinate system synchronous with one of the two stellar axial rotations, it is not possible to obtain a Jacobi integral and the Roche geometry cannot be further analyzed. In addition, a theoretical approach is summarized in order to use the axial rotations of the two component stars, even if the constants of the stellar structure (k₂)₁, (k₂)₂must be taken into consideration. So it is found that if the stellar angular velocities are higher than the corresponding Keplerian angular velocity (ω_i≫ ω_k, i= ), the problem of the rotational effect could be of practical consideration. Finally, a theoretical relationship between the two constants (k₂)₁and (k₂)₂of the stellar structure is established.     

Spectroscopic Analysis of the Eclipsing Binary α CrB

The eclipsing binary α CrB, is a well-known double-lined spectroscopic binary. The system is considered unique among main-sequence systems with respect to its small mass ratio and large magnitude difference between the components. Our aim in the present paper is to compute the orbital parameters and to model the atmospheric parameters of the system. Synthetic spectral analysis of both the individual and disentangled spectra has been performed and yielded effective temperatures T _eff?=?10000±250 K, surface gravities logg?=?4±0.25 and projected rotational velocities $\emph{v}$ sini?=?110±5 km/sec for the primary component, and T _eff?=?6000±250 K and logg?=?4.5±0.25 for the secondary component. Evolutionary state of the system is investigated using stellar models.     

Radial and rotational velocities for a sample of magnetic CP stars

The spectra taken with the Main Stellar Spectrograph (MSS) of the 6-m telescope with a resolution of R ～ 15000 and a signal-to-noise ratio of 200–300 are used to determine the radial velocities and projected rotational velocities (υ _e sin i) for 32 magnetic CP stars. Measured υ _e sin i values range from 18 km/s (the lower boundary determined by the instrumental profile) to 65 km/s. Measurements of standard stars demonstrate the absence of systematic differences between our and published data. Eight of the 32 magnetic stars are found or confirmed to be binary and binarity is suspected for another four stars. The components of tangential velocity are determined for 27 stars with known parallaxes.     

LU Vel (GJ 375): A M3.5Ve Flare and Double-Lined Spectroscopic Binary

High resolution echelle spectroscopic observations taken with the FEROS spectrograph at the 2.2 m telescope ESO confirm the binary nature of the flare M3.5V star LU Vel (GJ 375, RE J0958-462) previously reported by Christian and Mathioudakis (2002). Emission of similar intensity from both components is detected in the Balmer, Na i D₁&D₂, He i D₃, Ca ii H&K, and Ca ii IRT lines. We have determined precise radial velocities by cross correlation with radial velocity standard stars, which have allowed us to obtain for the first time the orbital solution of the system. The binary consists of two near-equal M3.5V components with an orbital period shorter than 2 days. We have analyzed the behaviour of the chromospheric activity indicators (variability and possible flares). In addition, we have determined its rotational velocity and kinematics.     

Stellarv sini and optical emission line widths in Be stars

I re-investigate empirical correlations between line widths of photospheric absorption lines — as a measure of the stellar projected rotational velocityv sini- and of circumstellar emission lines in Be stars. The degree of this correlation is a measure for the kinematic, i.e., rotational, contribution to the total emission line broadening.From the literature and from additional data, I have collected a sample of photoelectric measurements of Balmer and Feii emission lines of the 115 brightest Be stars in the sky, most of them observed several times during the past decade. I investigate the following emission line widths parameters: full width at half maximum, total width at the base, and double-peak separation. I find from the FWHM that the basic origin of emission line broadening in Be stars is undoubtedly rotational, the correlations withv sini being best for weaker emission lines while H shows considerable scatter. Total width at the base is uncorrelated withv sini except for the Feii lines. Peak separation is found to be a function both ofv sini and of equivalent width. The latter dependence can straightforwardly be understood by the fact that within Huang's disk model peak separation, normalized tov sini, is governed by the outer envelope radius.I conclude that observational evidence leaves no doubt that Be star envelopes as visible in optical emission lines are rotationally supported and have axisymmetric geometry.Partly based on observations obtained at the European Southern Observatory, La Silla, Chile.     

On the orbital and physical parameters of the HDE 226868/Cygnus X-1 binary system

In this paper we explore the consequences of the recent determination of the mass m=(8.7±0.8)M _⊙ of Cygnus X-1, obtained from the Quasi-Periodic Oscillation (QPO)-photon index correlation scaling, on the orbital and physical properties of the binary system HDE 226868/Cygnus X-1. By using such a result and the latest spectroscopic optical data of the HDE 226868 supergiant star we get M=(24±5)M _⊙ for its mass. It turns out that deviations from the third Kepler law significant at more than 1-sigma level would occur if the inclination i of the system’s orbital plane to the plane of the sky falls outside the range ≈41–56 deg: such deviations cannot be due to the first post-Newtonian (1PN) correction to the orbital period because of its smallness; interpreted in the framework of the Newtonian theory of gravitation as due to the stellar quadrupole mass moment Q, they are unphysical because Q would take unreasonably large values. By conservatively assuming that the third Kepler law is an adequate model for the orbital period we obtain i=(48±7) deg which yields for the relative semimajor axis a=(42±9)R _⊙ (≈0.2 AU).     

The dependence of brightness distribution on the inclination of galaxies

A sample of 92 galaxies with published surface photometric data inB band and inclined randomly to the line of sight is selected and used to compute the photometric parameterQ _N . The dependence ofQ _N on the apparent flatteningq is found and discussed for different morphological groups.Q _N is more sensitive toq in earlier-type galaxies.     

Measurement of spin in twenty binary systems

The spin velocities of 20 primaries and 5 secondaries in 20 binary systems were measured with the Condé Reticon on the McDonald 2.1 m telescope. 14 of the primaries and all 5 of the secondaries measured show synchronous rotation. The star, 62 Per, previously thought to have V sin i = 0,, turned out to have V sin i = 200 km/s. Results for other stars are in basic agreement with previous measurements (₀ Per has not been measured before). For TXUMa, the NaI D-line was found to be stronger in the secondary than in the primary, from which fact a mass-ratio of 0.32 was deduced.     

Early-type W UMa contact binary system: New data on V535 Ara

This paper presents the results of spectroscopic and photometric observations of the early-type W UMa system V535 Ara. New high-resolution spectra were taken at the Mt. John University Observatory in 2007. Radial velocities and spectroscopic orbital elements of the system were determined by applying KOREL spectral disentangling. The resulting orbital elements were: a₁sini = 0.0047 ± 0.0001 AU, a₂sini = 0.0146 ± 0.0001 AU, M₁sin³i = 1.85 ± 0.01 M_⊙, and M₂sin³i = 0.59 ± 0.01 M_⊙. The components were found to be in synchronous rotation following examination of their disentangled Hγ line profiles. Four photometric data-sets (1966 BV, 1967 BV, HIPPARCOS and ASAS) were modeled using the Wilson-Devinney method. The model describes V535 Ara as an A sub-type W UMa type eclipsing binary which has a fill out factor of 0.22 in marginal contact configuration. The simultaneous solution of light and radial velocity curves gave the following absolute parameters: M₁ = 1.94 ± 0.04 M_⊙, M₂ = 0.59 ± 0.02 M_⊙, R₁ = 2.09 ± 0.03 R_⊙, R₂ = 1.23 ± 0.02R_⊙, L₁ = 18 ± 3 L_⊙ and L₂ = 6 ± 1 L_⊙. The distance to V535 Ara was calculated as 123 ± 20 pc using distance modulus with correction for interstellar extinction.     

Spectrum of the star BM Ori at minimum light

Two spectra of the star BM Ori were obtained with the 2.6-m Crimean Astrophysical Observatory telescope near its maximum eclipse phase. The light detector was a CCD array. The wavelength range 5305–5373 Å was chosen in such a way that it contained no strong primary lines. Optimum filtration of the spectra yielded a signal-to-noise ratio of ～300. Eighteen secondary lines are seen in the spectrum. Atmospheric parameters of the secondary star were determined: T _eff=5740 K and logg=3.0; the secondary was classified by these parameters as being of spectral type G2 III. The best agreement between observed and synthetic spectra is achieved for metallicity [M/H]=?0.5 and microturbulence ξ_t=0 km s^?1. The projected rotational velocity is Vsini=60 km s^?, in agreement with the synchronous velocity in the hypothesis that assumes a total eclipse by the secondary star. Atmospheric elemental abundances in the secondary are estimated. Nickel, chromium, and iron exhibit an underabundance of ～1 dex.     

Another view of synodic solar rotation

Adding the angular velocity of sidereal solar rotation and the apparent rotational effect of the Earth's revolution vectorially, a new synodic solar rotation vector has been obtained. The sidereal and synodic solar rotation axes (and equators) are separated. Using the known parameters of the Earth's orbital motion, the synodic rotation angular velocity and the inclination of the synodic equator, the corresponding sidereal rotation parameters have been calculated (ω₁ = 2.915 × 10^#X2212;6 rad s^#X2212;1 and i ₁ = 6.076). Various linear rotational velocities at the solar globe are briefly described.     

On the Use of Roche Equipotentials in Analysing the Problems of Binary and Rotating Stars

Kopal (Adv. Astron. Astrophys., 9, 1, 1972) introduced the concept of Roche equipotentials to analyse the effects of rotational and tidal distortions in case of stars in binary systems. In this approach a mathematical expression for the potential of a star in a binary system is obtained by approximating its inner structure with Roche model. This expression for the potential has been used in subsequent analysis by various authors to analyse the problems of structures and oscillations of synchronous and nonsynchronus binary stars as well as single rotating stars. Occasionally, doubts have been expressed regarding the validity of the use of this approach for analysing nonsynchronous binaries and rotationally and tidally distorted single stars. In this paper we have tried to clarify these doubts.     

Astrometric study of the triple star ADS 9173

An approximate orbit of the wide visual binary star ADS 9173 A(Bb) with a period of ～6000 yr has been determined for the first time by the method of apparent motion parameters. The orbit was computed using a short (1982–2004) arc of photographic observations obtained with the 26-inch Pulkovo Observatory refractor and the Hipparcos parallax. Agreement of the new orbit with the observations from the WDS catalog beginning in 1832 serves as a check. The errors in the orbital elements are large, but the orientation elements of the orbital plane (i and Ω) were estimated reliably. Component B has an invisible spectroscopic companion with a period of 4.9 yr. An astrometric orbit of Bb consistent with radial velocity measurements was determined from the residuals to the relative orbital motion of A(Bb). The orbital planes are nearly coplanar. If the mass of component B is taken in accordance with the mass—luminosity relation, 1.5 M _⊙, and the parallax is 0.″021, then the mass of the secondary component is no less than 0.5M _⊙. Component A may also be a long-period binary system.     

An updated period analysis for ER Orionis: A definitive solution

An updated period analysis for the overcontact eclipsing binary ER Orionis is presented. Featured is an improved derivation of parameters for the light time effect (LTE) due to the third star (in actuality, a pair of stars) utilising the latest set of eclipse timings. The very good fit between the eclipse timing differences (ETD) plot (otherwise known as an O–C diagram) and the theoretical ETD curve makes possible an improved determination of the rate of mass interchange between the binary pair, dm₁/dt = +1.83(6) × 10⁻⁷ M_ʘ/year. In addition, the mass of the companion system (in actuality, m₃ sin i) and the elements of its orbit were computed. A suggestion is made for a method of future determination of the inclination of the orbit of the companion system.     

Determining the minimum sum of the component masses for a binary with a known parallax from observations of a short arc of its apparent motion

An inequality that allows the minimum sum of the component masses for a binary, M₀, to be determined was derived from simple geometric considerations. This quantity satisfies the observed orbital motion according to Newton's law with a known parallax. The M₀ value can be calculated if the apparent-motion parameters for the components, including the curvature of the observed short orbital arc, were determined from observations. We estimated M₀ for 14 Pulkovo program stars for which the apparent orbital arc covered with observations was no less than 10°. We compare M₀ with the masses estimated from the mass-luminosity relation. A significant mass excess was found for the star ADS 10329.     

Modeling the luminosity function of galactic low-mass X-ray binaries

The evolution of the family of binaries with a low-mass star and a compact neutron star companion (low-mass X-ray binaries (LMXBs) with neutron stars) ismodeled by the method of population synthesis. Continuous Roche-lobe filling by the optical star in LMXBs is assumed to be maintained by the removal of orbital angular momentum from the binary by a magnetic stellar wind from the optical star and the radiation of gravitational waves by the binary. The developed model of LMXB evolution has the following significant distinctions: (1) allowance for the effect of the rotational evolution of a magnetized compact remnant on themass transfer scenario in the binary, (2) amore accurate allowance for the response of the donor star to mass loss at the Roche-lobe filling stage. The results of theoretical calculations are shown to be in good agreement with the observed orbital period-X-ray luminosity diagrams for persistent Galactic LMXBs and their X-ray luminosity function. This suggests that the main elements of binary evolution, on the whole, are correctly reflected in the developed code. It is shown that most of the Galactic bulge LMXBs at luminosities L _x > 10³⁷ erg s^?1 should have a post-main-sequence Roche-lobe-filling secondary component (low-mass giants). Almost all of the models considered predict a deficit of LMXBs at X-ray luminosities near ～10^36.5 erg s^?1 due to the transition of the binary from the regime of angular momentum removal by a magnetic stellar wind to the regime of gravitational waves (analogous to the widely known period gap in cataclysmic variables, accreting white dwarfs). At low luminosities, the shape of the model luminosity function for LMXBs is affected significantly by their transient behavior-the accretion rate onto the compact companion is not always equal to the mass transfer rate due to instabilities in the accretion disk around the compact object. The best agreement with observed binaries is achieved in the models suggesting that heavy neutron stars with masses 1.4–1.9M _⊙ can be born.     

Absorption line profiles and rotational velocities for 59 stars

Absorption lines of Heii, Hei, Mgii, and other ions have been measured in coudé spectral tracings for 59 slowly and rapidly rotating sourthern O, B and A stars on the Main Sequence. All 668 separate line profiles have been analyzed with a procedure of differential corrections by least-squares to yield the following parameters and their error estimates: half-width, central depth, equivalent width, and shape parameter. The shape parameter includes Voigt profiles and also ‘super-Gaussian’ and ‘super-damping’ profiles. In addition, separately-measured line profiles in each star have been superimposed to yield better composite profiles with smaller errors. In addition, a preliminary value ofv sini is derived for each line by deconvolving it with both the intrinsic and instrumental profiles, and a mean value (including error bar) is derived for each star. The resulting mean values ofv sini are only about 2/3 as large as the earlier results presented by Buscombe (1969). The inadequacies of the traditional procedure are discussed, and plans for using calculated non-LTE intrinsic line profiles including line limb darkening and also effects of rotational distortion, will be outlined.     

Atmospheric Parameters and Abundances of sdB Stars

We summarize recent results of quantitative spectral analyses using NLTE and metal line-blanketed LTE model atmospheres. Temperatures and gravities derived for hundreds of sdB stars are now available and allow us to investigate systematic uncertainties of T _e ff, log g scales and to test the theory of stellar evolution and pulsations. Surface abundance patterns of about two dozen sdB stars are surprisingly homogenous. In particular the iron abundance is almost solar for most sdBs. We highlight one iron-deficient and three super metal-rich sdBs, a challenge to diffusion theory. sdB stars are slowly rotating stars unless they are in close binary systems, which is hard to understand if the sdB stars were formed in merger events. The only exception is the pulsator PG 1605+072 rotating at vsin i= 39 km/s. Signatures of stellar winds from sdB stars may have been found.