A Mechanism for Producing Short-Period Binaries

When three point masses form a hierarchical triple system, the short-period orbit can be severely modified by the long-period orbit if the two orbits are inclined to each other by more than about 39^deg (). Such an inclination can induce ‘Kozai cycles’ (Kozai, 1962), in which the eccentricity of the inner orbit cycles by a large amount while its period and therefore semimajor axis remains roughly constant. During those periastra when the eccentricity is largest, tidal friction may become important, and this can result in a secular shrinkage of the orbit, until it becomes circularised at a period of a few days.However, apsidal motion due to either GR or to the quadrupolar distortion of the components (if they are no longer treated as point masses) can reduce the range of eccentricity. We explore the limits on outer and inner orbital period that these perturbations imply.If the components are F/G/K/M dwarfs, then rotationally-driven dynamo activity can become important at the short periods that can occur in the right circumstances. It can cause the period to shorten further. The result may be a contact binary, and/or a merger in which the two stars of the inner pair coalesce to form a single rapidly rotating star. We suggest that this may be the origin of AB Dor, a very rapidly rotating K dwarf that is probably about 50 Myr old.     

Role of the Rossiter-McLaughlin effect in the study of close binaries

This paper is devoted to binary stars belonging to the class of eclipsing-variable systems.Photometric and spectroscopic analysis of eclipses allows us to determine geometric parameters of the orbit and physical characteristics of stellar components as well as inclinations of stellar equators to the orbital plane. Estimations of inclinations can be obtained from measurement of the Rossiter-McLaughlin effect, which is discussed using examples of some eccentric binaries with an anomalous apsidal effect. Our task is to find the complete spectrum of solutions of the equation of apsidal motion, depending on the inclinations of the polar axes of the components to the orbital one for these systems, based on their individual spectroscopic and photometric observational data. The matrix of solutions allows us to select those pairs of polar inclinations that provide agreement with the observational apsidal period.     

Dynamical Processes in the Neighborhood of the Herbig Ae Star MWC 480 Based on Spectral Monitoring Data

Spectral observations of the Herbig Ae star MWC 480 are reported. Observations were made on the 2.6 m telescope at the Crimean Astrophysical Observatory and the 6 m telescope at the Special Astrophysical Observatory in the neighborhoods of the sodium resonance doublet, the He I 5876 line, the oxygen O I 7774 line, the H line, and some others. The H line has a P Cyg-type profile which is typical of anisotropic decelerated material outflows. The parameters of the line profile vary on a time scale on the order of days or longer. The blue wing of the line profile, in which noticeable changes are detectable over times of a few hours, is subject to the greatest variation. An unusual line shape is observed in the sodium lines. Their profiles resemble type P Cyg profiles with discrete absorption components can be seen in the blue wing. The number, shape, and radial velocities of the components change with time. The maximum radial velocity is -330 km/s and the minimum, about -50 km/s. The high velocity components are subject to the greatest variability. An analysis of the spectral variability yields the following conclusions: (1) the inner layers of the accretion disk of MWC 480 reach right to the star. The maximum rotation velocity of the circumstellar gas derived from the oxygen OI 7774 line shape is close to 400-500 km/s, which corresponds roughly to the radius of the last Keplerian orbit. (2) A highly nonuniform, high velocity component of the disk wind, which contains dense fragments (microjets), develops in this region. They appear to form as a result of the unstable structure of the magnetic field in the layers of the accretion disk closest to the star. (3) The maximum velocities of the microjets are only slightly higher than the escape velocity at the star's surface. Thus, the bulk of the momentum which they acquire is expended in overcoming the star's gravity and this causes a deceleration in the radial motion of the gas. This kind of structure for the radiating region is consistent with magneto-centrifugal models of the disk wind in which the intrinsic magnetic field of the accretion disk plays a dominant role in the acceleration of the gas.     

Comparative Analysis of “Exact” and “Approximate” Methods for Estimating the Absolute and Relative Elements of Detached Close Binary Systems

In this paper the star characteristics (luminosities, spectra, masses, absolute and relative radii of the components, mass ratio, major semiaxis, and orbital inclination) of close binary systems (CBS) with detached components are compared element-by-element. Svechnikov and Perevozkina's Catalog of the orbital elements, masses, and luminosities of pre-main sequence-type eclipsing variable stars with known photometric and spectroscopic elements and Svechnikov and Kuznetsova's Catalog of approximate photometric and absolute elements of eclipsing variable stars are used as initial data. The orbital elements contained in the first catalog are determined from solutions of the known photometric light curves and the known radial velocity curves, while the orbital elements for the second catalog were estimated using data from the General Catalog of Variable Stars (GCVS) IV employing approximate statistical relationships such as mass-radius, mass-luminosity, and mass-spectrum, along with the dependence of the orbital inclination on the depth of the principal minimum and others. Possible reasons for discrepancies among the compared quantities are discussed.     

The eclipsing binary PV Cas: a case of strong differential rotation in depth

In this study, we show that only models with differential rotation, as opposed to non-rotation or solid-body rotation for the components of PV Cas, are in satisfactory agreement with the observations (including constraints on the apsidal advance rate and the synchronous rotation of the components in addition to their luminosities and radii). Internal rotation profiles found for solar and metal-rich chemical compositions are similar to each other in that only a small part of the outermost regions is rotating very slowly  ( v _eq∼ 65 km s ⁻¹)  and the rest is rotating very rapidly. Confirmation of Ap-like variations in the light curve of the system leads us to search for a connection between this type (and similar types) of internal rotation and chemically peculiar stars. The temperature difference between the blue sides of the main sequence for the normal and for the magnetic Ap stars may arise from such a connection, since we find a similar difference between the models with this kind of rotation and the non-rotating models of somewhat lower mass.     

Rotation of close binary system components

The rotation of close binary system components is investigated. The principal physical characteristics as well as the equatorial rotational velocities and the axial and orbital inclinations for 46 close binary systems were determined. It is found that the rotation axes of the individual stars in a pair cross the orbital plane under different angles. As a rule, the rotation and orbital periods of a vast majority of the systems investigated here do not coincide.     

Some Comments on the Magnetic Braking of CP Stars

The low rotation velocities of magnetic CP stars are discussed. Arguments against the involvement of the magnetic field in the loss of angular momentum are given: (1) the fields are not strong enough in young stars in the stage of evolution prior to the main sequence; (2) there is no significant statistical correlation between the magnetic field strength and the rotation period of CP stars; (3) stars with short periods have the highest fields; (4) a substantial number of stars with very low magnetic fields (B _e < 500 G) have rotation speeds that are typical of other CP stars; (5) simulations of the magnetic fields by Leroy and the author show that the orientation of dipoles inside rotating stars, both slow and fast, is consistent with an arbitrary orientation of the dipoles; and, (6) slow rotators with P>25 days, which form 12% of the total, probably lie at the edge of the velocity distribution for low mass stars. All of these properties conflict with the hypothesis of magnetic braking of CP stars.     

Estimation of the Time Scale of Merging of the Components of Contact Binaries of the W UMa Type

Time scales of the transition from contact binary systems of the W UMa type to single stars of the blue straggler type are estimated. A model of one-way mass transfer from the primary component to the companion inside a common envelope (Eggen et al.) and a model of a contact binary lying on the zero-age main sequence with a companion that is losing mass (F. van't Veer) are used to calculate these scales. The merging times of components were calculated for 304 contact systems of the W UMa type from the Catalog of Approximate Photometric and Absolute Elements of Eclipsing Variable Stars on a scale of loss of mass and orbital angular momentum due to magnetic braking, under the assumption of synchronization of the axial rotation and orbital revolution. On the basis of the resulting statistics, the characteristic merging scales are 0.4-0.6 and 0.5-0.7 Gyr, respectively, for the above two models. The results of a comparison with the work of other authors are discussed.     

UBVRI Photometry and Polarimetry of the Eclipsing Binary RY Per

Results are presented from multicolor photometric and polarimetric studies of the eclipsing binary RY Per during 2001-2003. Light curves in the UBVRI bands are shown. An analysis of the variations in the linear polarization makes it possible to separate it into interstellar and intrinsic components. The degree of intrinsic polarization of the system away from the eclipse attains a maximum (0.23%) in the B band and falls off rapidly with increasing wavelength. This dependence is indicative of the existence of optically thick gas in the system. An analysis of the polarimetric data also shows that: the total mass of optically thin gas in the system is about 2·10^-10 M , while the total mass of the shell must be several times that; and, the inclination of the orbital plane of the binary system relative to the galactic plane is 4° or 18°.     

Stable planetary orbits around one component in nearby binary stars. II

Numerical simulations are made within the framework of the plane restricted three-body problem, in order to find out if stable orbits for planets around one of the two components in double stars can exist. For any given set of initial parameters (the mass ratio of the two stars and the eccentricity of their orbit around each other), the phase-space of initial positions and velocities is systematically explored.In previous works, systematic exploration of the circular model as well as studies of more realistic (elliptic) cases such as Sun-Jupiter and the nearby Centauri and Sirius systems, large stable planetary orbits were found to exist around both components of the binary, up to distances from each star of the order or more than half the binary's periastron separation.The first results presented here for the Coronae Borealis system confirm the previous studies.     

Apsidal motion in the eclipsing binary system V 451 Ophiuchi

MulticolourWBVR photoelectric observations of the eclipsing binary V 451 Oph were carried out, and a highly accurate light curve was obtained. The angular velocity of the orbital rotation, =2.1 deg yr^–1, and the apsidal motion constantk ₂=0.0045 are given.     

Optical spectroscopy of X-Mega targets – II. The massive double-lined O-type binary HD 93205

A new high-quality set of orbital parameters for the O-type spectroscopic binary HD 93205 has been obtained combining échelle and coudé CCD observations. The radial velocity orbits derived from the He  ii λ 4686 Å (primary component) and He  i λ 4471 Å (secondary component) absorption lines yield semi-amplitudes of 133±2 and 314±2 km s⁻¹ for each binary component, resulting in minimum masses of 31 and 13 M_⊙ ( q =0.42) . We also confirm for the binary components the spectral classification of O3 V+ O8 V previously assigned. Assuming for the O8 V component a 'normal' mass of 22–25 M_⊙ we would derive for the primary O3 V a mass of 'only' 52–60 M_⊙ and an inclination of about 55° for the orbital plane. We have also determined for the first time a period of apsidal motion for this system, namely 185±16 yr using all available radial velocity data sets of HD 93205 (from 1975 to 1999). Phase-locked variations of the X-ray emission of HD 93205 consisting of a rise of the observed X-ray flux near periastron passage are also discussed.     

The BM Ori System. I. Anomaly in the Radial Velocity

The radial velocities of the star BM Ori are determined from spectra obtained by the HST and IUE satellites, as well as from spectra obtained with the BTA telescope. An analysis of this data shows that the radial velocities of the main star and its satellite experience an irregular positive shift by 20-30 km/s. This fact can only be interpreted in terms of the presence of yet another star in the binary system. The new observations have made it possible to significantly improve the accuracy of the spectroscopic elements of the orbit of the close binary system and to estimate the orbital characteristics of the third body. The preliminary values of the elements are: Ep=JD2444744, P=1302^d, =11km/s, e=0.92, K=20km/s, and =1.6rad.     

The effects of viscous friction on the precession and nutation of celestial bodies

The aim of the present study has been to set the system of differential equations which govern the precession and nutation of self-gravitating globes of compressible viscous fluid, due to the attraction exerted on the rotating configuration by its companion; and to construct their approximate solution which are correct to terms of the second order in small dependent variables of the problem. Section 2 contains an explicit formulation of the effects of viscosity arising in this connection, given exactly as far as the viscosity remains a function of radial distancer only; but irrespective of its magnitude. In Section 3 the equations of motion will be linearized for the case of near-circular orbits and small inclinations andi of the equator of the rotating configuration, and of its orbital plane, to the invariable plane of the system; while in Section 4 further simplifications will be introduced which are legitimate for studies of secular (or long-periodic) motions of the nodes and inclinations. The actual solutions of so simplified a system of equations are constructed in Section 5; and these represent a generalization of the results obtained in our previous investigation (Kopal, 1969) of the inviscid case.The physical significance of the new results will be discussed in the concluding Section 6. It is demonstrated that the axes of rotation of deformable components in close binary systems are initially inclined to the orbital plane, viscous dissipation produced by dynamical tides will tend secularly to rectify their positions until perpendicularity to the orbital plane has been established, and the equators as well as orbit made to coincide with the invariable plane of the system-in a similar manner as other effects of tidal friction are bound eventually to synchronize the velocity of axial rotation with that of orbital revolution in the course of time.An application of the results of the present study to the dynamics of the Earth-Moon system discloses that the observed inclination of 1°.5 of the lunar equator to the ecliptic cannot be regarded as being secularly constant, but representing the present deviations from perpendicularity of oscillatory motion of very long period.The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR-09-051-001 with the National Aeronautics and Space Administration. This paper constitutes the Lunar Science Institute Contribution No. 85.     

Tidal evolution in close binary systems

The aim of the present paper will be to give a mathematical outline of the theory of tidal evolution in close binary systems of secularly constant total momentum — an evolution activated by viscous friction of dynamical tides raised by the two components on each other. The first section contains a general outline of the problem; and in Section 2 we shall establish the basic expressions for the energy and momenta of close binaries consisting of components of arbitrary internal structure. In Section 3 we shall investigate the maximum and minimum values of the energy (kinetic and potential) which such systems can attain for given amount of total momentum; while in Section 4 we shall compare these results with the actual facts encountered in binaries with components whose internal structure (and, therefore, rotational momenta) are known to us from evidence furnished by the observed rates of apsidal advance.The results show that all such systems — be these of detached or semi-detached type — disclose that more than 99% of their total momenta are stored in the orbital momentum. The sum of the rotational momenta of the constituent components amounts to less than a percent of the total — a situation characteristic of a state close to the minimum energy for given total momentum. This appears, moreover, to be true not only of the systems with both components on the Main Sequence, but also of those possessing evolved components in contact with their Roche limits.Under such conditions, a synchronism between rotation and revolution (characteristic of both extreme states of maximum and minimum energy) is not only possible, but appears to have been actually approached — if not attained — in the majority of cases. In other words, it would appear that — in at least a large majority of known cases — the existing close binaries have already attained orbits of maximum distension consistent with their momenta; and tidal evolution alone can no longer increase the present separations of the components to any appreciable extent.The virtual absence, in the sky, of binary systems intermediate between the stages of maximum and minimum energy for given momentum leads us to conjecture that the process of dynamical evolution activated by viscous tides may enroll on a time-scale which is relatively short in comparison with their total age — even for systems like Y Cygni or AG Persei, whose total age can scarcely exceed 10⁷ yr. A secular increase of the semi-major axes of relative orbits is dynamically coupled with a corresponding variation in the velocity of axial rotation of both components through the tidal lag arising from the viscosity of stellar material. The differential equations of so coupled a system are given in Section 5; but their solution still constitutes a task for the future.The Lunar Science Institute Contribution No. 90. The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.     

Dusty disk wind in young binary systems viewed pole-on

A model of a young binary system with companions of unequal mass whose orbital plane is inclined at a large angle to the line of sight is examined. The system components are assumed to accrete matter from the remains of the protostellar cloud. It is found that eclipsing of the primary component by the disk wind of the secondary can be observed when the plane of the orbit is inclined at a large angle to the line of sight or even when the binary system is observed pole-on. __________ Translated from Astrofizika, Vol. 51, No. 2, pp. 267–275 (May 2008).     

The structure and evolution of M 51-type galaxies

We discuss the integrated kinematic parameters of 20 M 51-type binary galaxies. A comparison of the orbital masses of the galaxies with the sum of the individual masses suggests that moderately massive dark halos surround bright spiral galaxies. The relative velocities of the galaxies in binary systems were found to decrease with increasing relative luminosity of the satellite. We obtained evidence that the Tully-Fisher relation for binary members could be flatter than that for local field galaxies. An enhanced star formation rate in the binary members may be responsible for this effect. In most binary systems, the direction of the orbital motion of the satellite coincides with the direction of the rotation of the main galaxy. Seven candidates for distant M 51-type objects were found in the Northern and Southern Hubble Deep Fields. A comparison of this number with the statistics of nearby galaxies provides evidence for the rapid evolution of the space density of M 51-type galaxies with redshift z. We assume that M 51-type binary systems could be formed through the capture of a satellite by a massive spiral galaxy. It is also possible that the main galaxy and its satellite in some of the systems have a common cosmological origin.     

Coordinated monitoring of the eccentric O-star binary Iota Orionis: optical spectroscopy and photometry

With the objective of investigating the windwind collision phenomenon and supporting contemporaneous X-ray observations, we have organized a large-scale, coordinated optical monitoring campaign of the massive, highly eccentric O9 III+B1 III binary Iota Orionis. Successfully separating the spectra of the components, we refine the orbital elements and confirm the rapid apsidal motion in the system. We also see strong interaction between the components during periastron passage and detect phase-locked variability in the spectrum of the secondary star. However, we find no unambiguous signs of the bow shock crashing on the surface of the secondary, despite the predictions of hydrodynamic simulations. Combining all available photometric data, we find rapid, phase-locked variations and model them numerically, thus restricting the orbital inclination to 50° i 70°.     

The precession and nutation of deformable bodies,III

In preceding papers of this series (Kopal, 1968; 1969) the Eulerian equations have been set up which govern the precession and nutation of self-gravitating fluid globes of arbitrary structures in inertial coordinates (space-axes) as well as with respect to the rotating body axes; with due account being taken of the effects arising from equilibrium as well as dynamical tides.In Section 1 of the present paper, the explicit form of these equations is recapitulated for subsequent solations. Section 2 contains then a detailed discussion of the coplanar case (in which the equation of the rotating configuration and the plane of its orbit coincide with the invariable plane of the system); and small fluctuations in the angular velocity of axial rotation arising from the tidal breathing in eccentric binary systems are investigated.In Section 3, we consider the angular velocity of rotation about theZ-axis to be constant, but allow for finite inclination of the equator to the orbital plane. The differential equations governing such a problem are set up exactly in terms of the time-dependent Eulerian angles and , and their coefficients averaged over a cycle. In Section 4, these equations are linearized by the assumption that the inclinations of the equator and the orbit to the invariable plane of the system are small enough for their squares to be negligible; and the equations of motion reduced to their canonical form.The solution of these equations — giving the periods of precession and nutation of rotating components of close binary systems, as well as the rate of nodal regression which is synchronised with precession — are expressed in terms of the physical properties of the respective system and of its constituent components; while the concluding Section 6 contains a discussion of the results, in which the differences between the precession and nutation of rigid and fluid bodies are pointed out.     

Dynamical theory of viscous tides in close binary systems

The aim of the present paper has been to investigate quantitative aspects of the phenomenon of tidal lag in close binary systems, the components of which rotate (in a direct or retrograde sense) in periods which differ from that of orbital revolution. The components constituting the binary are regarded as self-gravitating configurations, consisting of viscous compressible fluid, the viscosity of which varies with the 2.5th power of local temperature (indicated by theoretical investigations of the viscosity of hydrogen plasma). The equilibrium structure of the components has been assumed to be polytropic of indexn; and numerical computations were carried out for the values ofn=1.5, 2.5, 3.5, and 4.5. The magnitudes of the tidal lag /2 – _i for these models and for different values of the ratio of the angular velocities of rotation and revolution are listed in Tables III–XLII in terms of six values of a non-dimensional parameterZ which is proportional to viscosity.