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.     

Contact binaries at different evolutionary stages

Contact binaries consist of two strongly interacting component stars where they are filling their critical Roche lobes and sharing a common envelope. Most of them are main-sequence stars, but some of them are post main-sequence systems. They are good astrophysical laboratories for studying several problems such as the merging of binary stars, evolution of the common envelope, the origin of luminous red nova outbursts and the formation of rapidly rotating single stars with possible planetary systems. A large number of contact binary candidates were detected by several photometric surveys around the world and many of them were observed by the LAMOST spectroscopic survey. Based on follow-up observations,the evolutionary states and geometrical structures of some systems were understood well. In this review,we will introduce and catalog new stellar atmospheric parameters(i.e., the effective temperature(Teff), the gravitational acceleration(log(g)), metallicity([Fe/H]) and radial velocity(Vr)) for 9149 EW-type contact binaries that were obtained based on low-and medium-resolution spectroscopic surveys of LAMOST. Then we will focus on several groups of contact binary stars, i.e., marginal contact binary systems, deep and low-mass ratio contact binary stars, binary systems below the short-period limit of contact binaries and evolved contact binaries. Marginal contact binaries are at the beginning of the contact stage, while deep and low-mass ratio contact binary stars are at the final evolutionary stage of tidally locked binaries. Several statistical relations including the period-temperature relation are determined well by applying LAMOST data and their formation and evolutionary states are reviewed. The period-color relation of M-type binaries reveals that there are contact binaries below the short-period limit. Searching for and investigating contact binaries near and below this limit will help us to understand the formation of contact binary systems and a new prediction for the short-period limit is about 0.15 d. Some evolved contact binaries were detected by the LAMOST survey where both components are sub-giants or giants. They provide a good opportunity to investigate evolution of the common envelope and are the progenitors of luminous red novae like V1309 Sco.     

On the binarity of Herbig Ae/Be stars

We present high-resolution spectro-astrometry of a sample of 28 Herbig Ae/Be and three F-type pre-main-sequence stars. The spectro-astrometry, which is essentially the study of unresolved features in long-slit spectra, is shown from both empirical and simulated data to be capable of detecting binary companions that are fainter by up to 6 mag at separations larger than ∼0.1 arcsec. The nine targets that were previously known to be binary are all detected. In addition, we report the discovery of six new binaries and present five further possible binaries. The resulting binary fraction is 68 ± 11 per cent. This overall binary fraction is the largest reported for any observed sample of Herbig Ae/Be stars, presumably because of the exquisite sensitivity of spectro-astrometry for detecting binary systems. The data hint that the binary frequency of the Herbig Be stars is larger than that of the Herbig Ae stars. The Appendix presents model simulations to assess the capabilities of spectro-astrometry and reinforces the empirical findings. Most spectro-astrometric signatures in this sample of Herbig Ae/Be stars can be explained by the presence of a binary system. Two objects, HD 87643 and Z CMa, display evidence for asymmetric outflows. Finally, the position angles of the binary systems have been compared with available orientations of the circumprimary disc and these appear to be coplanar. The alignment between the circumprimary discs and the binary systems strongly suggests that the formation of binaries with intermediate-mass primaries is due to fragmentation as the alternative, stellar capture, does not naturally predict aligned discs. The alignment extends to the most massive B-type stars in our sample. This leads us to conclude that formation mechanisms that do result in massive stars, but predict random angles between the binaries and the circumprimary discs, such as stellar collisions, are also ruled out for the same reason.     

Radius of the Roche equipotential surfaces

In literature, there is no exact analytical solution available for determining the radius of Roche equipotential surfaces of distorted close binary systems in synchronous rotation. However, Kopal (Roche Model and Its Application to Close Binary Systems, Advances in Astronomy and Astrophysics, Academic Press, New York 1972) and Morris (Publ. Astron. Soc. Pac. 106:154, 1994) have provided the approximate analytical solutions in the form of infinite mathematical series. These series expressions have been commonly used by various authors to determine the radius of the Roche equipotential surfaces, and hence the equilibrium structures of rotating stars and stars in the binary systems. However, numerical results obtained from these approximating series expressions are not very accurate. In the present paper, we have expanded these series expressions to higher orders so as to improve their accuracy. The objective of this paper is to check, whether, there is any effect on the accuracy of these series expressions when the terms of higher orders are considered. Our results show that in most of the cases these expanded series give better results than the earlier series. We have further used these expanded series to find numerically the volume radius of the Roche equipotential surfaces. The obtained results are in good agreement with the results available in literature. We have also presented simple and accurate approximating formulas to calculate the radius of the primary component in a close binary system. These formulas give very accurate results in a specified range of mass ratio.     

The Coma Morphology Due to an Extended Active Region and the Implications for the Spin State of Comet Hale-Bopp

We have compared the kinematics and metallicity of the main-sequence binary and single uvby F stars from the Hipparcos catalog to see if the populations of these stars originate from the same statistical ensemble. The velocity dispersions of the known unresolved binary F stars have been found to be dramatically smaller than those of the single F stars. This suggests that the population of these binaries is, in fact, younger than that of the single stars, which is further supported by the difference in metal abundance: the binaries turn out to be, on average, more metal rich than the single stars. So, we conclude that the population of these binaries is indeed younger than that of the single F stars. Comparison of the single F stars with the C binaries (binary candidates identified in Suchkov & McMaster) has shown, on the other hand, that the latter stars are, on average, older than the single F stars. We suggest that the age difference between the single F stars, known unresolved binaries, and C binaries is associated with the fact that stellar evolution in a binary systems depends on the binary components' mass ratio and separation, with these parameters being statistically very different for the known binaries and C binaries (e.g., mostly substellar secondaries in C binaries vs. stellar secondaries in known binaries). In general we conclude that the populations of known binaries, C binaries, and single F stars do not belong to the same statistical ensemble. The implications of the discovered age difference between these populations along with the corresponding differences in kinematics and metallicity should be important not only for understanding the evolution of stars but also for the history of star formation and the evolution of the local Galactic disk.     

Neutron Stars in X-ray Binaries and their Environments

Neutron stars in X-ray binary systems are fascinating objects that display a wide range of timing and spectral phenomena in the X-rays. Not only parameters of the neutron stars, like magnetic field strength and spin period evolve in their active binary phase, the neutron stars also affect the binary systems and their immediate surroundings in many ways. Here we discuss some aspects of the interactions of the neutron stars with their environments that are revelaed from their X-ray emission. We discuss some recent developments involving the process of accretion onto high magnetic field neutron stars: accretion stream structure and formation, shape of pulse profile and its changes with accretion torque. Various recent studies of reprocessing of X-rays in the accretion disk surface, vertical structures of the accretion disk and wind of companion star are also discussed here. The X-ray pulsars among the binary neutron stars provide excellent handle to make accurate measurement of the orbital parameters and thus also evolution of the binray orbits that take place over time scale of a fraction of a million years to tens of millions of years. The orbital period evolution of X-ray binaries have shown them to be rather complex systems. Orbital evolution of X-ray binaries can also be carried out from timing of the X-ray eclipses and there have been some surprising results in that direction, including orbital period glitches in two X-ray binaries and possible detection of the most massive circum-binary planet around a Low Mass X-ray Binary.     

Photometric light curve solutions of three ultra-short period eclipsing binaries

We present the results of our study of the eclipsing binary systems CSS J112237.1+395219,LINEAR 1286561 and LINEAR 2602707 based on new CCD B, V, Rcand Iccomplete light curves. The ultra-short period nature of these stars, as reported by Drake et al., is confirmed and the system's periods are revised. The light curves were modeled using the 2003 version of the Wilson-Devinney code. When necessary, cool spots on the surface of the primary component were introduced to account for asymmetries in the light curves. As a result, we found that CSS J112237.1+395219 is a W UMa type contact binary system belonging to W subclass with a mass ratio of q = 1.61 and a shallow degree of contact of 14.8%where the primary component is hotter than the secondary one by 500 K. LINEAR 1286561 and LINEAR2602707 are detached binary systems with mass ratios q = 3.467 and q = 0.987 respectively. These detached systems are low-mass M-type eclipsing binaries with similar temperatures. The marginal contact,fill-out factor and temperature difference between components of CSS J112237.1+395219 suggest that this system may be at a key evolutionary state predicted by thermal relaxation oscillation(TRO) theory. From the estimated absolute parameters, we conclude that our systems share common properties with other ultrashort period binaries.     

The proper-motion signal of unresolved binaries in the Hipparcos catalogue

We present an investigation of the differences between quasi-instantaneous stellar proper motions from the Hipparcos catalogue and long-term proper motions determined by combining Hipparcos and the Astrographic Catalogue. Our study is based on a sample of about 12000 stars of visual magnitude from 7 to 10 in two declination zones on the northern and equatorial sky. The distribution of the proper-motion differences shows an excess of large deviations. This is caused by the influence of orbital motion of unresolved binary systems. The proper-motion deviations provide statistical evidence for 360 astrometric binaries in the investigated zones, corresponding to about 2400 such binaries in the entire Hipparcos catalogue, in addition to those already known. In order to check whether the observed deviations are compatible with standard assumptions on the basic parameters of binary stars, we model the impact of orbital motion on the observed proper motions in a Monte Carlo simulation. We show that the simulation yields an acceptable approximation of the observations, if a binary frequency between 70% and 100% is assumed, i.e.if most of the stars in the sample are assumed to have a companion. Thus Hipparcos astrometric binaries confirm that the frequency of non-single stars among field stars is very high. We also investigate the influence of the mass function for the secondary component on the result of the simulation. A constant mass function and mass functions with moderate increase towards low masses lead to results, which are compatible with the observed proper-motion effects. A high preponderance of very-low-mass or substellar companions as produced, for example, by a M^—1 power law is not in agreement with the frequency of proper-motion deviations in our sample of stars.     

Disk wind in young binaries and the origin of the cyclic activity of young stars

We present the results of our numerical simulations of the cyclic brightness modulation in young binary systems with eccentric orbits and low-mass secondary components. We suggest that the binary components accrete matter from the remnants of the protostellar cloud, with the main accretor (according to current models) being the low-mass component. The brightness variations of the primary are attributable to the periodic extinction variations on the line of sight caused by the disk wind from the secondary and by the common envelope produced by this wind. The distribution of matter in the envelope was calculated in the ballistic approximation. When calculating the optical effects produced by the dust component of the disk wind, we adopted the dust-to-gas mass ratio of 1:100 characteristic of the interstellar medium and the optical parameters of the circumstellar dust typical of young stars. Our calculations show that the theoretical light curves for binaries with elliptical orbits exhibit a wider variety of shapes than those for binaries with circular orbits. In this case, the parameters of the photometric minima (their depth, duration, and shape of the light curve) depend not only on the disk-wind parameters and the orbital inclination of the binary to the line of sight, but also on the longitude of the periastron. We investigate the modulation of the scattered radiation from the common envelope with orbital phase in the single-scattering approximation. The modulation amplitude is shown to be at a maximum when the system is seen edge-on and to be also nonzero in binaries seen pole-on. We discuss possible applications of the theory to young stellar objects. In particular, several model light curves have been found to be similar to those of candidate FU Orionis stars (FUORs).     

Population Synthesis of Binary Be Stars with Degenerate Companions in the Galaxy

Using the numerical code (`Scenario Machine') we study of number and physical properties of binary Be stars. Evolutionary tracks leading to a formation of the observational binary systems are presented. We conclude that synchronization must be taken into account when calculating binary Be star evolution and calculate the minimal orbital period for Be/evolved companion binary. The obtained distributions over orbital parameters are in good agreement with the observational lack of short-period Be/X-ray binaries. According to our calculations 70% of all Be stars must have a white dwarf. The white dwarfs in these systems should be hot enough with the surface temperature distribution peaking at 10000–20000 K. Their detection is possible during the period of the lack of Be star envelope by the detection of white dwarf extremely UV and soft X-ray emission. This method of registration appears to be particularly promising for `single' early-type Be stars because in these systems the white dwarfs must have a very high surface temperature. However, the loss of the Be disc-like envelope does not often occur and it is a rather rare event for many Be stars. The best possibility of white dwarf detection is given by the study of helium spectral lines found in emission from several Be stars. The ultraviolet continuum energy of these Be stars is found to be not enough to produce the observed helium emission. Besides, we also discuss the orbital properties of binary Be star systems with other evolved companions such as helium stars and neutron stars and give a possible explanation for the lack of Be/black hole binaries. This revised version was published online in July 2006 with corrections to the Cover Date.     

Equilibrium structures of rotationally and tidally distorted stellar models

In this paper we present a method for computint the equilibrium structures of rotationally distorted stars as well as rotationally and tidally distorted primary components of the stars in binary systems. The method is based on the averaging technique of Kippenhahn and Thomas (1970) and utilizes the concepts of Roche equipotentials (Kopal, 1972). The method takes into account terms up to second-order of smallness in the rotational and tidal distortion parameters. The use of the method in obtaining the equilibrium structures of certain rotationally and (or) tidally distorted models of Main-Sequence stars is also illustrated.     

Close encounters in young stellar clusters: implications for planetary systems in the solar neighbourhood

The stars that populate the solar neighbourhood were formed in stellar clusters. Through N -body simulations of these clusters, we measure the rate of close encounters between stars. By monitoring the interaction histories of each star, we investigate the singleton fraction in the solar neighbourhood. A singleton is a star which formed as a single star, has never experienced any close encounters with other stars or binaries, or undergone an exchange encounter with a binary. We find that, of the stars which formed as single stars, a significant fraction is not singletons once the clusters have dispersed. If some of these stars had planetary systems, with properties similar to those of the Solar System, the planets' orbits may have been perturbed by the effects of close encounters with other stars or the effects of a companion star within a binary. Such perturbations can lead to strong planet–planet interactions which eject several planets, leaving the remaining planets on eccentric orbits. Some of the single stars exchange into binaries. Most of these binaries are broken up via subsequent interactions within the cluster, but some remain intact beyond the lifetime of the cluster. The properties of these binaries are similar to those of the observed binary systems containing extrasolar planets. Thus, dynamical processes in young stellar clusters will alter significantly any population of Solar System-like planetary systems. In addition, beginning with a population of planetary systems exactly resembling the Solar System around single stars, dynamical encounters in young stellar clusters may produce at least some of the extrasolar planetary systems observed in the solar neighbourhood.     

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.     

Frequency of Be and Ae stars in spectroscopic binaries

The frequency of Be and Ae stars in spectroscopic binaries and Algol binaries is examined based on the available catalogue data, and compared with that of stars in theBright Star Catalogue. It is shown that in binary systems Be and Ae stars reveal different statistical behaviours. The frequency of Be stars in spectroscopic binaries shows a notable peak in its orbital-period distribution in the range of 100–300 days, suggesting a statistical group separated from Algol systems. In contrast, most of Ae stars in spectroscopic binaries belong to the Algol systems.     

Accretion and dynamical interactions in small-N star-forming clusters: N= 5

We present results from high-resolution hydrodynamical simulations that explore the effects of small-scale clustering in star-forming regions. A large ensemble of small- N clusters with five stellar seeds have been modelled and the resulting properties of stars and brown dwarfs statistically derived and compared with observational data.
Close dynamical interactions between the protostars and competitive accretion driven by the cloud collapse are shown to produce a distribution of final masses that is bimodal, with most of the mass residing in the binary components. When convolved with a suitable core mass function, the final distribution of masses resembles the observed initial mass function, in both the stellar and substellar regimes. Binaries and single stars are found to constitute two kinematically distinct populations, with about half of the singles attaining velocities ≥2 km s⁻¹, which might deprive low-mass star-forming regions of their lightest members in a few crossing times. The eccentricity distribution of binaries and multiples is found to follow a distribution similar to that of observed long-period (uncircularized) binaries.
The results obtained support a mechanism in which a significant fraction of brown dwarfs form under similar circumstances as those of normal stars but are ejected from the common envelope of unstable multiple systems before their masses exceed the hydrogen burning limit. We predict that many close binary stars should have wide brown dwarf companions. Brown dwarfs, and, in general, very low-mass stars, would be rare as pure binary companions. The binary fraction should be a decreasing function of primary mass, with low-mass or substellar primaries being scarce. Where such binaries exist, they are expected either to be close enough (semimajor axis ∼10 au) to survive strong interactions with more massive binaries or to be born in very small molecular cloud cores.     

On evolution of contact eclipsing binaries

It is shown that during contact eclipsing binaries evolution under the influence of stellar wind, magnetic stellar wind and with matter transfer by gas flow, in binary stellar systems there may take place a process of star merger (low mass stars) within 10⁵–10⁷ yr and a fast increase of distance between stars of massive binaries. W UMa-type stars are a finite evolutionary stage of very close and low mass binary pairs. As for contact systems of early spectral types (CE-systems), they are more varied in evolution.     

Binary Population Synthesis

Binary interactions lead to the formation of intriguing objects, such as compact binaries, supernovae, gamma ray bursts, X-ray binaries, pulsars, novae, cataclysmic variables, hot subdwarf stars, barium stars and blue stragglers. To study the evolution of binary populations and the consequent formation of these objects, many methods have been developed over the years, for which a robust approach named binary population synthesis(BPS) warrants special attention. This approach has seen widespread application in many areas of astrophysics, including but not limited to analyses of the stellar content of galaxies, research on galactic chemical evolution and studies concerning star formation and cosmic re-ionization. In this review,we discuss the role of BPS, its general picture and the various components that comprise it. We pay special attention to the stability criteria for mass transfer in binaries, as this stability largely determines the fate of binary systems. We conclude with our perspectives regarding the future of this field.     

Light-curve analysis and eclipse mapping of the contact binaries KQ Gem and V412 Her

CCD photometry of the short-period binary stars KQ Gem and V412 Her is presented, together with some spectroscopic observations of KQ Gem. Although both systems are classified in the General Catalogue of Variable Stars as having light curves of EB/KW type, our data and analyses, involving light-curve synthesis and stellar surface imaging, show that KQ Gem is an EB system that is in marginal contact and has an enhanced bright region around the substellar point on the secondary component, whilst V412 Her is an EW system, a true contact binary with a mass ratio of 0.46 and both stars having the same surface brightness. The properties of the components of the two systems are compared with other marginal-contact and contact binaries, and a plea is repeated for more theoretical work on the mass/energy interchanges in contact binaries.     

The Brave New World of Binary Star Studies

In this paper we discuss some of the new and exciting developments in the study of binary stars. Recent technological advances (such as CCDs) now make it possible (even easy) to study faint, astrophysically important binaries that in the past could only be done with large 4 + meter class telescopes. Also, the panoramic nature of CCDs (and the use of mosaics), permit large numbers of stars to be imaged and studied. At this conference, most of the observational material discussed was secured typically with smaller aperture 0.5 – 2 m telescopes. Excellent examples are the discovery of over 10⁴ new ～13 – 20 mag eclipsing (and interacting) binaries now found in nearby galaxies from the EROS, OGLE, MACHO and DIRECT programs. As briefly discussed here, and in more detail in several papers in this volume, a small fraction of these extragalactic eclipsing binaries are now serving as “standard candles” to secure accurate distances to the Magellanic Clouds, as well as to M31 and M33. Moreover, the discovery of increasingly larger numbers of eclipsing binaries has stimulated the development of automatic methods for reducing and analyzing the light curves of thousands of systems. In the near future, hundreds of thousands (possibly millions) of additional systems are expected to be discovered by Pan-STARRS, the Large Synoptic Survey Telescopes (LSST), and later by GAIA. Over the last decade, new classes of binary systems have also been found which contain Jupiter-size planets and binaries containing pulsating stars. Some examples of these important binaries are discussed. Also discussed are the increasing numbers (now eight) of eclipsing binary planet–star systems that have been found from high precision photometry. These systems are very important since the radii and masses of the hosted planets can be directly measured. Moreover, from the upcoming COROT and KEPLER missions hundreds of additional transiting planet-star systems are expected to be found. All in all, we hope in this paper to highlight some of the current developments and new directions in the “Brave New World” of binary star studies.     

Variable stars in the open cluster NGC 2141

We report the results of a search for variable stars in the open cluster NGC 2141. Ten variable stars are detected, among which nine are new variable stars and they are classified as three short-period W UMa-type eclipsing binaries, two EAtype eclipsing binaries, one EB-type eclipsing binary, one very short-period RS CVntype eclipsing binary, one d-type RR Lyrae variable star, and one unknown type of variable star. The membership and physical properties are discussed, based on their light curves, positions in the color magnitude diagrams, spatial locations and periods.A known EB-type eclipsing binary is also identified as a blue straggler candidate in the cluster. Furthermore, we find that all eclipsing contact binaries have prominent asymmetric eclipses and display the O'Connell effect, which increases with a decrease in orbital periods. This suggests that the O'Connell effect is probably related to the evolution of the orbital period in short period eclipsing binary systems.