The dynamical stability of W Ursae Majoris-type systems

Theoretical study indicates that a contact binary system would merge into a rapidly rotating single star due to tidal instability when the spin angular momentum of the system is more than a third of its orbital angular momentum. Assuming that W Ursae Majoris (W UMa) contact binary systems rigorously comply with the Roche geometry and the dynamical stability limit is at a contact degree of about 70 per cent, we obtain that W UMa systems might suffer Darwin's instability when their mass ratios are in a region of about 0.076–0.078 and merge into the fast-rotating stars. This suggests that the W UMa systems with mass ratio   q ≤ 0.076  cannot be observed. Meanwhile, we find that the observed W UMa systems with a mass ratio of about 0.077, corresponding to a contact degree of about 86 per cent would suffer tidal instability and merge into the single fast-rotating stars. This suggests that the dynamical stability limit for the observed W UMa systems is higher than the theoretical value, implying that the observed systems have probably suffered the loss of angular momentum due to gravitational wave radiation (GR) or magnetic stellar wind (MSW).     

Orbital evolution with white-dwarf kicks

Recent observations of white dwarfs in globular clusters indicate that these stars may get a velocity kick during their time as giants. This velocity kick could originate naturally if the mass loss while on the asymptotic giant branch is slightly asymmetric. If white dwarfs get a kick comparable to the orbital velocity of the binary, the initial Runge–Lenz vector (eccentricity vector) of the orbit is damped to be replaced by a component pointing toward the cross-product of the initial angular momentum and the force. The final eccentricity may be of the order of unity and if the kick is sufficiently large, the system may be disrupted. These results may have important ramifications for the evolution of binary stars and planetary systems.     

Reconstructing the evolution of white dwarf binaries: further evidence for an alternative algorithm for the outcome of the common-envelope phase in close binaries

We determine the possible masses and radii of the progenitors of white dwarfs in binaries from fits to detailed stellar evolution models and use these to reconstruct the mass-transfer phase in which the white dwarf was formed. We confirm the earlier finding that in the first phase of mass transfer in the binary evolution leading to a close pair of white dwarfs, the standard common-envelope formalism (the α-formalism) equating the energy balance in the system (implicitly assuming angular momentum conservation) does not work. An algorithm equating the angular momentum balance (implicitly assuming energy conservation) can explain the observations. This conclusion is now based on 10 observed systems rather than three. With the latter algorithm (the γ-algorithm) the separation does not change much for approximately equal-mass binaries. Assuming constant efficiency in the standard α-formalism and a constant value of γ, we investigate the effect of both methods on the change in separation in general and conclude that when there is observational evidence for strong shrinkage of the orbit, the γ-algorithm also leads to this. We then extend our analysis to all close binaries with at least one white dwarf component and reconstruct the mass-transfer phases that lead to these binaries. In this way we find all possible values of the efficiency of the standard α-formalism and of γ that can explain the observed binaries for different progenitor and companion masses. We find that all observations can be explained with a single value of γ, making the γ-algorithm a useful tool to predict the outcome of common-envelope evolution. We discuss the consequences of our findings for different binary populations in the Galaxy, including massive binaries, for which the reconstruction method cannot be used.     

Structure and evolution of low-mass W Ursae Majoris type systems – III. The effects of the spins of the stars

In a previous paper, using Eggleton's stellar evolution code, we have discussed the structure and evolution of low-mass W Ursae Majoris (W UMa) type contact binaries with angular momentum loss owing to gravitational radiation or magnetic braking. We find that gravitational radiation is almost insignificant for cyclic evolution of low-mass W UMa type systems, and it is possible for angular momentum to be lost from W UMa systems in a magnetic stellar wind. The weaker magnetic activity shown by observations in W UMa systems is likely caused by the lower mass of the convective envelopes in these systems than in similar but non-contact binaries. The spin angular momentum cannot be neglected at any time for W UMa type systems, especially for those with extreme mass ratios. The spin angular momenta of both components are included in this paper and they are found to have a significant influence on the cyclic evolution of W UMa systems. We investigate the influence of the energy transfer on the common convective envelopes of both components in detail. We find that the mass of the convective envelope of the primary in contact evolution is slightly more than that in poor thermal contact evolution, and that the mass of the convective envelope of the secondary in contact evolution is much less than that in poor thermal contact evolution. Meanwhile, the rate of angular momentum loss of W UMa type systems is much lower than that of poor thermal contact systems. This is indeed caused by the lower masses of the convective envelopes of the components in W UMa type systems. Although the models with angular momentum loss for W UMa systems exhibit cyclic evolution, they seem to show that a W UMa system cannot continue this type of cyclic evolution indefinitely, and it might coalesce into a fast-rotating star after about 1200 cycles of evolution (about  7.0 × 10⁹ yr  ).     

Binary asteroid population: 1. Angular momentum content

We compiled a list of estimated parameters of binary systems among asteroids from near-Earth to trojan orbits. In this paper, we describe the construction of the list, and we present results of our study of angular momentum content in binary asteroids. The most abundant binary population is that of close binary systems among near-Earth, Mars-crossing, and main belt asteroids that have a primary diameter of about 10 km or smaller. They have a total angular momentum very close to, but not generally exceeding, the critical limit for a single body in a gravity regime. This suggests that they formed from parent bodies spinning at the critical rate (at the gravity spin limit for asteroids in the size range) by some sort of fission or mass shedding. The Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect is a candidate to be the dominant source of spin-up to instability. Gravitational interactions during close approaches to the terrestrial planets cannot be a primary mechanism of formation of the binaries, but it may affect properties of the NEA part of the binary population.     

大质量双星系统的非守恒演化

由于大质量双星系统有强大的星风物质损失,因而在研究其结构和演化时必须考虑星风物质损失,动量损失,物质交换以及由以上原因引起的轨道参量的变化,此外,天文观测又证实,一些大质量双星系统中存在星风冲击波,有Ｘ射线辐射以及有致密天体（白矮星,中子星）的存在,因此在研究大质量双星的演化时,又会遇到在星风冲击波理论及其对演化的影响,双星系统何时会演化成为公共外壳的系统,以及双星系统中如果发生超新星爆发,是否会     

Stability of Binary Asteroids

The stability and final outcome of a strongly interacting binary asteroid system is considered. We discuss the implications of the system transferring energy and angular momentum between rotational and translational motion while conserving the total system energy and angular momentum. Using these results we can develop a set of sufficient conditions for stability against escape and impact. These allow us to delineate several classes of final outcomes for a binary asteroid system, each of which may have implications for asteroid observations. The effects of energy dissipation on an asteroid binary system are also considered and are shown to be able to change the stability of the system against escape and impact. An example computation for the near-Earth asteroid binary 1996 FG3 is given along with a series of numerical explorations of an evolving binary system consisting of an ellipsoid and a sphere of equal mass.     

Merger of binary globular clusters: Case of unequal masses

Merger process of binary globular cluster is discussed for a pair of unequal-mass components. We calculated the case of mass ratio 10.5 by means of anN-body code with 6144 particles in total. We have found the followings. The mass exchange between the components takes place through the Roche-lobe overflow. In the early stages, however, the dynamical evolution is mainly governed by escape of particles from the system. As the particles escape carrying angular momentum with them, the separation between the component cluster shrinks. The time-scale of this shrinkage depends upon the size of the clusters. When a critical separation is reached, the orbital angular momentum is transferred unstably to the spins of the component clusters. This is the process of the synchronization instability which was found in a previous study on binary cluster of equal masses. As a result the component clusters merge into a single cluster. The structures of the mergers are quite similar among different cases except for the central cores which retain their initial central concentrations. In particular, the ellipticity and the rotation curve are quite close each other among models of different initial radii and of different mass ratios.     

Rayleigh-Taylor instability of a two-fluid layer under a general rotation field and a horizontal magnetic field

In this paper the Rayleigh-Taylor instability (RTI) of a two-fluid layer system under the simultaneous action of a general rotation field and a horizontal magnetic field is presented. An approximate and an exact solution of the eigenvalue equation are calculated. These solutions are important not only to understand more deeply the physical problem but also to determine the correct numerical solutions. Numerical calculations are done for an unstable density stratification in the cases of horizontal magnetic field parallel and perpendicular to the horizontal component of the angular velocity. For an adverse density stratification, it is shown that in comparison to previous works, the horizontal magnetic field creates new angular areas (of the angle of propagation of the perturbation) at which the perturbation is stable and propagates as traveling waves. It is also shown that the vertical component of the angular velocity has a destabilizing effect because it works to eliminate the stable angular areas.     

Co-accretion of the Earth-Moon system after the giant impact: reduction of the total angular momentum by lunar impact ejecta

Though the Moon is considered to have been formed by the so-called giant impact, the mass of the Earth immediately after the impact is still controversial. If the Moon was formed during the Earth's accretion, a subsequent accretion of residual heliocentric planetesimals onto the protoearth and the protomoon must have occurred. In this co-accretion stage, a significant amount of lunar-impact-ejecta would be ejected to circumterrestrial orbits, since the mean impact velocity of the planetesimals with the protomoon is much larger than the escape velocity of the protomoon. Orbital calculations of test particles ejected from the protomoon, whose semimajor axis is smaller than that of the present Moon, reveal that most of the particles escaping from the protomoon also escape from the Hill sphere of the protoearth and reduce the planetocentric angular momentum of the primordial Earth-Moon system. Using the results of the ejecta simulations, we investigate the evolution of the mass ratio and the total angular momentum (Earth's spin angular momentum + Moon's orbital angular momentum) of the Earth-Moon system during the co-accretion. We find that the mass of the protomoon is almost constant or rather decreases and the total angular momentum decreases significantly, if the random velocity of planetesimals is as large as the escape velocity of the protoearth. On the other hand, if the random velocity is the half of the escape velocity of the protoearth, the mass ratio is kept to be almost as large as the present value and the decrease of the total angular momentum is not so significant. Comparing with the results of giant impact simulations, we find that the mass of the protoearth immediately after the Moon-forming impact was 0.7-0.8 times the present value if the impactor-to-target mass ratio was 3:7, whereas the giant impact occurred almost in the end of the Earth's accretion if the impactor-to-target mass ratio was 1:9.     

Mass loss from the inner regions of accretion discs due to centrifugally driven magnetic wind flows

Wind flows and collimated jets are believed to be a feature of a range of disc accreting systems. These include active galactic nuclei, T Tauri stars, X-ray binaries and cataclysmic variables. The observed collimation implies large-scale magnetic fields and it is known that dipole-symmetry fields of sufficient strength can channel wind flows emanating from the surfaces of a disc. The disc inflow leads to the bending of the poloidal magnetic field lines, and centrifugally driven magnetic winds can be launched when the bending exceeds a critical value. Such winds can result in angular momentum transport at least as effective as turbulent viscosity, and hence they can play a major part in driving the disc inflow.
It is shown here that if the standard boundary condition of vanishing viscous stress close to the stellar surface is applied, together with the standard connection between viscosity and magnetic diffusivity, then poloidal magnetic field bending increases as the star is approached with a corresponding increase in the wind mass loss rate. A significant amount of material can be lost from the system via the enhanced wind from a narrow region close to the stellar surface. This occurs for a Keplerian angular velocity distribution and for a modified form of angular velocity, which allows for matching of the disc and stellar rotation rates through a boundary layer above the stellar surface. The enhanced mass loss is significantly affected by the behaviour of the disc angular velocity as the stellar surface is approached, and hence by the stellar rotation rate. Such a mechanism may be related to the production of jets from the inner regions of disc accreting systems.     

Dynamical model of binary asteroid systems using binary octahedrons

We used binary octahedrons to investigate the dynamical behaviors of binary asteroid systems. The mutual potential of the binary polyhedron method is derived from the fourth order to the sixth order. The irregular shapes, relative orbits, attitude angles, as well as the angular velocities of the binary asteroid system are included in the model. We investigated the relative trajectory of the secondary relative to the primary, the total angular momentum and total energy of the system, the three-axis attitude angular velocity of the binary system, as well as the angular momentum of the two components. The relative errors of the total angular momentum and the total energy indicate that the calculation has a high precision. It is found that the influence of the orbital and attitude motion of the primary from the gravitational force of the secondary is obvious. This study is useful in understanding the complicated dynamical behaviors of the binary asteroid systems discovered in our Solar system.     

Bounded motion for a modified three-body problem

The energy and the angular momentum integral of motion for the planar three point problem cannot assure bounded motion. In this paper it is shown that if one of the points is replaced by a homogeneous sphere then bounded motion can be found. The zero velocity surfaces for this modified problem are found and their evolution is described.     

A close-in substellar object orbiting the sd OB-type eclipsing-binary system NSVS 14256825

NSVS 14256825 is the second discovered sdOB+dM eclipsing-binary system with an orbital period of 2.65 h. This special binary was reported to contain circumbinary planets or brown dwarfs by using the timing method. However, different results were derived by different authors because of the insufficient coverage of eclipse timings. Since 2008, we have monitored this binary for about 10 yr using several telescopes and 84 new times of light minimum were obtained with high precision. It is found that the O-C curve has been increasing recently and it shows a cyclic variation with a period of 8.83 yr and an amplitude of 46.31 seconds. The cyclic change cannot be explained by magnetic activity cycles of the red dwarf component because the required energy is much larger than that radiated by this component in one whole period. This cyclic change detected in NSVS 14256825 could be explained by the light-travel time effect via the presence of a third body. The lowest mass of the third body is determined to be 14.15 Mjupwhich is in the transition range between planets and brown dwarfs. The substellar object is orbiting around this evolved binary at an orbital separation of around 3 AU with an eccentricity of 0.12. These results indicate that NSVS 14256825 is the first sdOB-type eclipsing binary consisting of a hierarchical substellar object.The detection of a close-in substellar companion to NSVS 14256825 will provide some insights on the formation and evolution of sdOB-type binaries and their companions.     

Rotational fission of contact binary asteroids

The energetics and dynamics of contact binary asteroids as they approach and pass the rotational fission limit is studied. We presume that the asteroids are subject to an external torque, such as from the YORP effect, that increases their angular momentum. Furthermore, we assume the asteroids can be described by a fairly minimal model comprised of a sphere and ellipsoid resting on each other. The minimum energy configurations for contact binary asteroids at different levels of angular momentum are computed and discussed. We find distinct transitions between different configurations as the angular momentum of the system is increased. These indicate that rapidly rotating contact binary asteroids may seek out clearly different relative configurations than slowly rotating systems. We find a single end state of the systems prior to rotational fission, and distinct dynamical outcomes as a function of mass distribution and shape when the rotational fission limit is exceeded. Our theoretical results agree qualitatively with observed properties of near-Earth asteroids, and can be used to help explain the spin-rate barrier, contact binaries, and the observed morphology of most NEO binaries.     

Observations of binaries and evolutionary implications

Comparison of the characteristics of groups of stars in various evolutionary phases and the study of individual systems allow to make estimates of the parameters governing mass loss and mass transfer. Observations enable us in a few cases to determine geometric models for binaries during or after the mass transfer phase (disks, rings, common envelopes, symbiotics, interacting binaries, compact components).From spectra taken at different phases, radial velocity curves can be derived and masses and radii can be determined. In special cases spectra in different spectral ranges (visual, UV, X-ray) are required for the determination of the radial velocities of the two components (for X-ray binaries, for systems with hot and cool components). Information on parameters related to the mass transfer process enables us to consider non conservative evolution — i.e. the computation of evolutionary sequences with the assumption that mass and angular momentum not only are transferred from one of the components towards the other one, but that also mass and angular momentum can leave the system. Careful and detailed analysis of the observations allows in certain cases to determine the parameters governing this mass and angular momentum loss, and for contact phases, to determine the degree of contact.Paper presented at the Lembang-Bamberg IAU Colloquium No. 80 on Double Stars: Physical Properties and Generic Relations, held at Bandung, Indonesia, 3–7 June, 1983.     

Where are the binary source gravitational microlensing events? II

Despite the same multiplicity of lenses and sources, the frequency of detection of binary source events is relatively very low compared with that of binary lens events. Dominik pointed out that the rarity of binary source events is caused mainly by the large difference in amplification between the component stars. In this paper, we determine that the fraction of events with similar source star amplifications is as large as ∼8 per cent, and thus show that the very low detection rate for binary source events cannot be explained by this effect alone. By carrying out realistic simulations of binary source events, we find that a significant number of binary source events are additionally missed from detection for various other reasons. First, if the flux ratio between the component stars is very large, the light curve of the bright star is hardly affected by the light from the faint star. Secondly, if the separation is too small, the binary source stars behave like a single star, making it difficult to separate the binary source event from a single source event. Finally, although the probability of detecting binary source events increases as the source separation increases, some fraction of binary source events will still be missed because the light curves of these events will mimic those of single source events with longer time-scales and larger values of the impact parameter.     

Tidal Angular Momentum in Close Binary Systems in presence of Wind Driven Non-conservative Mass Transfer with Uniform Mass Accretion Rate

A very well-known property of close binary stars is that they usually rotate slowly than a similar type single star. Massive stars in close binary systems are supposed to experience an exchange of mass and angular momentum via mass transfer and tidal interaction, and thus the evolution of binary stars becomes more complex than that of individual stars. In recent times, it has become clear that a large number of massive stars interact with binary companions before they die. The observation also reveals that in close pairs the rotation tends to be synchronized with the orbital motion and the companions are naturally tempted to invoke tidal friction. We here introduce the effect of tidal angular momentum in the model of wind driven non-conservative mass transfer taking mass accretion rate as uniform with respect to time. To model the angular momentum evolution of a low mass main sequence companion star can be a challenging task. So, to make the present study more interesting, we have considered initial masses of the donor and gainer stars at the proximity of bottom-line main sequence stars and they are taken with lower angular momentum. We have produced a graphical profile of the rate of change of tidal angular momentum and the variation of tidal angular momentum with respect to time under the present consideration.