Stable Triple Systems Research Articles

Binary–binary scattering in the secular limit

ABSTRACT Binary–binary interactions are important in a number of astrophysical contexts including dense stellar systems such as globular clusters. Although less frequent than binary–single encounters, binary–binary interactions lead to a much richer range of possibilities such as the formation of stable triple systems. Here, we focus on the regime of distant binary–binary encounters, i.e. two binaries approaching each other on an unbound orbit with a periapsis distance Q much larger than the internal binary separations. This ‘secular’ regime gives rise to changes in the orbital eccentricities and orientations, which we study using analytic considerations and numerical integrations. We show that ‘direct’ interactions between the three orbits only occur starting at a high expansion order of the Hamiltonian (hexadecupole order), and that the backreaction of the outer orbit on the inner two orbits at lower expansion orders is weak. Therefore, to good approximation, one can obtain the changes of each orbit by using previously known analytic results for binary–single interactions, and replacing the mass of the third body with the total mass of the companion binary. Nevertheless, we find some dependence of the ‘binarity’ of the companion binary, and derive explicit analytic expressions for the secular changes that are consistent with numerical integrations. In particular, the eccentricity and inclination changes of orbit 1 due to orbit 2 scale as ϵSA, 1(a2/Q)2[m3m4/(m3 + m4)2], where ϵSA, 1 is the approximate quadrupole-order change, and a2 and (m3, m4) are the companion binary orbital semimajor axis and component masses, respectively. Our results are implemented in several python scripts that are freely available.

THE FORMATION OF THE ECCENTRIC-ORBIT MILLISECOND PULSAR J1903+0327 AND THE ORIGIN OF SINGLE MILLISECOND PULSARS

The millisecond pulsar J1903+0327 is accompanied by an ordinary G-dwarf star in an unusually wide ($P_{\rm orb} \simeq 95.2$\,days) and eccentric ($e \simeq 0.44$) orbit. The standard model for producing MSPs fails to explain the orbital characteristics of this extraordinary binary, and alternative binary models are unable to explain the observables. We present a triple-star model for producing MSPs in relatively wide eccentric binaries with a normal (main-sequence) stellar companion. We start from a stable triple system consisting of a Low-Mass X-ray Binary (LMXB) with an orbital period of at least 1 day, accompanied by a G-dwarf in a wide and possibly eccentric orbit. Variations in the initial conditions naturally provide a satisfactory explanation for the unexplained triple component in the eclipsing soft X-ray transient 4U~2129+47 or the cataclysmic variable EC 19314-5915. The best explanation for J1903, however, results from the expansion of the orbit of the LMXB, driven by the mass transfer from the evolving donor star to its neutron star companion, which causes the triple eventually to becomes dynamically unstable. Using numerical computations we show that, depending on the precise system configuration at the moment the triple becomes dynamically unstable, the ejection of each of the three components is possible. If the donor star of the LMXB is ejected, a system resembling J1903, will result. If the neutron star is ejected, a single MSP results. This model therefore also provides a straightforward mechanism for forming single MSP in the Galactic disk. We conclude that the Galaxy contains some 30--300 binaries with characteristics similar to J1903, and about an order of magnitude fewer single millisecond pulsars produced with the proposed triple scenario.

Dynamical evolution of multiple stars: Influence of the initial parameters of the system

We have modeled the dynamical evolution of small stellar groups with N=6 components in the framework of the gravitational N-body problem, taking into account possible mergers of stars and ejection of single and binary stars. We study the influence of the initial global parameters of the systems (the mass spectrum, average size, virial factor) on their dynamical evolution. The distribution over states is analyzed for a time equal to 300 initial crossing times of the system. The parameters of binary and stable triple systems that form are studied, as well as the properties of ejected single and binary stars. The rate of dynamical evolution in both expanding and contracting groups is higher than in systems in a state of virial equilibrium. The dynamical evolution is more intense in the case of unequal masses than when the system initially consists of equal-mass stars. In most cases, the evolution of a group ends with the formation of a binary or stable triple system. The semimajor axes of the binaries range from several hundredths to several times the initial size of the system. The distribution of the eccentricities of the binaries formed is consistent with an f(e)=2e law. When the initial size of the group is small, the number of final binaries with large eccentricities, and also of stable triple systems with elongated inner-binary orbits, decreases due to merging. As a rule, stable triple systems are substantially hierarchical (the average ratio of the semimajor axes of the inner and outer binaries is 1: 20). On average, the eccentricities of the inner binaries exceed those of the outer binaries: they are equal to $$\overline {e_{in} } \approx 0.7$$ and $$\overline {e_{ex} } \approx 0.5$$ , respectively. The velocities of ejected stars are from several to several tens of km/s, and tend to increase as the initial size of the system, and hence its virial coefficient, decreases.

Dynamical evolution of multiple stars

We have modeled the dynamical evolution of small groups of N=3–18 stars in the framework of the gravitational N-body problem, taking into account possible coalescences of stars and the ejection of single and binary stars from the system. The distribution of states is analyzed for a time equal to 300 initial crossing times of the system. The parameters of the binaries and stable triple systems formed, as well as those of ejected single stars, are studied. In most cases, the evolution of the group results in the formation of a binary or stable triple system. The orbital eccentricities of the binaries formed are distributed according to the law f(e)=2e. As a rule, stable triple systems display pronounced hierarchy (the mean ratio of the semimajor axes of the outer and inner binaries is about 20:1). Stars are ejected with velocities from several km/s to several tens of km/s. The results of the modeling are compared with the parameters of observed wide binaries and triple systems.

Discovery of a New Companion and Evidence of a Circumprimary Disk: Adaptive Optics Imaging of the Young Multiple System VW Chamaeleon

Since a majority of young low-mass stars are members of multiple systems, the study of their stellar and disk configurations is crucial to our understanding of both star and planet formation processes. Here we present near-infrared adaptive optics observations of the young multiple star system VW Chamaeleon. The previously known 07 binary is clearly resolved already in our raw J- and K-band images. We report the discovery of a new faint companion to the secondary, at an apparent separation of only 01, or 16 AU. Our high-resolution photometric observations also make it possible to measure the J-K colors of each of the three components individually. We detect an infrared excess in the primary, consistent with theoretical models of a circumprimary disk. Analytical and numerical calculations of orbital stability show that VW Cha may be a stable triple system. Using models for the age and total mass of the secondary pair, we estimate the orbital period to be 74 yr. Thus, follow-up astrometric observations might yield direct dynamical masses within a few years and constrain evolutionary models of low-mass stars. Our results demonstrate that adaptive optics imaging in conjunction with deconvolution techniques is a powerful tool for probing close multiple systems.

On the Evolution of Close Triple Stars That Produce Type Ia Supernovae

Current observational estimates suggest that ~30% of all binary stars are in triple systems. In ~70% of these, the enclosed binary is close enough that the primary in the binary can evolve to fill its Roche lobe. In ~10%-20%, the third, more distant component can evolve to fill its Roche lobe, leading to configurations inaccessible to isolated binary stars. Triple stars are unstable if the ratio of the orbital period of the enclosed binary to the period of the third component exceeds a critical value. Hence, an increase in the orbital period of the binary due to conservative mass transfer between components or to wind mass loss from the binary can destabilize an initially stable triple system, causing it to decompose into a rapidly moving single star and an evolved binary recoiling in the opposite direction with a velocity large compared with velocities typical of primordial binaries. To highlight the different possibilities inherent in triple-star evolution, we discuss qualitatively several possible scenarios whereby triple stars with component masses in the range 1-10 M☉ can evolve into Type Ia supernovae, which we assume to be explosions of merging carbon-oxygen or oxygen-neon white dwarfs of total mass larger than 1.4 M☉. Before quantitative predictions of the likelihood of these scenarios can be made, it is necessary to determine the initial distribution of young triple stars over their masses and orbital separations and to calculate the reaction of the enclosed binary to matter transferred to it by the third component when it fills its Roche lobe or supports a strong wind.

Dynamical evolution of triple systems with big differences in the masses of bodies. A criterion for stability

The dynamical evolution of about 1.5 million planar hierarchical triple systems with a negative total energy and different-mass bodies is investigated by computer simulations. We considered both cases — prograde and retrograde motions of bodies. For every system, calculations were carried out either till a time when the Marchal'set al. (1984) criterion of escape of a body from a triple system was satisfied (the unstable triple systems) or during 1000 rotations of a total system (the stable triple systems). Computations were carried out on three computers-Sunstations in the Physical Research Laboratory, Ahmedabad, India during several months continuously. We changed smoothly the initial value of the coefficient of hierarchy of triples $$q = r_{3 - 12} /r_{12} $$

The present status of periodic orbits

Recent results on periodic orbits are presented and it is shown that the periodic orbits can be used in the study of planetary systems and triple or multiple stellar systems. Triple stellar systems are stable even for close approaches of the three components. Also stable triple systems exist with nearly zero angular momentum. For the planetary systems a global view is obtained from which it is clear which configurations are stable or unstable and also what factors affect the stability. Also, the relation between resonance and instability is studied by making use of periodic orbits.