Evolution Of Triple Systems Research Articles

Transition regions between stable periodic solutions of the general three-body problem

The behavior of triple systems in the transition zones located between regions of stability is studied in the framework of the general three-body problem with equal masses and zero angular momentum. It is well known that there are exist three stable periodic orbits, namely, the Schubart orbit for the rectilinear problem, the Broucke orbit for the isosceles problem, and the Moore eight-figure orbit. In the space of the initial conditions, these orbits are surrounded by sets of points where bounded motions are observed over substantial time intervals. The transition zones between the Schubart and Moore orbits and the Moore and Broucke orbits are studied. It is shown that the boundaries of the regions of stability can be either smooth and sharp or diffuse. Beyond these boundary regions, the dynamical evolution of triple systems results in a distant ejection of one of the components, or the decay of the system. The distribution of the times when the stability is lost is constructed, and obeys a power law for long time intervals. Three stages in the evolution of an unstable triple system are identified.

Disintegration process of hierarchical triple systems. I. Small-mass planet orbiting equal-mass binary

The stability of hierarchical triple system is studied in the case of an extrasolar planet or a brown dwarf orbiting a pair of main sequence stars. The evolution of triple system is well modelled by random walk (RW) diffusion, particularly in the cases where the third body is small and tracing an orbit with a large eccentricity. A RW model neglects the fact that there are many periodic orbits accompanied by stability islands, and hence inherently overestimates the instability of the system. The present work is motivated by the hope to clarify how far the RW model is applicable. Escape time and the surface section technique are used to analyse the outcome of numerical integrations. The analysis shows that the RW-like model explains escape of the third body if the initial configuration is directly outside of the KAM tori. A small gap exists in (q2/a1, e2)-plane between locations of the stability limit curves based on our numerical study and on RW-model (the former is shifted by –1.4 in q2/a1 direction from the latter).

A tertiary component in close binary systems

In this short review, the existence of third bodies in close binary systems is presented. Starting with the observational methods used to detect the tertiary component, we continue with the theoretical studies concerning the stability and evolution of triple systems and also of multiple systems in general. We next consider the type of tertiary component and give a list of catalogues for these systems; we end with a general discussion.

Metastability in the evolution of triple systems

The dynamical evolution of 15 000 equal-mass triple systems with zero initial velocities (the free-fall three-body problem) is considered. The equations of motion are numerically integrated using regularization of binary and triple encounters. We find 170 triple systems which reach a state where the motions take place within a limited region of phase space during a long time. These regions are concentrated in the zones of regular motions in the vicinities of stable periodic orbits: the von Schubart orbit in the rectilinear problem, the Broucke orbit in the isosceles problem, and the ‘Eight’ orbit. The classification of such metastable orbits is suggested. A change of the types is found during the dynamical evolution of some metastable systems. The triple system leaves the metastable regime after some time, and its evolution is finished by the escape of one body.

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 $$q = r_{3 - 12} /r_{12} $$

Main features of dynamical escape from three-dimensional triple systems

The dynamical evolution of triple systems with equal and unequal-mass components and different initial velocities is studied. It is shown that, in general, the statistical results for the planar and three-dimensional triple systems do not differ significantly. Most (about 85%) of the systems disrupt; the escape of one component occurs after a triple approach of the components. In a system with unequal masses, the escaping body usually has the smallest mass. A small fraction (about 15%) of stable or long-lived systems is formed if the angular momentum is non-zero. Averages, distributions and coefficients of correlations of evolutionary characteristics are presented: the life-time, angular momentum, numbers of wide and close triple approaches of bodies, relative energy of escapers, minimum perimeter during the last triple approach resulting in escape, elements of orbits of the final binary and escaper.

Strong triple interactions in the general three-body problem

Strong three-body interactions play a decisive role in the course of the dynamical evolution of triple systems having positive as well as negative total energies. These interactions may produce qualitative changes in the relative motions of the components. In triple systems with positive or zero total energies the processes of formation, disruption or exchange of the components of binaries take place as the result of close approaches of the three single bodies or as the result of the passages of single bodies past wide or hard binaries. In the triple systems with negative energies, the strong triple interactions may result in an escape from the system as well as a formation of a hard final binary. This paper summarizes the general results of the studies of the strong three-body interactions in the triple systems with positive and negative energies. These studies were conducted at the Leningrad University Observatory by computer simulations during 1968–1989.

Dynamical evolution of triple systems

Dynamical evolution of triple systems

Distribution of minima of the current size of the triple systems and their disruption

The dynamical evolution of triple systems has been studied by computer simulations. A function ρ(t) has been defined, where p is the maximum distance of the components from their centre of inertia, and t is the time. The value of ρ is used to indicate the current size of the triple system. The minima of ρ have been followed during the course of evolution of the triples. A distribution of f(ρmin) has been obtained, which is described by the following statistical parameters: the mode is equal to 0.65d, the mean value ρmin= 0.750d, r.m.s. is 0.477d, the asymmetry is 0.218, the excess is 2.04 where d is the mean harmonic distance between the bodies in the equilibrium state of the triple system. As a rule, escapes from triples occur only after close three-body approaches.

Numerical-experiment investigation of coalescence of gaseous protogalactic fragments in triple systems

The numerical-experiment approach in the framework of the general gravitational three-body problem has been used to investigate the dynamical evolution of triple systems of gaseous protogalactic fragments. The masses of the fragments are equal, the initial velocities zero. The initial positions were specified by uniform scanning in the region D of all possible initial configurations. Calculations were continued until the first two-body encounter of the fragments. Different values of the fragment radii at this times were considered, namely, r in the interval (0.001, 0.1)d, where d is the mean diameter of the system. It is shown that for such r the pair of gaseous fragments coalesces in the majority of cases (from 50.2% for r = 0.001d to 96.7% for r = 0.1d). The mean specific angular momentum of their relative motion, which becomes spin angular momentum of the coalescence product, is (0.8 /plus minus/ 1.0)/centered dot/10/sup 29//root//mu/l cm/sup 2/sec for the most probable value r = 10l kpc (the masses of the fragments are 5/centered dot/10/sup 10//mu/M/circled dot/; l and /mu/ are scale factors), this agreeing in order of magnitude with the specific angular momenta of disk galaxies if l, /mu/ /approximately/ 1. For each value of r, amore » continuous zone of initial configurations corresponding to coalescences is identified in the region D.« less

Influence of rotation on the evolution of triple systems

Influence of rotation on the evolution of triple systems