A. V. Rubinov

The disruption of three-body gravitational systems: lifetime statistics

We investigate the statistics of the decay process in an equal-mass three-body problem with randomized initial conditions. Contrary to earlier expectations of similarity with ‘radioactive decay’, the lifetime distributions obtained in our numerical experiments turn out to be heavy-tailed, i.e. the tails are not exponential but algebraic. The computed power-law index for the differential distribution is within a narrow range, approximately from −1.7 to −1.4, depending on the virial coefficient. Possible applications of our results to studies of the dynamics of triple stars known to be at the edge of disruption are considered.

The structure of non-hierarchical triple system stability regions

A detailed study of the two-dimensional initial conditions region section in the planar three-body problem is performed. The initial conditions for the three well-known stable periodic orbits (the Schubart’s orbit, the Broucke’s orbit and the eight-like orbit) belong to this section. Continuous stability regions (for the fixed integration interval) generated by these periodic orbits are found. Zones of the quick stability violation are outlined. The analysis of some concrete trajectories coming from various stability regions is performed. In particular, trajectories possessing varying number of “eights” formed by moving triple system components are discovered. Orbits with librations are also found. The new periodic orbit originated from the zone siding with the Schubart’s orbit region is discovered. This orbit has reversibility points (each of the outer bodies possess a reversibility point) and two points of close double approach of the central body to each of the outer bodies. The influence of the numerical integration accuracy on the results is studied. The stability regions structure is preserved during calculations with different values of the precision parameter, numerical integration methods and regularization algorithms of the equations of motion.

Dynamical stability of the quadruple systems HD 68255/6/7 and HD 76644

We analyze the dynamical stability of the hierarchical quadruple systems HD 68255/6/7 and HD 76644 via numerical integration of the equations of motion of the four-body problem, with a chainlike regularization of close stellar interactions. The observational errors were taken into account using Monte Carlo simulations, assuming that they possessed a Gaussian distribution. HD 68255/6/7 is probably stable, while HD 76644 is unstable with a probability exceeding 0.97 and with a disruption time of no more than 105 years. The influence of the observational errors and possible scenarios for the formation of unstable multiple stars are discussed.

The Problem of Three Stars: Stability Limit

The problem of three stars arises in many connections in stellar dynamics: threebody scattering drives the evolution of star clusters, and bound triple systems form long-lasting intermediate structures in them. Here we address the question of stability of triple stars. For a given system the stability is easy to determine by numerical orbit calculation. However, we often have only statistical knowledge of some of the parameters of the system. Then one needs a more general analytical formula. Here we start with the analytical calculation of the single encounter between a binary and a single star by Heggie (1975). Using some of the later developments we get a useful expression for the energy change per encounter as a function of the pericenter distance, masses, and relative inclination of the orbit. Then we assume that the orbital energy evolves by random walk in energy space until the accumulated energy change leads to instability. In this way we arrive at a stability limit in pericenter distance of the outer orbit for different mass combinations, outer orbit eccentricities and inclinations. The result is compared with numerical orbit calculations.

Disruption of the three-body gravitational systems: Lifetime statistics

We investigate the statistics of the decay process in an equal-mass three-body problem with randomized initial conditions. Contrary to earlier expectations of similarity with ‘radioactive decay’, the lifetime distributions obtained in our numerical experiments turn out to be heavy-tailed, i.e. the tails are not exponential but algebraic. The computed power-law index for the differential distribution is within a narrow range, approximately from −1.7 to −1.4, depending on the virial coefficient. Possible applications of our results to studies of the dynamics of triple stars known to be at the edge of disruption are considered.

Multiple Stars: Physics vs. Dynamics

We review physical and dynamical parameters of multiple stars. Possible scenaria of multiple star formation are discussed: their birth in dense cloud cores and the decay of small stellar groups and clusters. We compare physical and dynamical features of simulated multiple stars formed by these processes with the actual multiple stars. Multiplicity function, their period, eccentricity and mass ratio distributions, hierarchy of the structures are analysed. Also we discuss multiple systems where the apparent ages of the components are different. Such diferences can be explained by poor evolutionary tracks for low-mass stars, by formation of such systems by capture or by merging of components during dynamical evolution of multiple stars.

Periodic orbits in the general three-body problem and the relationship between them

We study the regions of finite motions in the vicinity of three simple stable periodic orbits in the general problem of three equal-mass bodies with a zero angular momentum. Their distinctive feature is that one of the moving bodies periodically passes through the center of mass of the triple system. We consider the dynamical evolution of plane nonrotating triple systems for which the initial conditions are specified in such a way that one of the bodies is located at the center of mass of the triple system. The initial conditions can then be specified by three parameters: the virial coefficient k and the two angles, φ1 and φ2, that characterize the orientation of the velocity vectors for the bodies. We scanned the region of variation in these parameters k∈(0, 1); φ1, φ2∈(0, π) at steps of δk=0.01; δφ1=δφ2=1° and identified the regions of finite motions surrounding the periodic orbits. These regions are isolated from one another in the space of parameters (k, φ1, φ2). There are bridges that correspond to unstable orbits with long lifetimes between the regions. During the evolution of these metastable systems, the phase trajectory can “stick” to the vicinity of one of the periodic orbits or move from one vicinity to another. The evolution of metastable systems ends with their breakup.

The disruption of three-body gravitational systems: lifetime statistics: The disruption of three-body systems

We investigate the statistics of the decay process in an equal-mass three-body problem with randomized initial conditions. Contrary to earlier expectations of similarity with ‘radioactive decay’, the lifetime distributions obtained in our numerical experiments turn out to be heavy-tailed, i.e. the tails are not exponential but algebraic. The computed power-law index for the differential distribution is within a narrow range, approximately from −1.7 to −1.4, depending on the virial coefficient. Possible applications of our results to studies of the dynamics of triple stars known to be at the edge of disruption are considered.