Dynamics of rotating triple systems: statistical escape theory versus numerical simulations

Abstract

Dynamical evolution of 120 000 equal‐mass rotating triple systems is investigated. The system rotation is described by the parameter w=−L20E0/G2m50, where G is the gravitational constant, m0 is the mass of a body, and L0 and E0 are the angular momentum and the total energy of the triple system, respectively. We consider the values of w= 0.005, 0.1, 1, 2, 4 and 6. For each w, 20 000 triple systems are studied. The initial coordinates and velocities of the components are randomly chosen. The initial data are chosen in two different ways: the first one assumes a hierarchical structure initially and the second one does not. The evolution of each triple system is calculated until either the escape of one of the bodies occurs or the time exceeds 1000 mean crossing times of the system. The orbital parameters of the final binary and the escaper are recorded for each run. We compare the results of numerical simulations and predictions of a statistical escape theory. The statistical theory is based on the assumption of ergodicity, that is, the only information on the initial conditions remaining at the time of the escape of the third body is contained in the conserved total energy, total angular momentum and the mass values. The distributions of various quantities are derived from the allowable phase‐space volumes. The distribution of binary energy agrees with earlier results by Heggie, with the angular momentum dependence of Mikkola & Valtonen being added. The eccentricities are distributed in general accordance with Monaghan's work, while the triple systems break up like in radioactive decay, as was previously found by Valtonen & Aarseth. The escape directions are preferentially perpendicular to the total angular momentum vector; the more so, the greater the angular momentum. The escape‐angle distributions are derived from the statistical theory and are found to be in agreement with the numerical data. The relative orientations and magnitudes of the binary and third‐body angular momenta are also explained based on the statistical theory.

Microlensing Discovery of a Tight, Low-Mass-Ratio Planetary-Mass Object Around an Old Field Brown Dwarf

“…Surveys for disks around young BD have found some systems with inferred disk masses up to and even slightly exceeding ∼M J (Harvey et al 2012), although these are relatively rare and the inferred masses are subject to considerable uncertainty. Such massive disks are likely to be near the limit of stability (e.g., Lodato et al 2005), arguing for a gravitational instability formation scenario rather than core accretion. On the other hand, the relatively close separation may pose a challenge for gravitational instability.…”

“…Therefore, it seems unlikely that these companions formed from the protoplanetary disk material via either of the popular giant planet formation mechanisms of core accretion (Pollack et al 1996) or disk fragmentation (Kuiper 1951;Cameron 1978;Boss 1997;Durisen et al 2007). Rather, these are more likely to have formed in the same way as stellar binaries through the process of gravitational fragmentation of massive primordial disks (Lodato et al 2005). Thus, according to a classification system based on their formation, they are not bona fide planets.…”

ALMA Observations of Polarized 872 μm Dust Emission from the Protostellar Systems VLA 1623 and L1527

“…The line-of-sightkinematic offset itself between the two parts of the system is 3−4 km/s. In three-body interactions wherein spin-orbit coupling is negligible, ejection preferentially occurs orthogonal to the total angular momentum of the system (Saari 1974;Valtonen et al 2005). Due to the extent of the circumbinary disk of VLA 1623A, the bulk of the angular momentum in the system should reside in the disks associated with VLA 1623AB.…”

A tertiary component in close binary systems

“…The initial coordinates and velocities of the components were chosen randomly. The initial data were chosen assuming that either there was an initial hierarchical structure or there was not [56].…”