Review of the Dynamical Aspects of Triple Systems

Abstract

A classification of possible motions of triple systems is presented emphasizing the transient phenomena occurring in addition to the final (asymptotic) outcome and clarifying the discrepancies between the astronomical and mathematical formulations. A conjectured possible instability is described and it is shown that systems with negative total energy and low angular momentum may lead to instability and to the formation of binaries. The ejected or escaping star may have high velocity if the triple close approach preceding the escape is sufficiently close. The computational results of several systematic series of such escapes are applied to various stellar configurations.The present status of the fundamental problem of partitioning the phase-space into stable and unstable regions is reviewed and a recently developed technique, applicable to stellar dynamics is described. Recently discovered families of periodic orbits and previously established classical configurations are shown to weaken the general instability conjecture.The possible existence of triple systems in states of dissolution offer intriguing observational challenges regarding the discovery of these projected temporary trapezium type systems.

Multiple Star Formation to the Bottom of the Initial Mass Function

“…Our solution includes several steps. First, we adopt the detection limits for a given primary star out to 3 times the projected separation ρ to its binary companion; we chose this limit because the minimum stable ratio of semimajor axes for a hierarchical triple is ∼2-3 (Szebehely & Zare 1977), and on a statistical basis, the projected separations for a sample of binary systems are similar to their semimajor axes (ρ ∼ 1.26a; Fischer & Marcy 1992). Second, in considering limits for additional companions at >3ρ, we sum the masses of the inner binary pair and treat it as a single, more massive primary.…”

The field high-amplitude SX Phe variable BL Cam: results from a multisite photometric campaign

“…Table 3) of BL Cam B, possibly resulting from the tidal circularization of its orbit (Claret & Cunha 1997); (ii) the respective closer (< 0.68 AU) and larger (> ∼4.5 AU) distances of BL Cam B and BL Cam C from the main star. In the case of a triple system, this scenario is consistent with a stable three-body system configuration over a Gyr timescale (e.g., Harrington 1968;Szebehely & Zare 1977;Quirrenbach 2006).…”

A Possible Third Component in the L Dwarf Binary System DENIS-P J020529.0-115925 Discovered with theHubble Space Telescope

“…′′ 055 (see Table 3). As stated by Harrington (1968) and then Szebehely & Zare (1977) in their analytical study, triple systems with moderate eccentricity and equal mass components are stable for ratios between the semi-major axes of the outer (a 2 ) and the inner orbits (a 1 ) greater than a 2 /a 1 ≥3.2. Assuming that the orbits of DENIS-P J020529.0-115925 components have moderate eccentricities, and considering that the 3 components must have similar masses as explained above, DENIS-P J020529.0-115925 would fit above the stability criterion, with a ratio between 3.6≤ a 2 /a 1 ≤7.1.…”

“…While case (a) cannot represent any Keplerian orbit, cases (b) and (c) could, with orbital periods comparable to the preliminary estimate we report here. Values are from Table 3. As stated by Harrington (1968) and then Szebehely & Zare (1977) in their analytical study, triple systems with moderate eccentricity and equal-mass components are stable for ratios between the semimajor axes of the outer (a 2 ) and the inner orbits (a 1 ) greater than a 2 =a 1 ! 3:2.…”