Resonant capture in quadruple stellar systems

Abstract

Some quadruple star systems in the hierarchical 2+2 configuration exhibit orbit-orbit resonances between the two compact binaries. We show that the most important resonances occur at period ratios of 1:1, 3:2 and 2:1. We describe the conditions required for capture and show that they can be satisfied at the 3:2 and 2:1 resonances in binaries that migrate significantly in semimajor axis after circularization, probably through magnetic braking or gravitational radiation.Quadruple stellar systems are almost always found in hierarchical configurations, since this is the only simple way to ensure long-term orbital stability. There are two possible architectures: the 3+1 configuration, in which a hierarchical triple system is orbited by an even more distant companion, and the 2+2 configuration, in which two relatively compact binaries orbit their common center of mass. In this paper we explore novel resonant phenomena that can arise in the 2+2 configuration.The best-studied 2+2 systems are those in which both compact binaries are eclipsing. These 'doubly eclipsing' systems are rare: the most recent compilation (Zasche et al. 2019) lists only 146 systems, and a significant fraction of these may be superimposed pairs of unrelated eclipsing binaries.Despite the modest sample size, Zasche et al. (2019) find significant peaks in the distribution of period ratios P B /P A near 1 and 1.5 (see Figure 1). There is no evidence for peaks near other resonances such as P B /P A = 2.Here are more complete descriptions of a few of the near-resonant systems from this sample.• V994 Her (Lee et al. 2008; Zasche & Uhlař 2016) consists of two detached eclipsing binary systems with periods P A = 1.4200 d, P B = 2.0833 d. (Here and throughout the paper, the labels 'A' and 'B' refer to the binaries with the shorter and longer periods, and 'C' refers to the mutual orbit of the centers of mass of binaries A and B. Not all authors follow this convention.) The distance is 320 ± 10 pc based on the Gaia DR2 parallax of 3.05 ± 0.13 mas and an assumed parallax offset of 0.05 mas. System A has spectral types A2V and A4V, while B has spectral types B8V and A0V. The stellar masses range from 1.8M to 3.0M ; the main-sequence lifetime of the most massive star is about 3 × 10 8 yr, suggesting that the age of the system is less than this. Both systems have non-zero eccentricities: e A = 0.125 ± 0.007 and e B = 0.031 ± 0.001. The mutual orbit has period P C = 2.91 ± 0.14 yr and eccentricity e C = 0.76 ± 0.07. The period ratio is close to but not exactly 3:2, with 1 − 2P B /3P A = 0.0220.• OGLE BLG-ECL-145467 (Zasche et al. 2019) has P A = 3.305 d, P B = 4.910 d, P C = 1540 ± 90 d. The distance is 3100 ± 400 pc based on the Gaia DR2 parallax of 0.374 ± 0.048 mas and the same assumed parallax offset. All three orbits have non-zero eccentricity, e A = 0.007 ± 0.001, e B = 0.068 ± 0.003, and e C = 0.395 ± 0.018. Apsidal motion is detected in binary A with 2π/ 125 yr. The stars appear to have spectral types near B9. The period ratio is close to a 3:2 resonance, ...

TIC 278956474: Two Close Binaries in One Young Quadruple System Identified by TESS

“…period ratio of the two binary orbits (P B /P A ∼ 1.03) is very close to unity. According to the results of Zasche et al (2019) there is a significant excess of 2+2 quadruple systems with near equal inner periods, however, the origin of this feature is still unknown (see also Breiter & Vokrouhlický 2018;Tremaine 2020). Turning to the other orbital parameters, as preliminary runs implied that eccentricities of both inner orbits should be less than 0.001, we assumed circular orbits for the further analysis.…”

Architecture of Hierarchical Stellar Systems and Their Formation

“…Later, if the masses become comparable, the gas is distributed more evenly and the inner binary also migrates. The inner and outer orbits, evolving jointly to closer separations, interact dynamically and can be trapped in a mean motion resonance (MMR), at least temporarily [49]. There is some analogy with the migration in multi-planet systems that also produces sometimes resonant or quasi-resonant architectures.…”

“…This can be explained by the interaction of both subsystems with their outer orbit, which is possible only in compact configurations. Yet another necessary condition for such resonances is migration of the orbits [49].…”

Architecture of Hierarchical Stellar Systems and their Formation

“…Later, if the masses become comparable, the gas is distributed more evenly and the inner binary also migrates. The inner and outer orbits, evolving jointly to closer separations, interact dynamically and can be trapped in a mean motion resonance (MMR), at least temporarily (Tremaine 2020). There is some analogy with the migration in multi-planet systems that also produces sometimes resonant or quasi-resonant architectures.…”

“…This can be explained by the interaction of both subsystems with their outer orbit, which is possible only in compact configurations. Yet another necessary condition for such resonances is migration of the orbits (Tremaine 2020).…”