Abstract
Context. Compact hierarchical systems are important because the effects caused by the dynamical interaction among its members occur ona human timescale. These interactions play a role in the formation of close binaries through Kozai cycles with tides. One such system is ξ Tauri: it has three hierarchical orbits: 7.14 d (eclipsing components Aa, Ab), 145 d (components Aa+Ab, B), and 51 yr (components Aa+Ab+B, C).Aims. We aim to obtain physical properties of the system and to study the dynamical interaction between its components.Methods. Our analysis is based on a large series of spectroscopic photometric (including space-borne) observations and long-baseline optical and infrared spectro-interferometric observations. We used two approaches to infer the system properties: a set of observation-specific models, where all components have elliptical trajectories, and an N -body model, which computes the trajectory of each component by integrating Newton’s equations of motion.Results. The triple subsystem exhibits clear signs of dynamical interaction. The most pronounced are the advance of the apsidal line and eclipse-timing variations. We determined the geometry of all three orbits using both observation-specific and N -body models. The latter correctly accounted for observed effects of the dynamical interaction, predicted cyclic variations of orbital inclinations, and determined the sense of motion of all orbits. Using perturbation theory, we demonstrate that prominent secular and periodic dynamical effects are explainable with a quadrupole interaction. We constrained the basic properties of all components, especially of members of the inner triple subsystem and detected rapid low-amplitude light variations that we attribute to co-rotating surface structures of component B. We also estimated the radius of component B. Properties of component C remain uncertain because of its low relative luminosity. We provide an independent estimate of the distance to the system.Conclusions. The accuracy and consistency of our results make ξ Tau an excellent test bed for models of formation and evolution of hierarchical systems.
Highlights
Binaries and multiple systems play a crucial role in our understanding of the formation, stability, and evolution of stars and their hierarchies, starting from simple binaries up to galaxies.Of all known binaries, those that eclipse have represented the most useful group because until recently, an accurate determination of component masses and radii was possible primarily for them
The system was observed by four different spectrointerferometers: the Mark III Stellar Interferometer1 (Mark III) (Shao et al 1988), the Navy Precision Optical Interferometer (NPOI) (Armstrong et al 1998), the Visible spEctroGraph and polArimeter (VEGA) (Mourard et al 2009) mounted at the Centre for High Angular Resolution Astronomy (CHARA), and the Astronomical Multi-BEam combineR (AMBER) (Petrov et al 2007) attached to the Very Large Telescope Interferometer (VLTI) (Glindemann et al 2004)
The first-order model of the physical delay (Eq (8) from Rappaport et al 2013), which is only a part of the total eclipse timing variations (ETVs), arising from dynamical interaction of two orbits in hierarchical triple systems, gives an estimate of the amplitude of the effect ∆tMODEL ≈ 0.02 d,. This is another proof of the dynamical interaction in ξ Tau and led us to develop an N-body model and a perturbation theory
Summary
Binaries and multiple systems play a crucial role in our understanding of the formation, stability, and evolution of stars and their hierarchies, starting from simple binaries up to galaxies. More accurate elements were given in a preliminary report by Bolton & Grunhut (2007), who obtained periods of 7.1466440(49) d and 145.1317(40) d They were the first to note that the inner binary is an eclipsing system, based on Hipparcos photometry. The first detailed, but still preliminary study of ξ Tau was published by Nemravová et al (2013) These authors analysed numerous spectral, photometric and interferometric observations and discovered the apsidal motion of the 145.2 d orbit with a period 224 ± 147 yr. They were able to separate the spectra of the two A stars and the broad-lined B star. We denote the faint and very distant F-type star as component C and its 51 yr orbit with the triple subsystem as orbit 3
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