ξTauri: a unique laboratory to study the dynamic interaction in a compact hierarchical quadruple system ^⋆,⋆⋆

¹ Astronomical Institute of the Charles University, Faculty of Mathematics and Physics, V Holešovičkách 2, 180 00 Praha 8, Troja, Czech Republic
² Laboratoire Lagrange, OCA/UNS/CNRS UMR 7293, BP 4229, 06304 Nice Cedex, France
³ European Southern Observatory, Karl–Schwarzschild–Str. 2, 85748 Garching bei München, Germany
⁴ Department of Mathematics, Physics & Geology, Cape Breton University, 1250 Grand Lake Road, Sydney, NS B1P 6L2, Canada
⁵ Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada
⁶ Department of Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, Ontario, M5S 3H4, Canada
⁷ Hvar Observatory, Faculty of Geodesy, Zagreb University, Kačićeva 26, 10000 Zagreb, Croatia
⁸ Astronomisches Institut, Ruhr-Universität Bochum, Universitätsstraße 150, 44780 Bochum, Germany
⁹ Instituto de Astronomía, Universidad Católica del Norte, Avenida Angamos 0610, Casilla 1280 Antofagasta, Chile
¹⁰ Department of Astronomy and Astrophysics, Villanova University, Villanova, PA 19085, USA
¹¹ CHARA Array, Mount Wilson Observatory, Mount Wilson, CA 91023, USA
¹² Department of Astronomy and Physics, Saint Mary’s University, Halifax, N.S., B3H 3C3, Canada
¹³ Astronomical Institute, Academy of Sciences of the Czech Republic, 251 65 Ondřejov, Czech Republic
¹⁴ Institute of Astronomy, University Vienna, Türkenschanzstrasse 17, 1180 Vienna, Austria
¹⁵ Department de Physique, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, QC H3C 3J7, Canada
¹⁶ Observatório do Instituto Geográfico do Exército, R. Venezuela 29 3 Esq., 1500-618, Lisbon, Portugal
¹⁷ NASA Ames Research Center, Moffett Field, CA 94035; SETI Institute, Mountain View, CA 94043, USA
¹⁸ Université de Lyon, Université Lyon 1, École Normale Supérieure de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR 5574, 69230 Saint-Genis-Laval, France
¹⁹ US Naval Observatory, Flagstaff Station, 10391 West Naval Observatory Road, Flagstaff, AZ 86005-8521, USA

Received: 5 May 2016
Accepted: 27 May 2016

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.