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Register a new userThe architecture of the hierarchical triple star KOI 928 from eclipse timing variations seen in Kepler photometry
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J. H. Steffen
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We present a hierarchical triple star system (KIC 9140402) where a low mass eclipsing binary orbits a more massive third star. The orbital period of the binary (4.98829 Days) is determined by the eclipse times seen in photometry from NASAs Kepler spacecraft. The periodically changing tidal field, due to the eccentric orbit of the binary about the tertiary, causes a change in the orbital period of the binary. The resulting eclipse timing variations provide insight into the dynamics and architecture of this system and allow the inference of the total mass of the binary ($0.424 pm 0.017 text{M}_odot$) and the orbital parameters of the binary about the central star.
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Field stars are frequently formed in pairs, and many of these binaries are part of triples or even higher-order systems. Even though, the principles of single stellar evolution and binary evolution, have been accepted for a long time, the long-term evolution of stellar triples is poorly understood. The presence of a third star in an orbit around a binary system can significantly alter the evolution of those stars and the binary system. The rich dynamical behavior in three-body systems can give rise to Lidov-Kozai cycles, in which the eccentricity of the inner orbit and the inclination between the inner and outer orbit vary periodically. In turn, this can lead to an enhancement of tidal effects (tidal friction), gravitational-wave emission and stellar interactions such as mass transfer and collisions. The lack of a self-consistent treatment of triple evolution, including both three-body dynamics as well as stellar evolution, hinders the systematic study and general understanding of the long-term evolution of triple systems. In this paper, we aim to address some of these hiatus, by discussing the dominant physical processes of hierarchical triple evolution, and presenting heuristic recipes for these processes. To improve our understanding on hierarchical stellar triples, these descriptions are implemented in a public source code TrES which combines three-body dynamics (based on the secular approach) with stellar evolution and their mutual influences. Note that modeling through a phase of stable mass transfer in an eccentric orbit is currently not implemented in TrES , but can be implemented with the appropriate methodology at a later stage.
We present the first results of a Kepler survey of 41 eclipsing binaries that we undertook to search for third star companions. Such tertiaries will periodically alter the eclipse timings through light travel time and dynamical effects. We discuss the prevalence of starspots and pulsation among these binaries and how these phenomena influence the eclipse times. There is no evidence of short period companions (P < 700 d) among this sample, but we do find evidence for long term timing variations in 14 targets (34%). We argue that this finding is consistent with the presence of tertiary companions among a significant fraction of the targets, especially if many have orbits measured in decades. This result supports the idea that the formation of close binaries involves the deposition of angular momentum into the orbital motion of a third star.
We present the results of a search through the photometric database of eclipsing Kepler binaries (Prsa et al. 2011; Slawson et al. 2011) looking for evidence of hierarchical triple star systems. The presence of a third star orbiting the binary can be inferred from eclipse timing variations. We apply a simple algorithm in an automated determination of the eclipse times for all 2157 binaries. The calculated eclipse times, based on a constant period model, are subtracted from those observed. The resulting O-C (observed minus calculated times) curves are then visually inspected for periodicities in order to find triple-star candidates. After eliminating false positives due to the beat frequency between the ~1/2-hour Kepler cadence and the binary period, 39 candidate triple systems were identified. The periodic O-C curves for these candidates were then fit for contributions from both the classical Roemer delay and so-called physical delay, in an attempt to extract a number of the system parameters of the triple. We discuss the limitations of the information that can be inferred from these O-C curves without further supplemental input, e.g., ground-based spectroscopy. Based on the limited range of orbital periods for the triple star systems to which this search is sensitive, we can extrapolate to estimate that at least 20% of all close binaries have tertiary companions.
We report eclipse timing variation analyses of 26 compact hierarchical triple stars comprised of an eccentric eclipsing (inner) binary and a relatively close tertiary component found in the {em Kepler} field. We simultaneously fit the primary and secondary $O-C$ curves of each system for the light-travel time effect (LTTE), as well as dynamical perturbations caused by the tertiary on different timescales. For the first time, we include those contributions of three-body interactions which originate from the eccentric nature of the inner binary. These effects manifest themselves both on the period of the triple system, $P_2$, and on the longer apse-node timescale. We demonstrate that consideration of the dynamically forced rapid apsidal motion yields an efficient and independent tool for the determination of the binary orbits eccentricity and orientation, as well as the 3D configuration of the triple. Modeling the forced apsidal motion also helps to resolve the degeneracy between the shapes of the LTTE and the dynamical delay terms on the $P_2$ timescale, due to the strong dependence of the apsidal motion period on the triples mass ratio. This can lead to the independent determination of the binary and tertiary masses without the need for independent radial velocity measurements. Through the use of our analytic method for fitting $O-C$ curves we have obtained robust solutions for system parameters for the ten most ideal triples of our sample, and only somewhat less robust, but yet acceptable, fits for the remaining systems. Finally we study the results of our 26 system parameter fits via a set of distributions of various physically important parameters, including mutual inclination angle, and mass and period ratios.
The eclipsing white dwarf plus main-sequence binary NN Serpentis provides one of the most convincing cases for the existence of circumbinary planets around evolved binaries. The exquisite timing precision provided by the deep eclipse of the white dwarf has revealed complex variations in the eclipse arrival times over the last few decades. These variations have been interpreted as the influence of two planets in orbit around the binary. Recent studies have proved that such a system is dynamically stable over the current lifetime of the binary. However, the existence of such planets is by no means proven and several alternative mechanisms have been proposed that could drive similar variations. One of these is apsidal precession, which causes the eclipse times of eccentric binaries to vary sinusoidally on many year timescales. In this paper we present timing data for the secondary eclipse of NN Ser and show that they follow the same trend seen in the primary eclipse times, ruling out apsidal precession as a possible cause for the variations. This result leaves no alternatives to the planetary interpretation for the observed period variations, although we still do not consider their existence as proven. Our data limits the eccentricity of NN Ser to e<0.001. We also detect a 3.3+/-1.0 second delay in the arrival times of the secondary eclipses relative to the best planetary model. This delay is consistent with the expected 2.84+/-0.04 second Romer delay of the binary, and is the first time this effect has been detected in a white dwarf plus M dwarf system.
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