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Register a new userThe evolution of hierarchical triple star-systems
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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.
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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.
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.
The SR24 multi-star system hosts both circumprimary and circumsecondary disks, which are strongly misaligned from each other. The circumsecondary disk is circumbinary in nature. Interestingly, both disks are interacting, and they possibly rotate in opposite directions. To investigate the nature of this unique twin disk system, we present 0.1 resolution near-infrared polarized intensity images of the circumstellar structures around SR24, obtained with HiCIAO mounted on the Subaru 8.2 m telescope. Both the circumprimary disk and the circumsecondary disk are resolved and have elongated features. While the position angle of the major axis and radius of the NIR polarization disk around SR24S are 55$^{circ}$ and 137 au, respectively, those around SR24N are 110$^{circ}$ and 34 au, respectively. With regard to overall morphology, the circumprimary disk around SR24S shows strong asymmetry, whereas the circumsecondary disk around SR24N shows relatively strong symmetry. Our NIR observations confirm the previous claim that the circumprimary and circumsecondary disks are misaligned from each other. Both the circumprimary and circumsecondary disks show similar structures in $^{12}$CO observations in terms of its size and elongation direction. This consistency is because both NIR and $^{12}$CO are tracing surface layers of the flared disks. As the radius of the polarization disk around SR24N is roughly consistent with the size of the outer Roche lobe, it is natural to interpret the polarization disk around SR24N as a circumbinary disk surrounding the SR24Nb-Nc system.
Under certain rather prevalent conditions (driven by dynamical orbital evolution), a hierarchical triple stellar system can be well approximated, from the standpoint of orbital parameter estimation, as two binary star systems combined. Even under this simplifying approximation, the inference of orbital elements is a challenging technical problem because of the high dimensionality of the parameter space, and the complex relationships between those parameters and the observations (astrometry and radial velocity). In this work we propose a new methodology for the study of triple hierarchical systems using a Bayesian Markov-Chain Monte Carlo-based framework. In particular, graphical models are introduced to describe the probabilistic relationship between parameters and observations in a dynamically self-consistent way. As information sources we consider the cases of isolated astrometry, isolated radial velocity, as well as the joint case with both types of measurements. Graphical models provide a novel way of performing a factorization of the joint distribution (of parameter and observations) in terms of conditional independent components (factors), so that the estimation can be performed in a two-stage process that combines different observations sequentially. Our framework is tested against three well-studied benchmark cases of triple systems, where we determine the inner and outer orbital elements, coupled with the mutual inclination of the orbits, and the individual stellar masses, along with posterior probability (density) distributions for all these parameters. Our results are found to be consistent with previous studies. We also provide a mathematical formalism to reduce the dimensionality in the parameter space for triple hierarchical stellar systems in general.
We report the discovery and complex analyses of the first two compact hierarchical triple star systems discovered with TESS in or near its southern continuous viewing zone during Year 1. Both TICs 167692429 and 220397947 were previously unknown eclipsing binaries, and the presence of a third companion star was inferred from eclipse timing variations exhibiting signatures of strong 3rd-body perturbations and, in the first system, also from eclipse depth variations. We carried out comprehensive analyses, including the simultaneous photodynamical modelling of TESS and archival ground-based WASP lightcurves, as well as eclipse timing variation curves. Also, for the first time, we included in the simultaneous fits multiple star spectral energy distribution data and theoretical PARSEC stellar isochrones, taking into account Gaia DR2 parallaxes and cataloged metallicities. We find that both systems have twin F-star binaries and a lower mass tertiary star. In the TIC 167692429 system the inner binary is moderately inclined ($i_{mut}=27^o$) with respect to the outer orbit, and the binary vs. outer (triple) orbital periods are 10.3 vs. 331 days, respectively. The mutually inclined orbits cause a driven precession of the binary orbital plane which leads to the disappearance of binary eclipses for long intervals. In the case of TIC 220397947 the two orbital planes are more nearly aligned and the inner vs. outer orbital periods are 3.5 and 77 days, respectively. In the absence of radial velocity observations, we were unable to calculate highly accurate masses and ages for the two systems. According to stellar isochrones TIC 167692429 might be either a pre-main sequence or an older post-MS system. In the case of TIC 220397947 our solution prefers a young, pre-MS scenario.
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