Dynamical evolution of triple stars.

Harrington, R. S.

doi:10.1086/110614

Cited by 228 publications

(177 citation statements)

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“…Harrington 1968Harrington , 1969Soderhjelm 1975;Breiter & Vokrouhlický 2015). Here n 1 and n 2 are the mean motion values of the orbits 1 and 2, both related to the semi-major axes a 1 and a 2 through the third Kepler law: n 2 1 a 3 1 = GM 1 and n 2 2 a 3 2 = GM 2 (G is the gravitational constant).…”

Section: Secular Effectsmentioning

confidence: 99%

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

Nemravová

Harmanec

Brož

et al. 2016

A&A

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Context. Compact hierarchical systems are important because the effects caused by the dynamical interaction among its members occur on a 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 eclipsetiming 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.

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Section: Secular Effectsmentioning

confidence: 99%

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

Nemravová

Harmanec

Brož

et al. 2016

A&A

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“…By the use of the theory of Harrington (1968Harrington ( , 1969, based on the von Zeipel averaging method of the canonical equations, Söderhjelm (1975Söderhjelm ( , 1982 derived analytical formulae for the long period perturbations in the standard Delaunay variables. Although these formulae are exact up to second order in the (a/a ) ratio, their practical use is limited, at least in their original forms.…”

Section: An Analytical Formula Of the Long Period Perturbation Of An mentioning

confidence: 99%

“…There the first two of our groups called together as "short period" perturbations, while the "apse-node terms" are called as "long period" ones. In the stellar three-body problem this latter classification was used by Harrington 1968Harrington , 1969.) These effects can be most easily detected in those triple systems, where the close binary happens to be an eclipsing one.…”

Section: Introductionmentioning

confidence: 99%

On the detectability of long period perturbations in close hierarchical triple stellar systems

Borkovits

Érdi

Forgács‐Dajka

et al. 2003

A&A

104

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Abstract.We study the possibility of the detection of the low amplitude long (P ) period perturbative effect of a distant third companion on the motion of a close binary. We give a new, more accurate analytical formula for this kind of perturbation affecting the moments of the times of minima in eclipsing binaries. The accuracy of this formula is tested by numerical integrations carried out for several initial configurations. We also describe a numerical method based on a non-linear Levenberg-Marquardt algorithm which makes it possible to separate this dynamical effect from the pure geometrical light-time effect in the eclipsing O−C diagram. The capabilities of this new method are demonstrated by the analysis of numerically simulated O−Cs for test systems having physical parameters very similar to Algol and IU Aur. The results show that the above mentioned effect would be detectable in these systems nowadays, observing almost each minima events in a 1-2 year-long interval.

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“…The Kozai resonance (recently and frequently referred to as Kozai cycle[s]) was first described by Kozai (1962) when investigating secular perturbations of asteroids. The first (theoretical) investigation of this phenomenon with respect to multiple stellar systems can be found in the studies by Harrington (1968Harrington ( , 1969, Mazeh & Saham (1979), and Söderhjelm (1982). A higher, third-order theory of Kozai cycles was given by Ford et al (2000), while the first application of KCTF to explain the present configuration of a close, hierarchical triple system (the emblematic Algol, itself) was presented by Kiseleva et al (1998).…”

Section: Introductionmentioning

confidence: 99%

Transit timing variations in eccentric hierarchical triple exoplanetary systems

Borkovits

Csizmadia

Forgács‐Dajka

et al. 2011

A&A

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Aims. We study the long-term time scale (i.e. period comparable to the orbital period of the outer perturber object) transit timing variations (TTVs) in transiting exoplanetary systems that contain another more distant (a 2 a 1 ) planetary or stellar companion. Methods. We give an analytical form of the O−C diagram (which describes such TTVs) in a trigonometric series, which is valid for arbitrary mutual inclinations, up to the sixth order in the inner eccentricity. Results. We show that the dependence of the O−C on the orbital and physical parameters can be separated into three parts. Two of these are independent of the real physical parameters (i.e. masses, separations, periods) of a concrete system and only depend on dimensionless orbital elements, so can be analysed in general. We find that, for a specific transiting system, where eccentricity (e 1 ) and the observable argument of periastron (ω 1 ) are known, say, from spectroscopy, the main characteristics of that TTV, which is caused by a possible third-body can be mapped simply. Moreover, as the physical attributes of a given system only occur as scaling parameters, the real amplitude of the O−C can also be estimated for a given system, simply as a function of the m 3 /P 2 ratio. We analyse the above-mentioned dimensionless amplitudes for different arbitrary initial parameters, as well as for two particular systems, CoRoT-9b and HD 80606b. We find in general that, while the shape of the O−C strongly varies with the angular orbital elements, the net amplitude (departing from some specific configurations) depends only weakly on these elements, but strongly on the eccentricities. As an application, we illustrate how the formulae work for the weakly eccentric CoRoT-9b and the highly eccentric HD 80606b. We also consider the question of detection, as well as the correct identification of such perturbations. Finally, we illustrate the operation and effectiveness of Kozai cycles with tidal friction (KCTF) in the case of HD 80606b.

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Dynamical evolution of triple stars.

Cited by 228 publications

References 0 publications

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

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

On the detectability of long period perturbations in close hierarchical triple stellar systems

Transit timing variations in eccentric hierarchical triple exoplanetary systems

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