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

Borkovits, T.; Érdi, Bálint; Forgács‐Dajka, E.; Kovács, Tímea

doi:10.1051/0004-6361:20021688

Cited by 83 publications

(116 citation statements)

References 14 publications

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“…However, our formulae can be practically applied even for the closest exoplanetary systems, because the tidal perturbations usually become effective on a notably longer time scale.) This work is a continuation and extension of the previous paper of Borkovits et al (2003). In that paper we formulated the long-period perturbations of an (arbitrarily eccentric and inclined) distant companion to the O−C diagram for a circular inner orbit.…”

Section: Introductionmentioning

confidence: 81%

“…orbital shrinking) to already be traced within a few decades. Furthermore, the larger the characteristic size of a multiple planetary, stellar (or mixed) system the greater the amplitude of even the shorter period perturbations in the TTVs, as shown in detail in the discussion of Borkovits et al (2003).…”

Section: Introductionmentioning

confidence: 99%

“…(A somewhat detailed description can be found in Borkovits et al 2003Borkovits et al , 2007; nevertheless for self-consistency of the present paper we provide a brief overview.) In Sect.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

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Transit timing variations in eccentric hierarchical triple exoplanetary systems

Borkovits

Csizmadia

Forgács‐Dajka

et al. 2011

A&A

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“…So far, the long-period effects, namely those with a period P 2 of orbit 2, have been extensively studied (e.g. Soderhjelm 1975Soderhjelm , 1982Borkovits et al 2003Borkovits et al , 2011Borkovits et al , 2015. We here focus on the ETVs, that is, on advances and delays δt LP in epochs of eclipse of orbit 1 that are due to the variations in its mean motion n 1 caused by component B.…”

Section: Long-and Short-period Eclipse Variationsmentioning

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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“…In consequence, if denotes a real-valued -continuous -measure of the orbital cycle (which also includes integer values when primary light minima are concerned, e.g., Gimenez & Garcia-Pelayo 1983;Borkovits et al 2003), the orbital period as a function of time, P(t), is converted into the orbital cycle domain, P( ), through the t = t( ) transformation that emerges by solving for t the following equation:…”

Section: Mathematical Proceduresmentioning

confidence: 99%

Efficiency of ETV diagrams as diagnostic tools for long-term period variations

Nanouris

Kalimeris

Antonopoulou

et al. 2015

A&A

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Context. The credibility of an eclipse timing variation (ETV) diagram analysis is investigated for various manifestations of the mass transfer and gravitational radiation processes in binary systems. The monotonicity of the period variations and the morphology of the respective ETV diagrams are thoroughly explored in both the direct impact and the accretion disk mode of mass transfer, accompanied by different types of mass and angular momentum losses (through a hot-spot emission from the gainer and via the L2/L3 points). Aims. Our primary objective concerns the traceability of each physical mechanism by means of an ETV diagram analysis. Also, possible critical mass ratio values are sought for those transfer modes that involve orbital angular momentum losses strong enough to dictate the secular period changes even when highly competitive mechanisms with the opposite direction act simultaneously. Methods. TheJ −Ṗ relation that governs the orbital evolution of a binary system is set to provide the exact solution for the period and the function expected to represent the subsequent eclipse timing variations. The angular momentum transport is parameterized through appropriate empirical relations, which are inferred from semi-analytical ballistic models. Then, we numerically determine the minimum temporal range over which a particular mechanism is rendered measurable, as well as the critical mass ratio values that signify monotonicity inversion in the period modulations. Results. Mass transfer rates comparable to or greater than 10 −8 M yr −1 are measurable for typical noise levels of the ETV diagrams, regardless of whether the process is conservative. However, the presence of a transient disk around the more massive component defines a critical mass ratio (q cr ≈ 0.83) above which the period turns out to decrease when still in the conservative regime, rendering the measurability of the anticipated variations a much more complicated task. The effects of gravitational radiation proved to be rather undetectable, except for systems with physical characteristics that only refer to cataclysmic variables. Conclusions. The monotonicity of the period variations and the curvature of the respective ETV diagrams depend strongly on the accretion mode and the degree of conservatism of the transfer process. Unlike the hot-spot effects, the Lagrangian points L2 and L3 support very efficient routes of strong angular momentum loss. It is further shown that escape of mass via the L3 point -when the donor is the less massive component -safely provides critical mass ratios above which the period is expected to decrease, no matter how intense the process is.

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

Cited by 83 publications

References 14 publications

Transit timing variations in eccentric hierarchical triple exoplanetary systems

Transit timing variations in eccentric hierarchical triple exoplanetary systems

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

Efficiency of ETV diagrams as diagnostic tools for long-term period variations

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