On the Motion of the Apsidal Line in Close Binary Systems

Cowling, T. G.

doi:10.1093/mnras/98.9.734

Cited by 91 publications

(77 citation statements)

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“…This effect has been known for a long time (Cowling 1938;Sterne 1939). The rate of motion of the apsis is dependent on the internal structure of each component.…”

Section: Apsidal Motion Analysismentioning

confidence: 99%

Relativistic apsidal motion in eccentric eclipsing binaries

Wolf¹,

Claret²,

Kotková

et al. 2010

A&A

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Context. The study of apsidal motion in detached eclipsing binary systems is known to be an important source of information about stellar internal structure as well as the possibility of verifying of General Relativity outside the Solar System. Aims. As part of the long-term Ondřejov and Ostrava observational projects, we aim to measure precise times of minima for eccentric eclipsing binaries, needed for the accurate determination of apsidal motion, providing a suitable test of the effects of General Relativity. Methods. About seventy new times of minimum light recorded with photoelectric or CCD photometers were obtained for ten eccentric-orbit eclipsing binaries with significant relativistic apsidal motion. Their O-C diagrams were analysed using all reliable timings found in the literature, and new or improved elements of apsidal motion were obtained. Results. We confirm very long periods of apsidal motion for all systems. For BF Dra and V1094 Tau, we present the first apsidalmotion solution. The relativistic effects are dominant, representing up to 100% of the total observable apsidal-motion rate in several systems. The theoretical and observed values of the internal structure constant k 2 were compared for systems with lower relativistic contribution. Using the light-time effect solution, we predict a faint third component for V1094 Tau orbiting with a short period of about 8 years.

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“…This effect has been known for a long time (Cowling 1938;Sterne 1939). The rate of motion of the apsis is dependent on the internal structure of each component.…”

Section: Apsidal Motion Analysismentioning

confidence: 99%

Relativistic apsidal motion in eccentric eclipsing binaries

Wolf¹,

Claret²,

Kotková

et al. 2010

A&A

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“…The rate of secular apsidal motion due to the tidal distortion of the components of a close binary is usually derived under the assumption that the orbital period is long in comparison to the periods of the free oscillation modes of the component stars (Cowling 1938;Sterne 1939). The resulting formula takes the forṁ…”

Section: The Influence Of Dynamic Tidesmentioning

confidence: 99%

“…The effect was first investigated by Russell in 1928, and subsequently by Cowling (1938) and Sterne (1939) who found the distortions to depend on the mass distribution of the stars. Comparison of theoretically predicted apsidalmotion rates with the rates derived from observations therefore provides a good tool to test current theories of stellar structure and evolution.…”

Section: Introductionmentioning

confidence: 99%

New results on the apsidal-motion test to stellar structure and evolution including the effects of dynamic tides

Claret

Willems²

2002

A&A

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Abstract. We revised the current status of the apsidal-motion test to stellar structure and evolution. The observational sample was increased by about 50% in comparison to previous studies. Classical and relativistic systems were analyzed simultaneously and only systems with accurate absolute dimensions were considered. New interior models incorporating recent opacity tables, stellar rotation, mass loss, and moderate core overshooting were used as theoretical tools to compare the predicted with the observed shifts of the position of the periastron. The stellar models were computed for the precise observed masses and the adopted chemical compositions are consistent with the corresponding tables of opacities to avoid the inherent problems of interpolation in mass and in (X, Z). The derived chemical composition for each individual system was used to infer the primordial helium content as well as a law of enrichment. The values found are in good agreement with those obtained from various independent sources. For the first time, the effects of dynamic tides are taken into account systematically to determine the contribution of the tidal distortion to the predicted apsidal-motion rate. The deviations between the apsidal-motion rates resulting from the classical formula and those determined by taking into account the effects of dynamic tides are presented as a function of the level of synchronism. For systems close to synchronisation, dynamic tides cause deviations with respect to the classical apsidal-motion formula due to the effects of the compressibility of the stellar fluid. For systems with higher rotational angular velocities, additional deviations due to resonances arise when the forcing frequencies of the dynamic tides come into the range of the free oscillation modes of the component stars. The resulting comparison shows a good agreement between the observed and theoretical apsidal-motion rates. No systematic effects in the sense that models are less mass concentrated than real stars and no correlations with the evolutionary status of the systems were detected.

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“…Miralda-Escudé (2002), A&A 528, A53 (2011) Heyl & Gladman (2007), and Jordán & Bakos (2008, and further references thereins). This effect has been studied since the pioneering works of Cowling (1938), and Sterne (1939), and besides its evident importance in the checking of the general relativity theory, it plays also an important role in studies of the inner mass distributions of stars (via their quadrupol moment); i.e. it provides observational verification of stellar models.…”

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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On the Motion of the Apsidal Line in Close Binary Systems

Cited by 91 publications

References 0 publications

Relativistic apsidal motion in eccentric eclipsing binaries

Relativistic apsidal motion in eccentric eclipsing binaries

New results on the apsidal-motion test to stellar structure and evolution including the effects of dynamic tides

Transit timing variations in eccentric hierarchical triple exoplanetary systems

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