Rapid apsidal motion in V381 Cassiopeiae

V381 Cas is a relatively bright and early-type eclipsing binary system. Several new times of its eclipses were measured as part of our long-term observational project of eccentric eclipsing binaries. Based on a current O–C diagram solution, we found for the first time that its orbit is slightly eccentric (e = 0.025) and shows a very rapid apsidal advance with short period of about 20 years only. The relativistic and third body effects are negligible, being about 3% of the total apsidal motion rate.     

New eccentric eclipsing binary in triple system: SY Phe

Analyzing available photometry from Hipparcos, ASAS, Pi of the sky and Super WASP, we found that the system SY Phe is a detached eclipsing binary with similar components and orbital period about 5.27089 days. It has a slightly eccentric orbit, however the apsidal motion is probably very slow. The system undergoes an additional photometric variation on longer time scales superimposed on the eclipsing light curve. It also contains one distant component, hence the third light was also considered.     

Photometry and Analysis of the Eclipsing Binary IQ Persei

Photoelectric observations of the eclipsing binary IQ Persei have been carried out in B and V colours at Ege University Observatory. The corresponding light curves were analyzed by synthesis techniques. The absolute physical parameters and apsidal motion period (122 yr) of the system were obtained. The results have been compared with theoretical evolutionary models which include both mass loss and convective overshooting. Theoretical evolutionary tracks of the component stars indicate an age of 1.3 × 10⁸ years and an apsidal motion constant of 0.0040 which is greater than its observed value by only about 5%. The A7 secondary of the eclipsing pair is still close to the zero-age main sequence but B7 primary is about halfway through its main sequence life-time. This revised version was published online in July 2006 with corrections to the Cover Date.     

Photometric light curves and physical paramters of the eclipsing binary systems IT Cas,CO Cep,AI Hya with possible apsidal motions

Multi-colourWBVR photoelectric observations of the eclipsing binaries IT Cas, CO Cep, and AI Hya were carried out. The photometric elements and the absolute parameters of the orbits and components were obtained. The valuation of the angular rate of the apsidal motion of AI Hya based on the comparison of our observations with the previous photoelectric light curve of this system was derived.     

The Unique Binary Star α Coronae Borealis

We present a new photoelectric light curve of α Coronae Borealis. The derived rate of apsidal motion differs from the theoretical prediction. A possible solution of the problem is suggested.     

Secular dynamics of the three-body problem: application to the υ Andromedae planetary system

The discovery of extra-solar planetary systems with multiple planets in highly eccentric orbits (∼0.1-0.6), in contrast with our own Solar System, makes classical secular perturbation analysis very limited. In this paper, we use a semi-numerical approach to study the secular behavior of a system composed of a central star and two massive planets in co-planar orbits. We show that the secular dynamics of this system can be described using only two parameters, the ratios of the semi-major axes and the planetary masses. The main dynamical features of the system are presented in geometrical pictures that allows us to investigate a large domain of the phase space of this three-body problem without time-expensive numerical integrations of the equations of motion, and without any restriction on the magnitude of the planetary eccentricities. The topology of the phase space is also investigated in detail by means of spectral map techniques, which allow us to detect the separatrix of a non-linear secular apsidal resonance. Finally, the qualitative study is supplemented by direct numerical integrations. Three different regimes of secular motion with respect to the secular angle Δ? are possible: they are circulation, oscillation (around 0° and 180°), and high eccentricity libration in a non-linear secular resonance. The first two regimes are a continuous extension of the classical linear secular perturbation theory; the last is a new feature, hitherto unknown, in the secular dynamics of the three-body problem. We apply the analysis to the case of the two outer planets in the υ Andromedae system, and obtain its periodic and ordinary orbits, the general structure of its secular phase space, and the boundaries of its secular stability; we find that this system is secularly stable over a large domain of eccentricities. Applying this analysis to a wide range of planetary mass and semi-major axis ratios (centered about the υ Andromedae parameters), we find that apsidal oscillation dominates the secular phase space of the three-body coplanar system, and that the non-linear secular resonance is also a common feature.     

Study of the contact binary AK Herculis: Light-curve analysis and orbital period investigation

AK Her is a very interesting contact binary exhibiting variable lightcurves and an obvious O'Connell effect, with max I greater than max II. Inthe present work an extensive study of this system is made covering notonly its light curve analysis, but also its orbital period changes in anattempt to give a definite answer regarding the apsidal motion of AK Her.Photoelectric observations of AK Her, obtained between 1985–1987 at theNational Observatory of Athens Greece, are presented, analysed anddiscussed. The light curve analysis was made with the W-D code and thegeometric and photometric elements of the system were derived. TheO'Connell effect was faced with a two dark spot model. Moreover, theorbital period of the system was examined and two periodicities weredetected. Since the first one corresponds to the time interval for whichobservational data exist and the second was found to be half of the first,it turns out that none of them is true. Two other significant results thatcame from the present analysis are that the orbital period of AK Her doesnot follow a sinusoidal variation and that, from the times of minimumlight at primary and secondary eclipses, it seems that there is no apsidalmotion.     

Pulsations in the eclipsing variable system AS Camelopardalis

We performed photoelectric observations of AS Cam in 2002–2004. Five new times of minima were obtained. Their positions are consistent with the previously found light equation for the system and with the hypothesis that the difference between the observed (15°/100 yr) and theoretical (44°/100 yr) rates of apsidal motion results from the presence of a third body in the system. A Fourier analysis of two observational data sets, 1968–1970 and 2002–2004, reveals, with a high significance, periodic light variations with a frequency of ω ₀ = 1.0950 ± 0.0001d^?1 and an amplitude of ～0 _. ^m 020, which are probably caused by the radial pulsations of one of the components. We found a seasonal phase shift of these oscillations that may be produced by other periodic processes in the system. We show that the fairly large scatter of observed times of minima about the theoretical curve of the light equation can be explained by the presence of pulsations. Using the 2002 and 2004 observations as an example, we show that including the pulsations reduces this scatter.     

The Eccentric Eclipsing Binary V889 Aquilae

Several new times of minimum light recorded with photoelectric or CCD means have been gathered for the eccentric eclipsing binary V889 Aql (P = 11.1 days, e = 0.37). Its O–C diagram is presented, and improved elements of the apsidal motion and the light-time effect (LITE) are given. We found a long apsidal motion period of about 24 400 ± 2400 years and a period of the third body of about 52 ± 2 years.     

Triple systems showing apsidal motion

Binary systems showing both apsidal motion and light travel time (LTT) effects which cause orbital period changes in close binaries were studied. 15 triple systems showing apsidal motion were found by searching the literature, and a table including the important parameters of these systems was constructed. Six of the systems given in this table were selected and observed photometrically. Existence of both apsidal motion and LTT effects in all selected systems was investigated by means of the analysis of their eclipse times. The mean observed internal structure constants,  log = k _2,obs  , and contributions to the apsidal motion from the theory of General Relativity and the third/fourth bodies were calculated. The masses of the third/fourth bodies and some characteristics of their orbits were also calculated.     

A Three Body Solution for the DI Her System

The DI Herculis system has been extensively studied over the past few decades because its observed rate of apsidal advance is less than a quarter of that which is expected from its physical and orbital properties. Work by Khaliullin et al. (1991) proposed that this slow rate of apsidal advance is a result of the presence of a third (stellar mass) body orbiting the system, however, observations by Guinan et al. (1994) severely restrict the orbital properties of such a solution. We show that a planetary mass object in a highly inclined orbit relative to the binary is capable of producing the observed apsidal motion, while remaining within the bounds of the most recent set of observations. A wide range of stable solutions are possible.     

U,B, V light curves of CO Lacertae

CO Lacertae is one of the very few known binaries with both a short period of apsidal motion and good M, L, R data. Our newU, B, V light curves provide two times of minima and a check on Semeniuk's value forP _aps. This is the first published example of an eclipsing binary analysed in terms of a physical model (as opposed to a model based on spherical or ellipsoidal star figures) which allows for eccentric orbit effects. The light curves show some peculiarities — particularly a large, probably intrinsic, scatter.     

A two-colour photoelectric investigation of the eclipsing binary system AG Persei

The detached eclipsing binary system AG Per was observed at Ege University Observatory on 12 nights from December 1974 to December 1975. Approximately 460 observations were obtained in each yellow and blue. AG Per has long been known to have an apsidal motion and eccentricities. New apsidal motion parameters based on the author's observations and all of the other minima are given. Solutions for its orbital elements were carried out using three different procedures: the Kitamura method, Wood triaxial ellipsoid model and Kopal's Fourier analysis method in the frequency-domain. By use of the available spectroscopic data for AG Per, the observational apsidal motion constant has been calculated.     

Photometric Observations and Apsidal Motion Study of V1143 Cyg

Photometric observations of the eccentric eclipsing binary V1143 Cyg were performed during Aug.–Sep. 2000 and July 2002, in Johnson B and V bands. The analysis of both light curves was made separately using the 1998 version of Wilson’s LC code. In order to find a new observed rate of apsidal motion, we followed the procedure described by Guinan and Maloney (1985). A new observed rate of apsidal motion of 3^∘.72/100 yr was computed, which is close to the one reported earlier by Khaliullin (1983), Gimenez and Margrave (1985), and Burns et al. (1996).     

An o-c diagram analysis of PV cassiopeiae

Basing on recent and old photoelectric times of minimum, a new slightly longer period of the apsidal motion for an eclipsing binary PV Cas has been obtained. A difference between observed and theoretical periods of the apsidal motion estimated on the base of Claret and Gimenez models growed up to 30 years is found.     

Remarks on the period variation of HS Herculis and SW Cygni

In order to get a satisfactory understanding of the periodic variation of the orbital period in the binary system HS Herculis, the study of this problem is resumed. Using recently observed primary and secondary minima, it is evident that after 1955 (E > -2000) the corresponding O – C diagram reflects the effect of apsidal motion. Any assumption on the presence of a third body is rejected, at least as long as the current aspect of the O–C diagram is concerned. For the interpretation of the sinusoidal period variation of the semi-detached system SW Cygni, 130 primary minima were compiled form the literature. Though it is considered as very likely that this variation of the period is primarily caused by apsidal motion, the hypothesis of a third body is analysed too. Further precise photometric and spectroscopic observations are recommended.     

A new method for the analysis of apsidal motions in eclipsing binaries

In this paper, a new method for the determination of apsidal motion parameters in eccentric eclipsing binaries is presented. A sequential procedure has been followed throughout allowing an automatized on-line computation of the elements and their accuracies as well as a more realistic fit to the observed times of minima. A determination of individual mean errors for the parameters of fit give us the possibility to compare the results with available theoretical models of stellar structure. In the procedure, we have introduced a determination of preliminary elements by means of Fourier transform and extended the practical equations to terms up to the fifth power of the eccentricity. An application to the well-known case of the eclipsing binary GL Car has been made. Our analysis shows an apsidal motion period of 25.3 years with a value of 0.152 for the orbital eccentricity.     

Apsidal motion in the close binary IT cassiopeiae

In 1982 and 1993, we carried out highly accurate photoelectric WBVR measurements for the close binary IT Cas. Based on these measurements and on the observations of other authors, we determined the apsidal motion $\left[ {\dot \omega _{obs} = {{(11\mathop .\limits^ \circ 0 \pm 2\mathop .\limits^ \circ 5)} \mathord{\left/ {\vphantom {{(11\mathop .\limits^ \circ 0 \pm 2\mathop .\limits^ \circ 5)} {100 years}}} \right. \kern-0em} {100 years}}} \right]$ . This value is in agreement with the theoretically calculated apsidal motion for these stars $\left[ {\dot \omega _{th} = {{(14^\circ \pm 3^\circ )} \mathord{\left/ {\vphantom {{(14^\circ \pm 3^\circ )} {100 years}}} \right. \kern-0em} {100 years}}} \right]$ .     

A remark on the apsidal motion in slose binary systems

Dynamics of the apsidal motion in close binary systems are discussed. A comparison between the solution for the perfect fluid system and the solution for the rigid system reveals that some overall viscosity in the interior of distorted star has a right tendency to reconcile the observation of apsidal motion with the theory of internal structure.     

HS Herculis: Not apsidal motion,but a third body

Todoran's (1992) postulate of apsidal motion to explain the observed minimum times of HS Her is shown to be physically inconsistent. Instead, a third body in the system is postulated. Minimum timings in the next few years can settle the matter.