Apsidal motion in the eclipsing binary system OX cas

Multi-colourWBVR photoelectric observations of the eclipsing binary OX Cas were carried out. The photometric elements, absolute parameters and the angular rate of the apsidal motion ( = 9.1 deg yr^–1 were obtained. The apsidal parameterk ₂ derived for this system is by 15–25% smaller than the theoretical parameterk ₂.     

Apsidal motion in the eclipsing binary system HP Aur

Multi-colourWBVR photoelectric observations of the eclipsing binary HP Aur were carried out. The photometric elements, the absolute parameters and the apsidal motion angular rate of HP Aur based on the comparison of our observations and the observations Meinunger (1980) obtained were presented. The derived value of is almost three times smaller than that predicted theoretically.     

Apsidal motion in the eclipsing binary system V 451 Ophiuchi

MulticolourWBVR photoelectric observations of the eclipsing binary V 451 Oph were carried out, and a highly accurate light curve was obtained. The angular velocity of the orbital rotation, =2.1 deg yr^–1, and the apsidal motion constantk ₂=0.0045 are given.     

Apsidal motion in the eclipsing binary system of BW AQR

The first photoelectric light curve of the eclipsing binary system BW Aqr (F71V+F81V;P=6^d.7;V=10 ^m .31), discovered by Miss Leavitt at the beginning of the century, was obtained. The photometric elements were detemined. The components of this system are considerably evolved stars: the age of the system is about 2×10⁹ yr. It follows from the photometric data that the secondary component should have greater mass than the primary one The zero-age spectral classes of components were F2V and F1V. The system has an elliptical orbit with the eccentricitye=0.18. The angular rate of the apsidal motion (_obs = 0.070 deg yr^–1) and the corresponding value of the apsidal parameterk ₂=0.0090 (the relativistic term included) were found. The derived valuek ₂ exceeds by more than a factor of 2 the theoretical coefficient obtained from the modern theory of internal structure of stars with moderate masses .     

Apsidal rotation in the eclipsing binary AG Persei

New three-filter light curves of AG Per are given. These yield times of minimum light in accord with the known rate of apsidal rotation but do not improve that rate. These light curves and all other published historical ones have been treated with the code EBOP and are shown to give largely consistent geometric and photometric parameters no matter which orientation of the orbit is displayed to the observer.     

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 $\left[ {\dot \omega _{th} = {{(14^\circ \pm 3^\circ )} \mathord{\left/ {\vphantom {{(14^\circ \pm 3^\circ )} {100 years}}} \right. \kern-0em} {100 years}}} \right]$ .     

The evolution of eccentricity in the eclipsing binary system AS Camelopardalis

In 2002,2004 and 2017 we conducted high precision CCD photometry observations of the eclipsing binary system AS Cam.By analysis of the light curves from 1967 to 2017(our data + data from the literature) we obtained photometric elements of the system and found a change in the system's orbital eccentricity of ?e = 0.03 ± 0.01.This change can indicate that there is a third companion in the system in a highly inclined orbit with respect to the orbital plane of the central binary,and its gravitational influence may cause the discrepancy between observed and theoretical apsidal motion rates of AS Cam.     

Study of the apsidal motion in the eclipsing binary MZ Lac

A series of highly accurate photoelectric observations of the eclipsing binary MZ Lac was obtained with a 48-cm AZT-14 reflector at the Tien-Shan High-Altitude Station of the Sternberg Astronomical Institute from 1985 to 2004 to study its apsidal motion. We constructed a consistent system of physical and geometrical parameters of the components and the binary’s orbit: we determined their masses (M₁ = 1.50M_⊙, M₂ = 1.29M_⊙), radii (R₁ = 1.86R_⊙, R₂ = 1.35R_⊙), luminosities (L₁ = 0.79L_⊙, L₂ = 0.45L_⊙), surface gravities (log_g1 = 4.06, log_g2 = 4.27), age (t = 1.9 × 10⁹ yr), and the distance to the binary (d = 510 pc). The binary exhibits apsidal motion with the period U_obs = 480 ± 40 yr, while its theoretically expected value is U_th = 450 ± 40 yr. Spectroscopic studies of MZ Lac and calculations of the absolute parameters of the components are required to test our conclusions.     

Photometric elements and apsidal motion of the eclipsing binary NSV 18773

The photometric elements of the eclipsing binary NSV 18773 (HD 99898) have been determined for the first time by analyzing its V-and I-band light curves from the ASAS-2 and ASAS-3 catalogs. Based on these elements and using other published spectroscopic and photometric data, we constructed a consistent system of geometrical and physical parameters for the system that consists of two stars (M ₁ = 20M _⊙, Sp₁=B0V, R ₁ = 5.0R _⊙ and M ₂ = 14M _⊙, Sp₂ = B1V, R ₂ = 6.5R _⊙) in elliptical orbits (P = 5 _. ^d 049, e = 0.365, a = 40.1R _⊙). The distance to the system is d = 3.3 kpc, the interstellar extinction is A _V = 2 _. ^m 0, and the age is t = 2.8 × 10⁶ yr. NSV 18773 is a visual binary with components V _A = 9 _. ^m 9 and V _B = 10 _. ^m 3 separated by 0 _. ^" 8. The third light (L ₃ = 0.61) that we found by analyzing the light curves shows that the eclipsing binary is the system’s fainter component B. We confirmed the rapid apsidal motion of the star detected by Otero and Wils (2006) and refined its observed period: U _obs = 150 ± 6 yr. Our photometric elements and physical parameters allowed the apsidal parameter $\bar k_2^{obs} = 0.0135(14)$ , which reflects the density distribution along the radii of the component stars, to be determined. Within the error limits, the derived parameter agrees with its theoretically expected value, $\bar k_2^{th} = 0.0119(8)$ , from current evolutionary models of stars of the corresponding masses and ages.     

Light-time orbit and apsidal motion of the eclipsing binary U Ophiuchi

A comprehensive period study of the times of minima observed from 1881 to 1985 has been performed. Previous interpretations of the O–C diagram based on light-time effect are confirmed. The light-time orbit of U Oph has been revised using a differential corrections procedure. We get an eccentric orbit withe=0.22±0.06,P=38.7±0.2 yr, and a mass function . In addition, our analysis has revealed short-period apsidal motion (U/P=4515±75) in a slightly eccentric close orbit (e=0.0031±0.0003), allowing a reliable determination of the density concentration coefficient,k ₂=0.0059±4. A comparison with stellar evolutionary models calculated by Jeffery (1984) yields the helium contentY=0.28±0.05 and an age of 3×10⁷ yr for the components of U Oph.     

On the relativistic motion of the periastron in the eclipsing binary system DI Herculis

An analysis of fifteen-year photoelectric observations of DI Herculis shows that the upper estimate for the relativistic part of apsidal motion in this binary system is almost three times lower than the theoretical value. The total observed angular velocity of apsidal rotation is 0 _. ^° 0124 yr^–1. The relativistic part is less than 0 _. ^° 008 yr^–1 instead of 0 _. ^° 023 yr^–1 required by the theory.     

Apsidal motion elements of three eccentric eclipsing binaries: V397 Cep,V493 Car and BW Aqr

The apsidal motion analysis of the eccentric eclipsing binaries: V397 Cep, V493 Car and BW Aqr have been presented. The method described by Lacy (1992) [Lacy, C.H S., 1992. AJ 104, 2213] has been used for the apsidal motion analysis. The apsidal motion periods have been found to be 174.2 ± 1.4, 277.3 ± 21.3 and 7195 ± 174 years for V397 Cep, V493 Car and BW Aqr, respectively.     

Envelopes in eclipsing binary systems

The present paper consists a discussion of (1) the relevance of envelopes to the study of the light curves of eclipsing binaries, (2) the disk envelope, and (3) the spherical envelope. They are separately considered in three sections, each of which is further divided into subsections. To the fourth section a brief concluding remark is appended.Originally presented at the IAU Colloquium No. 16 held at the University of Pennsylvania, Philadelphia, Pa, U.S.A., September 8–11, 1971.     

Gravitational lensing in eclipsing binary stars

I consider the effect of the gravitational deflection of light upon the light curves of eclipsing binary stars, focusing mainly upon systems containing at least one white dwarf component. In absolute terms the effects are small, however they are strongest at the time of secondary eclipse when the white dwarf transits its companion, and act to reduce the depth of this feature. If not accounted for, this may lead to under-estimation of the radius of the white dwarf compared with that of its companion. I show that the effect is significant for plausible binary parameters, and that it leads to ∼25 per cent reduction in the transit depth in the system KPD 1930+2752. The reduction of eclipse depth is degenerate with the stellar radius ratio, and therefore cannot be used to establish the existence of lensing. A second-order effect of the light bending is to steepen the ingress and egress features of the secondary eclipse relative to the primary eclipse, although it will be difficult to see this in practice. I consider also binaries containing neutron stars and black holes. I conclude that, although relatively large effects are possible in such systems, a combination of rarity, faintness and intrinsic variability makes it unlikely that lensing will be detectable in them.     

Convergence of eclipsing binary solutions

Attention is called to the fact that convergence to negligible corrections in differential corrections solutions usually can be achieved, provided that one or both of two common causes of poor convergence are recognized and properly dealt with.     

Photometric elements,apsidal motion,and a third body in the eclipsing binary HP Aur

Highly accurate W BV R photometric measurements of the eclipsing binary HP Aur were performed in 2002–2003 with the 48-cm AZT-14 reflector at the Tien-Shan High-Altitude Observatory to determine the rate of apsidal motion. A consistent system of physical and geometrical parameters of the components and the binary as a whole has been constructed for the first time by analyzing these new measurements together with other published data: we determined their radii (R₁ = 1.05R_⊙, R₂ = 0.82R_⊙) and luminosities (L₁ = 1.10L_⊙, L₂ = 0.46L_⊙), spectral types (G2V + G8V) and surface gravities (log g₁ = 4.38, log g₂ = 4.51), age (t = 9.5 × 10⁹ yr), and the distance to the binary (d = 197 pc). We detected an ultraviolet excess in the spectra of both components, \(\Delta (W - B) \simeq - 0\mathop .\limits^m 25\), that is probably attributable to a metal deficiency in the atmospheres of these stars. In this system of two solar-type stars, we found a third body with the mass M₃ sin i ₃ ³ = 0.17_M⊙ that revolved with the period P₃ = 13.7 yr around the eclipsing binary in a highly eccentric elliptical orbit: e₃ = 0.70 and A₃ sin i₃ ? 7 AU. The orbit of the eclipsing binary itself was shown to be also elliptical, but with a low eccentricity (e = 0.0025(5)), while apsidal motion with a period U_obs > 80 yr was observed at a theoretically expected period U_th ≈ 92 yr. At least 20 to 30 more years of photoelectric measurements of this star will be required to reliably determine U_obs.     

The eclipsing binary AB Andromedae

In this paper the two newB- andV-light curves of the eclipsing variable star AB Andromedae, obtained during 1979 with the 48 in reflector of the National Observatory of Athens, are represented and discussed. General information of the system is given in the Introduction, while in Section 2 some observational and reductional details are given and the new light curves are represented. Section 3 deals with the period of the system and, finally, in Section 4 a general discussion is given.     

The eclipsing binary BW Draconis

In this paper theB- andV-light curves of the eclipsing binary BW Draconis made at Kryonerion Station of the National Observatory of Athens during 1980 and 1981 are presented.     

The eclipsing binary WX Eridani

The Algol type eclipsing binary WX Eridani was observed on 21 nights with the 48-inch telescope of the Japal-Rangapur Observatory during 1973–74 and 1974–75 seasons in UBV colors. An improved period ofP=0^d.82327038 was obtained from the analysis of the times of five primary minima. Standstills between phase angles 50–80°, 100–130°, 230–260° and 280–310° were present in the light curves. The analysis of the light curves indicated the eclipses to be grazing with the primary a transit and the secondary an occultation. Elements derived from the solution of the light curve using Russell-Merrill method are given. From the comparison of the fractional radii with Roche lobes, it is concluded that none of the components has filled its respective Roche lobe. The spectral type of the primary component is estimated to be F3 and it is found to be a -scuti type variable pulsating with two periods equal to one-fifth and one-sixth of the orbital period.     

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.