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Home All issues Volume 527 (March 2011) A&A, 527 (2011) A43 Full HTML
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Issue
A&A
Volume 527, March 2011
Article Number A43
Number of page(s) 4
Section Stellar structure and evolution
DOI https://doi.org/10.1051/0004-6361/201015720
Published online 24 January 2011

© ESO, 2011

1. Introduction

The eccentric eclipsing binaries (EEBs) provide a great opportunity for studying the stellar structure of the stars as well as testing the General Relativity outside the solar system. The O − C diagram analysis, which investigates the revolution of the line of apsides in the system has been described elsewhere, e.g. 7, 8. Nevertheless, new contributions to this topic with new systems are still welcome, especially for cases where the apsidal motion period is adequately short and a few periods are covered. This is the case for the two somewhat neglected systems V456 Oph and V490 Cyg.

1.1. V456 Oph

V456 Oph (=AN 108.1935 = SAO 123842, Vmax = 9.95 mag) has been discovered as a variable star by 11, with the remark that it is a “short-periodic one, but probably not rapidly changing”. After than 9 incorrectly classified the star as a δ Cep one with a preliminary period of about 14.6 d. No such variation has been detected with the present data. The only spectral classification is that by 24, who indicated the spectral type A5, but with a remark that because of underexposed plates and uncertain ephemerides this classification is not very secure.

Although the first photoelectric light curve has been published by 5, there was no light curve analysis of the system performed until today. The same applies to the spectroscopic analysis, which has not yet been carried out, so the mass ratio of the pair in not known. 27 included the binary in the catalogue of systems located in the instability strip, which means that it possibly contains a δ Scu component. However, no indication of pulsations in V456 Oph has been detected.

1.2. V490 Cyg

V490 Cyg (=AN 76.1939, Vmax = 12.81 mag) is an Algol-type eclipsing binary, even though the SIMBAD database lists V490 Cyg as a β Lyrae one. The system has been discovered as a variable by 32, and its light curve coverage is too poor for any reliable analysis. Its spectral type was derived to be F8, while 28 give an estimate of the spectral types F8+[G4]. 10 included this system in his list of stars with possible apsidal motion, but since then it was not studied in detail. Other credible information about the physical properties of the components is missing because there is so little spectroscopy and photometry of this system.

2. The period analysis

2.1. V456 Oph

The set of published times of minima for V456 Oph is quite extensive, covering more than 70 years. Regrettably, the old minima are only photographic and their scatter is so large that one cannot use them for any reliable analysis. We used only the more precise photoelectric and CCD ones, which were published after 1970. These minima roughly follow the linear ephemerides given in GCVS, but there some variations are clearly visible.

We tried to collect all available minima times and also to derive some new ones. A few of the already published ones were recalculated once again and corrected for the final analysis. Besides these minima times, we also used the photometry of V456 Oph obtained with the robotized and automated telescopes working today. These are

thumbnail Fig.1

O − C diagram of V456 Oph. The lines represent the fit according to the apsidal motion hypothesis (see text and Table 2), the solid line stands for the primary, while the dashed line stands for the secondary minima, dots stand for primary and open circles for the secondary minima. The black line near the bottom axis represents the time interval covered with the OMC data used for the light curve analysis.

Sixteen new minima times were derived from these surveys, and some of the published ones were computed again (see Table 1). Our new minima times were observed in the Ondřejov observatory with the 65-cm telescope. We used the 17 method for all these minima. The mean linear light elements suitable for observations are Prim. Min.=2453923.9358+1.01600124·E,\begin{equation} \mathrm{Prim.~Min.} = 2453923.9358 + 1.01600124 \cdot \mathrm{E}, \end{equation}(1)which were also used for deriving the proper epochs and types of the minima times written in Table 1.

If we plot these data points in the O − C diagram, the difference between primary and secondary minima is clearly visible. Following the method of apsidal motion analysis as described in 7, we tried the computation with orbital inclination i = 90° for the first time. After that we used for the second attempt the inclination i = 87.88° (see Sect. 3), which resulted in almost the same parameters (owing to the term cot2(i), which is nearly 0 for our inclination). In Fig. 1 we plot the final fit with the apsidal motion hypothesis on all used data points. This leads to the parameters of the motion of apsides given in Table 2. All uncertainties of the parameters were calculated from the covariance matrix of the fit and from the uncertainty of the inclination. Evidently the apsidal period is very short, about only 23 yr, which places this system among one those with the shortest apsidal motion.

Table 1

New and recalculated CCD minima times of V456 Oph.

Table 2

The parameters of the apsidal motion fit for V456 Oph and V490 Cyg.

2.2. V490 Cyg

The system V490 Cyg has much lower published times of minima observations. The first rough times-of-minima estimates are those by 33 from his photometry in the 1930’s, but these have such a large scatter that they cannot be used for any reliable analysis. However, he also noticed that the secondary minimum is not symmetric with regards to the primary one. Nevertheless, a possible eccentricity and apsidal motion have never been studied since then. The more precise photoelectric and CCD observations have been measured since 1999, but there are only 12 published minima.

A few new CCD observations were obtained in the Ondřejov observatory with the same telescope as for V456 Oph, and two new minima times were also derived from the INTEGRAL/OMC data. The new measurements and the already published ones are presented in Table 3. The suitable linear ephemerides for observations are Prim. Min.=2451491.6075+1.14023698·E,Sec. Min.=2451491.5802+1.14023698·E.\begin{eqnarray} \mathrm{Prim.~Min.} & = & 2451491.6075 + 1.14023698 \cdot \mathrm{E}, \\ \mathrm{\,\,Sec.~Min.} & = & 2451491.5802 + 1.14023698 \cdot \mathrm{E}. \end{eqnarray}

Table 3

New and already published minima times of V490 Cyg.

The minima times presented in Table 3 were used for the period analysis, which we did by applying the apsidal motion hypothesis. The only difference in analysis between V490 Cyg and V456 Oph was the assumption of an inclination i = 90° for V490 Cyg because we had no light curve analysis. The difference between primary and secondary is clearly visible, reaching up to 47 minutes, which is surprisingly high for a binary with such a short orbital period. The analysis led to the parameters of the apsidal motion presented in Table 2. Obviously the resulting value of the apsidal motion period of about 18.8 years is even shorter than for V456 Oph; we are therefore dealing with the shortest apsidal motion period known among the EEBs today.

thumbnail Fig.2

O − C diagram of V490 Cyg. The lines represent the fit according to the apsidal motion hypothesis (see text and Table 2), the solid line stands for the primary, while the dashed line stands for the secondary minima, dots stand for the primary and open circles for the secondary minima.

3. Light curve analysis

The whole light curve of V456 Oph was observed with the OMC camera onboard the INTEGRAL satellite, a description of which is given in 20. The standard V filter was used, but the optical telescope has an aperture of only 5 cm in diameter. We obtained several hundred observations, of which we used 449 for the analysis.

The programme PHOEBE (ver. 0.29, Prša & Zwitter 2005), based on the Wilson-Devinney algorithm (Wilson & Devinney 1971) was used for the analysis. The “detached binary” mode (in Wilson & Devinney mode 2) was used with several assumptions. First, the ephemerides (HJD0 and P) and the apsidal motion parameters (e, ω, and $\dot \omega$) were adopted from the period analysis, because the minima times cover a longer time span, therefore these quantities are derived with higher precision. Secondly, the mass ratio q and temperature of the primary component T1 were set and the other relevant parameters were adjusted for the best fit. We changed the q and T1 values in the wide range of values to obtain the best fit according to the rms value and also the physical plausibility of the fit. This means during that the fitting process we scanned the parameter space in q ranging from 0.1 to 1.2 and in T1 from 15400 K to 6500 K.

We fitted the other light curve parameters, which are the luminosities L1 and L2 in the V filer, the temperature of the secondary T2, the inclination i, the Kopal’s modified potentials Ω1 and Ω2, the synchronicity parameters F1 and F2, the third light l3. The limb-darkening coefficients were automatically interpolated by the PHOEBE programme from van Hamme’s tables (see van Hamme 1993), using the linear cosine law for the values of Teff and log g of both components resulting from the analysis. The values of the gravity brightening and bolometric albedo coefficients were set at their suggested values for convective atmospheres (see Lucy 1968), i.e. G1 = G2 = 0.32, A1 = A2 = 0.5.

thumbnail Fig.3

PHOEBE light curve solution of V456 Oph based on the OMC data, the solid line represents our final solution (see the text and Table 4).

Table 4

The light curve parameters of V456 Oph.

The best fit was achieved with the light curve parameters given in Table 4, and the figure with the final fit is plotted in Fig. 3. Nonzero eccentricity is clearly visible from this plot, which is quite surprising in a binary with such a short orbital period. No other EEB with a shorter period is known today. The value of the third light is l3 = (0 ± 4)%, which indicates that there is no other visible companion to the system in the V filter (under the assumption that this component is also located on the main sequence). We made several attempts with nonzero values of the third light, but these did not lead to a satisfactory solution.

Because there is no spectroscopic analysis, the precise physical parameters cannot be computed directly, but need to be roughly estimated with the assumption that both components are located on the main sequence. We derived the following values: M1 = 1.46   M⊙, M2 = 1.41   M⊙, R1 = 1.51   R⊙, R2 = 1.49   R⊙. These are only very preliminary values, but lead to spectral types of about F1 + F2 for the two components. We obtained roughly the same result (F0+F1) with the standard mass-luminosity relation for the main sequence stars (e.g. Malkov 2007), applying the luminosity ratio derived from the light curve analysis.

The parameters are very different from what one could expect for a main sequence star of spectral type A5 (Roman 1956), and the masses are also different from those estimated by Brancewicz & Dworak (1980), but the presented values provided the best light curve fit, and the parameters of the apsidal motion also agree well with the theoretical values (see below). The spectral type presented by Roman (1956) was only estimated on the basis of poor photographic spectra. On the other hand, there is also the BVR photometry in the NOMAD catalogue (Zacharias et al. 2004), from which B − V = 0.279   mag and V − R = 0.165   mag. These values indicate (Houdashelt et al. 2000) that the temperature of the system is about 6500 K, therefore of the spectral type about of F5.

4. Discussion

For the light curve analysis of the system V456 Oph the ephemerides and the apsidal motion parameters were fixed, but another approach could be to compute these parameters directly also from the light curve. The problem is that the data coverage for the light curve is rather fairly in time (about only 1/5 of the apsidal period), and the data for the light curve have relatively high scatter as well.

The eclipsing binaries, V456 Oph and V490 Cyg, with their respective apsidal motion periods of about only 20 years place these systems among a few unique ones with apsidal periods below 30 years (see Table 5).

Table 5

The EEBs with the shortest apsidal motion period.

Our next task was to derive the averaged internal structure constant as well and to compare it with the theoretical value. This task was done after subtraction of the relativistic term, which resulted for V456 Oph in the value $\dot \omega_{\mathrm{rel}} = 0.0011~\mathrm{deg/cycle}$, about only 2.5% of the total apsidal motion rate. Therefore, the internal structure constant is

log k 2 ,   obs = − 2.44 ± 0.20. $$ \log k_{\mathrm{2,~obs}} = -2.44 \pm 0.20. $$

The surprisingly high value of the uncertainty is mainly caused by the error of the relative radii from the light curve analysis. We can compare this value with the stellar evolution grids (e.g. by Claret 2004) and the theoretical values of k2,theor. Using the value of log M = 0.1725 (M = 1.49   M⊙), we obtained the value of

log k 2 , theor = − 2.41 ± 0.05 $$ \log k_{\mathrm{2,theor}} =-2.41 \pm 0.05 $$

for the main sequence star with an age between 0 and 1.5    ×    109 yr. This could be interpreted as a rough estimation of maximum age for this system. No other eccentric eclipsing binary with such a late spectral type is known today. Therefore a detailed analysis of its spectra would be very welcome.

5. Conclusions

We performed the first detailed photometric and period analysis of the two eclipsing systems V456 Oph and V490 Cyg, which yielded the parameters of the apsidal motion with periods of about only 23 and 19 years. With the orbital period of V456 Oph of only about 1.016 days we are dealing with the shortest orbital period among the apsidal motion systems, while the period of apsidal motion of 18.8 years of V490 Cyg makes this system the shortest among the EEBs. However, because we lack a spectroscopic analysis, some of the physical parameters were only roughly estimated and apparently contradict each other. New times of minima observations as well as a detailed spectroscopic analysis are needed.

Acknowledgments

Based on data from the OMC Archive at LAEFF, pre-processed by ISDC. We thank the “ASAS” team and also the “Pi of the sky” team for making all of the observations easily public available. This work was supported by the Czech Science Foundation grant no. P209/10/0715 and also by the Research Programme MSM0021620860 of the Czech Ministry of Education. Mr. Anton Paschke is also acknowledged for sending us his photometric data and also Mr. Kamil Hornoch for the observational assistance. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and of NASA’s Astrophysics Data System Bibliographic Services.

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All Tables

Table 1

New and recalculated CCD minima times of V456 Oph.

In the text
Table 2

The parameters of the apsidal motion fit for V456 Oph and V490 Cyg.

In the text
Table 3

New and already published minima times of V490 Cyg.

In the text
Table 4

The light curve parameters of V456 Oph.

In the text
Table 5

The EEBs with the shortest apsidal motion period.

In the text

All Figures

thumbnail Fig.1

O − C diagram of V456 Oph. The lines represent the fit according to the apsidal motion hypothesis (see text and Table 2), the solid line stands for the primary, while the dashed line stands for the secondary minima, dots stand for primary and open circles for the secondary minima. The black line near the bottom axis represents the time interval covered with the OMC data used for the light curve analysis.
In the text
thumbnail Fig.2

O − C diagram of V490 Cyg. The lines represent the fit according to the apsidal motion hypothesis (see text and Table 2), the solid line stands for the primary, while the dashed line stands for the secondary minima, dots stand for the primary and open circles for the secondary minima.
In the text
thumbnail Fig.3

PHOEBE light curve solution of V456 Oph based on the OMC data, the solid line represents our final solution (see the text and Table 4).
In the text

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