Astron. Astrophys. 327, 11-21 (1997)

1. Introduction

Due to the tidal and rotational distortions present in stars which belong to eclipsing binaries there is a secular change in the position of the periastron if the orbit is eccentric. Such distortions can be described as a function of the internal structure constant - hereafter . Moreover, there is a relativistic contribution for the periastron shift in a similar way that occurs with the orbit of the planet Mercury.The resulting apsidal motion can be monitored by observing the time of minima. The apsidal motion test to the stellar structure and evolution has been used to contrast observational data of eclipsing binaries with theoretical predictions of the mass concentration derived from evolutionary models. Given the wide range of masses observed in eccentric binary systems it is possible to investigate the interior of the stars under different physical conditions. This test is also important since the direct comparison between the observed and theoretical predictions of the apsidal motion ate is performed only after previous tests concerning stellar models (like radii, effective temperatures and isochrones) have been done with success. In this sense it is a complementary test to the stellar evolution theory.

We have already performed a comparison between observations and theory for about 20 systems with accurate absolute dimensions and apsidal motion rate determinations (Claret & Giménez 1993a, 1993b). The importance of the good determination of absolute dimensions is obvious since the observed internal structure constant depends on the mass, eccentricity, rotational velocities, and more strongly, on the radius of the components (as R^-5). There are many systems showing observational evidence of apsidal motion (see for example Giménez 1994) but lacking a good scanning of time of minima and/or a good determination of masses and radii. This fact limits severely the study on the internal structure constants, although a sufficient number of adequate systems is now available.

The eclipsing binaries which present apsidal motion are also useful to test the predictions of the General Relativity - GR - for the periastron advance. In the papers quoted above we have only analysed the systems for which the relativistic contribution to the total apsidal motion were small. The results from these papers indicated that using new opacity calculations, core overshooting, rotation, improved orbital elements and recent apsidal motion rates the theoretical predictions are in good agree ment with observations. The old problem, that real stars seemed to be more mass concentrated than predicted by theory, was solved or at least minored. As we did not know a priori which was the cause for these discrepancies we have separated the systems presenting high relativistic contributions in order to avoid these disagreements with the theory to be attributed to relativistic effects. In this way we have divided our investigation in two parts: one concerning the non-relativistic systems (Claret & Giménez 1993a, b) and the present work probing the relativistic ones. As the name indicates, the relativistic systems are those for which the advance of the periastron predicted by the GR is comparable with the classical contribution. Moreover, the separation in two classes is justified given that the observations for some relativistic systems, DI Her and AS Cam, do not seem to be in agree nt with GR predictions. An alternative theory for the periastron shift was presented by Moffat (1984, 1989) and, in principle, it was able to explain such systems. However, such theory presents some problems which will be discussed later in this paper (Sect. 4).

The magnitude of the discrepancy found in DI Her (see for example Guinan & Maloney, 1985) demands an analysis in a separate paper (Claret 1997b). For this binary we have very good absolute dimensions determination and the discrepancy can not be attributed to errors in the radii and masses. Even if we take the mass point model to represent DI Her the disagreement remains. Another interesting case is AS Cam. But this system will not be analysed because it does not present the basic requirements this kind of investigation (good absolute dimension determination). Moreover, there are some discussions on the observed apsidal apsidal motion rate (Krzesinski et al. 1990; Maloney et al. 1991).

In this paper we perform a comparison of the observational data with the theoretical predictions concerning apsidal motion rates for the relativistic systems which fulfil the basic requirements. In the following sections we will discuss the astrophysical data for the eclipsing binaries used in the analysis, and the equations which govern the apsidal motion rate are presented. Next the observed astrophysical parameters are contrasted against the theoretical ones (including ages). Finally, we compare the observed apsidal motion rates with those predicted theoretically including the results based on the work by Moffat.

© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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