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

Abstract

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.

Relativistic apsidal motion in eccentric eclipsing binaries

“…Before comparing the theoretical and observed k 2 , we carried out a careful comparison of the theoretical and observed absolute dimensions of each system. The comparison with the absolute dimensions of some systems can be found in Claret & Willems (2002) and in Claret (1997). The absolute dimensions of the remaining systems were compared with theoretical values and we found good agreement between values for a given isochrone, as required.…”

Absolute dimensions of eclipsing binaries

“…Theoretical values of log k 2 have been computed for the C-04 models in the framework of static tides; for dynamical tides, the effects of the compressibility of the stellar fluid (and resonances, if present) should be also considered (Claret & Willems 2002). For both V760 Sco and U Oph, the observed and theoretical values are in good agreement.…”

Absolute dimensions of eclipsing binaries

“…7.1, V1130 Tau points towards a lower He abundance and/or enrichment ratio than the four different Y, Z prescriptions adopted by the model grids studied. We refer to Casagrande et al (2007) for at recent determination of ΔY/ΔZ based on K dwarfs (2.1 ± 0.9), to Blaser (2006) for a HII based study (1.41 ± 0.62) with references to a variety of methods and results, and to and Claret & Willems (2002) for determinations based on samples of eclipsing binaries (2.2 ± 0.8 and 1.9 ± 0.6, respectively). We believe binaries can give an even better constraint, provided detailed heavy element abundance determinations become available for a sufficiently large sample 10 .…”