2021A&A...654A..17C

Context. The measurement of apsidal motion rates in eccentric eclipsing binaries is a unique way to gain insight into the internal structure of stars through the internal density concentration parameter, k₂. High-quality physical parameters of the stellar components, together with precise measurements of the advance of the periastron, are needed for the comparison with values derived from models.
Aims. As a product of the Transiting Exoplanet Survey Satellite (TESS) mission, high-precision light curves of a large number of eclipsing binaries are now available. Using a selection of well-studied, double-lined eccentric eclipsing binary systems, we aim to determine their apsidal motion rates and place constraints on the internal density concentration and compare with the predictions from state-of-the-art theoretical models.
Methods. We computed times of minimum light using the TESS light curves of 34 eclipsing binaries with precise absolute parameters. We used the changing difference over time between primary and secondary eclipse timings to determine the apsidal motion rate. To extend the time baseline, we combined the high-precision TESS timings with reliable archival data. On the other hand, for each component of our sample of double-lined eclipsing binaries, we computed grids of evolutionary stellar models for the observed stellar mass exploring ranges of values of the overshooting parameter f_ov, the mixing-length parameter, and the metallicity. To find the best solution for the two components we adopted a χ² statistic to infer the optimal values of the overshooting parameter and the mixing-length parameter. The theoretical internal structure constants to be compared with the observed values were calculated by integrating the differential equations of Radau for each stellar model.
Results. We have determined the apsidal motion rate of 27 double-lined eclipsing binaries with precise physical parameters. The obtained values, corrected for their relativistic contribution, yield precise empirical parameters of the internal stellar density concentration. The comparison of these results with the predictions based on new theoretical models shows very good agreement. Small deviations are identified but remain within the observational uncertainties and the path for a refined comparison is indicated.