DI Herculis as a test of internal stellar structure and general relativity

Context. For the past three decades there has been a serious discrepancy between the observed and theoretical values of the apsidal motion rate $\dot\omega$ of the eccentric eclipsing binary DI Her, which has even been interpreted occasionally as a possible failure of general relativity (GR). A number of plausible explanations have been put forward. Recent observations of the Rossiter-McLaughlin effect have shown convincingly that the reason for the anomaly is that the rotational axes of the stars and the orbital axis are misaligned, which changes the predicted rate of precession significantly. Aims. Although the disagreement is now drastically smaller as a result of those measurements, it formally remains at the level of 50%, owing possibly to errors in the measured apsidal motion rate, outdated stellar models, or inaccuracies in the stellar parameters. The aim of this paper is to address each of these issues to improve the agreement even more. Methods. New times of minimum have been collected and used for redetermining of the apsidal motion rate. Based on the latest determinations of the absolute dimensions of the binary, we computed new stellar evolution models with updated physical inputs, and derived improved apsidal motion constants for the components. We performed Monte Carlo simulations to infer the theoretical distribution of $\dot\omega$, including the contributions from GR, as well as tidal and rotational distortions. All observational errors have been accounted for. Results. Our simulations yield a retrograde apsidal motion rate due to the rotationally-induced oblateness of - 0.00056 deg cycle-1 (mode of the distribution), a GR contribution of + 0.00068 deg cycle-1, and a tidal contribution of + 0.00034 deg cycle-1, leading to a total predicted rate of + 0.00046 deg cycle-1. This is in excellent agreement with the newly measured value of + 0.00042 deg cycle-1. The formal difference is now reduced to 10%, a small fraction of the observational uncertainties