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For the past three decades, and until recently, there has been a seriousdiscrepancy between the observed and theoretical values of the apsidal motionrate dw/dt of the eccentric eclipsing binary DI Her, which has even beeninterpreted occasionally as a possible failure of General Relativity (GR).Recent observations of the Rossiter-McLaughlin effect have shown convincinglythat the reason for the anomaly is that the rotational axes of the stars andthe orbital axis are misaligned, which changes the predicted rate of precessionsignificantly. Although as a result of those measurements the disagreement isnow drastically smaller, it remains formally at the level of 50%, possibly dueto errors in the measured apsidal motion rate, outdated stellar models, orinaccuracies in the stellar parameters. Here we address each of these issues inorder to improve the agreement further. New times of minimum have beencollected in order to redetermine the apsidal motion rate. We have computed newstellar evolution models with updated physical inputs, and derived improvedapsidal motion constants for the components. We have performed Monte Carlosimulations to infer the theoretical distribution of dw/dt, including thecontributions from GR as well as tidal and rotational distortions. Allobservational errors have been accounted for. Our simulations yield aretrograde apsidal motion rate due to the rotationally-induced oblateness of-0.00056 deg/cycle (mode of the distribution), a GR contribution of +0.00068deg/cycle, and a tidal contribution of +0.00034 deg/cycle, leading to a totalpredicted rate of +0.00046 deg/cycle. This is in excellent agreement with thenewly measured value of +0.00042 deg/cycle. The formal difference is nowreduced to 10%, a small fraction of the observational uncertainties. (abridged)

DI Her as a test of internal stellar structure and General Relativity: New apsidal motion rate and evolutionary models