DI Her作为恒星内部结构和广义相对论的检验：新的拱点运动速率和演化模型
DI Her as a test of internal stellar structure and General Relativity: New apsidal motion rate and evolutionary models
摘要：
在过去的三十年里，直到最近，偏心食双星DI Her的拱点运动速率dw/dt的观测值和理论值之间一直存在严重的差异，这甚至偶尔被解释为广义相对论（GR）的可能失败。最近对罗斯特-麦克劳克林效应的观测令人信服地表明，异常的原因是恒星的旋转轴和轨道轴不对齐，这会显着改变预测的岁差率。虽然由于这些测量的结果，现在的分歧大大减小，但它仍然保持在50%的水平，可能是由于测量的拱点运动速率的误差，过时的恒星模型，或恒星参数的不准确。在此，我们将逐一讨论这些问题，以便进一步改进协议。为了重新确定拱点运动速率，收集了新的最小时间。我们计算了新的恒星演化模型与更新的物理输入，并推导出改进的拱点运动常数的组件。我们已经进行了蒙特卡罗模拟来推断dw/dt的理论分布，包括来自GR以及潮汐和旋转畸变的贡献。所有的观测误差都已计算在内。我们的模拟产生了一个逆行拱点运动速率，由于旋转引起的扁率为-0.00056度/周期（分布模式），GR贡献为+0.00068度/周期，潮汐贡献为+0.00034度/周期，导致总预测速率为+0.00046度/周期。这与最新测量值+0.00042度/循环非常一致。形式上的差异现在减少到10%，这只是观测不确定性的一小部分。（节略）
英文摘要：
For the past three decades, and until recently, there has been a serious discrepancy between the observed and theoretical values of the apsidal motion rate dw/dt of the eccentric eclipsing binary DI Her, which has even been interpreted occasionally as a possible failure of General Relativity (GR). 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. Although as a result of those measurements the disagreement is now drastically smaller, it remains formally at the level of 50%, possibly due to errors in the measured apsidal motion rate, outdated stellar models, or inaccuracies in the stellar parameters. Here we address each of these issues in order to improve the agreement further. New times of minimum have been collected in order to redetermine the apsidal motion rate. We have computed new stellar evolution models with updated physical inputs, and derived improved apsidal motion constants for the components. We have performed Monte Carlo simulations to infer the theoretical distribution of dw/dt, including the contributions from GR as well as tidal and rotational distortions. All observational errors have been accounted for. Our simulations yield a retrograde apsidal motion rate due to the rotationally-induced oblateness of -0.00056 deg/cycle (mode of the distribution), a GR contribution of +0.00068 deg/cycle, and a tidal contribution of +0.00034 deg/cycle, leading to a total predicted rate of +0.00046 deg/cycle. This is in excellent agreement with the newly measured value of +0.00042 deg/cycle. The formal difference is now reduced to 10%, a small fraction of the observational uncertainties. (abridged)
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