[论文解读] DI Her as a test of internal stellar structure and General Relativity: New apsidal motion rate and evolutionary models

A. Claret, Guillermo Torres+1 more|arXiv (Cornell University)|Feb 15, 2010

Stellar, planetary, and galactic studies被引用 12

一句话总结

本研究通过结合新的光度观测、采用改进物理解释的更新版恒星演化模型，以及考虑自转轨道倾角偏差的蒙特卡洛模拟，解决了双星系统 DI Her 中长期存在的近日点运动速率差异问题。修订后的理论预测值为+0.00046°·cycle⁻¹，与新的观测速率+0.00042°·cycle⁻¹高度一致，理论与观测之间的差异仅剩10%，从而证实了广义相对论，并解决了天体物理学中持续数十年的谜题。

ABSTRACT

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smaller, it remains formally at the level of 50%, possibly due to errors in the measured apsidal motion rate, outdated stellar models, or inaccuracies in the stellar parameters.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)

研究动机与目标

• 解决广义相对论关键测试系统 DI Her 中观测与理论近日点运动速率之间长期存在的400%差异。
• 探究该异常是否源于测量误差、过时的恒星模型，或不准确的恒星参数。
• 通过整合近期关于自转轨道倾角偏差的 Rossiter-McLaughlin 测量结果，弥合观测数据与理论预测之间的差距。
• 利用更新的物理解释和绝对尺寸参数，提升近日点运动常数与演化模型的精度。
• 证明当前观测的近日点运动速率与理论预测高度一致，从而验证该系统中广义相对论的有效性。

提出的方法

• 收集新的最小时刻光度观测数据，以更高精度重新测定近日点运动速率。
• 基于更新的物理解释（如灰度、状态方程）和更精确的双星绝对尺寸，构建新的恒星演化模型。
• 根据新模型计算两颗恒星的近日点运动常数（k₂），并考虑中心集中效应。
• 执行蒙特卡洛模拟以传播观测不确定性，并计算总近日点运动速率的理论分布。
• 在模拟中纳入广义相对论、潮汐形变以及旋转引起的扁率贡献。
• 将 Albrecht 等人（2009年）提供的 Rossiter-McLaughlin 效应参数（λ, v sinβ）作为输入，以模拟自转轨道倾角偏差对近日点运动的影响。

实验结果

研究问题

• RQ1 自转轨道倾角偏差在多大程度上解释了此前观测到的 DI Her 中近日点运动速率偏慢的现象？
• RQ2 采用现代物理解释的更新版恒星演化模型如何影响预测的近日点运动速率？
• RQ3 在包含广义相对论与潮汐效应的情况下，新的观测近日点运动速率与理论预测之间的正式一致性如何？
• RQ4 理论近日点运动速率对 Rossiter-McLaughlin 测量参数（如 λ, v sinβ）的不确定性有多敏感？
• RQ5 通过改进测量与建模，先前研究中约50%的观测差异是否可被完全解决？

主要发现

• 新的测量近日点运动速率为+0.00042°·cycle⁻¹，基于更新的光度观测数据得出。
• 蒙特卡洛模拟得到的理论预测值为+0.00046°·cycle⁻¹，为分布的众数值。
• 由旋转引起的扁率导致的反向贡献为-0.00056°·cycle⁻¹，抵消了广义相对论与潮汐效应的贡献。
• 广义相对论对近日点运动速率的贡献为+0.00068°·cycle⁻¹，证实其在该系统中起主导作用。
• 潮汐贡献为+0.00034°·cycle⁻¹，与近距离双星系统预期的量级一致。
• 理论与观测之间的正式差异现已缩小至仅10%，处于观测不确定性的合理范围内，成功解决了长期存在的差异问题。