标题： 关于潮汐变形的经典近日点运动公式的有效性 显示英文标题

标题： On the Validity of the Classical Apsidal Motion Formula for Tidal Distortion

摘要： 我们通过比较近日点进动的动力学计算与静态潮汐公式，检验了广泛使用的经典近日点运动公式在轨道参数、恒星结构和恒星自转率方面的有效性。 我们发现，当低阶四极g、f和p模式的周期比近日点经过时间小约7倍或更多时，经典公式给出了非常准确的结果。 然而，当这一条件不满足时，经典公式与精确结果之间的差异可能相当大，甚至可能出现近日点退行的情况。 当恒星的一个低阶模式接近与轨道频率的整数倍减去恒星自转率的两倍共振时，会产生最大的差异。 高阶g模（径向节点数为$\gta 4$）与轨道的共振由于它们与潮汐力的耦合较弱，因此对近日点运动的贡献较小，所以不太可能导致偏离经典结果的显著偏差。 尽管恒星的旋转模具有与近日点经过时间相近的周期，但由于它们与潮汐力的重叠较小，因此对近日点运动的贡献也很小。 我们将我们的工作应用于两个著名的双星系统（AS Cam和DI Her），这两个系统显示出异常小的近日点运动，并得出结论，对于这些系统，动力学效应可以忽略不计，即静态潮汐假设是一个很好的近似。 显示英文摘要

摘要： We check the validity of the widely used classical apsidal motion formula as a function of orbital parameters, stellar structure, and stellar rotation rate by comparing dynamical calculations of the periastron advance with the static tidal formula. We find that the classical formula gives very accurate results when the periods of the low order quadrupole g, f and p modes are smaller than the periastron passage time by a factor of about 7 or more. However, when this condition is not satisfied, the difference between the classical formula and the exact result can be quite large, and even periastron recession can result. The largest difference arises when one of the low order modes of the star is nearly resonant with an integer multiple of the orbital frequency minus twice the rotation rate of the star. The resonance of higher order g-modes (number of radial nodes $\gta 4$) with the orbit is very unlikely to cause significant deviation from the classical result because of their weak coupling to the tidal force and thus their small contribution to the apsidal motion. Resonances involving rotational modes of the star are also unlikely to make much contribution to the apsidal motion because of their small overlap with the tidal force, even though they have periods comparable to the periastron passage time. We apply our work to two famous binary systems (AS Cam and DI Her) which show abnormally small apsidal motion, and conclude that dynamical effects are unimportant for these systems, i.e. the static tide assumption is an excellent approximation.