双星系统中的能量优化：近轨道等质量成员的解释
Energy Optimization in Binary Star Systems: Explanation for Equal Mass Members in Close Orbits
摘要：
观测表明，近距离双星的成员通常具有接近1的质量比，而较长周期的系统则表现出更均匀的质量比分布。本文通过确定双星系统的潮汐平衡态，在角动量守恒和总质量不变的约束下，对这一发现提供了理论解释。这项工作概括了以前的治疗方法，包括质量分数作为一个变量的优化问题。结果表明，该系统可达到的最低能量状态对应于圆形轨道上的等质量恒星，其中恒星自旋角速度与轨道同步且对齐。这些特征与观测到的密近双星系统的性质大致一致。我们还发现了这个最小能态存在的条件：[1]总角动量必须超过一个临界值，[2]轨道角动量必须是总自旋角动量的三倍，[3]半长轴从上面有界。最后一个条件意味着，足够宽的联星没有优化与等质量的恒星，在那里的限制联星分离发生在$a_0\approx16R_\ast$附近。
英文摘要：
Observations indicate that members of close stellar binaries often have mass ratios close to unity, while longer-period systems exhibit a more uniform mass-ratio distribution. This paper provides a theoretical explanation for this finding by determining the tidal equilibrium states for binary star systems --- subject to the constraints of conservation of angular momentum and constant total mass. This work generalizes previous treatments by including the mass fraction as a variable in the optimization problem. The results show that the lowest energy state accessible to the system corresponds to equal mass stars on a circular orbit, where the stellar spin angular velocities are both synchronized and aligned with the orbit. These features are roughly consistent with observed properties of close binary systems. We also find the conditions required for this minimum energy state to exist: [1] The total angular momentum must exceed a critical value, [2] the orbital angular momentum must be three times greater than the total spin angular momentum, and [3] the semimajor axis is bounded from above. The last condition implies that sufficiently wide binaries are not optimized with equal mass stars, where the limiting binary separation occurs near $a_0\approx16R_\ast$.
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