论文标题
世俗极限的二元二进制散射
Binary-binary scattering in the secular limit
论文作者
论文摘要
在许多天体物理环境中，包括密集的恒星系统，例如球状簇等二元相互作用很重要。尽管二进制二进制相互作用的频率少于二进制遇到的频率，但二进制二进制相互作用导致了更丰富的可能性，例如稳定的三重系统的形成。在这里，我们专注于遥远的二进制二进制相遇的政权，即，两个二进制文件在无束轨道上彼此接近的二进制距离，其距离距离距离Q远远大于内部二进制距离。这种“世俗”制度导致轨道偏心率和取向的变化，我们使用分析考虑因素和数值整合研究。我们表明，这三个轨道之间的“直接”相互作用仅以哈密顿量的高膨胀顺序（Hexadecupole Order）开始，并且在较低膨胀订单下的内部两个轨道上的外轨道反射是弱的。因此，为良好的近似值，可以通过使用先前已知的分析结果来获得每个轨道的变化，并用伴侣二进制的总质量代替第三体的质量。然而，我们发现伴侣二进制的“二进制”的某些依赖性，并为与数值集成一致的世俗变化提供了明确的分析表达式。特别是，由于轨道2的比例，轨道1的偏心和倾斜度变化为\ eps_ {sa1}（a_2/q）^2 [m_3 m_4/（m_3+m_4）^2]，其中\ eps_ {sa1}是大约quadrupole-rorder-order-rorder-rorder-rorder-rorde semim and and a_2 and a_2 and a_3 and a_3 and a_3，m4）轴和组件质量分别。我们的结果是在几个可自由可用的Python脚本中实现的。
Binary-binary interactions are important in a number of astrophysical contexts including dense stellar systems such as globular clusters. Although less frequent than binary-single encounters, binary-binary interactions lead to a much richer range of possibilities such as the formation of stable triple systems. Here, we focus on the regime of distant binary-binary encounters, i.e., two binaries approaching each other on an unbound orbit with a periapsis distance Q much larger than the internal binary separations. This `secular' regime gives rise to changes in the orbital eccentricities and orientations, which we study using analytic considerations and numerical integrations. We show that `direct' interactions between the three orbits only occur starting at a high expansion order of the Hamiltonian (hexadecupole order), and that the backreaction of the outer orbit on the inner two orbits at lower expansion orders is weak. Therefore, to good approximation, one can obtain the changes of each orbit by using previously-known analytic results for binary-single interactions, and replacing the mass of the third body with the total mass of the companion binary. Nevertheless, we find some dependence of the `binarity' of the companion binary, and derive explicit analytic expressions for the secular changes that are consistent with numerical integrations. In particular, the eccentricity and inclination changes of orbit 1 due to orbit 2 scale as \eps_{SA1} (a_2/Q)^2 [m_3 m_4/(m_3+m_4)^2], where \eps_{SA1} is the approximate quadrupole-order change, and a_2 and (m_3,m_4) are the companion binary orbital semimajor axis and component masses, respectively. Our results are implemented in several Python scripts that are freely available.
