论文标题
von Zeipel-Lidov-kozai在三杆系统处的振荡的特性：放松测试粒子近似
Properties of von Zeipel-Lidov-Kozai oscillations in triple systems at the quadrupole order: relaxing the test particle approximation
论文作者
论文摘要
分层三重系统中的von Zeipel-Lidov-Kozai（ZLK）振荡具有重要的天体物理意义，例如触发强烈的相互作用和产生，例如IA型超新星和引力波源。在考虑最低（四极）扩展顺序的ZLK振荡的分析特性以及由于高阶项而引起的并发症时，人们通常会假定测试粒子极限，其中内部二进制中的一个物体是无质量的。尽管这种近似值适用于例如行星系统，但对于具有更可比质量（例如恒星三元组）的系统，它的准确性较差。虽然通常在数值模拟中考虑了非测试粒子效应，但据我们所知，一种更加分析性的方法（以测试粒子和一般情况为单位）（在四极顺序下）尚未提出。在这里，我们在四倍扩展顺序下得出了三元的世俗振荡的几种分析性能。后者甚至适用于相对紧凑的三元组，只要内体的质量相似，以抑制八杆级效应。我们考虑振荡特征（圆形与图书馆），最小和最大偏心率以及时间尺度的一般条件，所有这些都是$γ\ equiv（1/2）l_1/g_2 $的函数，这是内部与轨道镜头角矩形变量的比率（在测试粒子限制中$γ= 0 $）。特别是，偏心振荡在非零$γ$的逆行方向方面更有效；假设初始内部偏心率为零，则最大偏心度在$ \ cos（i_ \ mathrm {rel，0}）=-γ$，其中$ i_ \ mathrm {rel，0} $是初始的相对倾向。我们提供了一个Python脚本，可用于快速计算这些属性。
Von Zeipel-Lidov-Kozai (ZLK) oscillations in hierarchical triple systems have important astrophysical implications such as triggering strong interactions and producing, e.g., Type Ia supernovae and gravitational wave sources. When considering analytic properties of ZLK oscillations at the lowest (quadrupole) expansion order, as well as complications due to higher-order terms, one usually assumes the test particle limit, in which one of the bodies in the inner binary is massless. Although this approximation holds well for, e.g., planetary systems, it is less accurate for systems with more comparable masses such as stellar triples. Whereas non-test-particle effects are usually taken into account in numerical simulations, a more analytic approach focusing on the differences between the test particle and general case (at quadrupole order) has, to our knowledge, not been presented. Here, we derive several analytic properties of secular oscillations in triples at the quadruple expansion order. The latter applies even to relatively compact triples, as long as the inner bodies are similar in mass such that octupole-order effects are suppressed. We consider general conditions for the character of the oscillations (circular versus librating), minimum and maximum eccentricities, and timescales, all as a function of $γ\equiv (1/2) L_1/G_2$, a ratio of inner-to-outer orbital angular momenta variables ($γ=0$ in the test particle limit). In particular, eccentricity oscillations are more effective at retrograde orientations for non-zero $γ$; assuming zero initial inner eccentricity, the maximum eccentricity peaks at $\cos(i_\mathrm{rel,0}) = -γ$, where $i_\mathrm{rel,0}$ is the initial relative inclination. We provide a Python script which can be used to quickly compute these properties.
