标题： 通过监测von Zeipel-Lidov-Kozai循环打破径向速度测量的质量倾角退化：在HD 41004系统中的意义 显示英文标题

标题： Breaking the Mass Inclination Degeneracy of Radial Velocity Measurements via Monitoring von Zeipel-Lidov-Kozai Cycles: Implications in the HD 41004 System

摘要： 我们研究了紧凑双星HD 41004中的S型行星的动力学稳定性。使用$N$体模拟，我们发现当相互轨道倾角达到$\sim75^\circ$时，该行星可能在动力学上是稳定的。当相互轨道倾角大于39.2$^\circ$时，von Zeipel-Lidov-Kozai（vZLK）机制开始起作用。高轨道倾角轨道表现出偏心率和倾角的耦合振荡，以及近日点进动。合成径向速度（RV）建模显示，这些长期变化在从完整vZLK周期到观测可及的几十年的时间尺度上产生可测量的特征。例如，在75$^\circ$的高相互倾角下，可以在圆形双星配置中引起每行星轨道超过5 m s$^{-1}$的RV漂移（$\sim 1.9 \,\text{m s}^{-1}\, \text{yr}^{-1}$）。偏心vZLK的存在进一步加速了这些漂移，提高了可检测性。对该系统的长期RV观测提供了一种独特的途径来动态约束轨道倾角，从而确定HD 41004 Ab的真实质量。仅使用RV测量时，质量-倾角的退化问题是众所周知的。我们的结果表明，HD 41004Ab以及可能其他紧凑双星中的S型行星是通过长期高精度RV监测研究由vZLK机制引起的动力学来打破这种退化的有希望的目标。 显示英文摘要

摘要： We investigate the dynamical stability of the S-type planet in the compact binary HD 41004. Using $N$-body simulations, we find that the planet could be dynamically stable at a mutual angle inclination up to $\sim75^\circ$. The von Zeipel-Lidov-Kozai (vZLK) mechanism becomes active when the mutual inclination is greater than 39.2$^\circ$. High-inclination orbits exhibit coupled oscillations in eccentricity and inclination, along with apsidal precession. Synthetic radial velocity (RV) modeling shows that these secular variations produce measurable signatures across a broad range of timescales, from full vZLK cycles to observationally accessible decades. For instance, a high mutual inclination at 75$^\circ$ can induce RV drifts exceeding 5 m s$^{-1}$ per planetary orbit ($\sim 1.9 \,\text{m s}^{-1}\, \text{yr}^{-1}$) in circular binary configurations. The presence of eccentric vZLK further accelerates these drifts, enhancing the detectability. Long-term RV observations of this system offer a unique pathway to dynamically constrain the orbital inclination, and thus determine the true mass of HD 41004 Ab. The degeneracy of mass-inclination is well known when using RV measurements alone. Our results highlight that HD 41004Ab and potentially other S-type planets in compact binaries are promising targets for breaking such a degeneracy by studying the dynamics induced by the vZLK mechanism through long-term high-precision RV monitoring.