An intriguing question in the context of dynamics arises: Could a moon possess a moon itself? Such a configuration does not exist in the Solar System, although this may be possible in theory. Kollmeier et al. (2019) determined the critical size of a satellite necessary to host a long-lived sub-satellite, or submoon. However, the orbital constraints for these submoons to exist are still undetermined. Domingos et al. (2006) indicated that moons are stable out to a fraction of the host planet Hill radius $R_{H,p}$, which in turn depends on the eccentricity of its host's orbit. Motivated by this, we simulate a system of exomoons and submoons for $10^5$ planetary orbits, while considering many initial orbital phases to obtain the critical semimajor axis in terms of $R_{H,p}$ or the hosts satellite's Hill radius $R_{H,sat}$, respectively. We find that, assuming circular coplanar orbits, the stability limit for exomoons is 0.40 $R_{H,p}$ and for a submoon is 0.33 $R_{H,sat}$. Additionally, we discuss the observational feasibility of detecting these sub-satellites through photometric, radial velocity, or direct imaging observations using the Neptunes-sized exomoon candidates Kepler 1625b-I (Teachey et al. 2018) and identify how stability can shape the identification of future candidates.

中文翻译：

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系外卫星和亚卫星的轨道稳定性以及 Kepler 1625b-I 的应用

在动力学的背景下出现了一个有趣的问题：月球能否拥有月球本身？这种配置在太阳系中并不存在，尽管这在理论上是可能的。科尔迈尔等人。(2019) 确定了承载长寿命子卫星或子月球所需的卫星的临界尺寸。然而，这些子卫星存在的轨道限制仍未确定。多明戈斯等。(2006) 指出卫星在宿主行星希尔半径 $R_{H,p}$ 的一小部分范围内是稳定的，这反过来取决于其宿主轨道的偏心率。受此启发，我们模拟了 $10^5$ 行星轨道的系外卫星和子卫星系统，同时考虑了许多初始轨道相位，以获得以 $R_{H,p}$ 或宿主卫星的希尔半径 $ 表示的临界半长轴分别为 R_{H,sat}$。我们发现，假设圆形共面轨道，系外卫星的稳定性极限为 0.40 $R_{H,p}$，而亚卫星的稳定性极限为 0.33 $R_{H,sat}$。此外，我们讨论了使用海王星大小的系外卫星候选者 Kepler 1625b-I（Teachey 等人，2018 年）通过光度、径向速度或直接成像观测来探测这些子卫星的观测可行性，并确定稳定性如何影响未来的候选人。