标题： 冷木星与内部超级地球之间的相互轨道倾角 显示英文标题

标题： Mutual Orbital Inclinations Between Cold Jupiters and Inner Super-Earths

摘要： 先前对多普勒和开普勒数据的分析发现，拥有“冷木星”（轨道周期大于 $a\gtrsim 1\,\mathrm{AU}$的巨行星）的类太阳恒星几乎总是拥有“内部超级地球”（1-$4\,R_\oplus$， $a\lesssim1\,\mathrm{AU}$）。 在这里，我们尝试确定冷木星和内部超级地球轨道平面之间的对齐程度。 关键的观测输入是开普勒恒星中既有凌日超级地球又具有凌日冷木星的比例。 这个比例既取决于冷木星在这些系统中出现的概率，也取决于相互轨道倾角。 由于出现概率已经在多普勒调查中被测量过，我们可以用这些数据来限制相互倾角分布的离散度。 我们发现 $\sigma=11.8^{+12.7}_{-5.5}\,\mathrm{deg}$ （68% 置信度）和 $\sigma>3.5\,\mathrm{deg}$ （95% 置信度），其中 $\sigma$是瑞利分布的尺度参数。 这表明拥有冷木星的行星系统的轨道倾向于共面——尽管不像太阳系中的行星那样共面，太阳系中的行星相对于不变平面的平均倾角为 $1.8\,\mathrm{deg}$。 我们还发现证据表明，冷木星相对于内层系统具有更低的相互倾角，这些内层系统的凌日多重性更高。 这表明内层和外层系统之间的动力激发存在联系。 例如，轨道不对齐的冷木星的扰动可能会动态加热或使内层超级地球系统变得不稳定。 显示英文摘要

摘要： Previous analyses of Doppler and Kepler data have found that Sun-like stars hosting "cold Jupiters" (giant planets with $a\gtrsim 1\,\mathrm{AU}$) almost always host "inner super-Earths" (1-$4\,R_\oplus$, $a\lesssim1\,\mathrm{AU}$). Here, we attempt to determine the degree of alignment between the orbital planes of the cold Jupiters and the inner super-Earths. The key observational input is the fraction of Kepler stars with transiting super-Earths that also have transiting cold Jupiters. This fraction depends on both the probability for cold Jupiters to occur in such systems, and on the mutual orbital inclinations. Since the probability of occurrence has already been measured in Doppler surveys, we can use the data to constrain the dispersion of the mutual inclination distribution. We find $\sigma=11.8^{+12.7}_{-5.5}\,\mathrm{deg}$ (68% confidence) and $\sigma>3.5\,\mathrm{deg}$ (95% confidence), where $\sigma$ is the scale parameter of the Rayleigh distribution. This suggests that planetary orbits in systems with cold Jupiters tend to be coplanar - although not quite as coplanar as those in the Solar System, which have a mean inclination from the invariable plane of $1.8\,\mathrm{deg}$. We also find evidence that cold Jupiters have lower mutual inclinations relative to inner systems with higher transit multiplicity. This suggests a link between the dynamical excitation in the inner and outer systems. For example, perturbations from misaligned cold Jupiters may dynamically heat or destabilize systems of inner super-Earths.