论文标题
在行星9的存在下，Kuiper带的平均平面超过50 au
Mean plane of the Kuiper belt beyond 50 AU in the presence of Planet 9
论文作者
论文摘要
语境。 Kuiper带对象（KBO）最近的观察普查已揭示了异常的轨道结构。这导致了一个假设，即存在一个额外的$ \ sim5-10〜m _ {\ oplus} $ Planet。这个行星被称为行星9，在数百个天文学单元上占据了一个古怪而倾斜的轨道。但是，正在考虑的KBO在$ a> 250 $ au中具有最大的已知半轴轴；因此，它们很难检测到。//// 目标。在拟议的行星9的背景下，我们旨在测量Kuiper Belt的平均平面，$ a> 50 $ au。在比较预期的和观察到的平均平面，将对未被发现的行星的质量和轨道施加一些限制。 方法。我们采用并开发了Volk＆Malhotra（2017）的理论方法与Kuiper带的预期平均平面与由八个已知行星确定的不变平面之间的相对角$δ$。构建数值模拟以验证我们的理论方法。然后类似于Volk＆Malhotra（2017），我们得出了$ 100 <a <200 $ au的真实观察到的KBO的角度$δ$，还估计了测量不确定性。最后，为了进行比较，为可能的行星9参数的不同组合创建了理论上预期的$δ$的地图。 结果。 Kuiper腰带的预期平均平均平均平均飞机几乎与上述不变的飞机内部相吻合至$ a = 90 $ au。但是这两架飞机在$ a> 100 $ au的情况下互相偏离，因为存在于行星9，因为相对角度$δ$可能大于$ \ sim10^{\ circ} $。将$1σ$上限的上限为$Δ<5^{\ circ} $作为约束，我们提出了行星9的最可能参数。
Context. A recent observational census of Kuiper belt objects (KBOs) has unveiled anomalous orbital structures. This has led to the hypothesis that an additional $\sim5-10~m_{\oplus}$ planet exists. This planet, known as Planet 9, occupies an eccentric and inclined orbit at hundreds of astronomical units. However, the KBOs under consideration have the largest known semimajor axes at $a>250$ AU; thus they are very difficult to detect.// Aims. In the context of the proposed Planet 9, we aim to measure the mean plane of the Kuiper belt at $a>50$ AU. In a comparison of the expected and observed mean planes, some constraints would be put on the mass and orbit of this undiscovered planet. Methods. We adopted and developed the theoretical approach of Volk & Malhotra (2017) to the relative angle $δ$ between the expected mean plane of the Kuiper belt and the invariable plane determined by the eight known planets. Numerical simulations were constructed to validate our theoretical approach. Then similar to Volk & Malhotra (2017), we derived the angle $δ$ for the real observed KBOs with $100<a<200$ AU, and the measurement uncertainties were also estimated. Finally, for comparison, maps of the theoretically expected $δ$ were created for different combinations of possible Planet 9 parameters. Results. The expected mean plane of the Kuiper belt nearly coincides with the said invariable plane interior to $a=90$ AU. But these two planes deviate noticeably from each other at $a>100$ AU owing to the presence of Planet 9 because the relative angle $δ$ could be as large as $\sim10^{\circ}$. Using the $1σ$ upper limit of $δ<5^{\circ}$ deduced from real KBO samples as a constraint, we present the most probable parameters of Planet 9.
