$\pi$ Men hosts a transiting super Earth ($P\approx6.27$ d, $m\approx4.82$ $M_{\oplus}$, $R\approx2.04$ $R_{\oplus}$) discovered by TESS and a cold Jupiter ($P\approx2093$ d, $m \sin I\approx10.02$ $M_{\rm{Jup}}$, $e\approx0.64$) discovered from radial velocity. We use Gaia DR2 and Hipparcos astrometry to derive the star's velocity caused by the orbiting planets and constrain the cold Jupiter's sky-projected inclination ($I_b=41-65^{\circ}$). From this we derive the mutual inclination ($\Delta I$) between the two planets, and find that $49^{\circ}< \Delta I < 131^{\circ}$ (1$\sigma$), and $28^{\circ} < \Delta I < 152^{\circ}$ (2$\sigma$). We examine the dynamics of the system using $N$-body simulations, and find that potentially large oscillations in the super Earth's eccentricity and inclination are suppressed by general relativistic precession. However, nodal precession of the inner orbit around the invariable plane causes the super Earth to only transit between 7-22 per cent of the time, and to usually be observed as misaligned with the stellar spin axis. We repeat our analysis for HAT-P-11, finding a large $\Delta I$ between its close-in Neptune and cold Jupiter and similar dynamics. $\pi$ Men and HAT-P-11 are prime examples of systems where dynamically hot outer planets excite their inner planets, with the effects of increasing planet eccentricities, planet-star misalignments, and potentially reducing the transit multiplicity. Formation of such systems likely involves scattering between multiple giant planets or misaligned protoplanetary discs. Future imaging of the faint debris disc in $\pi$ Men and precise constraints on the stellar spin orientation would provide strong tests for these formation scenarios.

中文翻译：

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冷木星和过境超级地球轨道 π 人之间相互高度倾斜的证据

$\pi$ 人类拥有一个过境超级地球（$P\approx6.27$ d, $m\approx4.82$ $M_{\oplus}$, $R\approx2.04$ $R_{\oplus}$）由 TESS 和从径向速度发现的冷木星 ($P\approx2093$ d, $m \sin I\approx10.02$ $M_{\rm{Jup}}$, $e\approx0.64$) 发现。我们使用 Gaia DR2 和 Hipparcos 天体测量法来推导出由轨道行星引起的恒星速度并限制冷木星的天空投影倾角（$I_b=41-65^{\circ}$）。由此我们推导出两颗行星之间的相互倾角($\Delta I$)，发现$49^{\circ}< \Delta I < 131^{\circ}$ (1$\sigma$)，并且$28 ^{\circ} < \Delta I < 152^{\circ}$ (2$\sigma$)。我们使用 $N$-body 模拟检查系统的动力学，并发现超级地球中潜在的大振荡 一般的相对论进动抑制了偏心和倾向。然而，围绕不变平面的内部轨道的节点进动导致超级地球仅在 7-22% 的时间内通过，并且通常被观察到与恒星自旋轴不对齐。我们重复我们对 HAT-P-11 的分析，发现它靠近海王星和冷木星之间的大 $\Delta I$ 以及类似的动力学。$\pi$ Men 和 HAT-P-11 是动态热外行星激发其内行星的系统的主要例子，其影响是增加行星离心率、行星-恒星错位，并可能减少凌日多样性。这种系统的形成可能涉及多个巨行星或未对准的原行星盘之间的散射。