Colombo's Top的照片：潮汐耗散和共振俘获，及其在倾斜超级地球、超短周期行星和螺旋热彗星上的应用
Dynamics of Colombo's Top: Tidal Dissipation and Resonance Capture, With Applications to Oblique Super-Earths, Ultra-Short-Period Planets and Inspiraling Hot Jupiters
摘要：
本文对行星在潮汐耗散和外部伴星引力扰动共同作用下的自旋演化进行了全面的理论研究。这样的“自旋+伴星”系统（称为科伦坡顶）出现在许多行星环境中。潮汐力矩（驱动自旋-轨道对齐和同步）和来自伴星的引力力矩（驱动行星的轨道进动）之间的竞争产生了两种可能的自旋平衡（“潮汐卡西尼平衡”，tCE），它们是稳定和吸引的：“简单”tCE 1，通常具有较低的自旋重复性，和“共振”tCE 2，可以具有显著的重复性。后者是由自旋轨道共振引起的，当潮汐对准力矩强于伴星的岁差力矩时，它会被打破。我们描述了任意初始自旋方向的行星自旋的长期演化（包括星等和旋度），并发展了一种新的理论方法来解析地获得由潮汐耗散驱动的共振俘获几率.将我们的一般理论结果应用于系外行星系统，我们发现具有外部伴星的超级地球（SE）可能有很大的概率被困在高密度tCE 2中，假设SE具有广泛的原始密度。我们还评估了最近提出的“潮汐”的超短周期地球质量的行星的形成和热木星WASP-12 b的轨道衰变的情况。我们发现，在这两种情况下，共振捕获到tCE 2的概率一般是低的，这样一个高的dielity状态可以很容易地打破所需的轨道衰变。
英文摘要：
We present a comprehensive theoretical study on the spin evolution of a planet under the combined effects of tidal dissipation and gravitational perturbation from an external companion. Such a "spin + companion" system (called Colombo's top) appears in many [exo]planetary contexts. The competition between the tidal torque (which drives spin-orbit alignment and synchronization) and the gravitational torque from the companion (which drives orbital precession of the planet) gives rise to two possible spin equilibria ("Tidal Cassini Equilibria", tCE) that are stable and attracting: the "simple" tCE1, which typically has a low spin obliquity, and the "resonant" tCE2, which can have a significant obliquity. The latter arises from a spin-orbit resonance and can be broken when the tidal alignment torque is stronger than the precessional torque from the companion. We characterize the long-term evolution of the planetary spin (both magnitude and obliquity) for an arbitrary initial spin orientation, and develop a new theoretical method to analytically obtain the probability of resonance capture driven by tidal dissipation. Applying our general theoretical results to exoplanetary systems, we find that a super-Earth (SE) with an exterior companion can have a substantial probability of being trapped in the high-obliquity tCE2, assuming that SEs have a wide range of primordial obliquities. We also evaluate the recently proposed "obliquity tide" scenarios for the formation of ultra-short-period Earth-mass planets and for the orbital decay of hot Jupiter WASP-12b. We find in both cases that the probability of resonant capture into tCE2 is generally low and that such a high-obliquity state can be easily broken by the required orbital decay.
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