论文标题
Trappist-1系统的长期潮汐演变
Long-term tidal evolution of the TRAPPIST-1 system
论文作者
论文摘要
Ultracool M-Dwarf Star Trappist-1周围环绕着谐振链中的七个行星。过渡时期的变化表明，行星以多种三体共振捕获，它们的轨道略微偏心，这可能是由共振强迫引起的。偏心率的当前值可能是其形成中的残余。在这里，我们使用虚拟力进行数值模拟，以将完全生长的行星捕获在气盘中迁移时，然后进行详细介绍其潮汐进化的数值模拟。对于降低的圆盘尺度高度$ h \ sim 0.03 $ -0.05，捕获时行星的偏心率比少数因素高于其当前值。我们表明，当前行星D到H的偏心率和间距是耦合的潮汐演化的自然结果，其中，行星同时湿透了它们的偏心率，并且由于它们的共振相互作用而分开。我们进一步表明，行星沿着半轴轴的一组平衡曲线演化 - 由共振定义的幼体相位空间，并保存角动量。因此，当前的8：5--5：3-（3：2）$^2 $ - 4：3--3：2不能从原始的（3：2）$^4 $ -4 $ - 4：3--3：2复制的谐振构型，仅在星球中的潮汐耗散。我们使用仿真来将长期的潮汐参数限制为行星B到E的长期潮汐参数$ k_2/q $，该参数在$ 10^{ - 3} $的范围内至$ 10^{ - 2} $，并证明这些范围与合理假设后的内部建模所获得的大多数是一致的。
The ultracool M-dwarf star TRAPPIST-1 is surrounded by seven planets configured in a resonant chain. Transit-timing variations have shown that the planets are caught in multiple three-body resonances and that their orbits are slightly eccentric, probably caused by resonant forcing. The current values of the eccentricities could be a remnant from their formation. Here we run numerical simulations using fictitious forces of trapping the fully-grown planets in resonances as they migrated in the gas disc, followed by numerical simulations detailing their tidal evolution. For a reduced disc scale height $h\sim 0.03$--0.05, the eccentricities of the planets upon capture in resonance are higher than their current values by factors of a few. We show that the current eccentricities and spacing of planets d to h are natural outcomes of coupled tidal evolution wherein the planets simultaneously damp their eccentricities and separate due to their resonant interaction. We further show that the planets evolve along a set of equilibrium curves in semimajor axis--eccentricity phase space that are defined by the resonances, and that conserve angular momentum. As such, the current 8:5--5:3--(3:2)$^2$--4:3--3:2 resonant configuration cannot be reproduced from a primordial (3:2)$^4$--4:3--3:2 resonant configuration from tidal dissipation in the planets alone. We use our simulations to constrain the long-term tidal parameters $k_2/Q$ for planets b to e, which are in the range $10^{-3}$ to $10^{-2}$, and show that these are mostly consistent with those obtained from interior modelling following reasonable assumptions.
