解开参数空间：行星多重性在触发白矮星周围行星系动力学不稳定性中的作用
Disentangling the parameter space: The role of planet multiplicity in triggering dynamical instabilities on planetary systems around white dwarfs
摘要：
围绕中低质量恒星运行的行星由于其恒星宿主演化为白矮星（WD）而处于危险之中，因为恒星质量损失后行星与恒星质量比的增加会导致行星系的动力学发生变化。为了了解行星多样性如何影响后主序星（MS）系统的动力学稳定性，我们进行了数千次N体模拟，涉及行星多样性作为变量，并具有受控的物理和轨道参数空间：等质量行星;相邻行星对之间的相同轨道间距;以及具有小偏心率和倾角的轨道。我们发展的主恒星从MS WD阶段的系统动力学为10 Gyr。我们发现，对于两行星系统，WD阶段的动力学活动模拟的分数是$10.2^{+1.2}_{-1.0}$ - $25.2^{+2.5}_{-2.2}$ $\%$，对于六行星系统，动态活动模拟的分数增加到$33.6^{+2.3}_{-2.2}$ - $74.1^{+3.7}_{-4.6}$ $\%$。我们的模拟表明，当恒星成为WD时，系统拥有的行星越多，系统就越不稳定，而不管行星的质量和分离范围如何。额外的结果表明，模拟与低质量的行星（1，10 $\mathrm{M_\oplus}$）失去了最多两个行星，有一个很大的分数的系统进行轨道交叉没有行星损失，并动态活跃的陀螺仪时间尺度上的WD的冷却轨道。另一方面，拥有大质量行星（100，1000 $\mathrm{M_\oplus}$）的系统最多会失去5颗行星，最好是通过喷射，并在WD形成后的最初几百万年变得不稳定。
英文摘要：
Planets orbiting intermediate and low-mass stars are in jeopardy as their stellar hosts evolve to white dwarfs (WDs) because the dynamics of the planetary system changes due to the increase of the planet:star mass ratio after stellar mass-loss. In order to understand how the planet multiplicity affects the dynamical stability of post-main sequence (MS) systems, we perform thousands of N-body simulations involving planetary multiplicity as the variable and with a controlled physical and orbital parameter space: equal-mass planets; the same orbital spacing between adjacent planet's pairs; and orbits with small eccentricities and inclinations. We evolve the host star from the MS to the WD phase following the system dynamics for 10 Gyr. We find that the fraction of dynamically active simulations on the WD phase for two-planet systems is $10.2^{+1.2}_{-1.0}$-$25.2^{+2.5}_{-2.2}$ $\%$ and increases to $33.6^{+2.3}_{-2.2}$-$74.1^{+3.7}_{-4.6}$ $\%$ for the six-planet systems, where the ranges cover different ranges of initial orbital separations. Our simulations show that the more planets the system has, the more systems become unstable when the star becomes a WD, regardless of the planet masses and range of separations. Additional results evince that simulations with low-mass planets (1, 10 $\mathrm{M_\oplus}$) lose at most two planets, have a large fraction of systems undergoing orbit crossing without planet losses, and are dynamically active for Gyr time-scales on the WD's cooling track. On the other hand, systems with high-mass planets (100, 1000 $\mathrm{M_\oplus}$) lose up to five planets, preferably by ejections, and become unstable in the first few hundred Myr after the formation of the WD.
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