Between 25-50 % of white dwarfs (WD) present atmospheric pollution by metals, mainly by rocky material, which has been detected as gas/dust discs, or in the form of photometric transits in some WDs. Planets might be responsible for scattering minor bodies that can reach stargazing orbits, where the tidal forces of the WD can disrupt them and enhance the chances of debris to fall onto the WD surface. The planet-planet scattering process can be triggered by the stellar mass-loss during the post main-sequence evolution of planetary systems. In this work, we continue the exploration of the dynamical instabilities that can lead to WD pollution. In a previous work we explored two-planet systems found around main-sequence (MS) stars and here we extend the study to three-planet system architectures. We evolved 135 detected three-planet systems orbiting MS stars to the WD phase by scaling their orbital architectures in a way that their dynamical properties are preserved by using the $N$-body integrator package Mercury. We find that 100 simulations (8.6 %) are dynamically active (having planet losses, orbit crossing and scattering) on the WD phase, where low mass planets (1-100 $\mathrm{M}_\oplus$) tend to have instabilities in Gyr timescales while high mass planets ($>100~\mathrm{M}_\oplus$) decrease the dynamical events more rapidly as the WD ages. Besides, 19 simulations (1.6 %) were found to have planets crossing the Roche radius of the WD, where 9 of them had planet-star collisions. Our three-planet simulations have an slight increase percentage of simulations that may contribute to the WD pollution than the previous study involving two-planet systems and have shown that planet-planet scattering is responsible of sending planets close to the WD, where they may collide directly to the WD, become tidally disrupted or circularize their orbits, hence producing pollution on the WD atmosphere.

中文翻译：

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通过基于探测到的三行星系统的动力学模拟了解白矮星大气污染的起源

25-50% 的白矮星 (WD) 存在金属污染，主要是岩石物质，已被检测为气体/尘埃盘，或在某些白矮星中以光度凌日的形式存在。行星可能是散射小天体的原因，这些小天体可以到达观星轨道，WD 的潮汐力可以在那里扰乱它们并增加碎片落到 WD 表面的机会。在行星系统的后主序演化过程中，恒星质量损失可以触发行星-行星散射过程。在这项工作中，我们继续探索可能导致 WD 污染的动力学不稳定性。在之前的工作中，我们探索了在主序 (MS) 恒星周围发现的两行星系统，在这里我们将研究扩展到三行星系统架构。我们将 135 个探测到的围绕 MS 恒星运行的三行星系统进化到 WD 阶段，通过缩放它们的轨道结构，以使用 $N$-body 积分器包 Mercury 保留它们的动力学特性。我们发现 100 次模拟 (8.6 %) 在 WD 阶段是动态活跃的（有行星损失、轨道交叉和散射），其中低质量行星（1-100 $\mathrm{M}_\oplus$）往往具有不稳定性在 Gyr 时间尺度中，而大质量行星（$>100~\mathrm{M}_\oplus$）随着 WD 年龄的增长而更快地减少动力事件。此外，19 次模拟（1.6 %）被发现有行星穿过西洋的罗氏半径，其中 9 次发生了行星与恒星的碰撞。