发表机构
Institute for Astronomy, School of Physics, Zhejiang University（浙江大学物理学院天体物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究盘扩散对行星共振过稳定的影响，通过引入指数增长的时标描述盘扩散，结合N体积分发现局地盘扩散足够快时可冻结过稳定共振天平动，使行星对维持共振。
AI 中文摘要
背景：气态原行星盘中的收敛迁移可将行星对捕获入平均运动共振，随后的偏心率阻尼会使共振天平动变为过稳定状态，导致该对行星脱离共振。然而，大多数相关研究均假设盘是静态的。目的：本文研究盘扩散过程中盘力矩的衰减如何改变这一结果，以及是否能在行星对脱离前冻结过稳定天平动。方法：通过让迁移和偏心率阻尼时标在局地时标τ_d上呈指数增长来描述盘扩散，对时变增长率进行积分可预测τ_d,crit∝τ_e,0，本文通过直接N体积分检验该标度关系，并将τ_d与光蒸发腔边缘穿过局地力矩产生区所需的时间关联起来。结果：模拟在已探索参数范围内得到线性边界τ_d,crit≃Sτ_e,0，其中S≃3；在基准最小质量太阳星云中，腔边缘的更快传播缩短了局地扩散时间，且τ_d/τ_d,crit之比随轨道半径减小，这两种效应均有利于共振的保留。结论：当局地盘扩散足够迅速时，天平动振幅可被冻结，行星对可保持共振而非通过过稳定状态脱离，因此盘的后期演化可改变共振过稳定的结果。
英文摘要
Context. Convergent migration in a gaseous protoplanetary disk can capture a planet pair into mean-motion resonance. Eccentricity damping can subsequently make the resonant libration overstable and drive the pair out of resonance. Most studies of this process, however, assume a static disk. Aims. We examine how the decay of disk torques during dispersal changes this outcome and whether it can freeze an overstable libration before the pair escapes. Methods. We describe disk dispersal by allowing the migration and eccentricity-damping timescales to increase exponentially on a local timescale $τ_{\rm d}$. Integrating the time-dependent growth rate predicts $τ_{\rm d,crit}\proptoτ_{e,0}$. We test this scaling with direct $N$-body integrations and relate $τ_{\rm d}$ to the time taken by a photoevaporative cavity edge to cross the local torque-producing region. Results. The simulations recover a linear boundary, $τ_{\rm d,crit}\simeq Sτ_{e,0}$, with $S\simeq3$ over the explored parameter range. In a fiducial minimum-mass solar nebula, faster propagation of the cavity edge shortens the local dispersal time. The ratio $τ_{\rm d}/τ_{\rm d,crit}$ also decreases with orbital radius, so both effects favour resonant survival. Conclusions. When local disk dispersal is sufficiently rapid, the libration amplitude can freeze and the planet pair can remain in resonance instead of escaping through overstability. Late disk evolution can therefore alter the outcome of resonant overstability.
Comments5 pages, 3figures, submitted to A&A Letter
