发表机构
Anhui Normal University（安徽师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过N体模拟发现，在气体盘消散后，碰撞合并可驱动平均运动共振形成，且该机制对初始质量分布不敏感，但更倾向于产生近共振而非真正共振。
AI 中文摘要
平均运动共振（MMRs）传统上被认为是在原行星盘富含气体的阶段通过盘驱动的迁移形成的。在盘消散后，仅通过碰撞阻尼能否形成MMRs尚未被系统研究。为了研究后气体盘时代的MMR形成，我们进行了一组大规模的N体模拟，每个模拟包含10,000个星子围绕一颗M矮星运行，并演化超过10百万年。我们比较了两组仅在初始质量分布上不同的模拟。每组包含10次运行，具有统计上相同的初始星子轨道分布，使用不同的随机种子生成。一组采用均匀的星子质量分布，而另一组则具有双峰分布，其中大质量胚胎嵌入在较小星子的群体中。在1百万年时，40%的系统（8/20）表现出近共振周期比，但到10百万年时，这一比例降至25%（5/20），因为高阶共振关系逐渐消散。共振角追踪显示，所有持续存在的系统在10百万年时具有循环共振角，尽管有一个系统在约2至7百万年间经历短暂的振动阶段，然后恢复循环。这些结果表明，即使没有气体盘，碰撞合并也能驱动MMR形成，尽管在这种情况下，近共振构型比真正共振更受青睐。此外，这种机制在两组中产生了相似的MMR比例，表明MMR形成对初始质量分布不敏感，尽管后者可能在有限程度上调节形成路径。
英文摘要
Mean motion resonances (MMRs) are traditionally thought to form during the gas-rich phase of protoplanetary disks via disk-driven migration. Whether MMRs can form solely through collisional damping after disk dispersal has not been systematically investigated. To study MMR formation in the post-gas-disk era, we perform a large suite of N-body simulations, each containing 10,000 planetesimals around an M-dwarf star and evolving over 10 Myr. We compare two groups of simulations that differ only in their initial mass distributions. Each group consists of 10 runs with statistically identical initial planetesimal orbital distributions, generated using different random seeds. One group adopts a uniform planetesimal mass distribution, whereas the other features a bimodal distribution with massive embryos embedded in a swarm of smaller planetesimals. At 1 Myr, 40% of systems (8/20) exhibit near-resonant period ratios, but this fraction drops to 25% (5/20) by 10 Myr as higher-order commensurabilities dissolve. Resonant-angle tracking shows that all persistent systems have circulating resonant angles at 10 Myr, although one system undergoes a transient libration phase between about 2 and 7 Myr before returning to circulation. These results demonstrate that collisional merging can drive MMR formation even without a gas disk, although in this scenario near-resonant configurations are strongly favored over true resonances. Furthermore, this mechanism produces similar MMR fractions in both groups, suggesting that MMR formation is insensitive to the initial mass distribution, although the latter may modulate the formation pathway to a limited extent.
Comments18 pages, 3 figures; accepted for publication in Research in Astronomy and Astrophysics
