e >~ H/r的原行星偏心率可以减缓或逆转迁移，但以前的二维研究表明，引力散射不能保持显着的行星偏心率，以对抗盘诱导的阻尼。我们在三维空间模拟了低质量原行星群的演化。其目的是研究原行星的存活率和由此产生的行星系统的动力学结构，并将其与2D模拟进行比较。我们目前的结果从一个三维流体动力学模拟的八个原行星嵌入在一个原行星盘。我们还提出了一套使用N体代码进行的模拟，修改，包括处方行星迁移和偏心率和倾斜阻尼。这些处方是通过拟合分析公式，以流体动力学模拟嵌入盘与初始偏心和/或倾斜轨道的行星。正如在二维空间中发现的那样，差异迁移产生了稳定的原行星群，多重平均运动共振，它们步调一致地迁移，防止了长时间的引力散射。在几乎所有的模拟中，这导致了原行星群在缺乏可行的停止机制的情况下大规模迁移到中央恒星。这种演化包括相互碰撞，偶尔的大规模散射，以及在所有运行中出现超过30%的长寿共轨行星系统的频繁形成。盘诱导阻尼抑制了行星间相互作用引起的偏心和倾角增长。共轨行星是在强耗散环境中动力学松弛的自然结果，如果在自然界中观察到，将意味着这样一个演化时期通常出现在行星形成期间。
英文摘要：
Protoplanet eccentricities of e >~ H/r can slow or reverse migration, but previous 2D studies have shown that gravitational scattering cannot maintain significant planet eccentricities against disc-induced damping. We simulate the evolution of low-mass protoplanetary swarms in three dimensions. The aim is to examine both protoplanet survival rates and the dynamical structure of the resulting planetary systems, and to compare them with 2D simulations. We present results from a 3D hydrodynamic simulation of eight protoplanets embedded in a protoplanetary disc. We also present a suite of simulations performed using an N-body code, modified to include prescriptions for planetary migration and for eccentricity and inclination damping. These prescriptions were obtained by fitting analytic formulae to hydrodynamic simulations of planets embedded in discs with initially eccentric and/or inclined orbits. As was found in two dimensions, differential migration produces groups of protoplanets in stable, multiple mean-motion resonances that migrate in lockstep, preventing prolonged periods of gravitational scattering. In almost all simulations, this leads to large-scale migration of the protoplanet swarm into the central star in the absence of a viable stopping mechanism. The evolution involves mutual collisions, occasional instances of large-scale scattering, and the frequent formation of the long-lived, co-orbital planet systems that arise in > 30% of all runs. Disc-induced damping overwhelms eccentricity and inclination growth due to planet-planet interactions. Co-orbital planets are a natural outcome of dynamical relaxation in a strongly dissipative environment, and if observed in nature would imply that such a period of evolution commonly arises during planetary formation.
