论文标题
行星形成模拟中非相互作用粒子之间的相互作用
Interactions Among Non-Interacting Particles in Planet Formation Simulations
论文作者
论文摘要
在最近几十年的整个过程中,$ n $体体模拟已成为量化在构成行星磁盘中随之而来的重力扰动的标准工具。在此类模拟的背景下,大规模的非中心物体通常被分类为“大”和“小”粒子,其中大物体会自以为是与所有其他对象相互作用,而小物体与大物体相互作用,但彼此之间没有相互作用。重要的是,这种分组转化为近似方案,其中小体的轨道演变完全由大物体的动力学决定,从而产生了相当大的计算优势,而在天体物理准确性方面几乎没有成本。但是,在这里我们指出,该方案也可以产生虚假的动力学行为,即使在模拟中没有大物体的情况下,小体之间的间接耦合也会导致构成“非相互作用”轨道的激发。我们通过执行一系列数值实验来证明这种自我刺激性,并确认此效果在很大程度上独立于时间步长或使用的集成算法。此外,我们采用角动量不足作为动态激发的代理,我们探索了其对时间的依赖性,系统的累积质量以及模拟中存在的粒子总数。最后,我们在常规的陆地行星形成计算的背景下检查了这种间接激发的程度,并得出结论,尽管可能有必要谨慎,但这种效果在推动模拟动力学演化中起着可忽略的作用。
Over the course of the recent decades, $N$-body simulations have become a standard tool for quantifying the gravitational perturbations that ensue in planet-forming disks. Within the context of such simulations, massive non-central bodies are routinely classified into "big" and "small" particles, where big objects interact with all other objects self-consistently, while small bodies interact with big bodies but not with each other. Importantly, this grouping translates to an approximation scheme where the orbital evolution of small bodies is dictated entirely by the dynamics of the big bodies, yielding considerable computational advantages with little added cost in terms of astrophysical accuracy. Here we point out, however, that this scheme can also yield spurious dynamical behaviour, where even in absence of big bodies within a simulation, indirect coupling among small bodies can lead to excitation of the constituent "non-interacting" orbits. We demonstrate this self-stirring by carrying out a sequence of numerical experiments, and confirm that this effect is largely independent of the time-step or the employed integration algorithm. Furthermore, adopting the growth of angular momentum deficit as a proxy for dynamical excitation, we explore its dependence on time, the cumulative mass of the system, as well as the total number of particles present in the simulation. Finally, we examine the degree of such indirect excitation within the context of conventional terrestrial planet formation calculations, and conclude that although some level of caution may be warranted, this effect plays a negligible role in driving the simulated dynamical evolution.