Interactions among Noninteracting Particles in Planet Formation Simulations

Abstract

Over the course of 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 noncentral 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 behavior where, even in the 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 integration algorithm employed. 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.

Formation of rocky super-earths from a narrow ring of planetesimals

“…Following conventional practice of N -body calculations of planet formation, we break up our simulations into two classes of particles: fully selfgravitating planetary "embryos" and semi-active "planetesimals", which interact with embryos but not one-another (strictly speaking, only direct coupling between planetesimals is suppressed; indirect interactions among these particles -that are transmitted through the reflex motion of the central body -remain, and drive a minor but non-physical excitation of the planetesimals' velocity dispersion [29]). The computational cost of a given numerical experiment scales quadratically with the number of embryos (∝ N 2 emb ) and linearly with the number of planetesimals (∝ N emb N pl ).…”

The Resonance Hopping Effect in the Neptune-planet Nine System

“…Note that if the TNOs are treated as massive non-interacting test particles, numerical (non-physical) complications can arise depending on the integration scheme-seePeng & Batygin (2020) for a discussion of this potentially problematic effect.…”

A Lopsided Outer Solar System

“…In these test particle simulations we have a test particle, a background disk, and a central body (with/without added J 2 ). The background disk particles are given the REBOUND/MERCURY 'small particle' designation meaning they do not interact with each other; they only interact with the test particle and the central body (they do actually interact with each other indirectly through the central body as mentioned in Peng & Batygin (2020); this effect is small). Paradoxically, we must give the test particle mass in order for it to interact with the background disk.…”