A Lagrangian Integrator for Planetary Accretion and Dynamics (LIPAD)

TL;DR

LIPAD is a novel particle-based Lagrangian code that simulates the entire process of planetary formation from km-sized planetesimals to planets, incorporating statistical algorithms and tracer particles for efficient large-scale modeling.

Contribution

It introduces the concept of tracer particles and statistical algorithms to efficiently simulate planetesimal evolution within a Lagrangian framework built on SyMBA.

Findings

Successfully models redistribution of planetesimals due to gravitational interactions.

Accurately reproduces results comparable to Eulerian and N-body codes.

Demonstrates the importance of gravitational redistribution in planetary growth.

Abstract

We presented the first particle based, Lagrangian code that can follow the collisional/accretional/dynamical evolution of a large number of km-sized planetesimals through the entire growth process to become planets. We refer to it as the 'Lagrangian Integrator for Planetary Accretion and Dynamics' or LIPAD. LIPAD is built on top of SyMBA, which is a symplectic $N$-body integrator. In order to handle the very large number of planetesimals required by planet formation simulations, we introduce the concept of a `tracer' particle. Each tracer is intended to represent a large number of disk particles on roughly the same orbit and size as one another, and is characterized by three numbers: the physical radius, the bulk density, and the total mass of the disk particles represented by the tracer. We developed statistical algorithms that follow the dynamical and collisional evolution of the tracers due to the presence of one another. The tracers mainly dynamically interact with the larger objects (`planetary embryos') in the normal N-body way. LIPAD's greatest strength is that it can accurately model the wholesale redistribution of planetesimals due to gravitational interaction with the embryos, which has recently been shown to significantly affect the growth rate of planetary embryos . We verify the code via a comprehensive set of tests which compare our results with those of Eulerian and/or direct N-body codes.