A close-encounter method for simulating the dynamics of planetesimals

Abstract

The dynamics of planetesimals plays an important role in planet formation, because their velocity distribution sets the growth rate to larger bodies. When planetesimals form in protoplanetary discs, their orbits are nearly circular and planar due to the effect of gas drag. However, mutual close encounters of the planetesimals increase eccentricities and inclinations until an equilibrium between stirring and damping is reached. After disc dissipation, there is no more gas drag and mutual close encounters as well as encounters with planets stir the orbits again. The high number of planetesimals in protoplanetary discs renders it difficult to simulate their dynamics by means of direct N-body simulations of planet formation. Therefore, we developed a novel method for the dynamical evolution of planetesimals that is based on following close encounters between planetesimal-mass bodies and gravitational stirring by planet-mass bodies. To separate the orbital motion from the close encounters, we employ a Hamiltonian splitting scheme as used in symplectic N-body integrators. Close encounters are identified using a cell algorithm with linear scaling in the number of bodies. A grouping algorithm is used to create small groups of interacting bodies which are integrated separately. Our method allows simulating a high number of planetesimals interacting through gravity and collisions with low computational cost. The typical computational time is of the order of minutes or hours, up to a few days for more complex simulations, as compared to several hours or even weeks for the same setup with full N-body. The dynamical evolution of the bodies is sufficiently well reproduced. This will make it possible to study the growth of planetesimals through collisions and pebble accretion coupled to their dynamics for a much higher number of bodies than previously accessible with full N-body simulations.

arXiv commentaccepted for publication in A&A

References in corpus (28)

• Rapid planetesimal formation in turbulent circumstellar discs
• Streaming Instabilities in Protoplanetary Disks
• Rapid growth of gas-giant cores by pebble accretion
• A simple model for the evolution of the dust population in protoplanetary disks
• Coagulation, fragmentation and radial motion of solid particles in protoplanetary disks
• The effect of gas drag on the growth of protoplanets -- Analytical expressions for the accretion of small bodies in laminar disks
• The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? II. Introducing the bouncing barrier
• The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? I. Mapping the zoo of laboratory collision experiments
• WHFast: A fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations
• Building the Terrestrial Planets: Constrained Accretion in the Inner Solar System
• The Mass and Size Distribution of Planetesimals Formed by the Streaming Instability. I. The Role of Self-Gravity
• Concentrating small particles in protoplanetary disks through the streaming instability
• How to form planetesimals from mm-sized chondrules and chondrule aggregates
• Formation of planetary systems by pebble accretion and migration: How the radial pebble flux determines a terrestrial-planet or super-Earth growth mode
• Three-dimensional simulations of multiple protoplanets embedded in a protostellar disc
• Initial mass function of planetesimals formed by the streaming instability
• Adding particle collisions to the formation of asteroids and Kuiper belt objects via streaming instabilities
• Formation of planetary systems by pebble accretion and migration: Growth of gas giants
• Hybrid Symplectic Integrators for Planetary Dynamics
• How planetary growth outperforms migration
• The GENGA Code: Gravitational Encounters in N-body simulations with GPU Acceleration
• Influence of sub- and super-solar metallicities on the compositions of solid planetary building blocks
• Planet Formation with Migration
• Understanding how planets become massive. I. Description and validation of a new toy model
• Growth after the streaming instability: from planetesimal accretion to pebble accretion
• Global 3D radiation-hydrodynamic simulations of gas accretion: The opacity dependent growth of Saturn-mass planets
• A Fast and Accurate Universal Kepler Solver without Stumpff Series
• A study of symplectic integrators for planetary system problems: error analysis and comparisons