N-body Simulations for Planet Formation with 10 Million Particles

Masaki Iwasawa (RIKEN)Shoichi Oshino (NAOJ)Yasunori Hori (ABC, NAOJ)

Collaborators:

Michiko FujiiUTokyo

1000万体を用いた惑星形成シミュレーション

Outline

• PENTACLE• New Direct-Tree Hybrid code

• Ring model up to 10M particles

• Disk model up to 1M paricles

• Summary

Planetesimals are collisional system

Close encounters between particles governs

the dynamical evolution of the system

• Small time steps

• O(N2) per etep

Special-purpose computers has been used

GRAPE-DR

N = 0.1M

This Study

Inte

grat

ion

tim

e (y

r)

Number of particles

Ex. Ring model

• Hayashi model (ΔR=0.1AU@1AU) ~ 0.16 earth mass

• Initially equal mass

2万年後N=5000

0.94 0.96 0.98 1 1.02 1.04 1.06

N=1,000,000

0.012

0.01

0.008

0.006

0.004

0.002

0

2万年後

1 AU

Parallelized Particle-Particle Particle-tree code for

PENTACLE

Planet formation (岩澤, 押野, 藤井 & 堀, PASJ, 69, id81)

: MIT Licenceで公開https://github.com/PENTACLE-Team/PENTACLE

FDPS (Framework for Developing Particle Simulator)

Particle-Particle Particle-Tree (P3T) method : O(N2) → O(NlogN)(Oshino et al. 2011)

(Iwasawa et al. 2016)

PENTACLE

(1)

w/ Kepler solver

(2)

Split Hamiltonian depending on the particle distances

hard part — 4th-order Hermite (distance < Rcut )

soft part — Barnes-Hut tree (distance > Rcut)

(1) Hybrid symplectic integrator using 4th-order Hermite + Tree

(2) FDPS library: Library for N-body calculation

Ring model

• Hayashi model (ΔR=0.1AU@1AU) ~ 0.16 earth mass

• Initially equal mass

1 AU

• Rayleigh distribution

(Adachi et al. 1976)

Time (yr)Semi-major axis (au)

Ecce

ntr

icity

Ma

xim

um

ma

ss (

ME)

• Equal masses

Ring model (Hayashi model)

• N=5,000

• Two different random seeds (red, blue)

4th-order Hermite

PENTACLE

Nu

mb

er

of

par

ticl

es

Time (yr) Time (yr)

Max

imu

m m

ass

Ring model (Hayashi model@1AU)

Ener

gy e

rro

r

Time (yr)

Ring model (Hayashi model@1AU)

Number of CPU cores

Tim

e p

er s

tep

(se

c)We have Improved the parallel scheme for the direct part from this.

Random velocity vs. Hill velocity

(Morishima 2017)

u : random velocity of minimum-mass planetesimals (here, initial-mass)

vH : Hill velocity of the maximum-mass planetesimal

(Goldreich et al. 2004)

u>vH : dispersion dominantu<vH : shear dominant

Pla

net

ary

mas

s (g

)

Initial planetesimal mass (g)

Does protoplanetmass at the onset of oligarchic growth depend on the initial planetesimalmass?

Morishima (2017)

Independent

∝m03/7

1020

10K

100K

1M

10MRunaway growth

Oligarchic growth

Evolution of the Maximum mass

With 10M, we might see a different evolution mode

Transition phase

10K

100K

1M

Maximum planetesimal mass [g]

u/v

H

u/vH ~1 : transition phase

u/vH >1 : dispersion dominant

10M (up to ~0.1Myr)

u/v

H

Time

Runaway collision

Oligarchic growth?

• 0.4-20au, m~1023g

• What is expected?• Mixing of planetsimals

• Migration of planetesimals from outward of snow line

• The origin of water on the earth

• A large number of particles is required to cover a wide region with a sufficiently high mass resolution

Now working!

a (au)

e

• Protoplanets has not formed yet.

• If protoplanets form outer than snow line, we might see the migration of planetesimals.

• We have done up to 1M yr• We expect 3M yr for the formation of outer planets

• PENTAGLE• PENTACLE + GPU = PENTAGLE

• We are developing now!

• PENTACLE: Direct + Tree Hybrid code

• Ring model with up to 10M particles• We might see a different evolution mode of planetesimals

• Disk model with up to 1M particles• 0.4-20 au

• Now calculating

• PENTAGLE (Parallelized Particle-Particle Particle-tree code for

Planet formation on a GPU cluster) will be ready in the near future