Chris Ormel – Planetesimal Accretion: Runaway Growth & Transition to Oligarchy – Kavli IAA, PKU – 16.12.09

Planetesimal Accretion: Runaway Growth & Transition to Oligarchy

Chris OrmelMPIA Heidelberg

w/ Kees Dullemond, Marco Spaans

Planetary distance ladder

μm mm m km

ChondrulesChondrulesISM-dustISM-dust BouldersBoulders PlanetesimalsPlanetesimals

103 km

(proto)Planets

(proto)Planets

1. Surface forces (direct sticking)1. Surface forces (direct sticking)

2. Gravity2. Gravity

1 1? 2?

Growth mechanisms:

3. Particle concentration + collapse (GI)3. Particle concentration + collapse (GI)

3?

Chris Ormel – Planetesimal Accretion: Runaway Growth & Transition to Oligarchy – Kavli IAA, PKU – 16.12.09

Gravitational focusing● Accretion rate

● Growth timescale● Runaway growth, T1<T2

● T1: growth timescale most-massive body

● T2: ----------- 2nd most massive body

T ac=M

dM /dt

dM big

dt=Rbig

2 1 vesc2

u2 Gravitational focusing

Rbig

Chris Ormel – Planetesimal Accretion: Runaway Growth & Transition to Oligarchy – Kavli IAA, PKU – 16.12.09

Runaway & Oligarchy

Log (mass)

Log (mass)

T1 = T2 :neutral growth

T1 = ½ T2:runaway growth

Oligarchy

Dynamically hot (large u), cool (low u)

T1 < T2 in same zone: RGT1 > T2 different zones:

no RG

Chris Ormel – Planetesimal Accretion: Runaway Growth & Transition to Oligarchy – Kavli IAA, PKU – 16.12.09

Planetesimal accretion (Results)

size(dot) ~ (total mass in swarm)1/3

Gra

v. F

ocu

sin

g ~

(u

/ves

c)

1. Emergence of RG-bodies (“seeds”)2. Grav. Focusing increases (RG-phase)3. Grav. Focusing decreases (Oligarchy) &

& transition to 2-component system

12 3

Chris Ormel – Planetesimal Accretion: Runaway Growth & Transition to Oligarchy – Kavli IAA, PKU – 16.12.09

Size distribution

1. Emergence of power-law w/ dN/dm ~ m- 2 . 5

2. Mass separation (2-component oligarchy)

1

2

Increasing time

Chris Ormel – Planetesimal Accretion: Runaway Growth & Transition to Oligarchy – Kavli IAA, PKU – 16.12.09

Runaway growth statistics

(in

vers

e)

Gra

vit

ati

on

al

focu

sin

g f

acto

r

R1(t): size of largest body

1. Runaway Growth: GF (u/vesc) decreases2. Transition to slower growth phase3. RG exponential @ Trg

1

2

3

RG Oligarchy

Chris Ormel – Planetesimal Accretion: Runaway Growth & Transition to Oligarchy – Kavli IAA, PKU – 16.12.09

Summary

● Runaway growth (RG) is fast; we find:

● Krg = constant <<1

● Equate Trg with timescale of 2-component model to find transition RG-oligarchy:

T rg=K rg

R0

Rtr≈300 km aAU 5 /7

1 g cm−3 1 /7

R0

10 km 3 /7

10 g cm−2 2 /7

R0: initial planetesimal size: internal densityρ

Ω: orbital frequency: surface density (solids)Σ

a: disk radius

Chris Ormel – Planetesimal Accretion: Runaway Growth & Transition to Oligarchy – Kavli IAA, PKU – 16.12.09

RG-Oligarchy transition

Insert MSN-profile:

Transition in outer solar system @ sizes ~103 km

Larger than previous works

∝a3 /2 ;=3g cm−3 ; R0=10 km

Previous equation