Planetesimal Accretion: Runaway Growth &...
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Chris Ormel – Planetesimal Accretion: Runaway Growth & Transition to Oligarchy – Kavli IAA, PKU – 16.12.09 Planetesimal Accretion: Runaway Growth & Transition to Oligarchy Chris Ormel MPIA Heidelberg w/ Kees Dullemond, Marco Spaans
Transcript of Planetesimal Accretion: Runaway Growth &...
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
