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Transcript of Planetesimal Accretionarchive.space.unibe.ch/fileadmin/media/pdf/wp/Seminars/C...Chris Ormel:...
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 1/46
Planetesimal Accretion
Chris W. Ormel
Max-Planck-Institute for Astronomy, Heidelberg
and
Kees Dullemond, Marco Spaans
MPIA + U. of Heidelberg || U. of Groningen
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 2/46
Contents
1. Introduction
2. Monte Carlo model for collisions
3. Planetesimal growth simulations
4. Transition between runaway growth & oligarchy
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 3/46
Contents
1.Introduction Planet formation stages
Gravitational focusing
Runaway growth & oligarchic growth
2.Monte Carlo model for collisional evolution
3.Planetesimal growth simulations
4.Application: transition to Oligarchy
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 4/46 [Michiel Hogerheijde]
Planet formation
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 5/46
Planetary distance ladder
μm mm m km
ChondrulesChondrulesISM-dustISM-dust BouldersBoulders PlanetesimalsPlanetesimals
103 km
(proto)Planets
(proto)Planets1 1? 2?
Growth mechanisms:1.Surface forces2.Gravity3.Particle concentration + collapse (GI)
3
– bind matter– timescales– observations
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 6/46
1. Dust to planetesimals
● Chondrule formation, planetesimal formation
● Sticking by surface forces [Blum & Wurm 2008]
● Relative velocity: gas drag– Meter size barrier
● (Particle) Instabilities [Johansen et al. 2007, 2009; Cuzzi et al. 2010]
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 7/46
Sound speedcg~105 cm/s
Turbulence strengthα~10-4
Pressure parameterη ~ 10-3
1mm 1cm 1m
radial drift
Velocities
[Weidenschilling 1977; Ormel & Cuzzi 2007]
10 m/s
1 cm/s
Stokes number
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 8/46
2. From planetesimals to protoplanets
● Sticking mechanism: gravity● Velocity: mutual grav. stirring
– Systematic (Kepl.) & random
● Runaway growth, oligarchic growth● Isolation mass:
M iso≈10−3M E
1 g cm2 3/2
R1 AU
3
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 9/46
3. Protoplanets → Planets
● Inner solar system: chaotic growth
● Outer solar system: Build-up of a ~10 ME core + gas accretion
– Planet synthesis[Mordasini et al. 2009a,b; Ida & Lin 2004, 2008...]
[e.g., Chambers 2001; Raymond 2006]
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 10/46
Gravitational focusing
Rc o l
Rg e o
dM big
dt=Rbig
2 1 vesc2
va2
Σ: Surface density planetesimals
Ω: orbital frequency
vesc : escape velocity of body
va: approach velocity Gravitational focusing factor(can be >> 1)
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 11/46
Keplerian shear (low v regime)
Ω(a)Ω(a+Rh)
va~vh
● Hill radius Rh
─ Minimum approach velocity va~vh
─ Max. GFF ~(vesc/vh)2 ~103
Rh=a M3Mc 1/3
; vh=Rh
dM big
dt=Rbig
2 1 vesc2
va2
Circu
lar orb
it
va=vran ~eaΩ
Relative velocity
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 12/46
Viscous stirring
● Collisionless gravitational encounters:
─ Convert potential energy to random E
─ Increases the random motion v (inclination+ eccentricities)
─ Decreases GF
Total motion
Low random motions
Total motion
Large random motions
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 13/46
GF – velocity regimes
Random velocity, v (mutual eccentricity)
Dispersion-dominated regimeShear-dominated regime
Superescape regime
Approach ve
locity,
v a
Rc o l
Rv s
Max GF
No GF
Hill velocity, vh Escape velocity, vesc
vran vranStirring
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 14/46
GF – velocity regimes
Random velocity, v (mutual eccentricity)
Dispersion-dominated regimeShear-dominated regime
Superescape regime
vran
Rc o l
Rv s
Growth
Escape velocity, vesc
Growth vran
Hill velocity, vh
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 15/46
Runaway & oligarchy
Log (mass)
Log (mass)
T1 = T2 :neutral growth
T1 = ½ T2:runaway growth
T ac=M
dM /dt
dM big
dt=Rbig
2 1 vesc2
va2 vesc= 2GM big
Rbig
T ac∝M big−1 /3
● Growth timescale
● RG (va = cnst):
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 16/46
Oligarchy
T1
T2
T2
Dynamically hot (large v), cool (low v)
T1 < T2 in same zone: RGT1 > T2 different zones:
no RG
mass
position
─ Heating locally slows down growth (viscous stirring)
─ Bodies in same spatial zone separate
─ ........... neighboring zones converge
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 17/46
Runaway growth/Oligarchy
● Chronologically, we expect: [Ida & Makino 1993; Kokubo Ida 1996,1998, 2000]
─ Runaway growth phase (GF-factor increases), big bodies grow quickly
─ Gradual heating of plts. through viscous-stirring of protoplanets
─ Transition to oligarchy, self-regulated [slow] growth “Oligarch heats its own food” [Goldreich et al. 2004]
2 component distribution of oligarchs & planetesimals
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 18/46
Contents
1.Introduction
2.Monte Carlo model for collisional evolution● Key ingredients
● Statistical codes
● Monte Carlo method
3.Planetesimal growth simulations
4.Application: transition to Oligarchy
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 19/46
Collisional evolution codes
● As function of time, resolve:
─ Masses
─ Random velocities (inclination, eccentricity)
─ Semi-major axis
─ (other properties of bodies)
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 20/46
Approaches
● N-body
─ Solve e.o.m. for every particle [e.g., Kokubo & Ida 1998 2000; Barnes et al. 2009]
● Monte Carlo (relaxation)
● Statistical/Particle in a box
─ Binning approach [e.g., Goldreich et al. 1978; Wetherill & Stewart 1989, Weidenschilling et
al. 1997; Inaba et al. 2001]
─ Monte Carlo (probability) [Ormel & Spaans 2008]
● Hybrid (statistical + N-body) [Bromley & Kenyon 2006; Glaschke et al. 2006]
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 21/46
Binning method
number density/unit mass
Continuous view(binning method)
Interactions between mass bins
Particle mass
● Group particles by mass (bins)
● Consider interactions between bins
─ Fast & easy to implement
─ Mass as only independent variable
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 22/46
Monte Carlo [OS08] approach I.
● Use representative bodies (RB)
─ Each RB represents Ng planetesimals
─ Fix: mass, eccentricity, inclination, semi-major axis
─ Randomize: phase angles
● Calculate the collision probability between each of these RB.
● Perform (group) collision; update probabilities
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 23/46
Monte Carlo approach II.Semi major axes, a
Comp. body: #total (physical) bodies
Particle type I: 30 bodies Particle type II: 5 bodies……Particle group N
CR=N 1N 2Rcol
2 va
2heff Area
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 24/46
Monte Carlo III. Collisions
+ →
● Bookkeeping:
─ Update collision rates
─ Number of collision partners
─ Add/remove new RB (=comp. bodies)
─ Dynamically change group size Ng: the number of physical particles a single RB represents
1 body of group 1 6 bodies of group 2 1 body of New group
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 25/46
Flexible grouping [Ormel & Spaans 2008]
mass
Mas
s de
nsity
Small particles still dominate(require little resolution)
Particles in tail will start runaway(resolve individually)
Sketch of particle distribution incipient to RG
groupingHigh Low/None
resolutionLow High
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 26/46
Contents
1.Introduction
2.Monte Carlo model for collisional evolution
3.Planetesimal growth simulations— Movies @1, 6, & 35 AU
— Low and high Σ
4.Application: transition to Oligarchy
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 27/46
Simulation Results
● Simulation properties
─ Single planetesimal size initially (e.g. r=8km)
─ Local (1 disk radius)
─ Multi-zone
─ Until 2000km
─ Viscous stirring, dynamical friction, gas drag, (fragmentation), etc.
─ NO: spatial scattering (close encounters)
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 28/46
1 AU simulation (w/o fragm.)
● Indicated are:
─ Radius plant. (X)
─ Position plant. (Y)
─ Group total mass: Area dot~m1/3tot; mtot = Ng midv
─ Grav. focusing factor w.r.t. biggest particle (v/vh, color)
Single body
Hill radius vh: Hill velocity of biggest body, vh~R1
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 30/46
1 AU simulation (no fragm.)
OligarchsLeftover plts.
Σ = 17 g cm-2
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 35/46
35 AU high density + fragmt.
High Σ Low Σ
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 38/46
Contents
1.Introduction
2.Monte Carlo model for collisional evolution
3.Planetesimal growth simulations
4.Application: transition to Oligarchy [Ormel et al. 2009]
— Runaway growth & oligarchy phase
— Runaway growth timescale, Trg
— New criterion for transition size, Rtr
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 40/46
Key statistics
Radius of biggest body(evolutionary parameter)
(inverse)Gravitational FF
Runaway growth Oligarchy
RG-timescale, Trg
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 41/46
Transition RG/Oligarchy?
1.Runaway growth ↔ increasing GF
2.Oligarchy ↔ decreasing GF
3.RG proceeds exponentially:
We find initially Tr g < Tv s :RG out-paces the stirring!
T rg=K rg
R0s
T vs=a
9Rh log vvh 5
[Ida & Makino 1993; Ormel et al. 2010]
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 42/46
Transition RG/Oligarchy II.
● Ida & Makino (1993) transition:
─ 2 component model
─ Comparison of stirring power among populations
● (Our) equate timescales:
─ The point where the 2comp approximation becomes first valid
2M =m
T rg=T vs-2c=T ac-2c
M,Σ: mass, surface density in big bodies
m,σ: mass, surface density of small bodies
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 43/46
Transition RG/Oligarchy III.
● Ida & Makino (1993) criterion:
● New criterion: [Ormel et al. 2010]
Rtr≈90 km
10 g cm2 1/5
a1 AU
2 /5
R0
10 km 3 /5
Rtr≈320 km
10 g cm2 2/7
a1 AU
5/7
R0
10 km 3 /7
Chris Ormel: planetesimal accretion || Bern 26.05.2010 || 45/46
Transition RG/Oligarchy
● New criterion provides conditions at transition:
─ Conditions for core accretion phase
─ Radii oligarchs, timescales, size distr. Planetesimals
─ Speculate Kuiper Belt' size distribution fossil of RG phase
Fraser & Kavelaars (2009)
Diameter [km]