Forming Protoplanets from Planetesimals · Forming Protoplanets from Planetesimals: The collisional...

Heidelberg Colloquium 29.06.2010

Forming Protoplanets from Planetesimals: The collisional evolution of planetary building blocks

Zoë Malka LeinhardtDepartment of Applied Mathematics and Theoretical Physics, University of CambridgeDepartment of Physics, University of Bristol

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Wednesday, June 30, 2010


Outline

The Context a. Observational Constraints - extrasolar planets, the solar system b. Planet Formation Story - “Once upon a time there was a cloud of gas ...” c. The Unknowns - planetesimal formation mechanism, initial conditions

Planetesimal Collisions a. Catastrophic Disruption Threshold - accretion or erosion? b. Velocity Dependent Collisional Response c. In Future - scaling laws

One Collisional Event in Detail (Haumea Family) a. Analytic determination of collisional regime b. Numerical confirmation

Discussion a. What does this all mean for planet formation?

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Observational Constraints: Exoplanets

• 464 planets outside our Solar System (29/06/10)

• Diverse: 68 hot Jupiters, 21 Super-Earths, 45 multiple systems, 69 around low mass stars (K & M), 4 around pulsars

• No exoplanet systems similar to the Solar System (yet)

• Planet formation is common: 5% of Sun-like stars have a Jupiter-mass planet (Marcy & Butler, 2000), 30% have a super-Earth (Lovis et al. 2009)

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Data from exoplanet catalog (http://exoplanet.eu/catalog.php)


http://exoplanet.eu/catalog.php



Observational Constraints: Exoplanets

• 464 planets outside our Solar System (29/06/10)

• Diverse: 68 hot Jupiters, 21 Super-Earths, 45 multiple systems, 69 around low mass stars (K & M), 4 around pulsars

• No exoplanet systems similar to the Solar System (yet)

• Planet formation is common: 5% of Sun-like stars have a Jupiter-mass planet (Marcy & Butler, 2000), 30% have a super-Earth (Lovis et al. 2009)

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Data from exoplanet catalog (http://exoplanet.eu/catalog.php)

The Solar System





The Problem

• Observations provide snapshots of early and late stages but cannot trace full history of planet formation

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Young Disk around HD142527

Fukagawa et al. 2006C. Marois et al. 2008

Multi-planet System

• No existing complete numerical model of planet formation that can connect early and late stages due to numerical limitations and incomplete physical models



Idealized Story: Planetesimal Theory

Planetesimal theory described by “isolated” phases - influence from the previous phase by its end state only

Planetesimal Formation

Planetesimal to Protoplanet

Protoplanet to Planet (or core)

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Planetesimal Formation: Hypotheses• Coagulation: growth accretion dominated collisions of dust

pro: consistent with meteoritescon: typical velocity dispersion is too fast (Blum & Wurm 2008) slow - meter-size will spiral into sun before decoupling from gas (Weidenschilling 1977) weak - km-sized very fragile could be ground down by collisions (Leinhardt & Stewart 2009, Stewart & Leinhardt 2009)

• Gravitational Instability: collapse of dust layer (Goldreich & Ward 1973)pro: fast - avoids intermediate sizescon: turbulence heats up the dust layer reducing the density solutions: turbulence at small scales (Cuzzi et al 2008) turbulence + streaming instability (Johansen et al 2007)

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Isolation of phases is a simplification - phases should interact & overlap



Multiple Generations: the Solar System

X-ray cross section of meteorite PCA 91082, chondrules in red (Mg), CAIs in blue (Al), Image from Krot Univ. of Hawaii

• Planetesimal formation occurs over long timescale (Hf/W chronology, Kleine 2009): differentiated planetesimals (iron meteorites) formed quickly after CAI + 1 Myr, ordinary chondrites (undifferentiated planetesimal) formed at least 1 Myr later.

• Chondrites formed slowly: Calcium aluminium rich inclusions (CAIs) oldest solar system material (4.56 Gyr), chondrules younger > 1 Myr find both in the same meteorite

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Planetesimal Evolution

Leinhardt et al. 2008

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• Planetesimal composition: changes with time and distance from sun - initially porous planetesimals compact (& melt) into solid planetesimals. Solid planetesimal may be disrupted into rubble piles.

• Impact speed: increases from subsonic to supersonic as solar system evolves

• QD*: will change during planet formation



Numerical Method for Subsonic Collisions

• Modelled with N-body code pkdgrav

• Target and projectile are gravitational aggregates, similar mass & ρ = 0.5 - 3.0 g/cm3

• Rubble-pile particles cannot fracture, only gravity and collisions (no cohesion)

• Inelastic collisions between particles governed by εn = 0.2 - 0.8

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Numerical Method for Supersonic Collisions

• Hybrid shock hydro (CTH) to N-body gravity (pkdgrav) to model gravitational re-accumulation

• Impacts into non-porous basalt targets with material strength (weak - strong)

• Impact speed kms/s, target radius = 1 - 50 km, mass of target much larger than mass of projectile

1s

1s

20s

20s

60s

60s

50 km

109

107

60s 110s 160s

0.44h 4.44h 139h

1A

1A

1B 1C

2A 2B 2C

3A 3B 3C

4A 4B 4C

50 km

50 km

Leinhardt & Stewart, 200911



First Order Collision Outcomes: Example QD*

102 103 104 105 106 107 108

Target Radius (cm)

104

105

106

107

108

109

1010

Proj

ectil

e Ki

netic

Ene

rgy

/ Tar

get M

ass

Q* D (e

rg/g

)

Solid Basalt (3 km/s, 5 km/s, 45o) [BA99]Solid Ice (3 km/s, 45o) [BA99]

0.001

0.010

0.100

1.000

10.00VI (km/s)

Filled: solid target

Open: porous target

#: porosity in %vol

Impact speeds of 3 - 5 km/s

Catastrophic Disrpution Threshold (QD*):Projectile Kinetic Energy/Target Mass needed to

permanently remove 50% of the target mass

Strength Regime:dominated by

tensile strength Gravity Regime:dominated bygravitational

binding energy

QD (e

rg/g

)

Target Radius (cm)

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100 102 104 106 108

RC1, Spherical Radius for Combined Mass at 1 g cm-3 (cm)

104

105

106

107

108

109

Q* RD

(e

rg/g

)

10-5 10-3 10-1 10 103RC1 (km)

<e>=0.001

<e>=0.01

Grav

itatio

nal b

indi

ng en

ergy

0.001

0.010

0.100

1.000

10.00VI (km/s)

Lab data:BasaltPorous glass

Modeling results:Strong Rock (Basalt) (3 km/s, 45o) [BA99]Weak Rock (1 km/s; 90o) [LS08]Rubble Piles (Mp<<Mtarg)Rubble Piles (Mp=Mtarg)Rubble Piles (Mp=1.5Mtarg)

Weak aggregates (Eq. 2)10 m/s

1 km/s


Collision Outcome: Velocity dependent QRD*

13Stewart & Leinhardt, 2009

Q∗RD = qsR

9µ/(3−2φ)C1 V 2−3µ

i

+qgR3µC1V

2−3µi



Collision Outcome: Universal Law for Mlr

0.0 0.5 1.0 1.5 2.0Q / Q*

D

0.00.5

1.0

1.5

2.02.5

Mlr /

Mta

rg

AMp = Mtarg slope = -1.45 (0.06)

Mp < Mtarg slope = -0.47 (0.05)

Mp > Mtarg slope = -2.32 (0.22)

0.0 0.5 1.0 1.5 2.0QR / Q*

RD

0.00.2

0.4

0.6

0.81.0

Mlr /

(Mp+

Mta

rg) Bslope = -0.5 (0.05)

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• Mass of the largest remnant is correlated with energy of impact (universal law)

• Universal law is effectively independent of mass ratio and impact angle when normalising by Mtot and Q*RD

Head-on20o

Shapes = mass ratios

45o



Collision Outcome: Universal Law for Mlr

0.0 0.5 1.0 1.5 2.0Q / Q*

D

0.00.5

1.0

1.5

2.02.5

Mlr /

Mta

rg

AMp = Mtarg slope = -1.45 (0.06)

Mp < Mtarg slope = -0.47 (0.05)

Mp > Mtarg slope = -2.32 (0.22)

0.0 0.5 1.0 1.5 2.0QR / Q*

RD

0.00.2

0.4

0.6

0.81.0

Mlr /

(Mp+

Mta

rg) Bslope = -0.5 (0.05)

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Mlr/Mtot = −0.5(QR/Q∗RD

−1) + 0.5

• Mass of the largest remnant is correlated with energy of impact (universal law)

• Universal law is effectively independent of mass ratio and impact angle when normalising by Mtot and Q*RD

Head-on20o

Shapes = mass ratios

45o



Size Distribution

• Cumulative size distribution for various impact speeds, impact parameters, and mass ratios

• Slope of fragment tail (~ -3.5) is independent of mass ratio and impact parameter

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μ = 1 b = 0

b = 0.35 b = 0.70 b = 0.90

μ = 0.25

μ = 0.025

1 10 1 101 101

10

100

1031

10

100

103

1

10

100

103

Diameter (km)

Cum

ulat

ive

N (>

D)

Super-catastrophic (Mlr ~10%)

Catastrophic (Mlr ~ 25%)

Catastrophic (Mlr ~ 75%)

Merging (Mlr ~ 90%)



Summary of Collision Outcome Model (to date)

• Q*RD varies by orders of magnitude during formation of solar system (Benz & Asphaug ‘99; Benz ‘00; Leinhardt & Stewart 2009; Stewart & Leinhardt 2009)

• Small gravity dominated bodies are weaker than previously assumed because of efficient energy coupling during low-speed collision events

• New variables define universal law for Mlr/Mtot vs QR/Q*RD that is relatively independent of impact parameter and mass ratio

• Size distribution of collisional tail independent of mass ratio and impact parameter (cumulative power-law index -3.5 differential -4.5)

• Leinhardt & Stewart (in prep) equations to fully characterise collision outcome as a function of mass ratio and impact parameter where relevant: universal law, catastrophic disruption curve, <v>, size distribution, transition to graze and run regime

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Haumea & Minions

• Large & elongated @ 43 AU: Radii ~1000 x 750 x 500 km

• Homogeneous surface & neutral colour

• Fast spin period ~ 4 hr

• 2 satellites + 8 family members (first “family” in the KB but many in the asteroid belt)

• Mass of Haumea satellites + family ~ 0.01 MH

• Family velocity dispersion low ~ 150 m/s(Refs: Rabinowitz 2006, Ragozzine & Brown 2007 & 2009, Schaller & Brown 2007 & 2008)

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14/12/2009 13:59A dark red spot on KBO Haumea

Page 1 of 6http://star.pst.qub.ac.uk/~pl/drs.html

back to homepage

A dark, red spot on KBO Haumea

Haumea, a

large, fast-

spinning

KBO

The Kuiperbelt objectknown asHaumea isveryinterestingbecause of itslarge size andvery fastrotation.Given itslarge size,about 2000km indiameter, andif not rotating,Haumeashould benearlyspherical likethe Earth orthe Moon.This isbecause itsself-gravitywouldcompress itequally in alldirections andso force itinto a giantball. ButHaumea spins

Figure 1 — Lightcurve of KBO Haumea in two broadbands, blue B andred R. The regular, quasi-sinusoidal shape of the lightcurve, together withthe rapid rotation (period P=3.9 hr) are strong indication that this object iselongated like a rugby ball. Two other important pieces of informationare the different heights (and depths) of the 2 peaks (and the 2 troughs),and the misalignment of the red and blue data points between the phases2.7 and 3.9 hr, approximately.

Figure 2 — Three simple models for the Haumea spot. All thesereproduce the lightcurve data well (see Fig. 3). Although color is notshown, the darker the spot the redder it is.

Lacerda et al. 2008

Brown et al. 2006

Haumea

Hi’iaka

Namaka



Slow Collision?

• Velocity dispersion of family members is small in comparison to escape speed from Haumea, Vdisp < Vesc from Haumea (900 m/s)

• Asteroid families have velocity dispersions ~ escape speed from largest remnant Mlr ~ 0.5 MTarg

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Vi = Vesc

BOOM!

V’esc = 0.7 Vesc

M M/2



What about the Spin?

• Assume all L of projectile and target goes into Haumea

• Analytic prediction of impact parameters

• Parameter space to attain required spin is narrow

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(Canup 2005)

MP/MTot

Imp

act

Par

amet

er, b

0.50.0

1

0.0

2.5

1.52.0

2.0 Vi = 1.25 Vesc

Bulk Density [g cm-3]


b =L

Lcrit

k√2f(γ)

V

Vesc



Numerical Method

• Numerically difficult problem - family members much smaller than Haumea (requiring high resolution), collision is slow (requiring long integration time), large amount of energy in impact (need equations of state)

• Refine parameter space: Low resolution numerical simulations (using a gravity code only) over a range of parameter space to locate best match to Haumea

• A few high resolution hybrid simulations (using two numerical methods) of the most promising scenarios to find the best match to entire family

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Graze and Merge

• Mproj = Mtarg

• R = 650 km

• Vi = 900 m/s

• b = 0.6

• Ice mantle over rock core (bulk density 2 g/cm3)

• Gadget + pkdgrav (hydrocode with EOS for ice & rock + N-body gravity code)

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Graze and Merge Cont.

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• Icy mantles blue, rocky cores grey

• Little mass loss on first impact

• Cores merge quickly on second impact

• Mass loss of mantle due to fission -largest remnant is initially spinning above critical spin rate

• Satellites and family members released close to escape speed



Results of Graze and Merge: Size Distribution

• Mass of observed family members derived assuming albedo of 0.7 and bulk density of 1.0

• Match mass, spin, and elongation of Haumea and mass largest family members

• Observed family is incomplete

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Cum

ulat

ive

N(>

M)/

Tota

l N

Fragment Mass/Total Mass

Namaka

Hi’iaka

Haumea

0.0001 1

0.01

1

0.01

0.1




Results of Graze and Merge: Velocity Dispersion

• 35 stable satellites after 2000 spin orbits of largest remnant

• Family mass small (.07 Mlr)

• Satellites and family made of mantle material (.8 MF)

• Satellites have low velocity dispersion (Vinf < 0.5 Vesc)

Fragment Mass/Total Mass

Cum

ulat

ive

N(>

M)/T

otal

N

Haumea

Hi’iaka

Namaka

0.0001 0.001 0.01 0.1 1

0.01

0.1

1

Observed family incomplete x10

V (km s-1)0 0.2 0.4 0.6 0.8

(Mass of Fragm

ents > V

)/Mfrag

1.0

0

0.4

0.2

0.6

0.8

(Mas

s of

Fra

gmen

ts >

V)/

Mlr

V/Vesc_lr

0.20 0.8 1.00.60.4

0.06

0.04

0.02

0

24Leinhardt et al. 2010



When and Where?

• If the collision scenario presented here is correct Haumea + family are old but not that old - the family could only have formed at the end Kuiper Belt excitation/sculpting event

• Dynamically hard to have the impact that is numerically the best fit --- still trying to figure out how to do it. Need two massive bodies for graze and merge collision modelled in this paper - not possible in recent past. Not clear that it is ever possible.

• Haumea is currently in classical belt but that could be the result of the impact: the impact could have occurred in scattered disk and the result ended up in classical belt (Levison et al. 2008) this collision is very slow though ...

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What does this all mean for planet formation?

• km-size range is weak: 1) km size needs to be avoided; 2) protected; or 3) the 1 km planetesimals do get ground down but a few are spared and grow fast by accreting the debris of those that were not so lucky (Paardekooper & Leinhardt 2010)

• Phases must overlap and interact our theoretical model is still too simple - in order to connect directly with observations our models of planetesimal evolution must become more realistic

• The Haumea collisional family is an extreme example of a collisional family in the Kuiper Belt there must be more in the Kuiper Belt when found would constrain the collisional and dynamical evolution of the outer solar system

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