Planetesimal Accretion

Transcription

1 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 /46

2 Contents 1. Introduction 2. Monte Carlo model for collisions 3. Planetesimal growth simulations 4. Transition between runaway growth & oligarchy Chris Ormel: planetesimal accretion Bern /46

3 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 /46

4 Planet formation Chris Ormel: planetesimal accretion Bern /46 [Michiel Hogerheijde]

5 Planetary distance ladder μm mm m km 103 km ISM-dust ISM-dust Chondrules Chondrules Boulders Boulders Planetesimals Planetesimals (proto) (proto) Planets Planets 1 1?? 2 3 bind matter timescales observations Growth mechanisms: 1. Surface forces 2. Gravity 3. Particle concentration + collapse (GI) Chris Ormel: planetesimal accretion Bern /46

6 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 /46

7 Velocities 1mm 1cm 1m radial drift 10 m/s Sound speed cg~105 cm/s Turbulence strength α~10-4 Pressure parameter η ~ cm/s [Weidenschilling 1977; Ormel & Cuzzi 2007] Chris Ormel: planetesimal accretion Bern /46 Stokes number

8 2. From planetesimals to protoplanets Sticking mechanism: gravity Velocity: mutual grav. stirring Systematic (Kepl.) & random Runaway growth, oligarchic growth Isolation mass: M iso 10 3 M E 1 g cm 2 3/ 2 3 Chris Ormel: planetesimal accretion Bern /46 R 1 AU

9 3. Protoplanets Planets Inner solar system: chaotic growth [e.g., Chambers 2001; Raymond 2006] Outer solar system: Build-up of a ~10 ME core + gas accretion Planet synthesis [Mordasini et al. 2009a,b; Ida & Lin 2004, ] Chris Ormel: planetesimal accretion Bern /46

10 Gravitational focusing Rc o l Rg e o Σ: Surface density planetesimals Ω: orbital frequency vesc : escape velocity of body 2 dm big v = R 2big 1 esc dt v 2a va: approach velocity Chris Ormel: planetesimal accretion Bern /46 Gravitational focusing factor (can be >> 1)

11 Keplerian shear (low v regime) Relative velocity M 3M c ; v h= R h Minimum approach velocity va~vh va~vh rbit R h=a 1/3 o Circular Hill radius Rh va=vran ~eaω 2 dm big v = R 2big 1 esc dt v 2a Max. GFF ~(vesc/vh)2 ~103 Chris Ormel: planetesimal accretion Bern /46 Ω(a) Ω(a+Rh)

12 Viscous stirring Total motion Collisionless gravitational encounters: Low random motions Convert potential energy to random E Increases the random motion v (inclination+ eccentricities) Decreases GF Chris Ormel: planetesimal accretion Bern /46 Total motion Large random motions

13 GF velocity regimes Shear-dominated regime Superescape regime Dispersion-dominated regime Rv s ch a o pr p A, va y t ci o l ve Rc o l Max GF No GF Stirring vran Hill velocity, vh Random velocity, v (mutual eccentricity) Chris Ormel: planetesimal accretion Bern /46 vran Escape velocity, vesc

14 GF velocity regimes Shear-dominated regime Dispersion-dominated regime Superescape regime Rv s Rc o l vran Growth Hill velocity, vh Random velocity, v (mutual eccentricity) Chris Ormel: planetesimal accretion Bern /46 Growth Escape velocity, vesc

15 Runaway & oligarchy M T ac = dm / dt Growth timescale 2 dm big v = R 2big 1 esc dt v 2a RG (va = cnst): 2G M big v esc = R big T ac M 1/3 big T1 = T2 :neutral growth Log (mass) T1 = ½ T2:runaway growth Log (mass) Chris Ormel: planetesimal accretion Bern /46

16 Oligarchy position Dynamically hot (large v), cool (low v) T1 < T2 in same zone: RG T1 > T2 different zones: no RG T2 T2 T1 mass Heating locally slows down growth (viscous stirring) Bodies in same spatial zone separate... neighboring zones converge Chris Ormel: planetesimal accretion Bern /46

17 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 /46

18 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 /46

19 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 /46

20 Approaches N-body Solve e.o.m. for every particle [e.g., Kokubo & Ida ; 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 /46

21 Binning method Group particles by mass (bins) Continuous view (binning method) number density/unit mass Consider interactions between bins Interactions between mass bins Fast & easy to implement Mass as only independent variable Particle mass Chris Ormel: planetesimal accretion Bern /46

22 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 /46

23 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 Chris Ormel: planetesimal accretion Bern /46 CR = N 1 N 2 R 2col v a 2 h eff Area

24 Monte Carlo III. Collisions + 1 body of group 1 6 bodies of group 2 1 body of New group 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 Chris Ormel: planetesimal accretion Bern /46

25 Flexible grouping [Ormel & Spaans 2008] Sketch of particle distribution incipient to RG Mass density Small particles still dominate (require little resolution) Particles in tail will start runaway (resolve individually) High Low grouping resolution mass Low/None High Chris Ormel: planetesimal accretion Bern /46

26 Contents 1.Introduction 2.Monte Carlo model for collisional evolution 3.Planetesimal growth simulations 6, & 35 AU Low and high Σ 4.Application: transition to Oligarchy Chris Ormel: planetesimal accretion Bern /46

27 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 /46

28 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 Chris Ormel: planetesimal accretion Bern /46 vh: Hill velocity of biggest body, vh~r1

29 Chris Ormel: planetesimal accretion Bern /46

30 1 AU simulation (no fragm.) Σ = 17 g cm-2 Leftover plts. Chris Ormel: planetesimal accretion Bern /46 Oligarchs

31 Chris Ormel: planetesimal accretion Bern /46

32 6 AU simulation (w/o fragm.) Chris Ormel: planetesimal accretion Bern /46

33 35 AU run (w/o fragm.) Chris Ormel: planetesimal accretion Bern /46

34 35 AU w/o fragm. Chris Ormel: planetesimal accretion Bern /46

35 35 AU high density + fragmt. High Σ Chris Ormel: planetesimal accretion Bern /46 Low Σ

36 35 AU: different Σ Chris Ormel: planetesimal accretion Bern /46

37 End states Chris Ormel: planetesimal accretion Bern /46

38 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 /46

39 Size distribution 1 AU Chris Ormel: planetesimal accretion Bern /46

40 Key statistics Runaway growth Oligarchy Gra (inve vita rse tio ) nal FF RG-timescale, Trg Radius of biggest body (evolutionary parameter) Chris Ormel: planetesimal accretion Bern /46

41 Transition RG/Oligarchy? 1.Runaway growth increasing GF 2.Oligarchy decreasing GF 3.RG proceeds exponentially: T rg =K rg R0 s 5 a v T vs = 9R h log v h [Ida & Makino 1993; Ormel et al. 2010] We find initially Tr g < Tv s :RG out-paces the stirring! Chris Ormel: planetesimal accretion Bern /46

42 Transition RG/Oligarchy II. Ida & Makino (1993) transition: 2 M =m 2 component model M,Σ: mass, surface density in big bodies m,σ: mass, surface density of small bodies Comparison of stirring power among populations (Our) equate timescales: T rg =T vs-2c =T ac-2c The point where the 2comp approximation becomes first valid Chris Ormel: planetesimal accretion Bern /46

43 Transition RG/Oligarchy III. Ida & Makino (1993) criterion: R tr 90 km 10 g cm 2 1/5 a 1 AU 2 /5 R0 10 km 3/5 New criterion: [Ormel et al. 2010] R tr 320 km 10 g cm 2 Chris Ormel: planetesimal accretion Bern /46 2/ 7 a 1 AU 5/7 R0 10 km 3/7

44 Chris Ormel: planetesimal accretion Bern /46

45 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 Chris Ormel: planetesimal accretion Bern /46 Diameter [km] Fraser & Kavelaars (2009)

46 Summary Investigated growth ~km ~103 km Introduced novel MC model Identified the runaway growth & oligarchy stages Set a new criterion for the transition size Chris Ormel: planetesimal accretion Bern /46