FORMATION OF PLANETESIMALS BY GRAVITATIONAL INSTABILITIES IN TURBULENT STRUCTURES: EVIDENCE FROM ASTEROID BELT CONSTRAINTS A.Morbidelli (OCA, Nice) D. Nesvorny, W.F. Bottke, H.F. Levison (SWRI, Boulder)

THE CLASSICAL VIEW ON PLANET FORMATION 1) Dust settles on the disk’s mid-plane and coagulates in pebbles 2) A miracle occurs: pebbles manage to form km-size planetesimals, somehow avoiding the so-called “meter-size barrier” 3) By pair-wise collisions, km-size planetesimals grow into larger bodies 4) This triggers a runaway/oligarchic growth process that leads to the formation of planetary embryos and cores of giant planets

However, recent work showed that planetesimals might have formed big

1. The Heidelberg model Johansen et al., 2007

However, recent work showed that planetesimals might have formed big 1. The NASA-Ames model D~100km Cuzzi et al., 2001 Cuzzi et al., 2008

WORK PLAN We have developed and tested a “classical” coagulation/fragmentation code This code accounts for viscous stirring, dynamical friction, gas drag, collisional damping and (optionally) turbulent stirring We simulate the process of classical collisional growth starting from a population planetesimals whose initial SFD is a free input of the simulation, and check the resulting SFD against those of small body reservoirs Here we focus on the asteroid belt, for which we have many information and constraints on the primordial size distribution resulting from the accretion process (see next slides)

ASTEROID BELT CONSTRAINTS Bottke et al. (2005) Primordial slope Primordial `bump’

ASTEROID BELT CONSTRAINTS Bottke et al. (2005)

ASTEROID BELT CONSTRAINTS x1,000

ASTEROID BELT CONSTRAINTS

Result of classical collisional growth from small (~km-size) planetesimals (1.5 Earth masses total)

Starting from 100km planetesimals

Case-A set-up

Starting from 100km planetesimals

Case-B set-up

Starting from 100km planetesimals

Effect of turbulent stirring Laughlin et al. (2004) from MHD simulations derived a recipe to model the stochastic surface density fluctuations of the disk Ogihara, Ida and Morbidelli (2006) used this recipe in N-body simulations and derived a formula for the turbulent stirring of eccentricities. de/dt is mass independent de/dt ÷ γ f γ: strength of turbulence f: density in MMSN f~1, γ~10 -3

Starting from 100km planetesimals

Starting from km planetesimals

Starting from 100-1,000km planetesimals

CONCLUSIONS Asteroids have to have been “born big” The initial planetesimals in the asteroid belt had to span the 100-1,000km size range This favors the Heidelberg model over the NASA-Ames model because the latter can only produce D~100km objects The current SFD slope in the 100-1,000km range is essentially the primordial slope: new challange for the Heidelberg model Classical collisional coagulation played only a minor role in asteroid belt accretion, maybe just that of forming Lunar-Martian mass embryos from a population of ~4,000 Ceres-size bodies. If the planetesimals formed in a sea of small boulders, runaway growth may be terrifically efficient: new hope to form the giant planets cores?

IMPLICATION The original asteroid belt was deficient in small bodies (10km or less) by orders of magnitude with respect to the extrapolation of the SFD of the “big guys” Thus, despite it was massive, its collisional activity was small Consistent with one basin on Vesta, lack of shock ages of meteorites prior to the LHB, absence of pre-LHB families

SPECULATION I Why aren’t all asteroids melted? Need for a delayed start of the gravitational instability process Scott, 2007

SPECULATION II What about the same happened in the Kuiper belt? The observed knee in the SFD at D~100km would be a primordial feature and not the consequence of collisional grinding, unlike what is usually accepted (from Kenyon & Bromley’s work) Then most of the initial mass would have been in large bodies; 30 Earth masses implies ~1,000 Pluto-size bodies, consistent with the Nice model, formation of the Kuiper belt and Oort cloud etc. A new mechanism to form binary TNOs?

Kuiper Belt Binaries here we focus on ~100-km-class binaries with equal size components and wide separations ~30% binary fraction among i 0.06’’ separations, <2 mag contrast) Large angular momentum and stability of binaries in the current KB environment suggest early formation by capture Different capture models make different assumptions: E.g., Goldreich et al. (2002) favored bimodal size distribution with  /  ~1000. Dynamical friction from s assures minimal encounter speeds of 100-km bodies and facilitates capture

Initial conditions and setup from Goldreich et al. (strong dynamical friction from small bodies promotes runaway growth) Initially bimodal size distribution s/S=1000, v=2 cm/s Coagulation Code Applied to KB

Like Kenyon & Luu (1999), we also obtain a very shallow size distribution slope for D>100 km. Inconsistent with observations. Reference slope with -5 index Size distribution after 1 Myr

Different possibility: Binaries formed during gravitational collapse in eddies of turbulent disk. Excess of angular momentum prevents formation of a single object. Fragmentation and formation of a binary with high angular momentum

N-body simulations of gravitational collapse with PKDGRAV (Richardson et al.) Quarter of Million 2.5-km bodies with 1 g/cm 3 density distributed in 200,000-km wide region initial rotation mimics turbulence-induced motion highly idealized: no gas

~10 5 km ~10 4 km triple system with ~120-km-radius gravitationally-bound bodies subsequent ejection of the outer body or collision of the inner pair leads to binary size of objects scaled for visibility

Formation of KB Binaries Similar to formation of binary stars in massive fragmenting disks (e.g., Alexander et al. 2008) Can explain why components of KB binaries have identical colors (Benecchi et al., #38.11) because they would form from the same local mixture of materials More work is needed to test this idea and make testable predictions (angular momentum budget, gas/solids interaction, realistic initial conditions, etc.)

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