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Earth and Planetary Science Letters xxx (2011) xxx–xxx

EPSL-10987; No of Pages 11

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Earth and Planetary Science Letters

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Chondrule formation during planetesimal accretion

Erik Asphaug ⁎, Martin Jutzi, Naor Movshovitz

⁎ Corresponding author at: Earth and Planetary ScienCalifornia, 1156 High St. Santa Cruz, CA 95064, United(voice); fax: +1 831 459 3074.

E-mail address: [email protected] (E. Asphaug).

0012-821X/$ – see front matter © 2011 Elsevier B.V. Adoi:10.1016/j.epsl.2011.06.007

Please cite this article as: Asphaug, E., et al.j.epsl.2011.06.007

a b s t r a c t
a r t i c l e i n f o
Article history:Received 10 January 2011Received in revised form 3 June 2011Accepted 6 June 2011Available online xxxx

Keywords:chondruleschondritesplanetesimalscollisionsorigins

We explore the idea that most chondrules formed as a consequence of inefficient pairwise accretion, whenmolten or partly molten planetesimals ~30–100 km diameter, similar in size, collided at velocities comparableto their two-body escape velocity ~100 m/s. Although too slow to produce shocks or disrupt targets, thesecollisions were messy, especially after ~1 Ma of dynamical excitation. In SPH simulations we find that theinnermost portion of the projectile decelerates into the target, while the rest continues downrange in massivesheets. Unloading from pre-collision hydrostatic pressure P0~1-100 bar into the nebula, the melt achievesequilibrium with the surface energy of chondrule-sized droplets. Cooling is regulated post collision by theexpansion of the optically thick sheets. on a timescale of hours–days. Much of the sheet rains back down ontothe target to be reprocessed; the rest is dispersed.

ces Department, University ofStates. Tel.: +1 831 459 2260

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, Chondrule formation during planetesimal ac

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

The formation of terrestrial planets left thousands of unaccretedbodies whose remnants are represented by chondrites, themajority ofmeteorites that fall to Earth. Chondrites consist predominately of~0.1-1 mm igneous silicate spherules known as chondrules (e.g.Hewins et al., 1996; Ringwood, 1961; Scott, 2007; Scott and Krot,2005; Sears, 2004; Sorby, 1864; Urey, 1967; Wood, 1963). What wasthe widespread cause of melting of these small spherules, in a nebulawhose pressures were far too low for liquids to be stable? Why didthey solidify in hours to days, instead of tens of seconds as expectedfor sub-mm droplets?Why are they so compositionally and texturallydiverse, when whole-rock chondrites are similar in aggregatechemistry (c.f. Hezel and Palme, 2010)? Why are chondrules ≳1 Mayounger than most of the iron meteorite parent bodies (Amelin andKrot, 2007; Wadhwa et al., 2007)? In light of the significantdeficiencies in all chondrule-forming models, including the presentlypopular idea that they formed in nebular shocks, we propose a newanswer to these questions.

1.1. Background

Physical models for chondrule formation must accommodateseveral facts. Chondrules formed as a rather narrow size distributionof spherules that were embedded in a fine-grained heterogeneousmatrix. This matrix is complementary (Hezel and Palme, 2010) in thatchondrite meteorites are much closer to solar composition thanchondrules or matrix separately (Wood, 1963). Chondrules solidified

in hours (Desch and Connolly, 2002) compared to seconds for asilicate droplet radiating into space. They are found to havecrystallized in evaporative equilibrium with sodium and othervolatiles (Alexander et al., 2008) and show evidence for plastic(almost-molten) pairwise collisions (Gooding and Keil, 1981) andmergers. These latter aspects argue significantly for their formation indense, self-gravitating particle swarms (Alexander et al., 2008).

Lead isotope ages of certain chondrules have been determined tohigh precision (Amelin and Krot, 2007; Villeneuve et al., 2009;Wadhwa et al., 2007). They postdate CAIs by ≳1 Ma and appear wellrepresented only after the first 1–2 Ma of solar system history. Ironmeteorites sample ~50–100 core-bearing parent bodies that melted≳0.5–1 Ma prior to chondrule formation (Bizzarro et al., 2005; Kleineet al., 2005; Qin et al., 2008), so the late time of formation and thewidespread presence of magmatic planetesimals frames the debate.

1.2. Nebular models

Nebular models of chondrule formation (Wood, 1963) haveevolved into the presently popular idea that low density mechanicalaggregates of solar-composition dust, or pre-chondrules of some sort,were melted when the nebula was heated by powerful shocks (e.g.Boss and Durisen 2005; Ciesla and Hood, 2002; Desch and Connolly,2002; Morris and Desch, 2010) whose cause is much debated.Planetesimals that had already formed by then, including the ironmeteorite parent bodies, were bystanders or formed elsewhere(Bottke et al., 2006), or were instrumental in causing the shocks.

Disks around sun-like stars persist for millions of years (Meyeret al., 2008). Planetary embryos excited by Jupiter (Weidenschillinget al., 1998) plowing supersonically through a dense nebula (e.g.ρnebula~10−9 g cm−3, v~8 km/s; Morris and Desch, 2010) can leadto shocks capable of melting dust and compressing the gas by a factorof ~10. However, Cuzzi and Alexander (2006) calculate that the

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2 E. Asphaug et al. / Earth and Planetary Science Letters xxx (2011) xxx–xxx

chondrule-forming shocks must have been 100s to 1000s of kmacross in order to experience limited isotopic fractionation; if so thenchondrule formation might require regional shocks, as are triggeredby density waves and gravitational instabilities (Boss and Durisen2005). To accommodate the timing of chondrule formation(Wadhwa et al., 2007) instabilities must take place for millions ofyears. If dynamically-excited embryos set up the chondrule-formingshocks, then likewise the cause of eccentric forcing, and the disk,must have persisted for millions of years.

The origin of pre-chondrule agglomerations is a puzzle. Parceling‘dust bunnies’ into monodisperse ~10–1000 μg accumulations re-quires size-dependent processing prior to melting, for instanceaerodynamical sorting (see Wood, 1988). It is more difficult toexplain in this context the stunning diversity of chondrule types andcompositions over intimate spatial domains (see e.g. Ciesla, 2010). Allchondrite groups show a wide range of chondrule compositions, andthe ratio of olivine to olivine+pyroxene in porphyritic (the mostcommon) chondrules ranges from b1% to N99% (see Scott and Krot,2005). Why should one dust bunny's chemistry or its shock be sodifferent from the one adjacent?

Chondrule-forming nebular shocks must leave behind a self-gravitating swarm according to the formation densities calculatedby Alexander et al. (2008). Assuming shock compaction by a factorof ~10, the pre-shocked swarms must be within an order ofmagnitude of instability already. Cuzzi et al. (2008) and Johansenet al. (2007) show how particles might coalesce in turbulent eddiesinto local-scale accumulations that might be close to self-gravitating,and like Morbidelli et al. (2009) we regard turbulent clumping as thelikely cause for the rapid accretion of the first planetesimals, bypassingthe problematic ‘one meter barrier’ (Benz, 2000; Weidenschilling et al.1977).

If this turbulent clumping happened after chondrule formation,the chondrules could not have formed in self-gravitating densities:the clumping would have occurred gravitationally already. If clump-ing coincided with the shock, then the turbulence must be tied to thelong range gravitational forcing (disk instability or forcing by distantplanets). We favor the scenario where turbulent clumping leadsdirectly to planetesimal formation, with chondrules forming laterfrom the planetesimals.

One challenge to nebularmodels is the inclusion of Mg-rich silicategrains that formed at elevated temperatures and pressures (Liboureland Krot, 2007; Villeneuve et al., 2011) within various CV-classchondrules. These might have derived from a precursor body, laterdisrupted and incorporated into chondrules. However, massive andenergetic collisions—reversing accretion—are required to disrupt≳10 km planetesimals into tiny bits. We favor an alternative wherethese inclusions derive from crusts and unmelted components (withtheir own complicated histories) of the same disrupted planetesimalsthat form the chondrules.

Nebular models require circumstances that have specific impli-cations for nebula physics and planet formation (e.g. Chambers,2004; Ciesla, 2010; Desch et al., 2005). The early nebula was acomplex place with diverse and coinciding processes competing fordominance. That said, we now turn to a process that certainlyoccurred in the first few Ma of solar system history: the pairwiseaccretion of molten planetesimals.

1.3. Planetesimal models

If chondrules formed in collisions or igneous eruptions (seeHutchison et al., 2005; Sorby, 1864; Urey and Craig, 1953) then thenebula played a background role, damping the relative motions andcontributing to the chondrite matrix. These models have not ascribeda satisfactory physics to their process. Appendix I of Wood (1963)debunks planetesimal models, and his arguments have been convinc-ing. While Krot et al. (2005) reason that some of the latest (~5 Ma

Please cite this article as: Asphaug, E., et al., Chondrule formation duringj.epsl.2011.06.007

post-CAI) iron-rich (CB, CH) chondrules formed in a single largeimpact, these chondrule types are uncommon; at question is notwhether impacts ever formed chondrules, but whether themajority ofcommon chondrites derive from disrupted planetesimals.

Molten spherules can be produced directly from solids, whenshock waves release during hypervelocity collisions. But impactspherules are physically and chemically distinct from chondrules(Melosh and Vickery, 1991). Furthermore, impact shock requiresrandom velocities orders of magnitude faster than vrand~vesc expectedduring accretion. Hypersonic collisions are characteristic of small-body populations that are eroding rather than accreting; present-dayasteroids do not produce chondrules. Thus we focus on already-melted planetesimals.

1.4. Melted bodies

According to thermal models, the radioactive decay of primeval26Al, with half-life τ1/2=0.72 Ma, led to the meltdown of planetes-imals ≳30 km diameter that accreted in the first ~1 Ma (Hevey andSanders, 2006; Sahijpal et al., 2007). This agrees with radioisotopic(Bizzarro et al., 2005; Kleine et al., 2005; Lee and Halliday, 1996) andpetrological (Keil, 2000) records. A planetesimal might have asignificant melt fraction in the timeframe of chondrule formation,beneath a solid carapace that started out thick (melting begins at thecenter), thinned rapidly during maximal heating, and then graduallythickened into a crust following several τ1/2.

Melted planetesimals can differentiate into cores and mantles.The chondrite parent bodies did experience signature variations inmetallic iron ranging from metal poor (L, LL) to high (H, CB/CH),although not complete differentiation. Varying levels of partialdifferentiation are expected for planetesimals ~30–100 km diameterbecause interfacial tension is high for metals and silicates, whereasgravity is smaller than achievable on most ‘zero gravity’ parabolicresearch flights. The driving force for core segregation could well bemuch smaller than the interfacial stresses borne bymetal percolatingthrough silicate, or by the immiscible components in a completemelt.

Gravity acting on a metal globule of radius r is 4/3πr3Δρg. Thedensity difference Δρ is ~4.5 g cm−3 for metallic iron suspended insilicates; lower for FeS. The Eödvös (Bond) number Eo=Δρgr2/γ isthe measure of the relative importance of interfacial stress γ/r to thegravity (or other body force) per unit area. Estimating r~1 mm,g~1 cm s−1, (a 30 km body) γ~400 dyn cm−1, and Δρ~4 g cm−3,we find Eo~10−4. Gravity-driven percolation is thus limited untilsome other process first agglomerates metals into ~10 cm blobs(m~10 kg), or increases the effective g by shaking. Capillary actioncan coalesce liquids if the dihedral (wetting) angle exceeds athreshold (typically ~60°), but experiments show that iron dropletsremain stuck to silicate junctures until pressures exceed ~400 kbar(Takafuji et al., 2004). Molten FeS alloys drain effectively at lowerpressures, corresponding to planetesimals larger than ~60 km(Yoshino et al., 2003), an interesting transition diameter.

The raining out of iron droplets may be slow even without a yieldstress, for instance the case of iron droplets. Suspended in a fullymelted basaltic magma (viscosity η~104P). The Stokes settlingtimescale to the core is ~η/Gr2ρΔρ (independent of planetesimalradius R) where ρ is the planetesimal bulk density, or ~0.1–1 Ma for0.1-1 mm diameter droplets, and longer for more viscous magmas.The solar-composition carapace might further sustain the primitivesignature in a melting body for some time. While collisional shakingmight dislodge and coalesce small droplets, larger collisions wouldstir up the settling mixture, as might thermal and magneticallyinduced convection. The above calculations suggest core formationoccurred with varying efficiency in melted planetesimals, consistentwith the wide range of metallic iron in chondrites.

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1.5. Splashing and eruption

The largest obstacle to forming chondrules from planetesimals isnot chemical or petrological but physical. Impact splashing (Sandersand Taylor, 2005) and volcanic eruption (Ringwood, 1961) have beenconsidered, but the physical models remain conceptual and facemajorchallenges. Either process would be inhibited by the presence of asubstantial unmelted carapace that could be kilometers thick.

Ignoring the carapace for a moment, consider splashing whichoccurs when a projectile strikes a target. The ejecta curtain shearsagainst the nebula, forming droplets if it attains high Weber numberWe=ρv2r/γ, the measure of inertial shear stress ρv2 relative to surfaceenergy γ/r for instabilities of dimension r (c.f. Yarin, 2006), whereρ=ρnebula. Impact splashing is not an efficient process for dropletproduction (Xu et al., 2005) in a nebula. For ρnebula~10−9 g cm−3,supersonic shearing velocities vN

ffiffiffiffiffiffiffiffiγ=ρ

p~6 km/s would be required to

achieve chondrule-sized instabilities. Moreover the variety of tubes,blobs and sheets produced by sheared-apart liquid curtains, inlaboratory and numerical experiments, would require further breakupsand size-sorting in the aftermath.

Suppose impact splashing could excavate through a carapace andcreate dense swarms of ~0.1–1 mm diameter chondrules. These wouldreaccumulate rapidly onto the target unless ejected at ≳vesc/√2. Giventhe steep mass-velocity distribution of crater ejecta, an impact velocity≫vesc is required for massively efficient chondrule production, at oddswith the quiescence of ongoing accretion. Atomization of droplets forindustrial applications (Sugiura et al., 2001) relies upon a nozzle togenerate a drop in downstream pressure, a concept we consider belowin the context of collisions (c.f. Kieffer, 1989).

Volcanic eruptions on Earth produce mm- to cm-sized lapilli,considered by Ringwood (1961) to be a terrestrial analog ofchondrules. This was disputed by Wood (1963) who argued that thecompositions, textures and sizes are very different (for instance, tuffsincluding all kinds of non-droplet sheets and strands). Morefundamentally, no plausible thermodynamic source has yet beenidentified that can account for massive scale chondrule-formingeruptions on planetesimals, even given the substantial evidence fortheir igneous interiors (Keil, 2000). Volcanoes on Earth and Mars canaccelerate eruptivematerials to velocities exceeding 100 m/s, but onlybecause of the large ΔP that is unavailable inside of planetesimals.

1.6. Inefficient accretion

Pairwise accretion is messy and lossy, and does a lot of‘unaccreting’ along the way. Shallow-incidence projectiles can skipdownrange in a half-space cratering geometry (Pierazzo and Melosh,2000), and when bodies are similar sized the majority of collisions are‘oblique’ (Asphaug, 2010) in the sense of projectiles overshootingtheir targets. The slowest possible collisions between ~30 and 100 kmbodies are violent, about the speed of a car crash, and in simulationsthey produce sheets of dispersed materials deriving mostly from theinterior of the smaller body. The outcome is sensitive to collisionalenergy above the binding energy, or equivalently the normalizedrandom velocity φ=vrand /vesc, where the two-body escape velocity

vesc =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2G Mp + MT

� �= RP + RTð Þ

q~30–100 m/s for 30–100 km plan-

etesimals where MP and MT are colliding (spherical) masses of radiiRTNRP, and G is the gravitational constant. Although fast, the collisionsoccur on a timescale ~R/vimp of several hours. If vimp~vesc then thecollision timescale is the self-gravitational timescale τgrav~(Gρ)−1/2,which is the time it takes for matter of density ρ to orbit itself.

When melted planetesimals collide in an early dynamicalenvironment strongly damped by gas and dust, φ~0 and almost allcollisional materials are ultimately bound to the final body. The finalmass Mfinal is simply the sum of the colliding masses MT+MP, so theaccretion efficiency ξ=(Mfinal−MT) /MP~1. The draping back of the


sheet can take days and leave layered structures (c.f. Jutzi andAsphaug, 2011). In all likelihood the aftermaths of the earliestaccretionary collisions were buried under subsequent collisions, tobe remelted and removed from the geologic record.

Later collisions, after the clearing of the gas and dust, were excitedby random self-stirring (Safronov, 1972) and by resonant couplingwith embryonic planets and gas giants (Weidenschilling et al., 1998).This led to random velocities φ~1 associated with the heyday ofoligarchic growth (Kokubo and Ida, 1998) and the giant impact phaseof terrestrial planet formation (Chambers, 2004). But in fact partialaccretion (ξb1) and hit and run (ξ~0) account for most collisionswhen φ~1 (Agnor and Asphaug, 2004).

To understand the prevalence of hit and run and partial accretionduring planetesimal growth, we have constructed a Monte Carlosimulation beginning with a swarm of planetesimals merging underrandom pairwise collisions until there are fewer. It is not dynamicallymeaningful, as there is equal probability of collision between any twoobjects, but allows us to analyze trends. We characterize theoutcomes of pairwise collisions using Fig. 8 of Asphaug (2010),approximating the gradation between efficient accretion, partialaccretion, and hit and run as a step function ξ=1 or 0. Collisionsinvolving much smaller bodies and larger targets are mergers, beingslow cratering events. Collisions between two bodies b1/30 thediameter of the largest are treated as catastrophic, because herevrand≫vesc. These have a minor effect. A planetesimal's hit-and-runtally h increases each time it collides into a larger body but does notaccrete; h is a simple representation of a complicated evolution, sinceeach surviving planetesimal can be partly accreted, or torn intomultiple bodies (e.g. Yang et al., 2007), or dispersed.

Results are shown (Fig. 1) for 105 initial planetesimals randomlyaccreting pairwise, assuming that (a) 50% (φ~1), (b) 70%, (c) 90% or(d) 98% (φ~0) of similar-sized collisions (SSCs) are perfect mergers.When90–98%are perfectmergersh remains small. Butwhen~1/4 to 1/2of the outcomes are hit and run (a, b) there evolves amajority ofmiddle-sized bodies with h≥1. When 50% of collisions are perfect mergers,characteristic for φ~1, nearly all of the next-largest bodies (NLBs, thefeedstock of the largest) have had 2–5 hit and run collisions. The overallimplication is great diversity of planetesimal evolution, and modes ofmass excavation and collisional interaction beyond the traditionalphysics of impact cratering and catastrophic disruption by shock.

While NLBs can be disrupted by hit and run collisions repeatedlyuntil they are accreted or destroyed, the growth of the largest bodiesproceeds apace (Kokubo and Genda, 2010). They do not encounterlarger bodies, and the random velocities of smaller projectiles withinthe population are too slow to disrupt them. But in detail they growfrom an increasingly evolved feedstock, NLBs stripped of mantles,oceans and atmospheres. Thus the more dynamically excited regionsof an accreting solar system might end with next-largest planets thatare drier and more reduced (Asphaug, 2010).

Likewise regarding chondrule formation, we expect a trendtowards iron-rich composition if accretion proceeds in the presenceof random stirring. This is supported by the late ages of the mostmetal-rich chondrules (Krot et al., 2005). Furthermore, the likelihoodof multiple hit and run collisions (Fig. 1) is consistent with evidencefor multi-stage formation, heating, alteration, and recycling ofchondrules and chondrites.

2. Simulation methods

We simulate collisions using a parallel 3D hydrocode running athigh resolution (~106 particles). The method is smooth particlehydrodynamics (SPH) with a grid-based self-gravity solver (Jutzi andAsphaug, 2011, in press; Jutzi et al., 2008). We use the Tillotsonequation of state for iron and basalt, and treat both colliding bodies asliquids except for the solid carapace, which wemodel using a granularrheology (Jop et al. 2006) that has Mohr–Coulomb type behavior.




a b

c d

Fig. 1. In a gravitationally stirred systemofplanetesimalswith vrand /vesc=φ~1, approximately half of similar-sized collisions are hit and run (Asphaug, 2010;Agnor andAsphaug, 2004). Ina highly damped system, on the other hand, φ~0 and most collisions are mergers. We assess the importance of hit and run and partial accretion with a simple model (see text) where100,000 initial bodies ranging a factor of10 inmass accrete by randompairwise collisions into1000, 100,30, 10, 3 andfinally 1 body. Theprobability ofperfectmerger is (a) 50%, (b) 70%, (c)90%, and (d) 98%. Objects that collide into a larger body are accreted (and removed from the list)with this probability, and otherwise have their hit and run tally h incremented by1,with hmass-averaged during accretion. For typical random stirring (a, b) the ten or so ‘next largest bodies’ (NLBs) have quite diverse histories, and typically hN1.


The goal of these simulations is to understand the global dynamicsand provenance of unaccreted material that might form chondrules.They are limited to the first ~10 h, a fewdynamical times. Because thereare no shocks, there is little thermal evolution other than advection. Thehydrodynamical model and its equation of state do not attempt tocapture phase transformation, phasemixing, solution of volatiles, or theradiative evolution of the expanding thick sheets of ejecta. Ironrepresents differentiated core material. In the absence of shocks, basaltis a suitable placeholder for primitive silicate-dominated materials ofsimilar bulk composition and density. Initial planetesimals are hydro-statically pre-compressed in separate initializations; although only ~1–10 bar this initial pressure P0 matters greatly to what follows.

Impact velocities are ~30–100 times below the sound speed(vesc=36m/s), so we can in principle use a softer bulk modulus bya factor of 103–104. We reduce it by 100, to 2.7×109 dyn/cm2 in themantle, improving the pressure resolution while increasing thetimestep—a trick for relatively incompressible flows (Monaghan,1994) that is needed to run the high resolution simulations tocompletion. The softened modulus does not greatly affect the pressureand dynamical history, as we have verified in lower resolutioncomparison simulations. With these simplifications each 106 particlerun takes a machine-day on 32 parallel processors.

Droplet formation is represented constitutively as a free expansionunder tension in the cold (condensed) curve of the equation of state.Zeroing out tensile pressure is common in giant impact simulations,


the assumption being that fragmentation takes place at low tensilestress. Surface tension is γ~400 dyn/cm for a wide range of magmatypes (Walker and Mullins, 1981); at the scale of a particle smoothinglength (r~300 m) surface stress γ/r is less than a micobar, and safelyignored. At chondrule-forming scales, however, the atomization of asilicate magma requires much greater surface energy ~104 erg/g,comparable to the hydrostatic pressure P0/ρ, an aspect addressed byour chondrule formation model (Section 4.1).

2.1. Rheological approach

Four of the simulations presented (Table 1) involve liquid planetes-imals, while a fifth includes a carapace of solidmaterial, modeled using agranular rheology in the outer 5 km (Jop et al. 2006; Jutzi and Asphaug,2011), assuming a clast size of 500 m (see Figs. 2–4). The stress-dependent shear strength makes the lid somewhat sluggish to deform;however, in our simulations itmoves almost as freely as a liquid rheology(Fig. 4). An intact lid supporting tensile stress should also be modeled(Benz andAsphaug ,1995; Jutzi et al., 2008); this is not yet achievable as itrequires a much smaller timestep for accurate damage integration andseveral times the resolution. However, at ~30 km scales solid rocks arequite weak under tension, with static tensile strength scaling as ~R−1/2

(e.g. Housen and Holsapple, 1999; see Asphaug, 2009); accordinglytensile strength would be b1 bar.




Table 1Summary of the high resolution (~106 particle) simulations. Each starts with the same target and projectile (RT=35 km and MT=54.4×1019 g; RP=15 km and MP=3.9×1019 g)but with varying impact velocity (1 to 4·vesc) and angle (30° and 60°, where 90° is head-on). Run 5 includes a 5 km granular solid carapace on both bodies, which is 69% of theprojectile mass and 33% of the target mass respectively. For each run we compute the fraction of the projectile and target that end up as chondrules. Material forms chondrules if it isoriginally molten (not part of either lid in Run 5) and its density fell below a critical value (2 gcm−3), indicating distension. A fraction are bound (a lower limit, given that no nebuladrag is considered) and a fraction escape. In Run 1 the random velocity is zero and only 2% of the projectile escapes. None of the target escapes, while 30% of the projectile turns intochondrule-sized droplets that collapse back down onto the target body. Run 2 is at twice the impact velocity; here almost half of the projectile escapes as a chondrule-forming plume.Run 3 is as fast as Run 2 but closer to head-on; it is less efficient at forming chondrules. Run 4 is the same as Run 3 but at twice the impact velocity; now a significant fraction of thetarget is dredged up with 7% of the target (equaling one projectile mass MP) escaping, resulting in net erosion, ξ=(Mfinal−MT) /MP=−0.4, even though 60% of the projectile iscontributed. Run 5 is very similar to Run 2 dynamically, but most of the materials in the sheet are solids.

Run Impact velocity(in vesc)

Impact angle(degree)

Lid Chondrite formation (in projectile masses MP) Total

From projectile From target

Escaping Bound Total Escaping Bound Total

1 1 30 – 0.01808 0.27378 0.2919 0.0019 0.0879 0.08972 0.381572 2 30 – 0.43652 0.21565 0.6522 0.1152 0.3682 0.48339 1.135573 2 60 – 0.14640 0.21587 0.3623 0.1223 0.5305 0.65274 1.015004 4 60 – 0.39109 0.27114 0.6622 0.9844 2.1345 3.11891 3.781145 2 30 5 km 0.10955 0.05936 0.1689 0.0000 0.0207 0.02066 0.18957


Regarding fluid behavior, if a planetesimal's resistance to defor-mation can be characterized by a linear viscosity η, then Asphaug et al.(2006) estimate that a terrestrial planetesimal of radius R, respondingto a gravity-regime encounter on a timescale ~(Gρ)−1/2, will undergoglobal scale deformation in response to a gravity-regimestress~Gρ2R2 only if η≲1013P(R/1000 km)2. Accordingly, planetesi-mals ~30 km diameter with viscosity b1010P can be approximated ina collision as inviscid fluids. Basaltic magmas are in the range ~104P,while silicic evolved magmas can be ≳1012P. Primitive melts areexpected to be ≪1010 P, but partial and clast-rich melts can havehigher viscosities. In addition, bubble nucleation can occur duringpressure unloading and initially stiffen an extruding magma. Highviscosity might hinder, or localize, the hours-long deformation of amolten planetesimal during similar-sized collisions.

Fig. 2. Snapshots of Runs 1–4 (Table 1) plotting pressure 2.2 h after contact. Slices define t(Fig. 3). Each plot is 500 km on a side. In each, a 30 km planetesimal has collided with a 70 kmslowest possible 2-body collision (vimp=vesc; 36 m/s for the bodies modeled) has 98% (orfalling back, some promptly and the rest after days-months. Plotted is log(P) in dyn cm−2 (=slower than the sound speed, so that even the 144 m/s collision (bottom right) maintains a


Generally speaking, rigid, granular and viscous responses aredominant for smaller, colder planetesimals, while powerful shocksrender rheological nuances inconsequential at the scales of giantimpacts: the stresses go as R2 while the global strains and strainrates are scale-similar. Furthermore, viscosity is not linear; it islower at the kilobar stresses inside of larger embryos and planets.Viscosity decreases further in response to pressure release melting—a minor effect for small bodies but of potentially great importancefor large ones (Asphaug et al., 2006).

We have shown that a comparatively simple rheology—a granularlid atop an inviscid interior—is appropriate for this initial explorationof our hypothesis. To simplify the study and its interpretation, ourbaseline calculations (Runs 1–4) do not involve the granular model.More comprehensive thermodynamical and rheological treatments

he symmetry plane of each 3D simulation. The long arms are sections of broad sheetsplanetesimal at 30° (top figures, nearly grazing) or 60° (bottom, nearly head-on). The

more, depending on nebula drag) of the depressurized (chondrule-forming) materialμbar); orange~1–10 bar while blue is effectively zero. The collisions are ~30–100 timespproximately hydrostatic pressure.




Fig. 3. A 3D rendition of Run 1, the same as Fig. 2a where impact angle is 30° and vimp=vesc, shown here at 1.1 h after initial contact (see also Fig. 6b and e). About 1/3 of the impactormass continues downrange, unloading into space. Nearly all of this material subsequently accretes into the final body over the next ~10 h. The top panels show log(P) in dyn/cm2

(=μbars) in two views along the symmetry plane illustrating the fan-like structure. Pressure remains close to the hydrostatic value deep within the target, while pressure drops tothe ambient nebula pressure in the projectile remnants. The bottom plots are log(ρ) in g/cm3; the swarm expands as a distended liquid.


are required to observe more directly the details of petrologicevolution during and after planetesimal collisions, and to modelspecific meteorite-forming scenarios involving clast-rich, viscous, orsmaller-scale igneous planetesimals.

Fig. 4. A comparison between Run 2 and Run 5 at 3.3 h post-impact. The bottom (Run 5)has a 5 km granular solid carapace on both the projectile and target. The 30 kmdiameter projectile is only ~1/3 molten in this case. As Table 1 summarizes, ~1/4 asmuch chondrule (melt droplet) mass is produced from the projectile in Run 5, andvirtually none from beneath the target lid. Run 5 is a much drier collision than Run 2,composed mostly of solids, though equally expansive.


2.2. Simulation parameters

We present five simulated collisions in an initial exploration of theparameter space: efficient accretion (φ=0, ξ~1), partial accretion(ξb1) including the casewhere both bodies have a 5 km solid carapace,and two cases of hit and run (ξ~0). Each collision involves essentiallythe sameprojectile and target, collidingateither 30° or60° (where 90° ishead-on), at impact velocities vimp=1, 2 and 4·vesc (φ=0, 1.7, 3.9),where vesc=36m/s. The projectile, from which most of the chondrulesderive, has radiusRP=15 km,massMP=54.4×1019 g, a silicatemantle,and a 3 wt.% iron core. The target is RT=35 km,MT=3.9×1019 g, withlarger (16 wt.%) iron core, and silicate mantle.

The core fractions are notional, representing states of incompletedifferentiation. The hydrodynamical evolution of the projectilematerial during the collision and downrange is not very sensitive tothe presence or absence of a small core, but core-mantle and core–core interplay can be dominant for collisions involving large corefraction (large h), perhaps relevant to the metal-rich CB and CHclasses and to the evolution of metallic meteorites.

For efficiency we begin each simulation by placing the twospherical, hydrostatic planetesimals into almost-contacting configu-ration, assigning the projectile the contacting impact velocityvimp =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiv2rand + v2esc

qcoming from the right. This introduces some

error, because fluid projectiles deform into a rugby-ball shape as theyfree-fall towards collision. This deformation is potentially importantto the specific outcome of any one collision, having an effectcomparable to pre-impact spin (which we also neglect for now). Butit is not important to understanding the general characteristics ofthese events.





3. Results

Table 1 lists impact velocity (vimp/vesc=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiφ2 þ 1

p), impact angle

(where 0° is grazing and 90° is head-on), lid thickness (Run 5 only),and chondrule formation efficiency, defined as the mass (in units ofMP) that has evolved to ρb2 g/cm3 by depressurization expansion.Fig. 2 shows Runs 1–4 (the cases with no lid), each at 2.2 h after initialcontact, plotting pressure in the symmetry plane of the collision. Theoverall trend in all simulations is to produce thick sheets ofdepressurized material, mostly from the projectile. Fig. 3 plots Run1 in 3D, showing the expansive sheets. The projectile core is seenfaintly in the lower left of Fig. 3, an arc of red material falling at~100 m/s towards the spherical target core after shearing apart in themantle.

The effect of a substantial solid carapace is seen in Fig. 4, where thetop is Run 2 at 3.3 h post impact, and the bottom is Run 5 with a 5 kmsolid lid on both bodies. The solid lid is ~2/3 the mass of the projectile,so the amount of melt in the sheet is replaced substantially by solids.But dynamically, for a Mohr–Coulomb type friction law with stress-dependent shear strength, the presence of a massive lid makessurprisingly little difference to the dynamics, for collisions at this scaleand larger.

We identify four candidate chondrule-forming regions: (1) meltsfrom the projectile that remain within the Hill sphere of the final bodyand are eventually accreted; (2) melts from the projectile that escapethe final body; (3) melts from the target that are ejected to vesc; and(4) melts from the target that become part of the depressurized sheetbut are reaccreted. The nebula interacts with chondrule-formingmaterials accordingly. There is also variation according to the depthfrom which chondrules were exhumed within their original bodies(see Figs. 6 and 7). Also, bound chondrules will accrete in layers, withthose ejected at ≲vesc/√2 landing in hours, and those ejected near vesccoming back in weeks to months.

Although we have yet to explain why chondrule droplets shouldform from these ejected melts, we have run enough simulations todemonstrate two key phenomena: the partial merger of one bodywith another (including its core), and the production of dense sheetsof unaccreted material going off into the nebula. The merged body ispart of a new,more fully differentiated planetesimal and is more likelythan before to end up as a planet. Chondrules, deriving in our modelfrom unaccreted planetesimals, have an opposite aspect to theirevolution.

4. Droplet formation

Droplet formation is approximated dynamically in our simulationsby zeroing out tensile pressure, reasoning that magma has negligibletensile strength across ~300 m scales (the SPH resolution). That is, thecavitation threshold is ≪P0. We now consider in somewhat moredetail what happens when P0 unloads in a disrupted magmaticplanetesimal as it transitions from a continuous volume of melt athydrostatic pressure, into a distributed mass or sheet with largesurface area supported by the near-vacuum pressure of the nebula.

4.1. Binding energy and surface energy

In accretionary collisions the strain rate ξ∼ffiffiffiffiffiffiGρ

p∼1h−1, orders of

magnitude slower than the rates associated with eruptive magmaticascent on Earth and thus a different physical regime. At very lowstrain rates, in milligravity, surface energy is expected to play adominant role in the energy balance. There is abundant evidence forsurface tension and interfacial tension acting between metals andsilicates in chondrules (Uesugi et al., 2008; Wasson and Rubin, 2010;Wood, 1963), and this motivates the following consideration ofsurface tension as the determinant of chondrule size.


The sheets of material in the simulations are exhumed from acharacteristic hydrostatic pressure P0~Gρ2R2, making availablespecific enthalpy that is derived ultimately from gravitational binding.Enthalpy is spent whenwater and other volatiles come out of solution,but this is limited by the availability of free surfaces. This leads to abalance of P0 by the Laplace pressure PL=2γ/r across the dropletinterface (c.f. Sugiura et al., 2001). According to this analysis, thelarger pressure drop from larger progenitors (VdP~GM/R) results insmaller droplet sizes r. This leads to a simple, though undoubtedlyapproximate, relationship between the radius R of a disruptingplanetesimal and the radius r of characteristic chondrules that derivefrom its unloaded magma:

R = 1 = ρffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2γ=GrE:

pð1Þ

where E is the fraction of VdP that is converted to surface energy.Given the high volatile abundances within certain primitive

chondrites, and expected in early planetesimals (Abe, 2011), a gas-driven aspect to the droplet-forming process is undoubtedly impor-tant, not least by lowering the threshold for cavitation. Also,surfactants (though not identified in terrestrial magmas; Rust et al.,2003) might exist and be expressed in interfacial chemistry andreduced γ (smaller, perhaps irregular chondrules). Enthalpy losses tovapor expansion, heat of dissolution and crystal growth might tend tolarger droplets. Thus much physics and chemistry is contained in E,and laboratory studies of basaltic magmas or their analogs arerequired under milligravity conditions and hours-long unloadingtimescales. Relatively low cost experiments should be feasible onorbital research platforms given the ~1 bar pressure conditions inplanetesimals and the availability of safe analog materials such aswater (see Pettit, 2003). For now we take E to be the ratio ofchondrule-forming mass to non-chondrule matrix in a chondrite,adopting E~1/2.

The surface tension of silicatemagma (γ~400 dyn/cm;Walker andMullins, 1981) is about equal to that of Hg, familiar to those who havebroken a glass thermometer. The viscosities are higher, and beadingby surface tension requires strains of order unity on the timescale ofthe pressure unloading (~τgrav). Thus the limiting viscosity is the sameas derived earlier (Section 2.1) for the global deformation, ηb~1010Pto allow beading (ε~1) to occur within an hour.

Eq. (1) is plotted in Fig. 5, from which we deduce that chondrule-sized droplets can derive from 10 to 20 km diameter bodies. This is alower estimate on R. A larger projectile (30 km) is modeled in Runs1–5 on the expectation that droplet–droplet accretion and Ostwaldripening (Tsang and Brock, 1984) will occur within the sheets prior tocooling, resulting in larger final droplets. In any case, gravity-dominated collisions are scale similar (Asphaug, 2010) so thedynamics will not change even if the droplet sizes are discrepant.The droplet sizes predicted for Runs 1 and 4 are shown in Figs. 6 and 7,along with the pressure and the depth within the original projectile.The smallest, most deeply-excavated droplets are found in the centralparts of the sheet.

4.2. Accumulation and dispersal

In the slowest collisions most ejecta remains gravitationally boundto the final body, although even for φ=0 the accretion efficiency ξ isnot quite 1. The distal fraction of the incoming projectile, 2% in Run 1,escapes the final body although it may be caught by nebula drag.About 60% is accreted without making chondrules, but 30% of it istransformed, if molten, into a large sheet of droplets according to ouranalysis. The droplet-rich sheet reaccretes over a period of hours todays onto the final body.

With increasing collisional energy the fraction that escapesincreases; this consequence depends sensitively upon the impactangle and energy (Asphaug, 2010). For φN2 only a fraction of




Fig. 5. The larger body disrupts the smaller in a hit and run collision, rather than theother way around. Assuming that this release from hydrostatic pressure is accommo-dated by droplet formation, then chondrule radius r can be estimated by equating theLaplace pressure 2γ/r to the initial hydrostatic pressure in the disrupted projectile(Eq. (1)). Here we assume an efficiency E=1/2 (see text). Surface tensionγ=400 dyn/cm is characteristic of silicate melts at 1 bar; liquid iron has γ ~3-4times higher, decreasing with oxygen abundance. Typical silicate chondrules are0.1–1 mm diameter, indicating in principle a ~5–10 km radius melted parentplanetesimal, disrupting by a target body several times larger. But droplet–dropletaccretion likely occurs as an intermediate step, and furthermore the internal pressureP0 is lower in the exterior, so Equation 1 underestimates R. We therefore consider a30 km diameter projectile as a representative chondrule-forming body in our SPHsimulations.

Fig. 6. Pressure and initial radius within the projectile (top two rows) plotted in the symmetimes 0, 4000, 8000 s after impact. Pressure (a–c) is log(P) in dyn/cm2 from millibars (blue)projectile unloads into a sheet. The core of the projectile is stopped by the target (e, f) whileMixing of projectile and target has begun (f). Droplet radius is plotted in (g–i), where P0 inplotted as brown until the material cavitates (Pb0) and expands to ρb2 gcm−3. The bottomgreen), to 0.1 mm (yellow), to 1 mm (red). Molten droplets will coalesce or ‘ripen’ after th



collisions result in mass growth; projectiles end up downrange (andusually disrupted). Direct hits at even higher velocity can result in theprojectile plowing through the target, sometimes undergoing a core–core grazing collision and escaping. Run 4 is a near-direct-hit (60°)at vimp=4·vesc (φ=3.9); it results in net erosion (ξ=−0.4) butcontributes more than half of the impactor and all its core. Muchhigher impact energies are required to catastrophically disrupt thetargets (Love and Ahrens, 1996), and are anticipated only later inaccretion. The ~30–100 km planetesimals required by our chondruleforming mechanism would likely have solidified before this time.

4.3. Chondrule fate and layering

Chondrule dispersal into the nebula is regulated by particle size,spatial distribution, ambient gas density, and the characteristicvelocity of the swarm. Individual escaping chondrules might easilybe stopped inside the planetesimal's Hill sphere by gas drag,accumulating matrix materials from the local environment beforecoalescing. Energetic plumes of chondrules might escape anddisperse, possibly to be collected onto other nearby planetesimals orinto discrete bodies. In the absence of a nebula, isolated chondrulesmight be swept by Poynting-Robertson drag into the Sun.

The rain of chondrules onto the target body lasts for hours to days,and tapers off with time. Re-accumulating chondrules would likely besolidified before impacting, although the interiors of dense sheetsmight remain molten. Reaccumulated chondrules might experiencesecondary heating after they are piled in massive layers upon thetarget, which is presumably also partly or largely molten. Thissecondary heating would be more gradual and much longer lastingthan the exhumation and cooling of the chondrules. Follow-on hit and

try plane of the escape-velocity collision (vimp=vesc=36 m/s; Figs. 2a and 3; Run 1) atto tens of bars (red). Hydrostatic pressure is largely maintained in the target while the~60% of the projectile continues downrange; of this ~2% has escaping velocity (Table 1).side the projectile and target converted into droplet radius r according to Eq. (1), butcolor bar is thus the equivalent droplet radius r(cm), logarithmically from 10 μm (blue-eir formation in the dense swarm, so Equation 1 is a lower limit to chondrule size.




Fig. 7. As Fig. 6, but showing Run 4, the highest energy collision we have studied (vimp=4·vesc=144 m/s; φ=3.9). At θ=60° the projectile plows through the target body: corebounces off core, and target mantle and crust are entrained in the sheet, which extends beyond the plot boundaries. The final body will end up kilometers-deep with chondrules inthe hours and days to come, in this case composed of materials extruded primarily (3:1 by mass) from inside the target. Coming from higher P0, the indicated chondrule sizes aresmaller, but as before these are a lower limit to size. This is a collision with ξ=−0.4 that erodes a net 0.4 of a projectile mass from the final body. However, in detail it adds 0.6 of theprojectile mass (and all its core) and removes to escaping speed about 1.0 projectile masses of target material (mostly from its exterior), altering the net mass balance by enhancingthe final body in deep projectile material. This is one example of a large parameter space of pairwise collisions to be explored.


run and partial accretion collisions (Fig. 1) would act to furtherscramble the stratigraphy and recycle these materials.

4.4. Cooling post formation

Cooling of chondrules in a swarm is limited by opacity (Cuzzi andAlexander, 2006). Because opacity ≫1 in the sheet (~100 km thick),cooling is regulated by the expansion timescale. The downrangevelocity of the overshooting part of the projectile is only slightlydecelerated by the impact, while the rest is stopped abruptly, givingan expansion timescale~R/vimp~τgrav of order 1 h (as evident in Figs. 6and 7). The cooling rate also depends on local swarm density andproximity to the boundary; significant variation in cooling time andalso isotopic variation are expected within smaller-scale swarms(Cuzzi and Alexander, 2006). For a fixed projectile diameter, fastercollisions produce faster-cooling ejecta.


Cooling time increases with projectile size. Opacity scales like theswarm radius, which is comparable to RP; it also scales inversely withdroplet size which goes as ~1/RP2 according to Eq. (1). The opacity thusoverall scales as ~RP3, allowing us to address a lingering question:where are the ‘chondrules’ from the completely differentiatedmantles of larger, later bodies? Large collisions were less commonthan small ones, but the mass produced was proportionately copious.One explanation is that 26Al heat production was diminished, by afactor of ~10 after ~2 Ma. Time ran out, and the ~100–300 kmplanetesimals solidified before there existed ~300–1000 km bodiesfor them to collide with.

Eq. (1) provides another explanation: droplets erupting fromP0~kbar would be dust-sized rather than chondrule sized. Clumpsaccumulating, or masses falling back onto the target body, would nothave a chance to cool below solidus given the very high opacity of aself-gravitating swarm of μm-sized droplets ~100–1000 km in extent.Heat could not get out during τgrav and the result would be igneous





rock. Escaping dust would be dragged into the Sun on a shorttimescale, in the absence of a nebula, and one or more such eventsmight contribute to the olivine and pyroxene rich dust found inmeteorites and IDPs.

4.5. Metal spheres and vesicles

The presence and distribution of reduced iron in the chondrule-forming melt can help us piece together the thermodynamic andphysical conditions of their formation (Wasson and Rubin, 2010). Butoutstanding questions remain. Why are iron-rich chondrules rare incomparison to silicate chondrules, and found only in a few subclassesof chondrites, when iron was abundant and subject to similarcollisional forces? One answer is that cores are harder to excavate(e.g. Love and Ahrens, 1996). Another is that molten silicate has lowersurface energy than Fe and FeS. Surface energy calculations by Uesugiet al. (2008) suggest that liquidmetallic iron, in the absence of gravity,would wet the surface of melted silicate chondrules, adhering ratherthan forming iron chondrules of its own. This would explain iron rims‘armoring’ many chondrules, and blebs of iron linked aroundchondrules in CR meteorites (Wasson and Rubin, 2010; Wood, 1963).

If iron was excavated in abundance, either by more energeticcollisions or by collisions involving high-h mantle-denuded pro-jectiles (Fig. 1), then iron chondrules might form by a process similarto that postulated for silicate chondrules. This requires metallic Fe tobe so abundant that there is comparatively little silicate surface, sothat metallic surface energy dominates. According to Eq. (1) ironchondrules should then be a few times larger, in proportion to iron'shigher (by a factor ~4) surface tension. Although again, iron-dominated melts are usually exhumed by more energetic events,from the higher-P0 interiors of larger bodies, resulting in smallerchondrules. At high enthalpies inside of larger, hotter planetesimals,iron droplets might evaporate, ultimately producing chondrules bycondensation from vapor (Petaev et al. 2001; Krot et al., 2005), or by amixed process of droplet formation followed by partial evaporationand recondensation (e.g. Tsang and Brock, 1984).

Bubbles obey similar physics as droplets. They are not stable inexpansive plumes but can be quenched in rapidly solidified magmas(Navon and Lyakhovsky, 1998). Bubbles are occasionally found inordinary chondrites (Benedix et al., 2008), and their occurrence isconsistent with our model of a pressure unloading origin. The scarcityof bubbles in chondrites and chondrules seems puzzling, although theLaplace pressure (~1–10 bars inside chondrule-sized droplets) wouldcause diffusion of gases across the interface.

5. Conclusions

The evidence for heating and melting of planetesimals by 26Alduring the same timeframe as collisional accretion appears undeni-able. We find it likely, in the extremely low gravity of planetesimals,that various degrees of differentiation would result. Given thisfavorable petrologic setting we make the case that most chondrulesformed in pairwise accretionary collisions, where ~half of the smallerunloaded from hydrostatic pressure P0 into magmatic sheetssupported by the low pressure of the nebula.

Occurring at b1/30 the sound speed, accretionary planetesimalcollisions are relatively incompressible. We argue that they aredominated at large scale by gravitation, momentum, and release fromhydrostatic pressure, and at small scale by the creation of surfaceenergy and release of volatiles. Most accretionary collisions involve acertain amount of ‘unaccretion,’ throwing much of the projectile (andsome of the target) back into the nebula, analogous to the splatter of aglancing water balloon in slow motion. Melts from the unaccretedprojectile expand to low pressure. Enthalpy is available for volatiledissolution, but because this requires surfaces (droplets) we arguethat the projectile hydrostatic pressure Gρ2R2 is balanced by the


Laplace pressure γ/r. For chondrule-sized droplets this is ~1–10 bar,corresponding to projectile diameter 2R~30 km, althoughmore likelysmaller droplets form first, then grow and coarsen until they solidify,cooling through solidus on a timescale of hours, regulated by theexpansion.

Varieties of chondrites emerge: piles massed rapidly onto thetarget body; sheets and clouds interacting with the nebula inside theHill sphere; free bodies ejected into the disk. Conversely a givenmeteorite might contain chondrules from diverse bodies, plus theaccumulated products of disk shock and solar events at theplanetesimal surface, together with layers of chondrules from pastcollisions. Solids entrained in the downrange sheet (solar-composi-tion carapace early on; layers of crustal cumulates after meltdown;layers of previous-generation chondrules with increasing h) wouldcommingle with the melts. Later collisions within the timeframe of26Al heat production would produce more chondrules, scramble thestratigraphy, and recycle the earliest solids.

In the earliest collisions, almost all the chondrules rained backdown (ξ~1) and were likely buried under subsequent accretionarycollisions, and remelted. Over time, gravitational stirring (higher φ)resulted in a greater fraction of collisional material escaping beyondthe Hill sphere, andmore chondrules overall. Chondrules raining backonto evolved targets with thick crusts would be better preserved,although probably highly altered. This setting, of chondrules atop adifferentiated core-forming planetesimal, has been envisioned byWeiss et al. (2011) to explain chondrules like those in Allende whichhave relatively strong unidirectional magnetization.

Acknowledgements

This research was sponsored by NASA's Planetary Geology andGeophysics Program. Simulations were performed on the NSF-sponsored pleiades supercomputer. We are grateful for detailedreviews and forthright advice by John Chambers and Fred Ciesla, andfor insightful conversations with many colleagues. The paper isdedicated in fond memory of Betty Pierazzo.

References

Abe, Y., 2011. Protoatmospheres and surface environment of protoplanets. Earth MoonPlanets 108, 9–14.

Agnor, C.B., Asphaug, E., 2004. Accretion efficiency during planetary collisions.Astrophys. J. 613, L157–L160.

Alexander, C.M.O.'.D., Grossman, J.N., Ebel, D.S., Ciesla, F.J., 2008. Formation conditionsof chondrules and chondrites. Science 320, 1617–1619.

Amelin, Y., Krot, A.N., 2007. Pb isotopic age of the Allende chondrules. Meteorit. Planet.Sci 42, 1321–1335.

Asphaug, E., 2009. Growth and evolution of asteroids. Ann. Rev. Earth Planet. Sci. 37,413–438.

Asphaug, E., 2010. Similar-sized collisions and the diversity of planets. Chem. Erde 70,199–219.

Asphaug, E., Agnor, C.B., Williams, Q., 2006. Hit and run planetary collisions. Nature 439,155–160.

Benedix, G.K., Ketcham, R.A., Wilson, L., McCoy, T.J., Bogard, D.D., Garrison, D.H., Herzog,G.F., Xue, S., Klein, J., Middleton, R., 2008. The formation and chronology of the PAT91501 impact-melt L chondrite with vesicle–metal–sulfide assemblages. Geochim.Cosmochim. Acta 72, 2417–2428.

Benz, W., 2000. Low velocity collisions and the growth of planetesimals. Space Sc. Rev.92, 279–294.

Benz, W., Asphaug, E., 1995. Simulations of brittle solids using smooth particlehydrodynamics. Comp. Phys. Comm. 87, 253–265.

Bizzarro, M., Baker, J.A., Haack, H., Lundgaard, K.L., 2005. Rapid timescales for accretionandmelting of differentiated planetesimals inferred from 26Al–26 Mg chronometry.Astrophys. J. 632, L41–L44.

Boss, A.P., Durisen, R.H., 2005. Sources of shock waves in the protoplanetary disk. In:Krot, A.N, et al. (Ed.), Chondrites and the Protoplanetary Disk. ASP ConferenceSeries, San Francisco, pp. 821–838.

Bottke, W.F., Nesvorný, D., Grimm, R.E., Morbidelli, A., O'Brien, D.P., 2006. Ironmeteorites as remnants of planetesimals formed in the terrestrial planet region.Nature 439, 821–824.

Chambers, J., 2004. Planetary accretion in the inner Solar System. Earth Planet. Sci. Lett.223, 241–252.

Ciesla, F.J., 2010. Residence times of particles in diffusive protoplanetary diskenvironments. I. Vertical motions. Astrophys. J. 723, 514–529.





Ciesla, F.J., Hood, L.L., 2002. The nebular shock wave model for chondrule formation:shock processing in a particle-gas suspension. Icarus 158, 281–293.

Cuzzi, J.N., Alexander, C.M.O'.D., 2006. Chondrule formation in particle-rich nebularregions at least hundreds of kilometres across. Nature 441, 483–485.

Cuzzi, J.N., Hogan, R.C., Shariff, K., 2008. Towards planetesimals: dense chondruleclumps in the protoplanetary nebula. Astrophys. J. 687, 1432–1447.

Desch, S.J., Connolly Jr., H.C., 2002. A model of the thermal processing of particles insolar nebula shocks: application to the cooling rates of chondrules. Meteorit. Planet.Sci. 37, 183–207.

Desch, S.J., Ciesla, F.J., Hood, L.L., Nakamoto, T., 2005. Heating of chondritic materials insolar nebula shocks. In: Krot, N., Scott, E.R.D., Reipurth, B. (Eds.), ASP ConferenceSeries 341: Chondrites and the Protoplanetary Disk (A). Astronomical Society of thePacific, San Francisco, pp. 849–872.

Gooding, J.L., Keil, K., 1981. Relative abundances of chondrule primary textural types inordinary chondrites and their bearing on conditions of chondrule formation.Meteoritics 16, 17–43.

Hevey, P., Sanders, I., 2006. A model for planetesimal meltdown by 26Al, and itsimplications for meteorite parent bodies. Meteorit. Planet. Sci. 41, 95–106.

Hewins, R.H., Jones, R.H., Scott, E.R.D. (Eds.), 1996. Chondrules and the ProtoplanetaryDisk. Cambridge University Press, UK.

Hezel, D.C., Palme, H., 2010. The chemical relationship between chondrules and matrixand the chondrule matrix complementarity. Earth Planet. Sci. Lett. 294, 85–93.

Housen, K.R., Holsapple, K.A., 1999. Scale effects in strength-dominated collisions ofrocky asteroids. Icarus 142, 21–33.

Hutchison, R., Bridges, J.C., Gilmour, J.D., 2005. Chondrules: chemical, petrographic, andchronologic clues to their origin by impact. Chondrites and the Protoplanetary Disk,ASP Conference Series, 341, pp. 933–953.

Johansen, A., Oishi, J.S., Low, M.-M.M., Klahr, H., Henning, T., Youdin, A., 2007. Rapidplanetesimal formation in turbulent circumstellar disks. Nature 448, 1022–1025.

Jop, P., Forterre, Y., Pouliquen, O., 2006. A constitutive law for dense granular flows.Nature 441, 727–730.

Jutzi, M., Asphaug, E., 2011. Mega-ejecta on asteroid Vesta. Geophys. Res. Lett. 38,L01102.

Jutzi, M., Asphaug, E., in press. Forming the lunar farside highlands by accretion of acompanion moon. Nature.

Jutzi, M., Benz, W., Michel, P., 2008. Numerical simulations of impacts involving porousbodies: I. Implementing sub-resolution porosity in a 3D SPH hydrocode. Icarus 198,242–255.

Keil, K., 2000. Thermal alteration of asteroids: evidence from meteorites. Planet. SpaceSci. 48, 887–903.

Kieffer, S.W., 1989. Geologic nozzles. Rev. Geophys. 27, 3–38.Kleine, T., Mezger, K., Palme, H., Scherer, E., Munker, C., 2005. Early core formation in

asteroids and late accretion of chondrite parent bodies: evidence from 182Hf–182 Win CAIs, metal-rich chondrites, and iron meteorites. Geochim. Cosmochim. Acta 69,5805–5818.

Kokubo, E., Genda, H., 2010. Formation of terrestrial planets from protoplanets under arealistic accretion condition. Appl. J. Lett. 714, L21–L25.

Kokubo, E., Ida, S., 1998. Oligarchic growth of protoplanets. Icarus 131, 171–178.Krot, A.N., Amelin, Y., Cassen, P., Meibom, A., 2005. Young chondrules in CB chondrites

from a giant impact in the early Solar System. Nature 436, 989–992.Lee, D.C., Halliday, A.N., 1996. Hf–W isotopic evidence for rapid accretion and

differentiation in the early solar system. Science 274, 1876–1879.Libourel, G., Krot, A.N., 2007. Evidence for the presence of planetesimal material among

the precursors of magnesian chondrules of nebular origin. Earth Planet. Sci. Lett.254, 1–8.

Love, S.G., Ahrens, T.J., 1996. Catastrophic impacts on gravity dominated asteroids.Icarus 124, 141–155.

Melosh, H.J., Vickery, A.M., 1991. Melt droplet formation in energetic impact events.Nature 350, 494–497.

Meyer, M., Carpenter, J., Mamajek, E., Hillenbrand, L., Hollenbach, D., Moro-Martin, A.,Kim, J., Silverstone, M., Najita, J., Hines, D., Pascucci, I., Stauffer, J., et al., 2008.Evolution of mid-infrared excess around sun-like stars: constraints on models ofterrestrial planet formation. Astrophys. J. Lett. 673, L181–84.

Monaghan, J.J., 1994. Simulating free surface flows with SPH. J. Comp. Phys. 110,399–406.

Morbidelli, A., Bottke, W.F., Nesvorny, D., Levison, H.F., 2009. Asteroids were born big.Icarus 204, 558–573.

Morris, M.A., Desch, S.J., 2010. Thermal histories of chondrules in solar nebula shocks.Astrophys. J. 722, 1474–1494.

Navon, O., Lyakhovsky, V., 1998. Vesiculation processes in silicic magmas. In: Gilbert,J.S., Sparks, R.S.J. (Eds.), The Physics of Explosive Volcanic Eruptions, 145. GeologicalSociety, London, pp. 27–50. Special Publications.

Petaev, M.I., Meibom, A., Krot, A.N., Wood, J.A., Keil, K., 2001. The condensation origin ofzoned metal grains in Queen Alexandra Range 94411: Implications for theformation of the Bencubbin-like chondrites. Meteorit. Planet. Sci. 36, 93–106.


Pettit, D., 2003. Saturday Morning Science (videos). NASA ISS Expedition Six. http://spaceflight.nasa.gov/station/crew/exp6/spacechronicles_videos.html.

Pierazzo, E., Melosh, H.J., 2000. Understanding oblique impacts from experiments,observations and modeling. Annu. Rev. Earth Planet. Sci. 28, 141–167.

Qin, L., Dauphas, N., Wadhwa, M., Masarik, J., Janney, P.E., 2008. Rapid accretion anddifferentiation of iron meteorite parent bodies inferred from 182Hf–182 Wchronometry and thermal modeling. Earth Planet. Sci. Lett. 273, 94–104.

Ringwood, A.E., 1961. Chemical and genetic relationships among meteorites. Geochim.Cosmochim. Acta 24, 159–197.

Rust, A.C., Manga, M., Cashman, K.V., 2003. Determining flow type, shear rate and shearstress in magmas from bubble shapes and orientations. J. Volcanol. Geotherm. Res.122, 111–132.

Safronov, V.S., 1972. Evolution of the Protoplanetary Cloud and Formation of the Earth andPlanets, NASA TT-F-677.

Sahijpal, S., Soni, P., Gupta, G., 2007. Numerical simulations of the differentiation ofaccreting planetesimals with 26Al and 60Fe as the heat sources. Meteorit. Planet. Sci.42, 1529.

Sanders, I.S., Taylor, G.J., 2005. Implications of 26Al in nebular dust: formation ofchondrules by disruption of molten planetesimals. Chondrites and the Protoplan-etary Disk, ASP Conference Series, 341, pp. 915–932.

Scott, E.R.D., 2007. Chondrites and the protoplanetary disk. Annu. Rev. Earth Planet. Sci.35, 577.

Scott, E.R.D., Krot, A.N., 2005. Chondritic meteorites and the high-temperature nebularorigins of their components. In: Krot, A., Scott, E., Reipurth, B. (Eds.), ASP Conf. Ser.341, Chondrules and the Protoplanetary Disk. ASP, San Francisco, pp. 15–53.

Sears, D., 2004. The Origin of Chondrules and Chondrites. Cambridge Planetary ScienceSeries, Cambridge, New York. 209 pp.

Sorby, H.C., 1864. On the microscopic structure of meteorites. Phil. Mag. 28, 157–159.Sugiura, S., Nakajima, M., Iwamoto, S., Seki, M., 2001. Interfacial tension driven

monodispersed droplet formation from microfabricated channel array. Langmuir17, 5562–5566.

Takafuji, N., Hirose, K., Ono, S., Xu, F., Mitome, M., Bando, Y., 2004. Segregation of coremelts by permeable flow in the lower mantle. Earth Planet. Sci. Lett. 224, 249–257.

Tsang, T.H., Brock, J.R., 1984. On Ostwald ripening. Aerosol Sci. Technol. 3, 283–292.Uesugi, M., Sekiya, M., Nakamura, T., 2008. Kinetic stability of a melted iron globule

during chondrule formation. I. Non-rotating model. Meteorit. Planet. Sci. 43,717–730.

Urey, H.C., 1967. Parent bodies of the meteorites and the origin of chondrules. Icarus 7,350–359.

Urey, H.C., Craig, H., 1953. The composition of the stone meteorites and the origin of themeteorites. Geochim. Cosmochim. Acta 4, 36–82.

Villeneuve, J., Chaussidon, M., Libourel, G., 2009. Homogeneous distribution of 26Al inthe solar system from the Mg isotopic composition of chondrules. Science 325,985–988.

Villeneuve, J., Chaussidon, M., Libourel, G., 2011. Magnesium isotopes constraints on theorigin of Mg-rich olivines from the Allende chondrite: nebular versus planetary?Earth Planet. Sci. Lett. 301, 107–116.

Wadhwa, M., Amelin, Y., Davis, A.M., Lugmair, G.W., Meyer, B., Gounelle, M., Desch, S.J.,2007. From dust to planetesimals: implications for the solar protoplanetary diskfrom short-lived radionuclides. In: Reipurth, B., Jewitt, D., Keil, K. (Eds.), Protostarsand Planets V. U. Arizona Press, p. 835.

Walker, D., Mullins, O., 1981. Surface tension of natural silicate melts from 1,200–1,500 C and implications for melt structure. Contrib. Mineral. Petrol. 76, 455–462.

Wasson, J.T., Rubin, A.E., 2010. Metal in CR chondrites. Geochim. Cosmochim. Acta 74,2212–2230.

Weidenschilling, S.J., 1977. Aerodynamics of solid bodies in the solar nebula. Mon. Not.Roy. Astron. Soc. 180, 57–70.

Weidenschilling, S.J., Marzari, F., Hood, L.L., 1998. The origin of chondrules at jovianresonances. Science 279, 681–684.

Weiss, B.P., Elkins-Tanton, L.T., Barucci, M.A., Sierks, H., Snodgrass, C., Vincent, J.-B.,Marchi, S., Pätzold, M., Richter, I., Weissman, P.R., Fulchignoni, M., Binzel, R.P., 2011.Evidence for Partial Differentiation of Asteroid Lutetia from Rosetta. Submitted.

Wood, J.A., 1963. On the origin of chondrules and chondrites. Icarus 2, 152–180.Wood, J.A., 1988. Chondritic meteorites and the solar nebula. Annu. Rev. Earth Planet

Sci. 16, 53–72.Xu, L., Zhang, W.W., Nagel, S.R., 2005. Drop splashing on a dry smooth surface. Phys.

Rev. Lett. 94 (18), 184505.Yang, J., Goldstein, J.I., Scott, E.R.D., 2007. Iron meteorite evidence for early formation

and catastrophic disruption of protoplanets. Nature 446, 888–891.Yarin, A.L., 2006. Drop impact dynamics: splashing, spreading, receding, bouncing….

Annu. Rev. Fluid Mech. 38, 159–192.Yoshino, T., Walter, M.J., Katsura, T., 2003. Core formation in planetesimals triggered by

permeable flow. Nature 422, 154–157.


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