EPSL-10987; No of Pages 11
Earth and Planetary Science Letters xxx (2011) xxx–xxx
Contents lists available at ScienceDirect
Earth and Planetary Science Letters
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e p s l
Chondrule formation during planetesimal accretion
Erik Asphaug ⁎, Martin Jutzi, Naor Movshovitz
a r t i c l e
i n f o
Article history:
Received 10 January 2011
Received in revised form 3 June 2011
Accepted 6 June 2011
Available online xxxx
Keywords:
chondrules
chondrites
planetesimals
collisions
origins
a b s t r a c t
We explore the idea that most chondrules formed as a consequence of inefficient pairwise accretion, when
molten or partly molten planetesimals ~ 30–100 km diameter, similar in size, collided at velocities comparable
to their two-body escape velocity ~ 100 m/s. Although too slow to produce shocks or disrupt targets, these
collisions were messy, especially after ~ 1 Ma of dynamical excitation. In SPH simulations we find that the
innermost portion of the projectile decelerates into the target, while the rest continues downrange in massive
sheets. Unloading from pre-collision hydrostatic pressure P0 ~ 1-100 bar into the nebula, the melt achieves
equilibrium with the surface energy of chondrule-sized droplets. Cooling is regulated post collision by the
expansion of the optically thick sheets. on a timescale of hours–days. Much of the sheet rains back down onto
the target to be reprocessed; the rest is dispersed.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
The formation of terrestrial planets left thousands of unaccreted
bodies whose remnants are represented by chondrites, the majority of
meteorites 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 was
the widespread cause of melting of these small spherules, in a nebula
whose pressures were far too low for liquids to be stable? Why did
they solidify in hours to days, instead of tens of seconds as expected
for sub-mm droplets? Why are they so compositionally and texturally
diverse, when whole-rock chondrites are similar in aggregate
chemistry (c.f. Hezel and Palme, 2010)? Why are chondrules ≳1 Ma
younger than most of the iron meteorite parent bodies (Amelin and
Krot, 2007; Wadhwa et al., 2007)? In light of the significant
deficiencies in all chondrule-forming models, including the presently
popular idea that they formed in nebular shocks, we propose a new
answer to these questions.
1.1. Background
Physical models for chondrule formation must accommodate
several facts. Chondrules formed as a rather narrow size distribution
of spherules that were embedded in a fine-grained heterogeneous
matrix. This matrix is complementary (Hezel and Palme, 2010) in that
chondrite meteorites are much closer to solar composition than
chondrules or matrix separately (Wood, 1963). Chondrules solidified
⁎ Corresponding author at: Earth and Planetary Sciences Department, University of
California, 1156 High St. Santa Cruz, CA 95064, United States. Tel.: + 1 831 459 2260
(voice); fax: + 1 831 459 3074.
E-mail address: [email protected] (E. Asphaug).
in hours (Desch and Connolly, 2002) compared to seconds for a
silicate droplet radiating into space. They are found to have
crystallized in evaporative equilibrium with sodium and other
volatiles (Alexander et al., 2008) and show evidence for plastic
(almost-molten) pairwise collisions (Gooding and Keil, 1981) and
mergers. These latter aspects argue significantly for their formation in
dense, self-gravitating particle swarms (Alexander et al., 2008).
Lead isotope ages of certain chondrules have been determined to
high precision (Amelin and Krot, 2007; Villeneuve et al., 2009;
Wadhwa et al., 2007). They postdate CAIs by ≳1 Ma and appear well
represented only after the first 1–2 Ma of solar system history. Iron
meteorites sample ~ 50–100 core-bearing parent bodies that melted
≳0.5–1 Ma prior to chondrule formation (Bizzarro et al., 2005; Kleine
et al., 2005; Qin et al., 2008), so the late time of formation and the
widespread presence of magmatic planetesimals frames the debate.
1.2. Nebular models
Nebular models of chondrule formation (Wood, 1963) have
evolved into the presently popular idea that low density mechanical
aggregates 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 iron
meteorite 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 (Meyer
et al., 2008). Planetary embryos excited by Jupiter (Weidenschilling
et 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 lead
to shocks capable of melting dust and compressing the gas by a factor
of ~ 10. However, Cuzzi and Alexander (2006) calculate that the
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Please cite this article as: Asphaug, E., et al., Chondrule formation during planetesimal accretion, Earth Planet. Sci. Lett. (2011), doi:10.1016/
j.epsl.2011.06.007
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E. Asphaug et al. / Earth and Planetary Science Letters xxx (2011) xxx–xxx
chondrule-forming shocks must have been 100s to 1000s of km
across in order to experience limited isotopic fractionation; if so then
chondrule formation might require regional shocks, as are triggered
by density waves and gravitational instabilities (Boss and Durisen
2005). To accommodate the timing of chondrule formation
(Wadhwa et al., 2007) instabilities must take place for millions of
years. If dynamically-excited embryos set up the chondrule-forming
shocks, 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 requires size-dependent processing prior to melting, for instance
aerodynamical sorting (see Wood, 1988). It is more difficult to
explain in this context the stunning diversity of chondrule types and
compositions over intimate spatial domains (see e.g. Ciesla, 2010). All
chondrite groups show a wide range of chondrule compositions, and
the ratio of olivine to olivine + pyroxene in porphyritic (the most
common) chondrules ranges from b1% to N99% (see Scott and Krot,
2005). Why should one dust bunny's chemistry or its shock be so
different from the one adjacent?
Chondrule-forming nebular shocks must leave behind a selfgravitating swarm according to the formation densities calculated
by Alexander et al. (2008). Assuming shock compaction by a factor
of ~ 10, the pre-shocked swarms must be within an order of
magnitude of instability already. Cuzzi et al. (2008) and Johansen
et al. (2007) show how particles might coalesce in turbulent eddies
into local-scale accumulations that might be close to self-gravitating,
and like Morbidelli et al. (2009) we regard turbulent clumping as the
likely cause for the rapid accretion of the first planetesimals, bypassing
the 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 clumping coincided with the shock, then the turbulence must be tied to the
long range gravitational forcing (disk instability or forcing by distant
planets). We favor the scenario where turbulent clumping leads
directly to planetesimal formation, with chondrules forming later
from the planetesimals.
One challenge to nebular models is the inclusion of Mg-rich silicate
grains that formed at elevated temperatures and pressures (Libourel
and Krot, 2007; Villeneuve et al., 2011) within various CV-class
chondrules. These might have derived from a precursor body, later
disrupted and incorporated into chondrules. However, massive and
energetic collisions—reversing accretion—are required to disrupt
≳ 10 km planetesimals into tiny bits. We favor an alternative where
these inclusions derive from crusts and unmelted components (with
their own complicated histories) of the same disrupted planetesimals
that form the chondrules.
Nebular models require circumstances that have specific implications for nebula physics and planet formation (e.g. Chambers,
2004; Ciesla, 2010; Desch et al., 2005). The early nebula was a
complex place with diverse and coinciding processes competing for
dominance. That said, we now turn to a process that certainly
occurred in the first few Ma of solar system history: the pairwise
accretion of molten planetesimals.
1.3. Planetesimal models
If chondrules formed in collisions or igneous eruptions (see
Hutchison et al., 2005; Sorby, 1864; Urey and Craig, 1953) then the
nebula played a background role, damping the relative motions and
contributing to the chondrite matrix. These models have not ascribed
a satisfactory physics to their process. Appendix I of Wood (1963)
debunks planetesimal models, and his arguments have been convincing. While Krot et al. (2005) reason that some of the latest (~5 Ma
post-CAI) iron-rich (CB, CH) chondrules formed in a single large
impact, these chondrule types are uncommon; at question is not
whether impacts ever formed chondrules, but whether the majority of
common chondrites derive from disrupted planetesimals.
Molten spherules can be produced directly from solids, when
shock waves release during hypervelocity collisions. But impact
spherules are physically and chemically distinct from chondrules
(Melosh and Vickery, 1991). Furthermore, impact shock requires
random velocities orders of magnitude faster than vrand ~ vesc expected
during accretion. Hypersonic collisions are characteristic of smallbody populations that are eroding rather than accreting; present-day
asteroids do not produce chondrules. Thus we focus on alreadymelted planetesimals.
1.4. Melted bodies
According to thermal models, the radioactive decay of primeval
Al, with half-life τ1/2 = 0.72 Ma, led to the meltdown of planetesimals ≳30 km diameter that accreted in the first ~1 Ma (Hevey and
Sanders, 2006; Sahijpal et al., 2007). This agrees with radioisotopic
(Bizzarro et al., 2005; Kleine et al., 2005; Lee and Halliday, 1996) and
petrological (Keil, 2000) records. A planetesimal might have a
significant melt fraction in the timeframe of chondrule formation,
beneath a solid carapace that started out thick (melting begins at the
center), thinned rapidly during maximal heating, and then gradually
thickened into a crust following several τ1/2.
Melted planetesimals can differentiate into cores and mantles.
The chondrite parent bodies did experience signature variations in
metallic iron ranging from metal poor (L, LL) to high (H, CB/CH),
although not complete differentiation. Varying levels of partial
differentiation are expected for planetesimals ~ 30–100 km diameter
because interfacial tension is high for metals and silicates, whereas
gravity is smaller than achievable on most ‘zero gravity’ parabolic
research flights. The driving force for core segregation could well be
much smaller than the interfacial stresses borne by metal percolating
through silicate, or by the immiscible components in a complete
melt.
Gravity acting on a metal globule of radius r is 4/3πr 3Δρg. The
density difference Δρ is ~ 4.5 g cm − 3 for metallic iron suspended in
silicates; lower for FeS. The Eödvös (Bond) number Eo = Δρgr 2/γ is
the measure of the relative importance of interfacial stress γ/r to the
gravity (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 until
some other process first agglomerates metals into ~ 10 cm blobs
(m ~ 10 kg), or increases the effective g by shaking. Capillary action
can coalesce liquids if the dihedral (wetting) angle exceeds a
threshold (typically ~ 60°), but experiments show that iron droplets
remain stuck to silicate junctures until pressures exceed ~ 400 kbar
(Takafuji et al., 2004). Molten FeS alloys drain effectively at lower
pressures, 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 yield
stress, for instance the case of iron droplets. Suspended in a fully
melted basaltic magma (viscosity η ~ 10 4 P). The Stokes settling
timescale to the core is ~ η/Gr 2ρΔρ (independent of planetesimal
radius R) where ρ is the planetesimal bulk density, or ~0.1–1 Ma for
0.1-1 mm diameter droplets, and longer for more viscous magmas.
The solar-composition carapace might further sustain the primitive
signature in a melting body for some time. While collisional shaking
might dislodge and coalesce small droplets, larger collisions would
stir up the settling mixture, as might thermal and magnetically
induced convection. The above calculations suggest core formation
occurred with varying efficiency in melted planetesimals, consistent
with the wide range of metallic iron in chondrites.
26
Please cite this article as: Asphaug, E., et al., Chondrule formation during planetesimal accretion, Earth Planet. Sci. Lett. (2011), doi:10.1016/
j.epsl.2011.06.007
E. Asphaug et al. / Earth and Planetary Science Letters xxx (2011) xxx–xxx
1.5. Splashing and eruption
The largest obstacle to forming chondrules from planetesimals is
not chemical or petrological but physical. Impact splashing (Sanders
and Taylor, 2005) and volcanic eruption (Ringwood, 1961) have been
considered, but the physical models remain conceptual and face major
challenges. Either process would be inhibited by the presence of a
substantial unmelted carapace that could be kilometers thick.
Ignoring the carapace for a moment, consider splashing which
occurs when a projectile strikes a target. The ejecta curtain shears
against the nebula, forming droplets if it attains high Weber number
We= ρv 2r/γ, the measure of inertial shear stress ρv 2 relative to surface
energy γ/r for instabilities of dimension r (c.f. Yarin, 2006), where
ρ = ρnebula. Impact splashing is not an efficient process for droplet
production (Xu et al., 2005) in p
a ffiffiffiffiffiffiffiffi
nebula. For ρnebula ~ 10− 9 g cm− 3,
supersonic shearing velocities v N γ=ρ ~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, in
laboratory and numerical experiments, would require further breakups
and size-sorting in the aftermath.
Suppose impact splashing could excavate through a carapace and
create dense swarms of ~0.1–1 mm diameter chondrules. These would
reaccumulate rapidly onto the target unless ejected at ≳vesc/√2. Given
the steep mass-velocity distribution of crater ejecta, an impact velocity
≫vesc is required for massively efficient chondrule production, at odds
with the quiescence of ongoing accretion. Atomization of droplets for
industrial applications (Sugiura et al., 2001) relies upon a nozzle to
generate a drop in downstream pressure, a concept we consider below
in 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 of
chondrules. This was disputed by Wood (1963) who argued that the
compositions, textures and sizes are very different (for instance, tuffs
including all kinds of non-droplet sheets and strands). More
fundamentally, no plausible thermodynamic source has yet been
identified that can account for massive scale chondrule-forming
eruptions on planetesimals, even given the substantial evidence for
their igneous interiors (Keil, 2000). Volcanoes on Earth and Mars can
accelerate eruptive materials to velocities exceeding 100 m/s, but only
because 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 skip
downrange 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 overshooting
their targets. The slowest possible collisions between ~30 and 100 km
bodies are violent, about the speed of a car crash, and in simulations
they produce sheets of dispersed materials deriving mostly from the
interior of the smaller body. The outcome is sensitive to collisional
energy above the binding energy, or equivalently the normalized
randomqvelocity
φ = vrand / vesc, where
the two-body escape velocity
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
vesc = 2G Mp + MT = ðRP + RT Þ ~ 30–100 m/s for 30–100 km planetesimals where MP and MT are colliding (spherical) masses of radii
RT N RP, and G is the gravitational constant. Although fast, the collisions
occur on a timescale ~R/vimp of several hours. If vimp ~ vesc then the
collision 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 dynamical
environment strongly damped by gas and dust, φ ~ 0 and almost all
collisional materials are ultimately bound to the final body. The final
mass Mfinal is simply the sum of the colliding masses MT + MP, so the
accretion efficiency ξ = (Mfinal − MT) / MP ~ 1. The draping back of the
3
sheet can take days and leave layered structures (c.f. Jutzi and
Asphaug, 2011). In all likelihood the aftermaths of the earliest
accretionary collisions were buried under subsequent collisions, to
be remelted and removed from the geologic record.
Later collisions, after the clearing of the gas and dust, were excited
by random self-stirring (Safronov, 1972) and by resonant coupling
with embryonic planets and gas giants (Weidenschilling et al., 1998).
This led to random velocities φ ~ 1 associated with the heyday of
oligarchic growth (Kokubo and Ida, 1998) and the giant impact phase
of terrestrial planet formation (Chambers, 2004). But in fact partial
accretion (ξ b 1) and hit and run (ξ ~ 0) account for most collisions
when φ ~ 1 (Agnor and Asphaug, 2004).
To understand the prevalence of hit and run and partial accretion
during planetesimal growth, we have constructed a Monte Carlo
simulation beginning with a swarm of planetesimals merging under
random pairwise collisions until there are fewer. It is not dynamically
meaningful, as there is equal probability of collision between any two
objects, but allows us to analyze trends. We characterize the
outcomes of pairwise collisions using Fig. 8 of Asphaug (2010),
approximating the gradation between efficient accretion, partial
accretion, and hit and run as a step function ξ = 1 or 0. Collisions
involving much smaller bodies and larger targets are mergers, being
slow cratering events. Collisions between two bodies b1/30 the
diameter of the largest are treated as catastrophic, because here
vrand ≫ vesc. These have a minor effect. A planetesimal's hit-and-run
tally h increases each time it collides into a larger body but does not
accrete; h is a simple representation of a complicated evolution, since
each surviving planetesimal can be partly accreted, or torn into
multiple bodies (e.g. Yang et al., 2007), or dispersed.
Results are shown (Fig. 1) for 10 5 initial planetesimals randomly
accreting pairwise, assuming that (a) 50% (φ ~ 1), (b) 70%, (c) 90% or
(d) 98% (φ ~ 0) of similar-sized collisions (SSCs) are perfect mergers.
When 90–98% are perfect mergers h remains small. But when ~1/4 to 1/2
of the outcomes are hit and run (a, b) there evolves a majority of middlesized bodies with h ≥1. When 50% of collisions are perfect mergers,
characteristic for φ ~ 1, nearly all of the next-largest bodies (NLBs, the
feedstock of the largest) have had 2–5 hit and run collisions. The overall
implication is great diversity of planetesimal evolution, and modes of
mass excavation and collisional interaction beyond the traditional
physics of impact cratering and catastrophic disruption by shock.
While NLBs can be disrupted by hit and run collisions repeatedly
until they are accreted or destroyed, the growth of the largest bodies
proceeds apace (Kokubo and Genda, 2010). They do not encounter
larger bodies, and the random velocities of smaller projectiles within
the population are too slow to disrupt them. But in detail they grow
from an increasingly evolved feedstock, NLBs stripped of mantles,
oceans and atmospheres. Thus the more dynamically excited regions
of an accreting solar system might end with next-largest planets that
are drier and more reduced (Asphaug, 2010).
Likewise regarding chondrule formation, we expect a trend
towards iron-rich composition if accretion proceeds in the presence
of random stirring. This is supported by the late ages of the most
metal-rich chondrules (Krot et al., 2005). Furthermore, the likelihood
of multiple hit and run collisions (Fig. 1) is consistent with evidence
for multi-stage formation, heating, alteration, and recycling of
chondrules and chondrites.
2. Simulation methods
We simulate collisions using a parallel 3D hydrocode running at
high resolution (~10 6 particles). The method is smooth particle
hydrodynamics (SPH) with a grid-based self-gravity solver (Jutzi and
Asphaug, 2011, in press; Jutzi et al., 2008). We use the Tillotson
equation of state for iron and basalt, and treat both colliding bodies as
liquids except for the solid carapace, which we model using a granular
rheology (Jop et al. 2006) that has Mohr–Coulomb type behavior.
Please cite this article as: Asphaug, E., et al., Chondrule formation during planetesimal accretion, Earth Planet. Sci. Lett. (2011), doi:10.1016/
j.epsl.2011.06.007
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E. Asphaug et al. / Earth and Planetary Science Letters xxx (2011) xxx–xxx
a
b
c
d
Fig. 1. In a gravitationally stirred system of planetesimals with vrand / vesc = φ ~ 1, approximately half of similar-sized collisions are hit and run (Asphaug, 2010; Agnor and Asphaug, 2004). In
a 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) where
100,000 initial bodies ranging a factor of 10 in mass accrete by random pairwise collisions into 1000, 100, 30, 10, 3 and finally 1 body. The probability of perfect merger 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 by 1, with h
mass-averaged during accretion. For typical random stirring (a, b) the ten or so ‘next largest bodies’ (NLBs) have quite diverse histories, and typically h N 1.
The goal of these simulations is to understand the global dynamics
and provenance of unaccreted material that might form chondrules.
They are limited to the first ~10 h, a few dynamical times. Because there
are no shocks, there is little thermal evolution other than advection. The
hydrodynamical model and its equation of state do not attempt to
capture phase transformation, phase mixing, solution of volatiles, or the
radiative evolution of the expanding thick sheets of ejecta. Iron
represents differentiated core material. In the absence of shocks, basalt
is a suitable placeholder for primitive silicate-dominated materials of
similar bulk composition and density. Initial planetesimals are hydrostatically 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 = 36 m/s), so we can in principle use a softer bulk modulus by
a factor of 103–104. We reduce it by 100, to 2.7× 109 dyn/cm2 in the
mantle, improving the pressure resolution while increasing the
timestep—a trick for relatively incompressible flows (Monaghan,
1994) that is needed to run the high resolution simulations to
completion. The softened modulus does not greatly affect the pressure
and dynamical history, as we have verified in lower resolution
comparison simulations. With these simplifications each 106 particle
run takes a machine-day on 32 parallel processors.
Droplet formation is represented constitutively as a free expansion
under 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 tensile
stress. Surface tension is γ ~ 400 dyn/cm for a wide range of magma
types (Walker and Mullins, 1981); at the scale of a particle smoothing
length (r ~ 300 m) surface stress γ/r is less than a micobar, and safely
ignored. At chondrule-forming scales, however, the atomization of a
silicate magma requires much greater surface energy ~10 4 erg/g,
comparable to the hydrostatic pressure P0/ρ, an aspect addressed by
our chondrule formation model (Section 4.1).
2.1. Rheological approach
Four of the simulations presented (Table 1) involve liquid planetesimals, while a fifth includes a carapace of solid material, modeled using a
granular 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 stressdependent shear strength makes the lid somewhat sluggish to deform;
however, in our simulations it moves almost as freely as a liquid rheology
(Fig. 4). An intact lid supporting tensile stress should also be modeled
(Benz and Asphaug ,1995; Jutzi et al., 2008); this is not yet achievable as it
requires a much smaller timestep for accurate damage integration and
several times the resolution. However, at ~30 km scales solid rocks are
quite weak under tension, with static tensile strength scaling as ~R− 1/2
(e.g. Housen and Holsapple, 1999; see Asphaug, 2009); accordingly
tensile strength would be b1 bar.
Please cite this article as: Asphaug, E., et al., Chondrule formation during planetesimal accretion, Earth Planet. Sci. Lett. (2011), doi:10.1016/
j.epsl.2011.06.007
E. Asphaug et al. / Earth and Planetary Science Letters xxx (2011) xxx–xxx
5
Table 1
Summary 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 the
projectile 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 is
originally molten (not part of either lid in Run 5) and its density fell below a critical value (2 g cm− 3), indicating distension. A fraction are bound (a lower limit, given that no nebula
drag 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 into
chondrule-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 the
target 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 is
contributed. Run 5 is very similar to Run 2 dynamically, but most of the materials in the sheet are solids.
Run
1
2
3
4
5
Impact velocity
(in vesc)
Impact angle
(degree)
Lid
1
2
2
4
2
30
30
60
60
30
–
–
–
–
5 km
Chondrite formation (in projectile masses MP)
From projectile
Total
From target
Escaping
Bound
Total
Escaping
Bound
Total
0.01808
0.43652
0.14640
0.39109
0.10955
0.27378
0.21565
0.21587
0.27114
0.05936
0.2919
0.6522
0.3623
0.6622
0.1689
0.0019
0.1152
0.1223
0.9844
0.0000
0.0879
0.3682
0.5305
2.1345
0.0207
0.08972
0.48339
0.65274
3.11891
0.02066
Regarding fluid behavior, if a planetesimal's resistance to deformation can be characterized by a linear viscosity η, then Asphaug et al.
(2006) estimate that a terrestrial planetesimal of radius R, responding
to a gravity-regime encounter on a timescale ~ (Gρ) − 1/2, will undergo
global scale deformation in response to a gravity-regime
stress ~ Gρ 2R 2 only if η ≲ 10 13P(R/1000 km) 2. Accordingly, planetesimals ~30 km diameter with viscosity b10 10 P can be approximated in
a collision as inviscid fluids. Basaltic magmas are in the range ~10 4 P,
while silicic evolved magmas can be ≳ 10 12 P. Primitive melts are
expected to be ≪10 10 P, but partial and clast-rich melts can have
higher viscosities. In addition, bubble nucleation can occur during
pressure unloading and initially stiffen an extruding magma. High
viscosity might hinder, or localize, the hours-long deformation of a
molten planetesimal during similar-sized collisions.
0.38157
1.13557
1.01500
3.78114
0.18957
Generally speaking, rigid, granular and viscous responses are
dominant for smaller, colder planetesimals, while powerful shocks
render rheological nuances inconsequential at the scales of giant
impacts: the stresses go as R 2 while the global strains and strain
rates are scale-similar. Furthermore, viscosity is not linear; it is
lower 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 importance
for large ones (Asphaug et al., 2006).
We have shown that a comparatively simple rheology—a granular
lid atop an inviscid interior—is appropriate for this initial exploration
of our hypothesis. To simplify the study and its interpretation, our
baseline calculations (Runs 1–4) do not involve the granular model.
More comprehensive thermodynamical and rheological treatments
Fig. 2. Snapshots of Runs 1–4 (Table 1) plotting pressure 2.2 h after contact. Slices define the symmetry plane of each 3D simulation. The long arms are sections of broad sheets
(Fig. 3). Each plot is 500 km on a side. In each, a 30 km planetesimal has collided with a 70 km planetesimal at 30° (top figures, nearly grazing) or 60° (bottom, nearly head-on). The
slowest possible 2-body collision (vimp = vesc; 36 m/s for the bodies modeled) has 98% (or more, depending on nebula drag) of the depressurized (chondrule-forming) material
falling back, some promptly and the rest after days-months. Plotted is log(P) in dyn cm− 2 (= μbar); orange ~ 1–10 bar while blue is effectively zero. The collisions are ~ 30–100 times
slower than the sound speed, so that even the 144 m/s collision (bottom right) maintains approximately hydrostatic pressure.
Please cite this article as: Asphaug, E., et al., Chondrule formation during planetesimal accretion, Earth Planet. Sci. Lett. (2011), doi:10.1016/
j.epsl.2011.06.007
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E. Asphaug et al. / Earth and Planetary Science Letters xxx (2011) xxx–xxx
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 impactor
mass 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 to
the 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 petrologic
evolution during and after planetesimal collisions, and to model
specific meteorite-forming scenarios involving clast-rich, viscous, or
smaller-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 km
diameter projectile is only ~ 1/3 molten in this case. As Table 1 summarizes, ~ 1/4 as
much chondrule (melt droplet) mass is produced from the projectile in Run 5, and
virtually 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 the
parameter space: efficient accretion (φ = 0, ξ ~ 1), partial accretion
(ξ b 1) including the case where both bodies have a 5 km solid carapace,
and two cases of hit and run (ξ ~ 0). Each collision involves essentially
the same projectile and target, colliding at either 30° or 60° (where 90° is
head-on), at impact velocities vimp = 1, 2 and 4·vesc (φ = 0, 1.7, 3.9),
where vesc = 36 m/s. The projectile, from which most of the chondrules
derive, has radius RP = 15 km, mass MP = 54.4× 1019 g, a silicate mantle,
and a 3 wt.% iron core. The target is RT = 35 km, MT = 3.9 × 1019 g, with
larger (16 wt.%) iron core, and silicate mantle.
The core fractions are notional, representing states of incomplete
differentiation. The hydrodynamical evolution of the projectile
material during the collision and downrange is not very sensitive to
the presence or absence of a small core, but core-mantle and core–
core interplay can be dominant for collisions involving large core
fraction (large h), perhaps relevant to the metal-rich CB and CH
classes and to the evolution of metallic meteorites.
For efficiency we begin each simulation by placing the two
spherical, hydrostatic planetesimals into almost-contacting configuration, q
assigning
the
projectile the contacting impact velocity
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
vimp = v2rand + v2esc coming from the right. This introduces some
error, because fluid projectiles deform into a rugby-ball shape as they
free-fall towards collision. This deformation is potentially important
to the specific outcome of any one collision, having an effect
comparable to pre-impact spin (which we also neglect for now). But
it is not important to understanding the general characteristics of
these events.
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3. Results
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Table 1 lists impact velocity (vimp/vesc = φ2 þ 1), 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 of
MP) that has evolved to ρ b 2 g/cm 3 by depressurization expansion.
Fig. 2 shows Runs 1–4 (the cases with no lid), each at 2.2 h after initial
contact, plotting pressure in the symmetry plane of the collision. The
overall trend in all simulations is to produce thick sheets of
depressurized material, mostly from the projectile. Fig. 3 plots Run
1 in 3D, showing the expansive sheets. The projectile core is seen
faintly 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 the
mantle.
The effect of a substantial solid carapace is seen in Fig. 4, where the
top is Run 2 at 3.3 h post impact, and the bottom is Run 5 with a 5 km
solid 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 stressdependent shear strength, the presence of a massive lid makes
surprisingly little difference to the dynamics, for collisions at this scale
and larger.
We identify four candidate chondrule-forming regions: (1) melts
from the projectile that remain within the Hill sphere of the final body
and are eventually accreted; (2) melts from the projectile that escape
the final body; (3) melts from the target that are ejected to vesc; and
(4) melts from the target that become part of the depressurized sheet
but are reaccreted. The nebula interacts with chondrule-forming
materials accordingly. There is also variation according to the depth
from which chondrules were exhumed within their original bodies
(see Figs. 6 and 7). Also, bound chondrules will accrete in layers, with
those ejected at ≲ vesc/√2 landing in hours, and those ejected near vesc
coming back in weeks to months.
Although we have yet to explain why chondrule droplets should
form from these ejected melts, we have run enough simulations to
demonstrate two key phenomena: the partial merger of one body
with another (including its core), and the production of dense sheets
of unaccreted material going off into the nebula. The merged body is
part of a new, more fully differentiated planetesimal and is more likely
than before to end up as a planet. Chondrules, deriving in our model
from unaccreted planetesimals, have an opposite aspect to their
evolution.
4. Droplet formation
Droplet formation is approximated dynamically in our simulations
by zeroing out tensile pressure, reasoning that magma has negligible
tensile strength across ~300 m scales (the SPH resolution). That is, the
cavitation threshold is ≪P0. We now consider in somewhat more
detail what happens when P0 unloads in a disrupted magmatic
planetesimal as it transitions from a continuous volume of melt at
hydrostatic pressure, into a distributed mass or sheet with large
surface area supported by the near-vacuum pressure of the nebula.
4.1. Binding energy and surface energy
pffiffiffiffiffiffi
In accretionary collisions the strain rate ξ∼ Gρ ∼1 h − 1, orders of
magnitude slower than the rates associated with eruptive magmatic
ascent on Earth and thus a different physical regime. At very low
strain rates, in milligravity, surface energy is expected to play a
dominant role in the energy balance. There is abundant evidence for
surface tension and interfacial tension acting between metals and
silicates in chondrules (Uesugi et al., 2008; Wasson and Rubin, 2010;
Wood, 1963), and this motivates the following consideration of
surface tension as the determinant of chondrule size.
7
The sheets of material in the simulations are exhumed from a
characteristic hydrostatic pressure P0 ~ Gρ 2R 2, making available
specific enthalpy that is derived ultimately from gravitational binding.
Enthalpy is spent when water and other volatiles come out of solution,
but this is limited by the availability of free surfaces. This leads to a
balance of P0 by the Laplace pressure PL = 2γ/r across the droplet
interface (c.f. Sugiura et al., 2001). According to this analysis, the
larger pressure drop from larger progenitors (VdP ~ GM/R) results in
smaller droplet sizes r. This leads to a simple, though undoubtedly
approximate, relationship between the radius R of a disrupting
planetesimal and the radius r of characteristic chondrules that derive
from its unloaded magma:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
R = 1 = ρ 2γ =GrE:
ð1Þ
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 gasdriven aspect to the droplet-forming process is undoubtedly important, 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 and
reduced γ (smaller, perhaps irregular chondrules). Enthalpy losses to
vapor expansion, heat of dissolution and crystal growth might tend to
larger droplets. Thus much physics and chemistry is contained in E,
and laboratory studies of basaltic magmas or their analogs are
required under milligravity conditions and hours-long unloading
timescales. Relatively low cost experiments should be feasible on
orbital research platforms given the ~1 bar pressure conditions in
planetesimals and the availability of safe analog materials such as
water (see Pettit, 2003). For now we take E to be the ratio of
chondrule-forming mass to non-chondrule matrix in a chondrite,
adopting E ~ 1/2.
The surface tension of silicate magma (γ ~ 400 dyn/cm; Walker and
Mullins, 1981) is about equal to that of Hg, familiar to those who have
broken a glass thermometer. The viscosities are higher, and beading
by surface tension requires strains of order unity on the timescale of
the pressure unloading (~ τgrav). Thus the limiting viscosity is the same
as derived earlier (Section 2.1) for the global deformation, η b ~10 10 P
to allow beading (ε ~ 1) to occur within an hour.
Eq. (1) is plotted in Fig. 5, from which we deduce that chondrulesized droplets can derive from 10 to 20 km diameter bodies. This is a
lower estimate on R. A larger projectile (30 km) is modeled in Runs
1–5 on the expectation that droplet–droplet accretion and Ostwald
ripening (Tsang and Brock, 1984) will occur within the sheets prior to
cooling, resulting in larger final droplets. In any case, gravitydominated collisions are scale similar (Asphaug, 2010) so the
dynamics 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 central
parts of the sheet.
4.2. Accumulation and dispersal
In the slowest collisions most ejecta remains gravitationally bound
to the final body, although even for φ = 0 the accretion efficiency ξ is
not 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 is
transformed, if molten, into a large sheet of droplets according to our
analysis. The droplet-rich sheet reaccretes over a period of hours to
days onto the final body.
With increasing collisional energy the fraction that escapes
increases; this consequence depends sensitively upon the impact
angle and energy (Asphaug, 2010). For φ N 2 only a fraction of
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collisions result in mass growth; projectiles end up downrange (and
usually disrupted). Direct hits at even higher velocity can result in the
projectile 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) but
contributes more than half of the impactor and all its core. Much
higher impact energies are required to catastrophically disrupt the
targets (Love and Ahrens, 1996), and are anticipated only later in
accretion. The ~ 30–100 km planetesimals required by our chondrule
forming mechanism would likely have solidified before this time.
4.3. Chondrule fate and layering
Fig. 5. The larger body disrupts the smaller in a hit and run collision, rather than the
other way around. Assuming that this release from hydrostatic pressure is accommodated by droplet formation, then chondrule radius r can be estimated by equating the
Laplace 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 tension
γ = 400 dyn/cm is characteristic of silicate melts at 1 bar; liquid iron has γ ~ 3-4
times higher, decreasing with oxygen abundance. Typical silicate chondrules are
0.1–1 mm diameter, indicating in principle a ~ 5–10 km radius melted parent
planetesimal, disrupting by a target body several times larger. But droplet–droplet
accretion likely occurs as an intermediate step, and furthermore the internal pressure
P0 is lower in the exterior, so Equation 1 underestimates R. We therefore consider a
30 km diameter projectile as a representative chondrule-forming body in our SPH
simulations.
Chondrule dispersal into the nebula is regulated by particle size,
spatial distribution, ambient gas density, and the characteristic
velocity of the swarm. Individual escaping chondrules might easily
be stopped inside the planetesimal's Hill sphere by gas drag,
accumulating matrix materials from the local environment before
coalescing. Energetic plumes of chondrules might escape and
disperse, possibly to be collected onto other nearby planetesimals or
into discrete bodies. In the absence of a nebula, isolated chondrules
might 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 be
solidified before impacting, although the interiors of dense sheets
might remain molten. Reaccumulated chondrules might experience
secondary heating after they are piled in massive layers upon the
target, which is presumably also partly or largely molten. This
secondary heating would be more gradual and much longer lasting
than the exhumation and cooling of the chondrules. Follow-on hit and
Fig. 6. Pressure and initial radius within the projectile (top two rows) plotted in the symmetry plane of the escape-velocity collision (vimp = vesc = 36 m/s; Figs. 2a and 3; Run 1) at
times 0, 4000, 8000 s after impact. Pressure (a–c) is log(P) in dyn/cm2 from millibars (blue) to tens of bars (red). Hydrostatic pressure is largely maintained in the target while the
projectile unloads into a sheet. The core of the projectile is stopped by the target (e, f) while ~ 60% of the projectile continues downrange; of this ~ 2% has escaping velocity (Table 1).
Mixing of projectile and target has begun (f). Droplet radius is plotted in (g–i), where P0 inside the projectile and target converted into droplet radius r according to Eq. (1), but
plotted as brown until the material cavitates (P b 0) and expands to ρ b 2 g cm− 3. The bottom color bar is thus the equivalent droplet radius r(cm), logarithmically from 10 μm (bluegreen), to 0.1 mm (yellow), to 1 mm (red). Molten droplets will coalesce or ‘ripen’ after their formation in the dense swarm, so Equation 1 is a lower limit to chondrule size.
Please cite this article as: Asphaug, E., et al., Chondrule formation during planetesimal accretion, Earth Planet. Sci. Lett. (2011), doi:10.1016/
j.epsl.2011.06.007
E. Asphaug et al. / Earth and Planetary Science Letters xxx (2011) xxx–xxx
9
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: core
bounces 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 in
the 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 are
smaller, 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 the
projectile 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 enhancing
the 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 further
scramble the stratigraphy and recycle these materials.
4.4. Cooling post formation
Cooling of chondrules in a swarm is limited by opacity (Cuzzi and
Alexander, 2006). Because opacity ≫1 in the sheet (~100 km thick),
cooling is regulated by the expansion timescale. The downrange
velocity of the overshooting part of the projectile is only slightly
decelerated by the impact, while the rest is stopped abruptly, giving
an expansion timescale ~ R/vimp ~ τgrav of order 1 h (as evident in Figs. 6
and 7). The cooling rate also depends on local swarm density and
proximity to the boundary; significant variation in cooling time and
also isotopic variation are expected within smaller-scale swarms
(Cuzzi and Alexander, 2006). For a fixed projectile diameter, faster
collisions produce faster-cooling ejecta.
Cooling time increases with projectile size. Opacity scales like the
swarm radius, which is comparable to RP; it also scales inversely with
droplet size which goes as ~ 1/RP2 according to Eq. (1). The opacity thus
overall scales as ~ RP3, allowing us to address a lingering question:
where are the ‘chondrules’ from the completely differentiated
mantles of larger, later bodies? Large collisions were less common
than small ones, but the mass produced was proportionately copious.
One explanation is that 26Al heat production was diminished, by a
factor of ~10 after ~ 2 Ma. Time ran out, and the ~ 100–300 km
planetesimals solidified before there existed ~ 300–1000 km bodies
for them to collide with.
Eq. (1) provides another explanation: droplets erupting from
P0 ~ kbar would be dust-sized rather than chondrule sized. Clumps
accumulating, or masses falling back onto the target body, would not
have a chance to cool below solidus given the very high opacity of a
self-gravitating swarm of μm-sized droplets ~ 100–1000 km in extent.
Heat could not get out during τgrav and the result would be igneous
Please cite this article as: Asphaug, E., et al., Chondrule formation during planetesimal accretion, Earth Planet. Sci. Lett. (2011), doi:10.1016/
j.epsl.2011.06.007
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E. Asphaug et al. / Earth and Planetary Science Letters xxx (2011) xxx–xxx
rock. Escaping dust would be dragged into the Sun on a short
timescale, in the absence of a nebula, and one or more such events
might contribute to the olivine and pyroxene rich dust found in
meteorites and IDPs.
4.5. Metal spheres and vesicles
The presence and distribution of reduced iron in the chondruleforming melt can help us piece together the thermodynamic and
physical conditions of their formation (Wasson and Rubin, 2010). But
outstanding questions remain. Why are iron-rich chondrules rare in
comparison to silicate chondrules, and found only in a few subclasses
of chondrites, when iron was abundant and subject to similar
collisional forces? One answer is that cores are harder to excavate
(e.g. Love and Ahrens, 1996). Another is that molten silicate has lower
surface energy than Fe and FeS. Surface energy calculations by Uesugi
et al. (2008) suggest that liquid metallic iron, in the absence of gravity,
would wet the surface of melted silicate chondrules, adhering rather
than forming iron chondrules of its own. This would explain iron rims
‘armoring’ many chondrules, and blebs of iron linked around
chondrules in CR meteorites (Wasson and Rubin, 2010; Wood, 1963).
If iron was excavated in abundance, either by more energetic
collisions or by collisions involving high-h mantle-denuded projectiles (Fig. 1), then iron chondrules might form by a process similar
to that postulated for silicate chondrules. This requires metallic Fe to
be so abundant that there is comparatively little silicate surface, so
that metallic surface energy dominates. According to Eq. (1) iron
chondrules should then be a few times larger, in proportion to iron's
higher (by a factor ~ 4) surface tension. Although again, irondominated melts are usually exhumed by more energetic events,
from the higher-P0 interiors of larger bodies, resulting in smaller
chondrules. At high enthalpies inside of larger, hotter planetesimals,
iron droplets might evaporate, ultimately producing chondrules by
condensation from vapor (Petaev et al. 2001; Krot et al., 2005), or by a
mixed process of droplet formation followed by partial evaporation
and recondensation (e.g. Tsang and Brock, 1984).
Bubbles obey similar physics as droplets. They are not stable in
expansive plumes but can be quenched in rapidly solidified magmas
(Navon and Lyakhovsky, 1998). Bubbles are occasionally found in
ordinary chondrites (Benedix et al., 2008), and their occurrence is
consistent with our model of a pressure unloading origin. The scarcity
of bubbles in chondrites and chondrules seems puzzling, although the
Laplace pressure (~1–10 bars inside chondrule-sized droplets) would
cause diffusion of gases across the interface.
5. Conclusions
The evidence for heating and melting of planetesimals by 26Al
during the same timeframe as collisional accretion appears undeniable. We find it likely, in the extremely low gravity of planetesimals,
that various degrees of differentiation would result. Given this
favorable petrologic setting we make the case that most chondrules
formed in pairwise accretionary collisions, where ~half of the smaller
unloaded from hydrostatic pressure P0 into magmatic sheets
supported by the low pressure of the nebula.
Occurring at b1/30 the sound speed, accretionary planetesimal
collisions are relatively incompressible. We argue that they are
dominated at large scale by gravitation, momentum, and release from
hydrostatic pressure, and at small scale by the creation of surface
energy and release of volatiles. Most accretionary collisions involve a
certain amount of ‘unaccretion,’ throwing much of the projectile (and
some of the target) back into the nebula, analogous to the splatter of a
glancing water balloon in slow motion. Melts from the unaccreted
projectile expand to low pressure. Enthalpy is available for volatile
dissolution, but because this requires surfaces (droplets) we argue
that the projectile hydrostatic pressure Gρ 2R 2 is balanced by the
Laplace pressure γ/r. For chondrule-sized droplets this is ~ 1–10 bar,
corresponding to projectile diameter 2R ~ 30 km, although more likely
smaller droplets form first, then grow and coarsen until they solidify,
cooling through solidus on a timescale of hours, regulated by the
expansion.
Varieties of chondrites emerge: piles massed rapidly onto the
target body; sheets and clouds interacting with the nebula inside the
Hill sphere; free bodies ejected into the disk. Conversely a given
meteorite might contain chondrules from diverse bodies, plus the
accumulated products of disk shock and solar events at the
planetesimal surface, together with layers of chondrules from past
collisions. Solids entrained in the downrange sheet (solar-composition carapace early on; layers of crustal cumulates after meltdown;
layers of previous-generation chondrules with increasing h) would
commingle with the melts. Later collisions within the timeframe of
26
Al heat production would produce more chondrules, scramble the
stratigraphy, and recycle the earliest solids.
In the earliest collisions, almost all the chondrules rained back
down (ξ ~ 1) and were likely buried under subsequent accretionary
collisions, and remelted. Over time, gravitational stirring (higher φ)
resulted in a greater fraction of collisional material escaping beyond
the Hill sphere, and more chondrules overall. Chondrules raining back
onto evolved targets with thick crusts would be better preserved,
although probably highly altered. This setting, of chondrules atop a
differentiated core-forming planetesimal, has been envisioned by
Weiss et al. (2011) to explain chondrules like those in Allende which
have relatively strong unidirectional magnetization.
Acknowledgements
This research was sponsored by NASA's Planetary Geology and
Geophysics Program. Simulations were performed on the NSFsponsored pleiades supercomputer. We are grateful for detailed
reviews and forthright advice by John Chambers and Fred Ciesla, and
for insightful conversations with many colleagues. The paper is
dedicated in fond memory of Betty Pierazzo.
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Please cite this article as: Asphaug, E., et al., Chondrule formation during planetesimal accretion, Earth Planet. Sci. Lett. (2011), doi:10.1016/
j.epsl.2011.06.007