# Chondrule Formation During Low-Speed Collisions of Planetesimals:
A Hybrid Splash-Flyby Framework

William Herbst Department of Astronomy, Wesleyan University, Middletown, CT,
06457, USA  James P. Greenwood  Department of Earth and Environmental
Sciences, Wesleyan University, Middletown, CT, 06457, USA

###### Abstract

Chondrules probably formed during a small window of time $\sim$1-4 Ma after
CAIs, when most solid matter in the asteroid belt was already in the form of
km-sized planetesimals. They are unlikely, therefore, to be “building blocks”
of planets or abundant on asteroids, but more likely to be a product of
energetic events common in the asteroid belt at that epoch. Laboratory
experiments indicate that they could have formed when solids of primitive
composition were heated to temperatures of $\sim$1600 K and then cooled for
minutes to hours. A plausible heat source for this is magma, which is likely
to have been abundant in the asteroid belt at that time, and only that time,
due to the trapping of 26Al decay energy in planetesimal interiors. Here we
propose that chondrules formed during low-speed ($\lesssim 1$ km s-1)
collisions between large planetesimals when heat from their interiors was
released into a stream of primitive debris from their surfaces. Heating would
have been essentially instantaneous and cooling would have been on the
dynamical time scale, 1/$\sqrt{(}G\rho)\sim 30$ minutes, where $\rho$ is the
mean density of a planetesimal. Many of the heated fragments would have
remained gravitationally bound to the merged object and could have suffered
additional heating events as they orbited and ultimately accreted to its
surface. This is a hybrid of the splash and flyby models: we propose that it
was the energy released from a body’s molten interior, not its mass, that was
responsible for chondrule formation by heating primitive debris that emerged
from the collision.

asteroids, chondrites, chondrules

##  1 Introduction

Chondrules are mm-scale igneous spherules that occupy 20-80% of the volume of
nearly all chondrites, the most common type of meteorite. Their existence
remains famously unexplained despite a major scientific effort spanning
decades (Russell et al., 2018). Unless and until we achieve a better
understanding of how chondrules and chondrites formed, it will be hard to be
confident about the initial stages of planet formation in the Solar System or
how to decode the wealth of information about it available from meteorite
studies.

For decades, models of chondrule formation have been categorized as either
nebular or planetary (Wood, 1963; Ciesla, 2005). Nebular models assume that
mm-scale pre-chondrule dust aggregates embedded in a protoplanetary disk of
originally solar composition were heated by shocks or some other process and
chondrules formed. The compositions and textures of chondrules strongly
support this view, which has been the dominant one (Hewins and Radomsky, 1990;
Jones et al., 2018). However, it is now well-established that most chondrules
formed in a relatively high pressure oxidizing atmosphere that is difficult to
reconcile with a H-rich solar disk (Grossman et al., 2008; Alexander et al.,
2008; Grossman et al., 2012; Fedkin et al., 2012; Fedkin and Grossman, 2016;
Ebel et al., 2018). It is also now clear that chondrules formed primarily or
exclusively during a narrow interval of time that did not begin until $\sim$1
Ma after CAIs and was over by $\sim$3 Ma later (Pape et al., 2019; Piralla et
al., 2023). The precursors of chondrules in the nebular model are pebble-sized
and smaller grains, which aggregate into larger objects on such a short
timescale, $\ll 0.1$ Ma (Weidenschilling, 2000), that it is hard to see how
they could still be dispersed in a nebular gas in any abundance by the time
most chondrules formed.

Planetary models, by contrast, see chondrules as a byproduct of the collisions
of planetesimals, with the required dense, oxidizing atmosphere being created
during the collision. In one version, which requires high-speed collisions
($\gtrsim$2.5 km s-1) and is known as the “jetting” model, there is sufficient
kinetic energy in the collision to heat some of the primitive surface material
on the colliders to chondrule-forming temperatures, and it has been verified
by numerical experiment that this would be expected (Johnson et al., 2018). It
has not been demonstrated, however, that objects with chondrule-like textures
and other properties could emerge from such jets, and there is no explanation
in such a model for why chondrule formation should be limited to $\sim$1-4 Ma.

Another type of planetary model, known as the “splash” or “dirty impact plume”
model invokes low-speed ($\lesssim$1 km s-1) collisions to release already-
molten material from the interiors of large planetesimals (Asphaug et al.,
2011; Sanders and Scott, 2012, 2018). It can be shown that, during the
chondrule formation epoch, planetesimals larger than $\sim$50 km in radius
would commonly have been substantially molten beneath an insulating outer
layer due to the decay of 26Al, making the model attractive. Whereas
collisions occur at all epochs, there is only a narrow window of time when
large planetesimals with molten interiors were common in the asteroid belt,
and that time is more or less coincident with the chondrule formation epoch. A
fundamental issue with the splash model is whether mm-scale solid spherules
will actually emerge from expanding sheets of magma released during such
collisions. One has only a sketch of how this might have occured (Asphaug et
al., 2011), with no detailed modeling or experiment to support the idea. A
counter-argument to the claim has been made by Lichtenberg et al. (2016, 2018)
who point out that chondrules have relatively iron metal-rich compositions
characteristic of primitive material. If their progenitors were molten
material inside planetesimals one would expect that at least some of them
would have largely been drained of their iron. Such “basaltic” chondrules are
rare in nature and the splash model needs to account for that fact.

A related model that also relies on the existence of hot material near the
surfaces of large planetesimals to account for chondrules is the flyby model,
proposed by Herbst and Greenwood (2016, 2019). Instead of positing chondrule
formation directly from the magma splash, these authors rely on the radiant
energy from magma, released to space by either volcanism or collision, to melt
primitive solid material orbiting closely past it during a “flyby”. The pre-
chondrule material in this case is primitive dust or m-scale porous boulders.
A challenge for this model is to produce enough chondrules, given that it
requires the presence of surface lava on a planetesimal at just the time that
primitive material is “flying by”. The model is tenable only if a large amount
of accretion in the 1-4 Ma time frame is through a circumplanetesimal disk. In
that case, the small chance of any individual dust grain or boulder being
irradiated by magma from a volcanic eruption or collisional rupture of the
carapace during a single orbit, may be multiplied by the millions of orbits it
may make before accreting to the surface of the planetesimal. If most
accretion is not through a disk then few chondrules could be formed in this
way.

The lack of progress to date in accounting for chondrules is not due to a lack
of observational constraints – there are now many (Connolly and Jones, 2016;
Russell et al., 2018). Pape et al. (2019) enumerate six: peak temperatures,
cooling rates, elevated alkali vapor pressures, chondrule reworking at high
temperatures, matrix-chondrule complementarity, and a chronology that places
chondrule formation in the context of planet formation. Other constraints
include the magnetic properties of chondrules and chondrites (Elkins-Tanton et
al., 2011; Fu et al., 2014, 2018; Shah et al., 2017), the phenomenon of size
sorting (Friedrich et al., 2015), the existence of compound chondrules
(Gooding and Keil, 1981; Wasson et al., 1995; Akaki and Nakamura, 2005;
Jacquet, 2021), cluster chondrites and “hot accretion” (Metzler, 2012;
Bigolski et al., 2019), and the overall abundance of chondrules in the near-
Earth Solar System today (discussed below).

In this paper we propose a framework for chondrule formation that is a hybrid
of the splash and flyby models. We point out that the dirty impact plumes of
the splash model are an attractive astrophysical site for forming chondrules
by the flyby mechanism – radiative heating of primitive material orbiting
close to the surface of a large planetesimal – although in this case the
proto-chondrules might be flying “with” the heat source (magma) rather than
“by” it. Our proposal differs from the splash model in that chondrules are not
presumed to form directly from the magma itself, but from primitive debris
heated by the magma. It differs from the flyby model in that a single event –
a low-speed collision – is responsible for both releasing the 26Al decay
energy stored in planetesimal interiors and generating the mm- to m-sized
primitive objects on ballistic orbits to be irradiated. In Section 2 we
describe the idea and its justification in more detail. In Section 3 we
discuss how the hybrid framework not only addresses the primary inadequacies
of the splash and flyby models, but offers a promising avenue for meeting the
full range of constraints on chondrule formation. Section 4 is a brief
summary.

##  2 The Case for a Splash-Flyby Hybrid Model

The fundamental issue in explaining chondrules is to identify a heat source
strong enough to melt solids that could also be modulated on a timescale of
minutes. The seeming plausibility of any particular scenario depends on one’s
views of the chondrule formation environment and the efficiency with which
they needed to be produced. We begin, therefore, with a review of the evidence
suggesting that chondrules formed in the asteroid belt between 1-4 Ma after
CAIs, at a time when most of the original solids had already formed into
planetesimals large enough to have molten interiors. In that case, chondrules
were not essential to planet formation, were never abundant on asteroids, do
not require an efficient production mechanism, and there is an obvious heat
source – magma encased in planetesimal interiors. It has the right temperature
and is present in abundance at the right time and place to serve as the heat
source. In the remainder of the Section, we sketch a proposal for how this
might have occurred.

###  2.1 Where and When did Chondrules Form?

We assume that chondrules formed in the asteroid belt, close to the locations
where their host chondrites are currently stored on surviving primitive
asteroids (Piralla et al., 2021). The more volatile-rich carbonaceous
chondrites (CCs) presumably formed at the outer edge of the belt and have
isotopic characteristics distinctly different from the ordinary chondrites
(OCs) that formed closer in and, perhaps, slightly earlier (Fukuda et al.,
2022). The distinctive isotopic characteristics of the CCs and OCs is
sometimes attributed to an early formation of Jupiter, which would dynamically
stir the planetesimals generating high speed collisions, but may instead
reflect other aspects of the evolution of the protosolar disk, such as the
location of the water ice line and/or the development of pressure bumps that
constrain the motion of pebbles (Lichtenberg et al., 2021; Izidoro et al.,
2022). D’Angelo et al. (2021) simulate the formation of Jupiter and find that
it is too slow to be a significant dynamical influence on the asteroid belt
until $\sim$3.4-4.2 Ma.

The Al-Mg dating technique has been applied to over 150 chondrules from a wide
range of meteorites (Villeneuve et al., 2009; Kita and Ushikubo, 2012;
Nagashima et al., 2018; Pape et al., 2019; Siron et al., 2022). Pape et al.
(2019) interpret the results as indicating a rather abrupt turn-on to the main
chondrule formation epoch at about t = 1.8 Ma, where t = 0 is set by the 26Al
abundance at the time of CAI formation, followed by some possible peaks at 2.0
and 2.3 Ma and an end to the process by $\sim$3 Ma. Allowing for some outliers
one might characterize the epoch broadly as between t = 1.5 - 4 Ma with a peak
near 2 Ma. A more recent analysis by Piralla et al. (2023) suggests that the
gap between CAI formation and the start of chondrule formation may be as small
as 0.7 Ma, but it remains clear in their data that CAIs formed in a separate
heating event or events that significantly pre-dated the main epoch of
chondrule formation.

One key aspect of this description that is vigorously debated is whether any
surviving chondrules at all formed before t$\sim$0.7 Ma. There are some
chondrules whose Pb-Pb ages appear to overlap with those of CAIs (Connelly et
al., 2012; Bollard et al., 2017; Connelly and Bizzaro, 2018). One
interpretation of this is that the chondrule formation epoch actually began at
t = 0, coincident with CAI formation and, since the 22 chondrule ages
determined by this technique are roughly evenly distributed over the 0 - 4 Ma
epoch, that chondrule formation was steady over this time. In the model
proposed here, no chondrule should be as old as CAIs, assuming they date the
beginning of planetesimal growth, since it does take at least a few hundred
thousand years for large planetesimals to form and generate molten interiors
(Hevey and Sanders, 2006), but chondrule formation could have begun earlier
than 0.7-1.8 Ma. Given that the canonical 26Al-abundance is about four times
larger than is necessary to fully melt planetesimals larger than 5 km or so
(Sanders and Scott, 2018), chondrules that formed earlier than 0.7-1.5 Ma
(about 1-2 half-lives of 26Al) may simply have not survived further
processing.

Ways of reconciling the discordant Al-Mg and Pb-Pb results are discussed in
several papers (Nagashima et al., 2018; Connelly and Bizzaro, 2018; Pignatale
et al., 2019; Pape et al., 2019; Desch et al., 2023; Piralla et al., 2023) and
need not be elaborated upon here. We simply note that there is no plausible
mechanism proposed in these papers for producing a heterogeneity of 26Al at
the level required and that accounting for all possible error sources in the
Pb-Pb ages, including possible systematic effects from environmental
contamination, is challenging. If the error bars on the individual Pb-Pb ages
are underestimated, then there may actually be no discordance. The average
time for chondrule formation by both techniques is about 2 Ma after CAIs, or 1
Ma if the analysis of Piralla et al. (2023) is correct.

###  2.2 The Implausibility of Nebular Models

Any successful model of chondrule formation must be consistent with what is
known about the early evolution of gas and solids in the Solar System. It is
widely accepted that dust grains aggregate to m-scale objects and settle
towards the disk plane of the solar nebula on a very short timescale, $<0.1$
Ma (Weidenschilling, 2000; Chiang and Youdin, 2010). Therefore, the
progenitors of chondrules in nebular models – mm-scale dust – are likely to be
rare by 1 Ma. Even the nebular gas in the 1.5-4 AU zone may be seriously
depleted by 1 Ma, since that is roughly the half-life of disks around solar
mass stars inferred from observations of young stars in the solar neighborhood
(Mamajek, 2009; Venuti et al., 2017). And, despite decades of effort, no
mechanism for heating nebular gas to the requisite temperatures for the
requisite times has yet gained widespread acceptance. Global nebular models
would be required if a large percentage of the original solids in the disk
needed to be turned into chondrules but, as we argue further below, that is
not the case.

####  2.2.1 Simulations of the Evolution of Solids and the Chemistry of the
Ambient Gas

It is increasingly clear that planetesimals large enough to contain their 26Al
decay energy emerged quickly in the proto-solar nebula with the result that
objects with molten interiors were common. Observational evidence for this
comes from the inferred ages of iron meteorites (Scott, 2020). Additional
evidence comes from simulations of planetesimal growth in the asteroid belt
during the first 2 Ma by Weidenschilling (2019). He assumes that bodies grow
by accretion alone from primary planetesimals in the 50 m to 5 km range and
adopts an initial mass of solids between 1.5 and 4 AU of $\leq 4.9$ M⊕,
consistent with a smooth surface density variation in the solar nebula. He
further assumes that Jupiter has not yet fully formed and that any dynamical
effects from it can be neglected.

One purpose of these simulations was to test whether the large, differentiated
planetesimals (LDPs) needed to account for iron meteorites could form quickly
enough to satisfy timing constraints imposed by their radioactive ages. This
turns out not to be a problem; for an initial planetesimal radius of 50 m,
tens of thousands of objects exceeding 50 km form quickly and then continue to
accrete at a slower pace. Somewhat counter-intuitively, he also finds that the
smaller the initial (primary) planetesimals, the faster the evolution
proceeds. For the 50 m simulation, the fraction of mass in planetesimals of
different size, based on that simulation, is shown in Fig. 1 at t = 1 Ma and 2
Ma. We note that the starting points, t = 0, for the simulation and for the
radioactive age scale are defined differently but assume that the actual time
difference is negligible for the purposes of the discussion in this paper. The
size distribution is truncated at 500 km because objects of this size and
larger are assumed to be ejected from the Solar System once Jupiter forms, at
perhaps 3-4 Ma. Again, nebular models require mm-scale objects to be embedded
in the disk gas and observation, theory and simulations suggest that would not
be the case in the asteroid belt at 1 Ma.

Figure 1: The mass fraction of planetesimals as a function of size in the
asteroid belt at 1 Ma (dashed lines, except in case of the 1-3.1 radius bin,
where the dashed and solid lines overlap) and 2 Ma (solid lines) based on a
simulation by Weidenschilling (2019) (see his Fig. 20). The distribution is
bimodal at both times. Between 1 and 2 Ma one sees a decline in the mass
fraction of primitive matter from about 10% to 8% as SPPs (small, primitive
planetesimals) accrete to LDPs (large differentiated planetesimals). The
accompanying rise in the mass fraction of LDP’s is not noticeable on the
figure due to the logarithmic scale. The larger LDPs are nearly fully molten
(red) while smaller ones may retain substantial primitive material in surface
layers (indicated by red to black shading). For this simulation it was assumed
by Weidenschilling (2019) that Jupiter formed after a few Ma and
gravitationally ejected a few very massive (r $\geq$500 km) objects, along
with numerous smaller objects that carried much less mass. The net result of
Jupiter’s action would be to enhance the ratio of primitive to differentiated
mass that was present at 2 Ma and is “preserved” in today’s Solar System from
0.25% to 8%.

There is another line of evidence that favors a planetary, as opposed to
nebular, origin for chondrules. While calculations of oxygen fugacity (fO2)
suggest CAIs solidified in a reducing gas, as expected for a nebular disk
(Grossman et al., 2008), FeO-poor chondrules formed in an O-rich gas, $\sim$5
orders of magnitude higher in fO2 (Grossman et al., 2012). This is a
challenging fact to explain for any nebular model of chondrule formation,
including those invoking shock waves (Fedkin et al., 2012). Fedkin and
Grossman (2016) show that CI-dust enrichment by about 4 orders of magnitude
and water-enrichment are required for FeO-rich chondrules and point to impacts
on water-rich parent bodies as a potential source of the gaseous conditions
indicated. Alexander et al. (2008) used measurements of Na abundance and
zonation in chondrules to argue that they must have formed in a gaseous
environment with a high partial pressure of Na, so high in fact that if the
system were of solar composition, these regions would have been self-
gravitating. Similar arguments can be made with respect to Fe and all
moderately volatile elements present in chondrules (Ebel et al., 2018). If
chondrules formed in a typical proto-planetary disk environment their more
volatile elements would be expected to have evaporated, resulting in elemental
depletion and isotopic fractionation effects that are not observed. The
conclusion of these authors is that chondrules formed in regions of space
where the density of solids was much higher than current nebular models can
explain.

####  2.2.2 Can a Planetary Setting Produce Enough Chondrules to Explain their
Prevalence in Chondrites?

An early objection to all planetary chondrule formation models was that they
cannot explain the seeming ubiquity of chondrules within primitive material.
If chondrules were as abundant in the early asteroid belt as they are in
chondrites, where they make up $\sim$50% of the mass, then they would need to
be made with high efficiency. However, it is increasingly clear that the
Earth’s atmosphere filters out a substantial amount of poorly-lithified (and
arguably chondrule-poor) primitive material that is present in space, so that
the actual mass fraction of primitive material in the form of chondrules near
the Earth today is probably more like 0.01-0.1% than 50%. This point was first
made by Sears (1998), who further noted that the transport processes needed to
bring material from the asteroid belt to 1 AU may also bias the near-Earth
sample in the direction of chondrule-rich material.

Recent results, including improved data on near-Earth asteroids and sample
returns, support the view that chondrules are probably much rarer in space
than they are among meteorites in the world’s collections. Based on the known
meteorite flux of 2900 - 7300 kg a-1 (Bland et al., 1996), and the fractional
abundance of chondrites among meteorites, 85-90% (Corrigan et al., 2017), the
flux of chondrules at the Earth’s surface is 1.3 - 3.3 $\times$ 103 kg a-1.
This may be compared to the total mass flux at the top of the atmosphere, 1 -
6 $\times$ 107 kg a-1, derived from meteor rates, impacts on space hardware
and other studies (Drolshagen et al., 2017). Chondrules, therefore, are only a
minor component of the material impacting the Earth at the top of the
atmosphere, $\sim$0.01% of the mass. Most of the impacting mass arrives in
particles much smaller than chondrules. It can be collected from space or the
upper atmosphere as IDPs and from the surface as micrometeorites and does not
resemble ground-down chondrules, in general being much more porous (Koschny et
al., 2019). Whether it is primarily from comets or from the asteroid belt is
unknown.

Another avenue for directly assessing the fractional abundance of chondrules
within chondritic material has recently opened, namely sample returns from the
surfaces of small asteroids. Regrettably, the Hayabusa mission did not return
enough material from the surface of Itokawa, an asteroid chemically similar to
LL-class OCs, to determine its chondrule abundance or even whether any
chondrules at all are present on its surface (Abe et al., 2006). Hayabusa2 was
much more successful, however, returning several grams of material from Ryugu.
The first analyses show that it is definitely composed of chondritic material
with zero chondrules present (Yada et al., 2021). Nakamura et al. (2022)
describe some very small particles in the sample as related to chondrules but
the relationship is uncertain. The rarity or complete absence of chondrules in
the Ryugu sample was predicted by Herbst et al. (2021) on the basis of its low
bulk density, 1.19 g cm-3, and its low macroporosity, $0.14\pm 0.04$,
calculated from linear-mixture packing theory (Yu and Standish, 1991). They
showed that, if the asteroid was reasonably homogeneous, its surface rocks
must be much less dense than any known meteorite, even the rare chondrule-free
CI class. Such low-density, micro-porous material is consistent with the
thermal properties of Ryugu (Grott et al., 2019), and argues against the
presence of many chondrules in the material, since their densities are in the
range 3.0 - 3.4 g cm-3 (Friedrich et al., 2015). Herbst and Greenwood (2019)
also correctly predicted, to within the margin of error, the mean density of
the particles returned by Hayabusa2 (Yada et al., 2021), and it is
significantly less than that of any known meteorite.

Could Ryugu be an unusual primitive asteroid with regard to its chondrule
content, or is it likely to be representative? A definitive answer will await
further results, but we note that a sample from Bennu obtained by the OSIRIS-
REx mission has recently arrived on Earth and that the bulk density of this
asteroid is also 1.19 g cm-3 (Lauretta et al., 2017). The general appearance
of its surface is also quite similar to that of Ryugu and even without
comparing their boulder-size distribution in detail, linear-mixture theory
suggests that the macroporosity and, therefore, the mean boulder densities of
the two asteroids will be much the same. That is because the macroporosity of
a granular aggregate depends primarily on the dispersion of grain sizes of its
component boulders, not on their actual size or even shapes, as long as they
are not extreme in some way. As Yu and Standish (1991) discuss, single-sized
grain piles typically have a porosity of around 40% but two factors cause the
porosity to decline if there is a range of grain sizes. Larger than average
particles displace void space, reducing porosity, a phenomenon known as
occupation, whereas smaller than average particles fill in void spaces, a
phenomenon known as sifting. Both effects act to lower the porosity of the
pile. The dependence of porosity on the range of grain sizes for a lognormal
distribution, which represents Ryugu very well (Herbst et al., 2021), is shown
in Fig. 2. Given the appearance of the surface of Bennu, with its wide range
of boulder sizes, linear-mixture theory indicates a macroporosity of about
0.15. We, therefore, predict the OSIRIS-REx sample will have particles similar
in density to Ryugu and contain few, if any, chondrules.

Is it possible that Ryugu and Bennu are not representative of primitive
asteroids in general because they are spectrally similar to CC’s rather than
OC’s and CC’s are only 5% of the meteorites in our museums? The best studied
S-type asteroid is Itokawa, which was visited by the original Hayabusa
mission. Unfortunately, its sample return mechanism did not function properly
so we do not know if it would have brought back chondrules or not. However,
given the asteroid’s low bulk density of $1.9\pm 0.1$ g cm-3 (Abe et al.,
2006), and assuming a macroporosity of 0.15 (Fig. 2), the predicted average
density of its boulders is only 2.2 g cm-3, much less than the density of its
analog meteorite class (LL; 3.2 g cm-3) again leaving little room for abundant
chondrules. Of course, if chondrules did not begin forming until t = 1 Ma,
when the planetesimals that evolved into asteroids were already large, we
should not expect to find chondrules in any abundance on any asteroid. To
summarize, a variety of arguments suggests that chondrules are not nearly as
abundant on asteroids as they are in chondrites and, therefore, a chondrule
formation mechanism need not be very efficient at making them. Based on
current knowledge, models should be judged on their ability to process
$\sim$0.01 - 0.1% of relevant material into chondrules, meaning that global
(nebular) models are not required.

Figure 2: A schematic figure showing how increasing the size range of grains
in a granular aggregate decreases the porosity of the pile. The curve
displayed is for a lognormal distribution (Yu and Standish, 1991) but the
principle applies to any physical system in which occupation and sifting
operate. The location of Ryugu, based on the surface boulder counts of
Michikami et al. (2019) and the analysis of Herbst et al. (2021) is shown. It
has FWHM = exp ($2\sqrt{2{\rm ln}2}\ \sigma$) = 285, which means that the
grain sizes of particles at half-maximum on the high side of its frequency
distribution are 285 times larger than those at half-maximum on its low side.
For Ryugu this corresponds to $\sim$20 m boulders on the high side and $\sim$7
cm cobbles on the low side. The width of the band is set by the fact that,
excluding extreme shapes or non-gravitational forces, piles of single-size
grains typically have a porosity of $40\%\pm 5\%$.

###  2.3 Jetting versus Magma as a Heat Source in Planetary Models

An alternative heat source to magma in planetary models is the kinetic energy
of the collision. Material could be raised to the melting point of solids by
high speed collisions, but it requires impact speeds of 2.5 km s-1 or larger
(Johnson et al., 2018). In the Weidenschilling (2019) simulations, such high
speeds do not occur because objects large enough to generate them have not yet
formed. Impact speeds in his model would be at roughly the escape velocity of
the larger planetesimal, which is

$v_{esc}=\sqrt{{2GM}\over R}=\sqrt{{8\pi G\rho}\over{3}}R={{1.3}\
\big{(}{{R}\over{1\ \rm{km}}}\big{)}}\ \rm{m}\ \rm{s}^{-1}$

where M, R and $\rho$ are the mass, radius and mean density of the larger
planetesimal and we have adopted $\rho=3000$ kg m-3. As Fig. 1 shows, most
collisions will be between objects with $R\leq 300$ km, so typical collision
speeds will be under 0.4 km s-1, insufficient to form chondrules by jetting.
If, contrary to an assumption on which the Weidenschilling (2019) simulations
are based, Jupiter had formed by the beginning of the chondrule formation
epoch then a jetting model would be viable from 1 Ma on. However, a question
would remain – why does chondrule formation end, at about 4 Ma? High speed
collisions between planetesimal-sized objects would presumably continue beyond
that time and, if such collisions can generate chondrules between 1 and 4 Ma,
why would they not do so at later times? And, of course, it has not been shown
experimentally or by simulation that objects with the distinctive properties
of chondrules could emerge from any high speed collision.

Herbst and Greenwood (2016, 2019) proposed near-IR radiation from magma as the
heat source for chondrule formation, noting that it has the right temperature
and is arguably quite abundant in the asteroid belt during the chondrule
formation epoch. Asphaug et al. (2011) and Sanders and Scott (2012) proposed
that chondrules actually form directly from such hot magma. Thermal evolution
calculations indicate that objects with $R\geq 50$ km will be largely molten
within $\leq$0.5 Ma of their formation, assuming a canonical value for the
initial 26Al abundance (Hevey and Sanders, 2006; Sanders and Scott, 2012,
2018). According to the Weidenschilling (2019) simulations more than 90% of
the original mass of the asteroid belt was already encased in planetesimals
large enough to grow substantial molten interiors by t = 1 Ma. The ages of
iron meteorites provide additional support for the prediction that molten
interiors were a feature of planetesimals at that time (Scott, 2020), as noted
above. By about 1.5 Ma, the 26Al level would have dropped to the point where
cooling would dominate heating, and by the end of the chondrule formation
epoch at 4 Ma, one can expect that the amount of magma in the asteroid belt
would have diminished significantly and the insulating carapaces grown thick
enough that remaining interior heat would rarely be exposed to space. Fig. 3
is a schematic representation of the situation.

Figure 3: A schematic chronology of the early asteroid belt based on the
evidence discussed in the text. CAI formation defines t = 0 and primary
planetesimals are assumed to form quickly. Within a few hundred thousand years
most of the mass is in the form of large planetesimals, which become dominated
by magma interiors, as shown by the red line labeled magma fraction. The
energy source is 26Al, whose level declines with a half-life of 0.717 Ma from
an assumed initial value of 4 at t = 0, where a level of 1 corresponds to the
amount of energy (1.6 kJ/g) needed to just reach the liquidus of a perfectly
insulated cold primitive starting material. Chondrules formed between
$\sim$1-4 Ma when exposed to hot magma released during a collision, as
illustrated by the drawing in the right hand panel by David A. Harvey
(astroart.com) originally depicting the formation of a ring around the Earth.
Chondrule formation ends when the LDPs have cooled sufficiently that magma
does not reach their surfaces even during collisions. Jupiter may form at
around 3-4 Ma and begin clearing the asteroid belt of many of its larger
objects.

###  2.4 The Hybrid Model

There are two planetary models that rely on the trapped energy from the decay
of 26Al as the heat source – the splash and flyby models, and each faces
challenges. As noted in the Introduction, there is little evidence to support
the idea that chondrules would form in a splash of magma and the rarity of
basaltic chondrules is a problem for the model. Relict grains and dusty rims
are observed features of some chondrules that are also challenging for the
splash model (or jetting model) to explain. Even if mm-scale drops of molten
material do emerge from ejecta sheets, they must absorb primitive material
from the “dirty plume” in the proper amounts to account for these observed
features of chondrules. It seems that the splash model involves two so-far
unverified assumptions: the creation of mm-sized molten drops from expanding
sheets of magma and the absorption by those drops of primitive material during
the splash.

By contrast, in the flyby model chondrules formed conventionally during a
brief, intense heating of primitive material and magma was involved only as
the heat source. But the required radiation can only be liberated to space
briefly and episodically by rupturing the surface of an LDP and the pre-
chondrule material (primitive dust or porous blocks) must be within kilometers
of it to receive a sufficient dose of energy to melt. Herbst and Greenwood
(2019) envisioned a volcanic magma extrusion on the surface of an LDP, modeled
as a circular hot spot, irradiating orbiting material within a
circumplanetesimal accretion disk. They calculated the heating/cooling curves
expected in such a case and demonstrated via laboratory experiments that
objects with realistic chondrule textures could be synthesized from mineral
precursors, building on the classic work of Hewins and Radomsky (1990) and
complementing the more recent studies reviewed by Jones et al. (2018).

While there is little doubt that chondrule-like objects could have been made
in this manner, it would have been exceedingly inefficient unless there were a
mechanism to break primitive material into mm- to m-size objects and accrete
them through a circumplanetesimal ring, since any surface extrusions of lava
would be rare and short-lived. One way to do this would be by tidal capture
and disruption of small, primitive planetesimals. Quantitative analysis of
this mechanism indicates, however, that it is not likely to be important
during the kind of planetesimal growth phase simulated, for example, by
Weidenschilling (2019); it is not part of his simulations. The other
possibility is that a single event, an oblique collision of two planetesimals,
both created the swarm of m-scale or smaller debris to be irradiated and
released the requisite energy stored in the interior of one or both colliders.
It is this hybrid of the splash and flyby models, that we propose here as
worthy of more computational attention, and discuss below in qualitative form.

The idea is based on the oblique collisions described by Asphaug et al. (2011)
and Asphaug (2023) that are a basis for the splash model. As the authors point
out, in the 1-4 Ma time frame there will be many collisions between large
planetesimals, and most will be sufficiently oblique that a debris field will
emerge downstream from the event. If one or both of the colliders has a large
molten interior below a primitive surface the debris field may contain both
incandescent magma and primitive solids. High spatial resolution simulations
are not available to confirm the size distribution of the primitive debris but
it is reasonable to expect it will include everything from dust to boulders.
These objects will be on ballistic orbits, most of which will be closed. A
visual representation of such an event, originally inspired by a model of the
formation of the Moon, is included in Fig. 3.

Based on the simulation by Asphaug et al. (2011) one might expect that shortly
after the collision, primitive material with a range of sizes will find itself
immersed in an expanding, $\sim$2000 K black body radiation field whose source
is the magma spray within the debris field. In a matter of minutes one can
expect significant cooling, as the fan of material expands, becomes optically
thin and the magma cools and solidifies, perhaps as small droplets (Asphaug et
al., 2011). Although we are not aware of any simulations that are sufficiently
detailed to predict heating/cooling curves in such a scenario that could be
tested in the laboratory, it seems likely to us that they would be quite
similar to what has been modeled successfully by Herbst and Greenwood (2019).
In particular, the initial fan-shaped spray of hot magma from the interior(s)
should have a peak temperature exceeding 1600 K, which is what is required to
form chondrules. It should then cool on a timescale of minutes as it expands
(Asphaug et al., 2011). Much of the debris will presumably remain bound to the
merged planetesimal and orbit on the dynamical timescale of
1/$\sqrt{(}G\rho)\sim 30$ minutes. If the magma interior of the merged
planetesimal remains exposed, there could be multiple episodes of heating as
this material orbits past the impact site every 30-60 minutes or so.
Eventually, much of the processed debris, would be expected to accrete to the
surface of the merged planetesimal, as chondrules, matrix grains condensed
from the cooling vapor and perhaps even already-lithified chondrites. Without
higher resolution simulations covering a wider swath of parameter space it
will not be possible to test this idea quantitatively but, qualitatively, it
seems promising to us as a framework for understanding many of the observed
constraints on chondrule and chondrite formation, as we now discuss.

##  3 Discussion: Testing a Splash-Flyby Hybrid Framework

There is a substantial number of strong constraints on the formation of
chondrules and chondrites, a fact that has led some to describe the problem as
“over-constrained” and others to assert that no single model of chondrule
formation is likely to be able to account for all of them. In this section we
briefly describe how the hybrid splash-flyby framework proposed here may be a
promising one for addressing these constraints. Unless and until numerical
simulations of the proposed events are carried out, it is only possible to
make qualitative arguments.

###  3.1 Density of Solids in Chondrule Formation Zones

It has been recognized for decades that some chondrules must have interacted
with at least one other chondrule while both were still hot and plastic
(Gooding and Keil, 1981; Wasson et al., 1995; Akaki and Nakamura, 2005). Such
objects are referred to as compound chondrules and their existence provides an
important constraint on chondrule formation since it proves that the number of
chondrules forming within a given volume at the same time must have been high
enough that soft collisions could have occurred. The work referred to above
found that the fraction of chondrules suffering such collisions was of the
order of a few percent. Recently, Jacquet (2021) has argued that the actual
fraction of chondrules suffering an interaction with another chondrule during
their formation is much higher than previous estimates. Based on his analysis
of lobate chondrules in two CO3 meteorites, he argues that the percentage of
chondrules that could be called compound, because they interacted with another
chondrule while both were still in the process of formation, has been
underestimated by an order of magnitude or more. He argues that, in fact,
almost all chondrules may be compound. If true, this places a constraint on
the density of solids in the chondrule formation zone that is is difficult to
account for by any nebular model. The dust to gas ratio would need to be
increased by such a large factor that there would be insufficient gas
remaining to heat the dust sufficiently by any mechanism for chondrule
formation. In the hybrid model prosoed here, gas density is irrelevant and the
formation of molten and partially molten droplets that will solidify into
chondrules can occur with whatever concentration of them is needed to allow
their interaction and formation into the number of lobate chondrules observed.
There is no need to bring hot chondrules together from any substantial
distance, since the proto-chondrules are already in close proximity to one
another.

###  3.2 Magnetic Properties

Some chondrules retain a record of the strength and direction of the magnetic
field at the time their iron-bearing minerals last cooled through their Curie
points, typically $\sim$1000 K (Fu et al., 2018). Field strengths recorded are
in the range 10 - 100 $\mu$T and field directions may or may not be coherent
across the meteorite. The detection of these natural remanent magnetizations
shows that there was a stable magnetic field present at the time and location
of chondrule formation and that it was weaker than predicted by some models of
chondrule formation, such as those relying on electric currents or being close
to the Sun for heating (Fu et al., 2014). If the fields detected can be
confidently attributed to the solar nebula then inferences about its nature
can be drawn (Bryson et al., 2020). However, another likely source of magnetic
fields in the chondrule formation zone and epoch is an LDP dynamo (Elkins-
Tanton et al., 2011). They are commonly invoked to explain meteorite-wide
alignments of the field on a parent body after chondrite formation. In the
model proposed here, all chondrule formation occurs close to an LDP so the
magnetic field source could be an LDP, and no nebular field would be required.
The pre-chondrule material may also be packaged in larger units, meter-scale
blocks, than single chondrules and the predicted cooling rates near 1000 K are
likely to be high, up to 6000 K/h. Both of these factors increase the
probability that an individual chondrule could remain sufficiently stationery
as it cools through its Curie point to retain a magnetic record of the field.
Moreover, the fact that chondrite lithification may occur simultaneously with
chondrule formation (see subsection below on chondrite lithification) allows
for the possibility of meteorite-wide coherence of magnetic field direction
without having to postulate a second episode of heating. If this view is
correct, the remanent magnetizations detected in meteorites would be telling
us about the dynamos of large, primitive asteroids, not the nebular disk. This
is one reason that it remains important to understand chondrule formation even
if they are not the building blocks of planets.

###  3.3 Complementarity

It has been known for decades that a complementary chemical relationship
exists between the chondrules and matrix in chondrites (Palme et al., 2015).
While the bulk composition of chondrites matches expectation based on the Sun
closely, their two main components, chondrules and matrix, do not. Volatile
elements are depleted in the chondrules and enhanced within the matrix, while
more refractory elements show the opposite trend (Hezel et al., 2018). Any
successful chondrule formation model needs to account for this widely-observed
phenomenon. Isotopic complementarity also may exist (Budde et al., 2016),
however see Sanders and Scott (2022).

Complementarity appears to demand the confinement of atoms released by melting
chondrules within a gas from which matrix grains later condense. The
confinement could be immediate and local, if there is a mechanism to trap
them. It could also be on a scale of AUs if the evaporates escape back into
the solar disk but are confined within a ring by pressure gradients. If most
of the original solids in the solar nebula were processed through chondrule
melting, then the evaporated atoms might be sufficiently abundant that later-
condensing matrix grains could bear the signature of complementarity. However,
if only a tiny percentage of primitive material ever gets processed into
chondrules, as argued above, then their evaporated atoms would be heavily
diluted by diffusion into the nebular gas and it is hard to see how a
complementarity signal could survive. Assuming chondrules are actually a rare
form of primitive solids then one requires some immediate confinement of vapor
released during their formation followed by rapid condensation into matrix
grains to explain complementarity. The hybrid splash-flyby model described in
this paper offers two possibilities for such confinement. There will be a
relatively high pressure, oxidizing gas present during the collision, derived
from the more volatile solids. It could serve to limit dispersal of atoms
released by chondrule formation sufficiently that they could recondense as
matrix grains during the expansion and cooling phase of the cloud following
the collision. Alternatively, as Herbst and Greenwood (2019) have proposed,
the gas confinement could be by the unmelted portions of meter-scale blocks of
primitive material inside of which the chondrule formation occurs. In either
case, it appears that the demands of complementarity could be met with the
model of chondrule formation proposed here.

###  3.4 Cluster Chondrites and Hot Accretion

Cluster chondrites are portions of OCs that are so densely populated with
chondrules that their shapes depart from the normal spherules and take complex
forms dictated by the chondrules around them. It appears that these parts of
the OC formed and solidified while their chondrules were still warm and
pliable, allowing them to mold into the spaces available for them. Metzler
(2012) has described these objects and reports that they are found in all
types of OC and that they are quite common. The implication of cluster
chondrites is that the lithification of the chondrite into its current
structure must have occurred very shortly after the formation of the
chondrules, since they needed to still be hot and pliable. Given that cooling
times for chondrules must be minutes to hours, this is a very significant
constraint on what happened. Recent work by Bigolski et al. (2019) has
confirmed these findings and expanded the evidence for what is often called
“hot accretion”. That descriptor is meant to signify that the chondrules must
still have been hot when they accreted to the parent body on which the
meteorite formed. In the model described here, still-warm chondrules and just-
formed matrix grains could accrete to a portion of the surface of the merged
planetesimal that was not molten and chondrite lithification could occur
there. Another possibility, as discussed by Herbst and Greenwood (2019) is
that chondrite lithification could occur while material was still in orbit,
through hot isostatic pressing (HIPping). In either case, the formation of
multiple chondrules in close proximity to one another and their rapid
incorporation into a chondrite does not seem surprising or difficult to
account for in terms of the model of chondrule formation proposed here.

###  3.5 CAI and Pre-solar Grain Storage

Most chondrites contain CAIs and other highly refractory inclusions, including
pre-solar grains, which formed 0.7 Ma or more before the chondrules
(MacPherson et al., 2005; MacPherson, 2007; Whattam et al., 2022; Piralla et
al., 2023). CAIs are believed to be condensates of a brief, hot phase of the
solar nebula, although the cause and spatial extent of this hot phase are
uncertain. Assuming they were present in the asteroid belt at t = 0 they would
have accumulated like everything else into km-sized planetesimals and could
have survived with other primitive material on the smaller objects or within
surface layers of the larger ones. They would be among the last things to melt
and could survive if peak temperatures were low enough. In fact, the presence
of CAIs during chondrule formation, close to the heat source, may be revealed
by several facts: 1) some have an igneous texture which indicates they were
melted, 2) dusty rims are present in some, which could have the same cause as
the dusty rims of chondrules discussed below, 3) some chondrules have
apparently absorbed some CAIs during their formation, as evidenced by an
enhanced abundance of rare Earths, and 4) CAI-like relicts (if mostly only
isotopically recognizable) may be present in some chondrules. (Krot et al.,
2006; MacPherson, 2007; Marrocchi et al., 2019). The hybrid model described
here does not appear to require any special storage history for CAIs or pre-
solar grains.

###  3.6 Chondrite Lithification and Chondrule Age Spread

Remarkably little has been written about the subject of chondrite
lithification, especially when compared to the body of literature on chondrule
formation. Lithification is the process of converting loose sediment into hard
rock, which generally means reducing microporosity, increasing density and
increasing tensile strength. It requires some degree of heat and pressure and
may be facilitated by chemical processes. Consolmagno and Britt (1999) and
Consolmagno et al. (2002) have briefly elaborated on the basic problem – there
is not much heat or pressure available in the asteroid belt to accomplish
lithification. It is generally assumed that the lithification of chondrites
occurred on host bodies after the components (chondrules, matrix, CAIs, etc.)
had accreted to them. It is also assumed that pressure and temperature spikes
from impact shocks must have been, although there is little evidence for that
in chondrites and the process has many problems (Beitz et al., 2016).

The hybrid model proposed here has two potential paths to chondrite
lithification: it could have occurred on the solid portion of the merged
planetesimal by a process mentioned in the paragraph above, or it could have
occurred while the material was still in orbit by HIPping, as Herbst and
Greenwood (2019) have proposed. In either case, metamorphism may have followed
on the still-warm surface of the merged planetesimal as it continued to cool
over millions of years. In the hybrid framework chondrites would be expected
to contain mostly chondrules formed during a single collision event, so all
the chondrules in a particular chondrite might be expected to be coeval.
However, since a planetesimal could experience more than one chondrule-forming
collision, it is conceivable that exceptions might exist. While Pb-Pb ages do
vary widely for chondrules within a single chondrite, the significance of
those differences depends on the accuracy of the error estimates. Recent high
precision age measurements based on Al-Mg chronology have not detected any
significant age differences among chondrules within the same chondrite in a
group of UOCs (unequilibrated ordinary chondrules) (Siron et al., 2022),
although Tenner et al. (2019) claim a spread of at least 1.1 Ma among
chondrules in two CR meteorites.

###  3.7 Relict Grains

Type I (Fe-O poor) chondrules often contain olivine grains with isotopic and
minor element abundances that differ significantly from that of the majority
of olivine grains in the same chondrule. In particular, the anomalous olivine
grains are enriched in 16O and depleted in elements such as Ca, Al and Ti that
are abundant in high temperature condensates such as CAIs and AOAs. They are
known as relict grains (Rambaldi, 1981; Nagahara, 1981; Jones, 1992; Marrocchi
et al., 2018) because these attributes suggest that they are remnants of an
original condensate from the hot gas that somehow avoided remelting during the
formation of the chondrule. Piralla et al. (2021) have recently argued that
precursor recycling and vapor-melt interactions were involved in the formation
of relict grains found in both CC and OC chondrules. They describe a detailed
chondrule formation scenario consistent with their high spatial resolution
elemental and isotopic mapping of LL3 chondrules. It begins with an assemblage
of primitive materials that are partially melted and evolve chemically and
isotopically by interacting with their own vapor as they cool. More than one
cycle of melting may be required. If this interpretation of relict grains is
correct it is a strong argument that chondrules formed by melting primitive
precursors, as proposed here. If the heating is primarily radiative, we might
expect the temperature of material in the debris field to vary substantially
on length scales of cms and timescales of minutes. This would be caused by the
orbital motion of the debris, the highly variable attenuation resulting from
self-shielding, and the possible dispersal of the heat source if there is a
spray of hot material mixed with the primitive debris. High resolution
simulations of low speed collisions are required to say anything more specific
about what kind of heating/cooling curves would be expected but, again, the
temperatures involved ($\geq$1600 K), the timescales ($\sim$30 minutes) and
the expected variability on short length scales expected in a splash-flyby
hybrid seem consistent with expectation based on observations of relict
grains.

###  3.8 Size and Size Sorting

Chondrules have a remarkably narrow size distribution centered around 0.5 mm
and small but significant differences between classes of different chemistry
(Jacquet, 2014; Friedrich et al., 2015). A successful model of chondrule
formation should account for that fact. If chondrules are born from sheets of
expanding magma released during low speed collisions, as the splash model
posits, their distinctive size could derive from a balance between surface
tension of forming droplets and the ambient pressure of the gas, as Asphaug et
al. (2011) have suggested. Presumably there could be a slight variation of
conditions depending on chemical composition that could explain the
observations. If chondrules formed by melting primitive solids one can also
expect that drop formation will involve a balance between surface tension and
ambient pressure, although the size and chemical composition dependence of
radiative absorption efficiency could also affect the size distribution on its
small end (Eisenhour and Buseck, 1995). This is clearly an important issue
that deserves more attention both theoretically and, perhaps, experimentally.
No aerodynamic or other sorting of chondrules by size appears necessary in the
hybrid model, since most or all of the chondrules in any chondrite would have
formed together in the same location with the same chemistry under the same
conditions and have a size distribution set by those conditions.

##  4 Summary

We propose that chondrules formed when primitive debris from low-speed ($\leq
1$ km s-1) collisions of large (10-100 km radius) planetesimals, in the form
of dust to m-scale boulders, was exposed to near-IR radiation from molten
planetesimal interiors released by the collision. The exposure could have been
immediate, to magma ejected along with the primitive debris, and/or occurred
later (and possibly repeatedly), as the solids orbited past exposed lava that
remained on the surface of the merged object. This is a hybrid of the splash
(Sanders and Scott, 2012, 2018) and flyby (Herbst and Greenwood, 2016, 2019)
models. As Asphaug et al. (2011), Weidenschilling (2019) and Asphaug (2023)
have discussed, low-speed collisions are expected to be common during the
chondrule-forming epoch, 1-4 Ma after CAIs, as long as a proto-Jupiter was not
yet affecting orbits in the asteroid belt. Typical collision velocities would
be close to the escape speed of the larger planetesimals, around 450 km h-1,
comparable to what can be achieved by Formula 1 race cars. Such impacts are
too slow, by a factor of about 25, to raise the temperature of material
sufficiently to form chondrules by the “jetting” mechanism (Johnson et al.,
2018), but they should generate substantial debris fields, similar to what was
observed during the DART mission when the rubble-pile asteroid Dimorphos was
impacted by a spacecraft (Jewitt et al., 2023). Testing this hypothesis will
presumably require detailed numerical simulations of planetesimal collisions
with high enough spatial resolution to follow the evolution of small-scale
debris as it moves within an evolving thermal environment. As Asphaug (2023)
notes, these collisions are complex and the parameter space large enough to
accommodate a wide range of outcomes.

It remains an important task to firmly establish the setting or settings of
chondrule formation, so that the vast store of information the chondrules
harbor can be confidently decoded. For example, if the framework proposed here
is correct then their magnetic properties may constrain a local field, not a
global one. A collisional setting also suggests that, far from being the
building blocks of planets, chondrules were never abundant in the asteroid
belt, and today comprise $\leq$ 0.1% of its preserved primitive mass. In that
case, we have just begun to tap the main repositories of primitive matter in
the Solar System, through the Hayabusa2 and OSIRIS-REx missions, and should
not be surprised if chondrules and chondrites continue to be rare or absent in
returned samples. Asteroids and their spectrally-related meteorites clearly
have similar chemical compositions, but based on bulk densities and inferred
macroporosities (15% or less), we expect the primary granular material of
asteroids to be of lower density, lower tensile strength, less lithified and
harboring many fewer chondrules than the chondrites in our museums.

We thank Erik Asphaug for some helpful conversations and Ian Sanders and an
anonymous referee for their insightful criticisms of the original version of
this paper. We gratefully acknowledge the contributions of Ed Scott to the
work presented here; it would not have been possible without him.

## References

  * Abe et al. (2006) Abe, S. et al. 2006. “Mass and Local Topography Measurements of Itokawa by Hayabusa”, Science, 312(5778): 1344–1349 https://doi.org/10.1126/science.1126272.
  * Akaki and Nakamura (2005) Akaki, T. and Nakamura, T. 2005. “Formation processes of compound chondrules in CV3 carbonaceous chondrites: Constraints from oxygen isotope ratios and major element concentrations”, Geochimica et Cosmochimica Acta 69(11): 2907–2929 https://doi.org/10.1016/j.gca.2004.12.025.
  * Alexander et al. (2008) Alexander, C. M. O. ’D ., Grossman, J. N., Ebel, D. S., and Ciesla, F. J. 2005. “The Formation Conditions of Chondrules and Chondrites”, Science 320(5883): 1617-1619. https://doi.org/10.1126/science.1156561.
  * Asphaug et al. (2011) Asphaug, E., Jutzi, M., and Movshovitz, N. 2011. “Chondrule formation during planetesimal accretion”, Earth and Planetary Science Letters 308(3): 369–379. https://doi.org/10.1016/j.epsl.2011.06.007.
  * Asphaug (2023) Asphaug, E. 2023 “Why meteorites are so weird may be due to hysteretic growth”, 54th Lunar and Planetary Science Conference LPI Contribution No. 2806, id.1686.
  * Beitz et al. (2016) Beitz, E., Blum, J., Parisi, M. G., and Trigo-Rodriguez, J. 2016. “The Collisional Evolution of Undifferentiated Asteroids and the Formation of Chondritic Meteoroids”, The Astrophysical Journal 824(12): (18pp). https://doi.org/10.3847/0004-637X/824/1/12.
  * Bigolski et al. (2019) Bigolski, J. N., Weisberg, M. K., and Ebel, D. S. 2019. “Plastic Deformation of Chondrules in Ordinary and Enstatite Chondrites: Evidence of Hot Accretion or Impact-Related Regolith Processing?” 82nd Annual Meeting of The Meteoritical Society, LPI Contribution No. 2157, id.6413.
  * Bland et al. (1996) Bland, P. A., Berry, F. J., Smith, T. B., Skinner, S. J., and Pillinger, C. T. 1996. “The flux of meteorites to the Earth and weathering in hot desert ordinary chondrite finds”, Geochimica et Cosmochimica Acta 60(11): 2053–2059. https://doi.org/10.1016/0016-7037(96)00125-1.
  * Bollard et al. (2017) Bollard, J., Connelly, N., Whitehouse, M. J., Pringle, E. A., Bonal, L., Jørgensen, J. K., Nordlund, A., Moynier, F. and Bizzarro, M. 2017. “Early formation of planetary building blocks inferred from Pb isotopic ages of chondrules” Science Advances 3(8, e1700407, 09 Aug 2017). https://doi.org/10.1126/sciadv.1700407.
  * Bryson et al. (2020) Bryson, J. F. J., Weiss, B. P., Biersteker, J. B., King, A. J., and Russell, S. S.. 2020. “Constraints on the Distances and Timescales of Solid Migration in the Early Solar System from Meteorite Magnetism”, The Astrophysical Journal 896(2): 103 (26pp) https://doi.org/10.3847/1538-4357/ab91ab.
  * Budde et al. (2016) Budde, G., Kleine, T., Kruijer, T. S., Burkhardt, C., and Metzler, K.. 2016. “Tungsten isotopic constraints on the age and origin of chondrules”, Proceedings of the National Academy of Science, 113(13): 2886–2891. https://doi.org/10.1073/pnas.1524980113.
  * Chiang and Youdin (2010) Chiang, E., Youdin, A. N. 2010. “Forming Planetesimals in Solar and Extrasolar Nebulae”, Annual Review of Earth and Planetary Sciences 38, 493–522. doi:10.1146/annurev-earth-040809-152513.
  * Ciesla (2005) Ciesla, F. J. 2005. “Chondrule-forming Processes–An Overview.” in Chondrites and the Protoplanetary Disk, edited by A. N. Krot, E. R. D. Scott and B. Reipurth, Astronomical Society of the Pacific Conference Series 341: 811.
  * Connelly and Bizzaro (2018) Connelly, J. N. and Bizzaro, M. 2018. “The Absolute Pb-Pb Isotope Ages of Chondrules: Insights into the Dynamics of the Solar Protoplanetary Disk” in Chondrules: Records of Protoplanetary Disk Processes, edited by Sara S. Russell, Harold C. Connolly, Jr., and Alexander N. Krot, 300-323 Cambridge: Cambridge University Press.
  * Connelly et al. (2012) Connelly, J. N., Bizzarro, M., Krot, A. N., Nordlund, Å., Wielandt, D., and Ivanova, M. A. 2012. “The Absolute Chronology and Thermal Processing of Solids in the Solar Protoplanetary Disk”, Science 338(6107): 651-655. https://doi.org/10.1126/science.1226919.
  * Connolly and Jones (2016) Connolly, H. C. and Jones, R. H. 2016. “Chondrules: The canonical and noncanonical views”, Journal of Geophysical Research (Planets) 121(10): 1885–1899. https://doi.org/10.1002/2016JE005113.
  * Consolmagno and Britt (1999) Consolmagno, G. J., Britt, D. T. 1999. “Turning Meteorites into Rock: Constraints on Asteroid Physical Evolution” 30th Lunar and Planetary Science Conference abstract #1137.
  * Consolmagno et al. (2002) Consolmagno, G. J., Weidenschilling, S. J., Britt, D. T. 2002. “Forming Well-compacted Meteorites in the Solar Nebula” American Astronomical Society, Division of Planetary Sciences Meeting #34 id.28.07 Bulletin of the American Astronomical Society 34: 890.
  * Corrigan et al. (2017) Corrigan, C. M., Welzenbach, L. C., Righter, K., et al. 2017. “A Statistical Examination of 40 Years of U.S. Antarctic Meteorites” 80th Annual Meeting of the Meteoritical Society LPI Contribution No. 1987, id.6308.
  * D’Angelo et al. (2021) D’Angelo, G., Weidenschilling, S. J., Lissauer, J. J., and Bodenheimer, P. 2021. “Growth of Jupiter: Formation in disks of gas and solids and evolution to the present epoch”, Icarus 355: 114087. https://doi.org/10.1016/j.icarus.2020.114087.
  * Desch et al. (2023) Desch, S. J., Young, E. D., Dunham, E. T., et al. 2023. “Short-Lived Radionuclides in Meteorites and the Sun’s Birth Environment” in Proceedings of Protostars and Planets VII preprint https://doi.org/10.48550/arXiv.2203.11169.
  * Drolshagen et al. (2017) Drolshagen, G., Koschny, D., Drolshagen, S., Kretschmer, J., and Poppe, B. 2017. “Mass accumulation of earth from interplanetary dust, meteoroids, asteroids and comets”, Planetary and Space Science 143: 21–27. https://doi.org/10.1016/j.pss.2016.12.010.
  * Ebel et al. (2018) Ebel, D. S., Alexander, C. M. O. ’D. and Libourel, G. 2018. “Vapor-Melt Exchange: Constraints on Chondrite Formation Conditions and Processes” in Chondrules: Records of Protoplanetary Disk Processes, edited by Sara S. Russell, Harold C. Connolly, Jr., and Alexander N. Krot, 151-173 Cambridge: Cambridge University Press.
  * Eisenhour and Buseck (1995) Eisenhour, D. D. and Buseck, P. R. 1995. “Chondrule formation by radiative heating: A numerical model.”, Icarus 117(1): 197–211. https://doi.org/10.1006/icar.1995.1151.
  * Elkins-Tanton et al. (2011) Elkins-Tanton, L. T., Weiss, B. P., and Zuber, M. T. 2011. “Chondrites as samples of differentiated planetesimals”, Earth and Planetary Science Letters 305(1–2): 1–10. https://doi.org/10.1016/j.epsl.2011.03.010.
  * Fedkin et al. (2012) Fedkin, A. V., Grossman, L., Ciesla, F. J., and Simon, S. B. 2012. “Mineralogical and isotopic constraints on chondrule formation from shock wave thermal histories”, Geochimica et Cosmochimica Acta 87: 81–116. https://doi.org/10.1016/j.gca.2012.03.020.
  * Fedkin and Grossman (2016) Fedkin, A. V. and Grossman, L. 2016. “Effects of dust enrichment on oxygen fugacity of cosmic gases”, Meteoritics and Planetary Science 51(5): 843–850. https://doi.org/10.1111/maps.12627.
  * Friedrich et al. (2015) Friedrich, J. M. et al. 2015. “Chondrule size and related physical properties: A compilation and evaluation of current data across all meteorite groups” Chemie der Erde Geochemistry 75: 419–443. https://doi.org/10.1016/j.chemer.2014.08.003.
  * Fu et al. (2014) Fu, R. F. et al. 2014. ”Solar nebula magnetic fields recorded in the Semarkona meteorite” Science 346: 1089-1092. http://dx.doi.org/10.1126/science.1258022.
  * Fu et al. (2018) Fu, R. F., Weiss, B. P., Schrader, D. L. and Johnson, B. C. 2018. “Records of Magnetic Fields in the Chondrule Formation Environment” in Chondrules: Records of Protoplanetary Disk Processes, edited by Sara S. Russell, Harold C. Connolly, Jr., and Alexander N. Krot, 324-339 Cambridge: Cambridge University Press.
  * Fukuda et al. (2022) Fukuda, K. et al. 2022. “A temporal shift of chondrule generation from the inner to outer Solar System inferred from oxygen isotopes and Al-Mg chronology of chondrules from primitive CM and CO chondrites”, Geochimica et Cosmochimica Acta 322: 194–226, 2022. https://doi.org/10.1016/j.gca.2021.12.027.
  * Gooding and Keil (1981) Gooding, J. L., Keil, K., Fukuoka, T., and Schmitt, R. A. 1981. “Correlations Between Physical and Petrological Properties of Chondrules”, Meteoritics 16: 318.
  * Grossman et al. (2008) Grossman, L., Beckett, J. R., Fedkin, A. V., Simon, S. B., and Ciesla, F. J. 2008. “Redox Conditions in the Solar Nebula: Observational, Experimental and Theoretical Constraints”, Reviews in Mineralogy and Geochemistry 68: 93-140. https://doi.org/10.2138/rmg.2008.68.7.
  * Grossman et al. (2012) Grossman, L., Fedkin, A. V., and Simon, S. B. 2012. “Formation of the first oxidized iron in the solar system”, Meteoritics and Planetary Science 47(12): 2160–2169. https://doi.org/10.1111/j.1945-5100.2012.01353.x.
  * Grott et al. (2019) Grott, M. et al. 2019. “Low thermal conductivity boulder with high porosity identified on C-type asteroid (162173) Ryugu”, Nature Astronomy 3: 971–976. https://doi.org/10.1038/s41550-019-0832-x.
  * Herbst and Greenwood (2016) Herbst, W. and Greenwood, J. P. 2016. “A new mechanism for chondrule formation: Radiative heating by hot planetesimals”, Icarus 267: 364–367. https://doi.org/10.1016/j.icarus.2015.11.026.
  * Herbst and Greenwood (2019) Herbst, W. and Greenwood, J. P. 2019. “A radiative heating model for chondrule and chondrite formation”, Icarus 329: 166–181. https://doi.org/10.1016/j.icarus.2019.03.039.
  * Herbst et al. (2021) Herbst, W., Greenwood, J. P., and Yap, T. E. 2021. “The Macroporosity of Rubble Pile Asteroid Ryugu and Implications for the Origin of Chondrules”, The Planetary Science Journal 2: 110 (16pp) https://doi.org/10.3847/PSJ/abf7c0.
  * Hevey and Sanders (2006) Hevey, P. J. and Sanders, I. S. 2006. “A model for planetesimal meltdown by 26Al and its implications for meteorite parent bodies”, Meteoritics and Planetary Science 41(1): 95–106. https://doi.org/10.1111/j.1945-5100.2006.tb00195.x.
  * Hewins and Radomsky (1990) Hewins, R. H. and Radomsky, P. M. 1990. “Temperature Conditions for Chondrule Formation”, Meteoritics 25(4):309-318. https://doi.org/10.1111/j.1945-5100.1990.tb00715.x.
  * Hezel et al. (2018) Hezel, D. C., Bland, P. A., Palme, H., Jacquet, E., and Bigolski, J. 2018. “Composition of Chondrules and Matrix and Their Complementary Relationship in Chondrites” in Chondrules: Records of Protoplanetary Disk Processes, edited by Sara S. Russell, Harold C. Connolly, Jr., and Alexander N. Krot, 91-120 Cambridge: Cambridge University Press.
  * Izidoro et al. (2022) Izidoro, A., Dasgupta, R., Raymond, S. N., Deienno, R., Bitsch, B., and Isella, A. 2022. “Planetesimal rings as the cause of the Solar System’s planetary architecture”, Nature Astronomy 6: 357–366. https://doi.org/10.1038/s41550-021-01557-z.
  * Jacquet (2014) Jacquet, E. 2014. “The quasi-universality of chondrule size as a constraint for chondrule formation models”, Icarus, 232: 176–186. https://doi.org/10.1016/j.icarus.2014.01.012.
  * Jacquet (2021) Jacquet, E. 2021. “Collisions and compositional variability in chondrule-forming events”, Geochimica et Cosmochimica Acta 296: 18–37. https://doi.org/10.1016/j.gca.2020.12.025.
  * Jewitt et al. (2023) Jewitt, D., Kim, Y., Li, J., and Mutchler, M. 2023. “The Dimorphos Boulder Swarm”, The Astrophysical Journal 952(1) L12 (10pp) https://doi/10.3847/2041-8213/ace1ec.
  * Johnson et al. (2018) Johnson, B. C., Ciesla, F. J., Dullemond, C. P. and Melosh, H. J. 2018. ”Formation of Chondrules by Planetesimal Collisions” in Chondrules: Records of Protoplanetary Disk Processes, edited by Sara S. Russell, Harold C. Connolly, Jr., and Alexander N. Krot, 343-359 Cambridge: Cambridge University Press.
  * Jones (1992) Jones, R. H. 1992. “On the relationship between isolated and chondrule olivine grains in the carbonaceous chondrite ALHA77307”, Geochimica et Cosmochimica Acta 56(1): 467–482. https://doi.org/10.1016/0016-7037(92)90145-9.
  * Jones et al. (2018) Jones, R. H., Villaneuve, J. and Libourel, G. 2018. ”Thermal Histories of Chondrules: Petrologic Observations and Experimental Constraints” in Chondrules: Records of Protoplanetary Disk Processes, edited by Sara S. Russell, Harold C. Connolly, Jr., and Alexander N. Krot, 57-90 Cambridge: Cambridge University Press.
  * Kita and Ushikubo (2012) Kita, N. T. and Ushikubo, T. 2012. “Evolution of protoplanetary disk inferred from 26Al chronology of individual chondrules”, Meteoritics and Planetary Science 47(7): 1108–1119. https://doi.org/10.1111/j.1945-5100.2011.01264.x.
  * Koschny et al. (2019) Koschny, D. 2019. “Interplanetary Dust, Meteoroids, Meteors and Meteorites”, Space Science Reviews 215(4): 34 https://doi.org/10.1007/s11214-019-0597-7.
  * Krot et al. (2006) Krot, A. N. et al. 2006. “Aluminum-Magnesium and Oxygen Isotope Study of Relict Ca-Al-rich Inclusions in Chondrules”, The Astrophysical Journal 639(2): 1227–1237 https://doi.org/10.1086/498610.
  * Lauretta et al. (2017) Lauretta, D. S. and 47 colleagues. 2017. “OSIRIS-REx: Sample Return from Asteroid (101955) Bennu.” Space Science Reviews 212: 925–984. https://doi.org/10.1007/s11214-017-0405-1.
  * Lichtenberg et al. (2016) Lichtenberg, T., Golabek, G. J., Gerya, T. V., and Meyer, M. R. 2016. “The effects of short-lived radionuclides and porosity on the early thermo-mechanical evolution of planetesimals”, Icarus 274: 350–365. https://doi.org/10.1016/j.icarus.2016.03.004.
  * Lichtenberg et al. (2018) Lichtenberg, T., Golabek, G. J., Dullemond, C. P., Schönbächler, M., Gerya, T. V., and Meyer, M. R. 2018. “Impact splash chondrule formation during planetesimal recycling”, Icarus 302: 27–43. https://doi.org/10.1016/j.icarus.2017.11.004.
  * Lichtenberg et al. (2021) Lichtenberg, T., Drazkowska, J., Schonbachler, M., Golabek, G. J., and Hands, T. O. 2021. “Bifurcation of planetary building blocks during Solar System formation”, Science 371(6527): 365–370. https://doi.org/10.1126/science.abb3091.
  * MacPherson (2007) MacPherson, G. J. 2007. “Calcium-Aluminum Rich Inclusions in Chondritic Meteorites” Treatise on Geochemistry 1: 1-47. https://doi.org/10.1016/B0-08-043751-6/01065-3.
  * MacPherson et al. (2005) MacPherson, G. J., Simon, S. B., Davis, A. M., et al. 2005. “Calcium-Aluminum-rich Inclusions: Major Unanswered Questions” in Chondrites and the Protoplanetary Disk: Astronomical Society of the Pacific Conference Series 341, 225-250, edited by Alexander N. Krot, Edward R. D. Scott and Bo Reipurth, Tucson: Astronomical Society of the Pacific.
  * Mamajek (2009) Mamajek, E. E. 2009. “Initial Conditions of Planet Formation: Lifetimes of Primordial Disks” in Exoplanets and Disks: Their Formation and Diversity, AIP Conference Proceedings 1158(1), 3-10. https://doi.org/10.1063/1.3215910.
  * Marrocchi et al. (2018) Marrocchi, Y., Villeneuve, J., Batanova, V., Piani, L., and Jacquet, E. 2018. “Oxygen isotopic diversity of chondrule precursors and the nebular origin of chondrules”, Earth and Planetary Science Letters 496: 132–141. https://doi.org/10.1016/j.epsl.2018.05.042.
  * Marrocchi et al. (2019) Marrocchi, Y. et al. 2019. “Formation of CV chondrules by recycling of amoeboid olivine aggregate-like precursors”, Geochimica et Cosmochimica Acta 247: 121–141 https://doi.org/10.1016/j.gca.2018.12.038.
  * Metzler (2012) Metzler, K. 2012. “Ultrarapid chondrite formation by hot chondrule accretion? Evidence from unequilibrated ordinary chondrites”, Meteoritics and Planetary Science 47(12): 2193–2217. https://doi.org/10.1111/maps.12009.
  * Michikami et al. (2019) Michikami, T. et al. 2019. “Boulder size and shape distributions on asteroid Ryugu”, Icarus 331: 179–191. https://doi.org/10.1016/j.icarus.2019.05.019.
  * Nagahara (1981) Nagahara, H. 1981. “Evidence for secondary origin of chondrules”, Nature 292(5819): 135–136. https://doi.org/10.1038/292135a0.
  * Nagashima et al. (2018) Nagashima, K., Kita, N. T. and Luu, T.-H. 2018. “26Al-26Mg Systematics of Chondrules” in Chondrules: Records of Protoplanetary Disk Processes, edited by Sara S. Russell, Harold C. Connolly, Jr., and Alexander N. Krot, 247-274 Cambridge: Cambridge University Press.
  * Nakamura et al. (2022) Nakamura, T. et al. 2022. “Formation and evolution of carbonaceous asteroid Ryugu: direct evidence from returned samples Science 379(6634): eabn8671. https://doi.org/10.1126/science.abn8671.
  * Palme et al. (2015) Palme, H., Hezel, D. C., and Ebel, D. S. 2015. “The origin of chondrules: Constraints from matrix composition and matrix-chondrule complementarity”, Earth and Planetary Science Letters 411: 11–19. https://doi.org/10.1016/j.epsl.2014.11.033.
  * Pape et al. (2019) Pape, J., Mezger, K., Bouvier, A.-S., and Baumgartner, L. P. 2019. “Time and duration of chondrule formation: Constraints from 26Al-me26Mg ages of individual chondrules”, Geochimica et Cosmochimica Acta 244: 416–436. https://doi.org/10.1016/j.gca.2018.10.017.
  * Pignatale et al. (2019) Pignatale, F. C., Jacquet, E., Chaussidon, M., and Charnoz, S. 2019. “Fingerprints of the Protosolar Cloud Collapse in the Solar System. I. Distribution of Presolar Short-lived 26Al”, The Astrophysical Journal 884(1): 31 (8pp). https://doi.org/10.3847/1538-4357/ab3c1f.
  * Piralla et al. (2021) Piralla, M., Villeneuve, J., Batanova, V., Jacquet, E., and Marrocchi, Y. 2021. “Conditions of chondrule formation in ordinary chondrites”, Geochimica et Cosmochimica Acta 313: 295–312. https://doi.org/10.1016/j.gca.2021.08.007.
  * Piralla et al. (2023) Piralla, M., Villeneuve, J., Schnuriger, N., Bekaert, D. V., and Marrocchi, Y. 2023. “A unified chronology of dust formation in the early solar system”, Icarus 394: 115427. https://doi.org/10.1016/j.icarus.2023.115427.
  * Rambaldi (1981) Rambaldi, E. R. 1981. “Relict grains in chondrules”, Nature 293(5833): 558–561. https://doi.org/10.1038/293558a0.
  * Russell et al. (2018) Russell, S. S., Connolly, H. C., and Krot, A. N. 2018. Chondrules: Records of Protoplanetary Disk Processes. Cambridge: Cambridge university Press.
  * Sanders and Scott (2012) Sanders, I. S. and Scott, E. R. D. 2012. “The origin of chondrules and chondrites: Debris from low-velocity impacts between molten planetesimals?”, Meteoritics and Planetary Science 47(12): 2170–2192. https://doi.org/10.1111/maps.12002.
  * Sanders and Scott (2018) Sanders, I. S. and Scott, E. R. D. 2018. “Making Chondrules by Splashing Molten Planetesimals: The Dirty Impact Plume Model”, in Chondrules: Records of Protoplanetary Disk Processes, edited by Sara S. Russell, Harold C. Connolly, Jr., and Alexander N. Krot, 361-374 Cambridge: Cambridge University Press.
  * Sanders and Scott (2022) Sanders, I. S. and Scott, E. R. D. 2022. “Complementary nucleosynthetic isotope anomalies of Mo and W in chondrules and matrix in the Allende carbonaceous chondrite: The case for hydrothermal metamorphism and its implications”, Meteoritics and Planetary Science 57(2): 450–471. https://doi.org/10.1111/maps.13742.
  * Scott (2020) Scott, E. R. D. 2020 ”Iron Meteorites: Composition, Age, and Origin.” Oxford Research Encyclopedia of Planetary Science. Oxford University Press. https://doi.org/10.1093/acrefore/9780190647926.013.206.
  * Sears (1998) Sears, D. W. G. 1998. “The Case for Rarity of Chondrules and Calcium-Aluminum-rich Inclusions in the Early Solar System and Some Implications for Astrophysical Models”, The Astrophysical Journal 498(2): 73–778 https://doi.org/10.1086/305589.
  * Shah et al. (2017) Shah, J., Bates, H. C., Muxworthy, A. R., Hezel, D. C., Russell, S. S., and Genge, M. J. 2017. “Long-lived magnetism on chondrite parent bodies”, Earth and Planetary Science Letters 475: 106–118. https://doi.org/10.1016/j.epsl.2017.07.035.
  * Siron et al. (2022) Siron, G., Fukuda, K., Kimura, M., and Kita, N. T. 2022. “High precision 26Al-26Mg chronology of chondrules in unequilibrated ordinary chondrites: Evidence for restricted formation ages”, Geochimica et Cosmochimica Acta 324: 312–345. https://doi.org/10.1016/j.gca.2022.02.010.
  * Tenner et al. (2019) Tenner, T. J. et al. 2019. “Extended chondrule formation intervals in distinct physicochemical environments: Evidence from Al-Mg isotope systematics of CR chondrite chondrules with unaltered plagioclase.” Geochimica et Cosmochimica Acta 260: 133–160. https://doi:10.1016/j.gca.2019.06.023.
  * Venuti et al. (2017) Venuti, L. et al. 2017. “CSI 2264: Investigating rotation and its connection with disk accretion in the young open cluster NGC 2264”, Astronomy and Astrophysics 599: A23 (44 pp). https://doi.org/10.1051/0004-6361/201629537.
  * Villeneuve et al. (2009) Villeneuve, J., Chaussidon, M., and Libourel, G. 2009. “Homogeneous Distribution of 26Al in the Solar System from the Mg Isotopic Composition of Chondrules”, Science 325(5943): 985-988. https://doi.org/10.1126/science.1173907.
  * Wasson et al. (1995) Wasson, J. T., Krot, A. N., Lee, M. S., and Rubin, A. E. 1995. “Compound chondrules”, Geochimica et Cosmochimica Acta 59(9): 1847–1869. https://doi.org/10.1016/0016-7037(95)00087-G.
  * Weidenschilling (2000) Weidenschilling, S. J. 2000. “Formation of Planetesimals and Accretion of the Terrestrial Planets”, Space Science Reviews 92: 295–310. https://doi.org/10.1023/A:1005259615299.
  * Weidenschilling (2019) Weidenschilling, S. J. 2019. “Accretion of the asteroids: Implications for their thermal evolution”, Meteoritics and Planetary Science 54(5): 1115–1132. https://doi.org/10.1111/maps.13270.
  * Wood (1963) Wood, J. A. 1963. “On the Origin of Chondrules and Chondrites”, Icarus 2: 152–180. https://doi.org/10.1016/0019-1035(63)90013-7.
  * Whattam et al. (2022) Whattam, S. A., Hewins, R. H., Seo, J., and Devouard, B. 2022. “Refractory inclusions as Type IA chondrule precursors: Constraints from melting experiments”, Geochimica et Cosmochimica Acta 319: 30–55. https://doi.org/10.1016/j.gca.2021.12.022.
  * Yada et al. (2021) Yada, T. 2021. “Preliminary analysis of the Hayabusa2 samples returned from C-type asteroid Ryugu”, Nature Astronomy 6: 214–220. https://doi.org/10.1038/s41550-021-01550-6.
  * Yu and Standish (1991) Yu, A. B. and Standish, N. 1991. “Estimation of Porosity of Particle Mixtures by a Linear-Mixture Packing Model”, Industrial Engineering Chem. Res. 30: 1372-1385. https://doi.org/10.1021/ie00054a045.