Hashimoto and Nakano Progress in Earth and Planetary Science
https://doi.org/10.1186/s40645-020-00382-8(2021) 8:9

RESEARCH ARTICLE

Progress in Earth andPlanetary Science

Open Access

Bubbles to Chondrites-II. Chemical
fractionations in chondrites
Akihiko Hashimoto1

and Yuki Nakano2*

Abstract
We attempt to develop a possible theory of chemical fractionations in chondrites, that is consistent with various
features of chondritic components and current observation of protoplanetary disks (PPD). Combining the 3+2
component fitting calculation that simulates chondrule formation process proposed in paper (I) with additional
mixing procedures, we investigate essential causes that made various types of chondrites evolve from the uniform
solar system composition, the CI-chondritic composition. Seven chemical types of chondrites (CM, CV, CO, E, LL, L andH) are examined, for which reliable chemical compositions for both bulk chondrites and chondrules therein are
known. High vaporization degree of the primordial dust aggregates (dustons) required by the calculation vindicatesthat the chondrule formation was the driving force for the chemical fractionations in all chondrites examined. Various
initial redox states in dustons and different timings of CAIs’ invasion to the chondrule formation zone are identified for
different chondrite types. These results, together with a good correlation with the D/H ratios of chondrites measured
previously, lead us to the notion that PPD evolved from reducing to oxidizing. We explore the heating mechanism forthe chondrule formation and the place it occurred. Only heat source being consistent with our chondrule formation
model is lightning discharge. We postulate that large vortices encompassing the snow-line are ideal places for large
charge separation to occur between dustons and small ice particles, and that direct strikes on dustons should makethem boil for ten seconds and longer and allow a swarm of chondrules released from their surfaces. Chemical
fractionations are completed by an aerodynamic separation of dustons from chondrules inside the vortex, in such a
way that the dustons fall fast into the vortex center and form a planetesimal immediately, while chondrules with dust
mantles fall slow and form a thin veneer on the planetesimal surface. During collisional episodes, the veneers are
preferentially fragmented and reassemble themselves by a weak self-gravity to form a rubble-piled chondritic
asteroid, i.e. chondrite.
Keywords: Chondrites, Chondrules, Chemical fractionations, Protoplanetary disk, CAIs, D/H ratio, Lightning
discharge, Planetesimal, 26 Al, Redox state

1 Introduction
In pursuit of fundamental rules of chemical fractionations
caused by evaporation and condensation of primordialdust aggregates, we have discovered an alternative andcompelling route in evolution of chondritic materials inthe solar system protoplanetary disk.
From late 1960’s to early 1980’s, Anders and his group
sent out an outstanding array of their research works*Correspondence: yudaruma@ep.sci.hokudai.ac.jp
Department of Cosmosciences, Hokkaido University, N10 W8, 060-0810,
Sapporo, Japan
Full list of author information is available at the end of the article2

on meteorites (e.g., a series of ‘Chemical fractionations
in meteorites’; Anders 1971), particularly on chondrites,
deciphered a wealth of chemical codes about the originof our solar system materials, and established an idea thatchondritic materials are building-blocks of the planets.
Their core idea, the equilibrium condensation of a hot anddense gas, initially above 2000 K, with the solar elemental
abundance, was inspired by Cameron’s solar nebula model(Cameron 1962; 1963).
Recent theories and observations indicate much colder
protoplanetary disks (PPD) with much smaller masses, as
Williams and Cieza (2011) in their review paper described,© The Author(s). 2021 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
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Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9“Initially, disks rapidly funnel material onto the star but,as the surrounding molecular core is used up or otherwise disperses, the accretion rate decreases and a small
amount of material persists. That these discs can be considered protoplanetary is apparent through not only thegeometry of the Solar System but also the high detection
rate of exoplanets”. On the other hand, accretion during
the protostellar phase, while the protostellar envelope isstill falling onto the disk, is much less well understood(Hartmann et al. 2016), and thus a theoretical possibility
may exist that the planet- and meteorite-forming materials had gone through a high temperature phase when all
the preexisting dust once became a gas.
This possibility, however, is denied because the meteorites retain presolar grains with large isotopic anomalies
intact (e.g., Zinner 1998) and because the D/H ratios ofchondritic water and organic compounds exhibit ∼ 10−4
or higher values (e.g., Alexander et al. 2012) as opposedto the solar value ∼ 2 × 10−5 , which should be homogenized to the solar value if heated above 500 K (Lécluse
and Robert 1994). Therefore, the equilibrium condensation model of chondritic materials has lost its basis and weare in need of a new mechanism to explain the chemical
fractionations in chondrites.
Chondrules, once molten silicate droplets of 0.1-3 mm
in size that constitute more than 60% of the chondrites
in volume, have been generally regarded as nothing but asimple melted product of preexisting dust (e.g., Larimer
and Anders 1970; Jacquet 2014), and only their heatsources are a matter of concern for most researchers.
However, the chondrule formation event is only opportunity for causing chemical fractionations in chondrites
because the idea of the nebular-scaled, high temperaturephase is no longer valid.
In the companion paper (I) (Nakano and Hashimoto2020), we have demonstrated that primordial dust aggregates that are dense and large (>3 cm in diameter), named
dustons, are needed to generate jet-droplets, viz., chondrule nuclei, upon bursting of boiling bubbles on theirsurfaces. We have developed a model that a vapor cloudthat forms around a boiling duston provides the environment where jet-droplets react with vapor and condensed
particles on their way out and complete their chemical integrity as chondrules. This new model of chondrule formation explains the 3.5 fundamental featuresof chondrules, including their chemistry, size range andfrequency distribution, and textures.
Here we extend our model to cover the bulk chemistryof chondrites and propose a new mechanism of chemical fractionations in chondrites starting with the chemicalcomposition of CI chondrite.
This paper starts as a sequel to paper (I), in that basicallythe same model and calculation procedure are applied tothe bulk chemistry of chondrites, but having gained anPage 2 of 32

entirely new perspective on the origin of chondrites, we
expand our view to the evolution of PPD materials fromdust to planetesimals. We also investigate a possible heatsource of chondrule formation that should be consistent
with our model.

2 Numerical model of chemical fractionation
In our chondrite formation model, we assume the initialmaterial to be primordial dust aggregate having a CI-likecomposition, CIsil , just as in our paper (I). CIsil is thesilicate composition made of the ten oxide elements in CIchondritic proportions, Na, Mg, Al, Si, K, Ca, Ti, Cr, Mn
and Fe, only controlled with a parameter fs that is a fraction of Fe oxide in the total Fe in CI. We do this, since
Fe can also exist in other redox states such as metal andsulfide (See the detail in paper I).
In our paper (I), as a consequence of jet-droplet ejection in the vapor cloud that enshrouds the duston,
we have recognized the three components: jet-droplets,
vapor in the cloud (named differential vapor), and finecondensed particles (named integrated vapor). We havemodeled chondrule chemistry as a mixture of the three,and successfully reproduced chemical compositions of
75% of the 600 real chondrules. We extend the same
method with two more components, on account of thematrix material that coexists with chondrules insidechondrites.
2.1 Methods

We wish to solve the five simultaneous linear equations
just as in paper (I),Am,n Fn = Bm (m = 1−5

and n = 1−5).

(1)Here Bm represents a molar fraction of element m = 1-4(Na, Mg, Al and Si in ascending order) in a ‘bulk silicatechondrite’. B5 = 1. Fn , an unknown to be determined, represents a mixing proportion (in molar basis) of the fivecomponents n = 1-5 (1: jet-droplet, 2: differential vapor,
3: integrated vapor,
4: final integrated vapor and 5: CI∗ ).

By definition n Fn = 1. Am,n is a matrix to describe
molar fractions of Na, Mg, Al and Si (m = 1-4) among
the ten elements in each of the five components (n = 1-5).
A5,n = 1 (n =1-5).
The three components (n = 1-3) are for reproducing achemical composition of individual chondrules in paper(I). This time they are for an average composition of as
many chondrules as available from a single chondrite orfrom a specified type of chondrites.
The two components (n = 4 and 5) are for making the matrix material in that single chondrite or inthat specific type of chondrites. The fourth component (n = 4) represents the integrated vapor composition (viz., a weighted average composition of the total
condensed particles) at the end of evaporation from

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

the duston. For simplicity, the vapor lost (both differential and integrated) by reaction with jet-droplets is
assumed minimal or zero. The termination of evaporation is signaled with the final VD (vaporization degree)
reached by MLB (mother liquid body, viz., melted surface) of the duston, which is made equal to twice the
VD that produces the average chondrule composition.
It presupposes that the VD for the average chondrulecomposition is just the halfway of the total evaporation
process.
CI∗ (the fifth component) represents the average silicate composition of primordial CI-like dust that has tobe mixed with the fourth component to form the matrix
material after chondrule formation. CI∗ is assumed to beomnipresent in PPD, but is distinguished from CIsil which
is an immediate source of dustons. We take fs = 0.5 temporarily for CI∗ . In the following investigation, we havefound that Eq. 1 have solutions as long as CI∗ with fs =0.3-1.0, but not for CI∗ with fs < 0.3 for ordinary chondrites. The fs value of CI∗ has an effect on the relative
proportion of the matrix to chondrules, but otherwise it
does not affect the calculation result. Hence it is taken asa constant.
Am,n (m = 1-4; n = 1-4) are obtained by calculating
the evaporative chemical fractionation similar to the one
described in “Model calculation of chondrule chemistry”
of paper (I). Am,4 (m = 1-4) is the chemical composition of
the final integrated vapor described above and Am,5 (m =1-4) is that of CI∗ .
Calculation proceeds with a step size q = 1.001 starting with CIsil for a specified fs , and obtains a set ofAm,n at every step number, as described in Paper (I).
The q is defined as XAl,k /XAl,k−1 , where XAl is a molar
fraction of AlO1.5 in the MLB and k is an evaporation
step number, as described in Paper (I). Equation 1 aresolved at every step number to give the molar fractions
Fn . Computation is repeated with fs and step number(viz., VD%) as parameters so as to satisfy the requirement: Fn (n = 1 − 5) to be all positive. Only with thisrequirement, however, multiple solutions exist. We add
another constraint to the calculation, the average composition of chondrules. A unique solution is looked forwith the parameters fs and VD, that should reproduce
the molar fractions of Na and Fe in the average chondrule composition. The choice of Fe is obvious since itis related to the parameter fs . The Na concentration has
the largest dynamic range and monotonously changes
with VD% over the multiple solutions, making it easy tofind a single solution to fit the exact chondrule averagevalue.
The final solution is the one that should satisfy thebulk composition of chondrite as well as the average composition of chondrules included in that chondrite. The
number of constraints for the chondrule is two, while

Page 3 of 32

four (viz., Na, Mg, Al and Si concentrations) for thebulk chondrite. As explained in paper (I), the four constraints is good enough to fit the composition. However,
the two constraints are not enough. For this reason a best
fitting is not expected for the average chondrule composition. As it turned out, however, the fitting to thechondrule is also quite satisfactory for the two types ofchondrites, L and H.
2.2 Handling of CAIs

Unlike fitting individual chondrules in paper (I), the bulk
chondrite fitting has two sources of complexity, which arenonetheless very important to understand the chemical
fractionations in chondrites. The first one is the existence of inclusions in the bulk chondrites: CAIs (Ca-,Al-rich inclusions) and amoeboid olivine aggregates. They
are generally thought to be of foreign origin, from theiroxygen isotope composition (e.g., Clayton and Mayeda
1977; Hiyagon and Hashimoto 1999) and other isotopic
anomalies (e.g., Wasserburg et al. 1977; Wasserburg et al.
2012), having invaded into the chondrite formation zone.
CAIs are very enriched in refractory elements and affectthe Al, Ca and Ti concentrations in the bulk chondrite
composition (e.g., MacPherson 2014, references therein).
Amoeboid aggregates are mostly made of forsterite withsome refractory elements (e.g., Grossman and Steele 1976;
Hashimoto and Grossman 1987). Their compositions are
not so different from the bulk chondrite composition andthus hard to be distinguished from the latter in the calculation. For this reason, they are not considered in thecalculation.
We identify two types of CAIs: the ones that later
invaded into the chondritic materials and the ones which
invaded before the chondrule formation. The former are
recognized as CAIs as they are clearly visible in certain
types of chondrites (mostly carbonaceous chondrites),
while the latter are invisible but only manifest their presence as unusual enrichment in refractory elements inchondrules in certain types of chondrites (e.g., CO chondrites; see Table 1). We call the latter ‘ghost CAIs’ as wefound their existence for the first time.
For the sake of fitting the bulk composition of chondritethat is assumed to consist only of chondrules and matrix,
we need to subtract the apparent effect of CAIs that would
erroneously raise the concentrations in Al, Ca and Ti inthe bulk composition. Therefore, a due amount of CAI is
presupposed and subtracted from the bulk composition
beforehand. The corrected composition is renormalized
to 100 mol% (only the silicate with the ten elements) andthen applied with the aforementioned calculation procedure. We try typical CAI compositions and then someatypical composition until a best fit is found. The fitted
result should give both the CAI-free bulk chondrite composition and the composition of CAI and its amount, and(2021) 8:9

Hashimoto and Nakano Progress in Earth and Planetary Science

Page 4 of 32

Table 1 Bulk (silicate) chemical compositions of chondrites and average chemical compositions of chondrules (mol%)ChondriteType

NaO0.5

MgO

AlO1.5

SiO2

KO0.5

L

1.917

38.3662.760

41.335

0.146

H

1.921

39.9382.905

42.155LL

1.838

37.5122.634

40.508CV

0.518

39.356

4.243

E

1.956

39.890

3.811

CO

1.369

36.873CM

1.422

35.450

CI

1.835

CI∗

2.128

L
H

CaO

TiO2

CrO1.5

MnO

FeO

Total

2.063

0.094

0.436

0.300

12.584

100

0.132

2.147

0.104

0.474

0.302

9.921

100

0.127

2.053

0.098

0.426

0.296

14.510100

36.656

0.041

3.045

0.137

0.465

0.172

15.368100

49.636

0.119

1.595

0.098

0.387

0.259

2.248

100

3.629

35.612

0.084

2.431

0.105

0.391

0.221

19.285100

3.188

35.180

0.082

2.383

0.112

0.403

0.244

21.536100

33.2082.653

31.931

0.114

1.906

0.077

0.419

0.293

27.563100

38.5173.077

37.035

0.133

2.210

0.090

0.486

0.340

15.984100

1.765

39.3582.631

42.223

0.134

1.864

0.089

0.456

0.284

11.197100

1.913

39.3932.735

43.740

0.147

2.023

0.104

0.435

0.301

9.208

100

Bulk chondrite

Chondrule

LL

1.763

41.2382.415

42.859

0.175

1.654

0.097

0.627

0.295

8.878

100

CV

0.485

51.8842.814

40.330

0.041

2.782

0.145

0.228

0.058

1.233

100

E

1.237

43.8531.939

48.802

0.129

1.373

0.046

0.257

0.155

2.208

100

CO

1.386

41.7174.240

40.456

0.047

3.689

0.145

0.440

0.167

7.712

100

CM

0.039

52.7751.422

41.518

0.000

2.161

0.203

0.328

0.087

1.467

100

also the whole rock composition including CAIs, whichshould be identical to the bulk chondrite composition on
the ten element basis.
Ghost CAIs are handled in the opposite way. Extra Al,
Ca and Ti (and also Mg and Si if necessary) in due amounts
are added to the initial composition CIsil , and renormalized to 100 mol% to give a corrected initial composition
for the calculation. This corrected initial composition isapplied to the aforementioned calculation procedure inorder to fit the bulk chondrite composition. We try thesimplest Al:Ca:Ti proportion for the added CAIs, which is
identical to the CI-chondritic (or solar abundance) ratio
and then some atypical proportion until a best fit is found.
The fitted result should give the composition of ghost
CAI and its amount and also the whole rock composition which should be identical with the bulk chondrite
composition.
As will be shown later, both CAIs and ghost CAIs are
identified in two types of chondrites (CO and LL). To
these chondrites the combination of the two procedures
described above is applied.
2.3 Correction for the Effect of Aqueous Alteration in the
Bulk Chondrites

Another source of complexity is the aqueous alteration of
bulk chondrites suggested for certain types of chondrites(e.g., Tomeoka and Buseck 1985; Krot et al. 1998), thatshould have occurred after accumulation of chondritic
components onto a large body, or meteorite parent bodyas usually supposed. This would have changed the redox
state of Fe-bearing phases towards more oxidizing. Specifically Fe metals would have been changed into Fe oxides
that could be accommodated into silicate or exist as acertain hydrous oxide phase. The oxidation should be far
more effective for matrix materials because of their finegrained and porous nature than for chondrules which
are coarse-grained and non-porous. This effect should
be removed for the present calculation to be properly
executed because it is a secondary effect that has nothing to do with the chondrule formation. The problem
is how to recognize and distinguish it from the original redox state of chondrite forming materials before
alteration.
A hint is the difference in redox state between thechondrules and the matrix (or the bulk chondrite). The
wet-chemical analyses of chondrites distinguish Fe oxides
from metals and sulfides. Therefore, the FeO content in
the bulk chondrite is known. If it is too abundant ascompared with the average FeO content in the chondrules, we should suspect the effect of alteration in thematrix. In order to compensate the FeO content in thebulk chondrite for the effect of alteration, we introduce aHashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

factor fw which is the ratio of the FeO concentration in
the alteration-free bulk chondrite relative to that in the
wet-chemical data.
The fw is a factor which is imposed on the FeO concentration in the wet-chemical bulk chondrite data, but
not on the average composition of chondrules which
are contained in that chondrite. We parameterize fw justlike fs in the calculation and find a best fitting value.
As it turned out, it is rather easy to find the best fit
value within relative errors of 10% or so since other values just do not allow equations to have solutions. As
shown later, fw is unity for E, H and L chondrites, whileother four types of chondrites have values smaller thanunity, implying that aqueous alteration was in action in
the latter four chondrites after their accretion to large
bodies.
2.4 Data

Table 1 shows (in the upper columns) the bulk chemicalcompositions of seven types of chondrites, as well as two
CI compositions, on the ten oxide element basis, and also
shows (in the lower columns) the average compositions ofchondrules contained in each type of chondrites, used in
the calculation. The data sources and some adjustments todata are explained in Appendix A.

3 Results
In the followings we explain the results of numerical fittings in detail for chondrites temporarily grouped according to the fitting procedure commonly applied.
3.1 Ordinary Chondrites (L, H and LL types)

Ordinary chondrites are generally presumed CAI-free.
Thus the fitting procedure is simple. We obtained a single
solution for each chondrite. Figure 1 shows the results ofnumerical fittings for L, H and LL types of chondrites, by
normalizing the abundance of the elements to the CI and
Si abundance. The determined parameters as well as proportions of the five components and compositions thereof
are thoroughly examined in Section 3.5.
Here we investigate status of the fitting element by
element. The four elements calculated, Na, Mg, Al andSi fit exactly the bulk chondrite composition simply
because their concentrations are given as known values
in the five simultaneous linear equations. The Fe alsofits nearly perfectly because it is controlled with parameter fs . The remaining five elements, K, Ca, Ti, Cr and
Mn, are left free of preset constraints. As shown in Fig. 1(‘calc bulk’ on the left panels), the calculated concentrations in these elements are more or less different fromthe bulk chondrite values, except for Ca in L and H
chondrites. There must be reason or cause for the elements that are not fitted well, which will be explored
below.

Page 5 of 32

There are at least two kinds of causes possible. The
first is the possibility that the bulk composition and/or
the average chondrule composition adopted for the calculation is in error. As long as the bulk compositionsof ordinary chondrites are concerned, this possibility
is small because only the ‘falls’ meteorites are used
and the average of many chondrite wet-chemical analyses (see Appendix A) are used in the calculation. On
the other hand, the EPMA analyses of chondrule compositions may have their own source of error, especially the broad-beam corrections as described in paper(I). Minor elements, i.e., K, Ti, Cr and Mn, may suffer from the problem of detection limits in the EPMA
analysis.
Another possibility may be related with the validity
including our original experiments that were translated
to the volatilities of elements used in the present calculation and our model assumptions about the chondrule andchondrite formation, or with some essential problem suchas the initial composition assumed for the primordial dust
and some possible effect not included in the calculation.
A survey of the bulk chondrite fitting in Fig. 1 indicatesthe same trends in all three ordinary chondrites that 1) K,
Ti (and maybe Ca) are depleted in the calculation relative
to the actual chondrites and 2) Cr and Mn in the calculation are too enriched. The same trends are also seen in
the average chondrule fitting in Fig. 1 (‘calc cdl ave’ on theright panels). The fact implies that these trends are notrelated with analytical errors in the chondrite and chondrule analyses. They might be attributed to some problem
in our calculation, although we cannot think of any defectat the moment. Let us try to find a positive reason for theobserved trends. They could originate in the chondrule
formation process or be ascribed to the primary featuresof the dust.
The depletion in Cr and Mn in the actual chondrites andchondrules relative to the calculation may be due to theirhaving partially existed as sulfides in the primordial dust
just like Fe-sulfide, which would decrease their concentrations in the silicate dust. Mn and Cr are multi-valent elements like Fe, although they are usually considered moststable as oxides (viz., silicate) in PPD. Mn-bearing and Crbearing iron sulfides are often observed in a reduced typeof chondrites such as E chondrites. Some Cr can dissolve
into Fe-Ni alloy. For fitting the Cr and Mn concentrations in the bulk ordinary chondrites, ∼20% of Cr and∼25% of Mn must be removed from the initial CIsil composition. There are two possibilities. (1) Mn and Cr are
partially removed in the form of metal and/or sulfide by
the metal (+sulfide) - silicate fractionation process, as proposed for explaining the Fe depletion in bulk chondrites
relative to CI (Urey and Craig 1953; Larimer and Anders1970). (2) The wet chemical analyses of bulk chondrites by
Jarosewich (1990) do not include the Mn and Cr contents

(2021) 8:9

Hashimoto and Nakano Progress in Earth and Planetary Science

Table 2 Depletion factors for Cr and Mn
Chondrite Type
CV

CM

E

CO

LL

H

L

Cr

1.17

1

0.55

0.95

0.8

0.83

0.78

Mn

0.5

0.75

0.46

0.65

0.72

0.73

0.74

contributed by sulfide and metal. The both possibilities
are likely combined to make Mn and Cr depleted in thebulk chondrite compositions relative to the calculation.
Table 2 shows the depletion factors to be imposed on
the initial CIsil for Cr and Mn to fit the bulk chondrite
compositions for seven types of chondrites investigatedhere. E chondrite, the most reduced type, requires nearly

Page 6 of 32

halves of Cr and Mn to be removed from the initial silicate composition. On the other hand, CV and CM (andpossibly CO) requires no depletion in Cr, contrary to
Mn. This might suggest that Cr favors oxide more thanMn does.
The consistent depletion in K in the calculation (Fig. 1)
as compared to the bulk composition and the averagechondrule composition is mysterious, especially knowing the fact that the fitting of K is nearly perfect for theother four types of chondrites as will be shown later. Reexamination on the relative volatilities indicates that a factor of two or three more reduction in the relative volatilityof K compared to Na is required to explain the K enrichment in the bulk ordinary chondrites. Such an adjustment
is against our experimental results which indicated similar
relative volatilities for Na and K within errors of a few tens

Fig. 1 Results of numerical fittings for L, H and LL chondrites, as compared to the composition of real chondrites. (E/Si)/(E/Si)CI indicates (element
concentration normalized to Si concentration) of a substance divided by (element concentration normalized to Si concentration) of CI chondrite.
Initial: initial composition used in the calculation. Bulk chondrite: average bulk composition of a specified chondrite type (e.g., L chondrite).
Chondrule ave: average composition of chondrules which belong to a specified chondrite type. Calc bulk: calculated bulk composition of a
specified chondrite type. Calc cdl ave: calculated average composition of chondrules of a specified chondrite type

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

of percent (Nakano and Hashimoto 2020). If the relative
volatility of K was adjusted to fit the ordinary chondrites,
it should fail for the other four chondrite types.
We observe a consistent depletion in Ti (and possibly in Ca) in the calculation relative to both the bulk
composition and the average chondrule composition ofordinary chondrites. This implies some enrichment inthese elements before the chondrule forming process. It
should be related to a CAI invasion before the formationof chondrules, although ordinary chondrites are generally
thought being free of CAIs. We will re-examine ordinarychondrites later.
3.2 Carbonaceous Chondrites and Enstatite Chondrites

Carbonaceous chondrites contain CAIs up to several volume percent, and need subtraction of their effects before
fitting their bulk compositions and average chondrulecompositions. Fitting is a process of trial and error byassuming the composition and amounts of CAIs to subtract from the wet-chemical composition of bulk silicatechondrite, while surveying the other parameters, VD, fs
and fw at the same time. Let such a tentative, CAI-freebulk composition to be fitted be called, a ‘CAI-subtracted
bulk composition’. We apply the regular calculation procedure to the CAI-subtracted bulk composition and theaverage chondrule composition. When the best fitting
parameters and appropriate CAI component are found,the bulk composition of chondrite is reconstructed byadding the CAI component, called ‘the calculated bulk
composition’.
Chondrules in CO chondrites are unusually rich in
Al, Ca and Ti as compared to chondrules in any othertypes of chondrites, as shown in Table 1. The abundances of these elements are 1.6-1.9 times as high as
those in CI. This fact suggests that the initial composition of the primordial dust had been pre-enriched inthese refractory elements, most probably in the form ofinvaded CAIs, before the chondrule formation of CO
chondrites. We call those CAIs ‘ghost CAIs’ because
they should have become invisible by mixing with theprimordial dust during high-temperature melting in thechondrule forming process, but would only appear in
the chemistry of the chondrules thus formed. Therefore, CAIs with an adequate composition in an adequate
amount must be added to the initial composition CIsil
before fitting the bulk and chondrule composition of
CO chondrites. We call such a mixed composition a‘CAI-loaded CI silicate composition’. CO chondrites also
contain visible CAIs, which can be handled with subtraction of due amounts of CAI just as other carbonaceouschondrites.
Enstatite chondrites are rich in Al in their bulk composition, next to CV as shown in Table 1, although they
do not belong to carbonaceous chondrites. As a matter ofPage 7 of 32

fact, no solution is obtained without subtracting (Al-rich)
CAI before fitting. We have found that 2.3 mol% of an Alrich CAI (Al0.79 Ca0.19 Ti0.02 ; a mixture of more than twophases is possible) is needed to mix after the chondrule
formation to reproduce the bulk and chondrule composition of E chondrites. The Ca/Al ratio of E chondrites
far lower than that of CI has been an enigma for long. It
has been suggested that Ca was mobilized by shock andlocalized somewhere in the chondrite (Rubin et al. 2009).
However, no such occurrence has been found yet. We
suggest that E chondrite is unusually enriched in Al dueto the incorporation of Al-rich CAI after the chondrule
formation.
Figure 2 shows the results of numerical fittings for
CV, CM, CO and E chondrite. In all of these figures,
the bulk Cr and Mn abundances are already fitted withthe depletion factors shown in Table 2. The bulk Al, Ca
and Ti abundances are fitted with the CAI composition
and its amount of subtraction or addition as describedabove. CV, CM and E chondrites require mixing of CAIs
after the chondrule formation. CO chondrites require preenrichment in Al, Ca and Ti (as ghost CAIs) twice asabundant as CI before the chondrule formation, while
only a few percent addition of CAIs to the bulk chondrite afterwards. K is left with no fitting effort, which
nevertheless shows an extraordinary match between thecalculation and the bulk chondrite for all four types ofchondrites, as seen in Fig. 2. This is in contrast withthe result for ordinary chondrites, which clearly showsa disagreement between the calculation and the bulk
chondrites.
The CAIs in CV, CM and CO chondrites predictedby the calculation have chemical compositions of rather
common CAIs with the Al:Ca:Ti ratio similar to that of CI
composition, consistent with the observation in the realchondrites. The ghost CAIs predicted for CO chondrites
also have the same Al:Ca:Ti ratio as CI. The CAIs predicted in E chondrites, however, are very rich in Al andmost probably poor in Mg and Si. Such a CAI exists incarbonaceous chondrites, though extremely small in concentration (e.g., MacPherson et al. 1983; Ireland 1988), as
compared with common CAIs. In this sense E chondrites,
having only Al-rich CAIs predicted, are quite unique andrequire μm-scaled petrographic study since Al-rich CAIs
are usually very small in size. Actually Bischoff et al. (1984)
and Guan et al. (2000) have reported such occurrences.
The average chondrule compositions are not so well
reproduced by the calculation compared to the bulk compositions, particularly for CV and CM chondrites. It isvery likely that the number of chondrules used for averaging is too small, only eight for CV and ten for CM, tobe representative of chondrules in those chondrites. Nevertheless the matching to the average chondrule is quite
good for Mg and Si, reconfirming the validity of our study.

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

Page 8 of 32

Fig. 2 Results of numerical fittings for CV, E, CO and CM chondrites, as compared to the composition of real chondrites. CAI-subt bulk: ‘CAI-subtracted
bulk composition’ of a specified chondrite type (see text). Calc CAI-subt bulk: calculated CAI-subtracted bulk composition of a specified chondrite
type. Subtracted CAI: mol% of CAI-forming elements in the bulk chondrite, normalized to its CI abundance (refer to CAI/CI on the right hand scale).
The initial composition used for CO chondrite is ‘CAI-loaded CI silicate composition’ described in text. See the caption of Fig. 1 for other notations

3.3 Ordinary Chondrites Revisited

Knowing a possible existence of ghost CAIs before thechondrule formation in CO chondrites, we hypothesize
a pre-mixing of Ti-rich CAI into the primordial dust
before chondrule formation, to explain the depletion in
Ti and possibly in Ca in the calculation for ordinarychondrites.

Figure 3 shows the calculated bulk compositions as wellas the calculated average chondrule compositions for thethree types of ordinary chondrites, along with the realchondrite compositions for comparison. As in Fig. 2, thebulk Cr and Mn abundances are fitted with the depletion factors shown in Table 2. The CAI-loaded CI silicatecomposition explained in Section 3.2, shown in bold black(2021) 8:9

Hashimoto and Nakano Progress in Earth and Planetary Science

Page 9 of 32

calculated for the four types of chondrites. CO chondrites
require ghost CAIs as much as 9 mol% in their initial
silicate composition. The best fitting was made with acommon CAI composition, viz., having the Al:Ca:Ti ratio
being identical to that of CI composition and the Mg
and Si in half or equal amount of Ca, respectively. LL, H
and L chondrites, however, require Ti-enriched, Al-Ca-Ti
oxides for their ghost CAIs. The required mass for theghost CAIs, relative to the CIsil , before chondrule formation is only 0.1, 0.15 and 0.2 mol% for H, L and LL,
respectively.
In Section 3.2 we suggested invasion of the Al-rich CAI
to E chondrites after chondrule formation. Its mass, 2.3
mol%, however, is far larger than those for ghost CAIs
for ordinary chondrites, and its composition is not Tienriched but Ca-depleted relative to the CI composition.
Thus the ghost CAIs for ordinary chondrites are not only
different from that for CO chondrites but from the Al-rich
CAI in E chondrites.
3.4 Question of CI versus Solar Photosphere

Fig. 3 Results of numerical fittings for L, H and LL chondrites, thatincorporate the effect of CAIs and ghost CAIs. See the captions of
Figs. 1 and 2 for notationslines in the figures, includes the contribution of ghost
CAIs to the CIsil . In case of LL chondrites, the CAI composition to be added after chondrule formation is also
shown in thin gray line. The final matching is quite satisfactory for the bulk compositions with the K problem
remaining persistently, and is fairly good for the averagechondrule compositions.
Table 3 shows the amount of oxide elements to beentered as ghost CAIs to the primordial CI-like silicate,

So far we have assumed that the initial composition of theprimordial silicate dust was the CI composition throughout the present work, with the FeO content controlledwith the parameter fs . Figure 4 shows the elemental abundances in bulk CI chondrites and those in the solar
photosphere, in various compilations by Lodders (2003);
Lodders et al. (2009); Palme et al. (2014), normalized to
the CI chondritic abundances and the element Si of Lodders (2003), viz., those used in the present work. They
more or less agree with each other, with exceptions of Ti
and Mn.
The most important in the chemical fractionation is the
Mg/Si ratio since they are the most abundant elements inthe silicate. The solar photospheric elemental abundance(SP) in Lodders (2003) has Mg/Si = 1.00 as compared to
Mg/Si = 1.04 in CI in Lodders (2003). The difference of 4%

Table 3 Oxide elements entered as Ghost CAIs to CIsil before
chondrule fromation (mol%)Chondrite

AlO1.5

CaO

TiO2

MgO

SiO2

CO

3.109

2.234

0.091

1.117

2.234

LL

0.102

0.073

0.028

–

–

H

–

0.073

0.024

–

–

L

–

0.131

0.020

–

–

Fig. 4 The elemental abundances from various sources, normalized
to the CI elemental abundances of Lodders (2003). CI: CI chondrite.
SP: solar photosphere. L2003: Lodders (2003). L2009: Lodders et al.
(2009). P2014: Palme et al. (2014)

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

has only a small effect on the fitted parameters such as VD
and fs , as we performed calculations using both SP and CI
abundances.
The Ti abundance is questioned. Is the Ti in CI anomalously low? Or is the Ti in SP in Lodders (2003) anomalously high? The CI composition is the average of the three
CI chondrites. Its Ti concentration has a very small dispersion relative to its average value, δTi/Ti ∼0.02, muchsmaller than the normal analytical error in Ti analysis.
Therefore the Ti abundance in CI is trusted. If, on theother hand, the Ti in SP (Lodders 2003) is used in thepresent calculation, invasion of the Ti-enriched, Al-Ca-Ti
oxides is not needed to fit the bulk compositions of ordinary chondrites, because of the high abundance of Ti in
SP relative to CI as seen in Fig. 4. In a new compilationof SP abundances by Palme et al. (2014), the Ti abundance is revised to the value nearly identical to that of the
CI in Lodders (2003). Then the problem of the high Tiabundance for ordinary chondrites persists, and should be
explained by the invasion of Ti-enriched, Al-Ca-Ti oxides
as ghost CAIs as described in Section 3.3.
The Mn abundance in SP (Palme et al. 2014) has notbeen revised. Hence Mn in SP is still ∼25% lower than its
CI abundance. If the SP abundance was used for Mn, thedepletion factors imposed on it for ordinary chondrites,
0.72-0.74 would become ∼1, requiring no depletion for
Mn. For those chondrites with larger depletion factors
such as CV, E and CO, however, the depletion problem
would remain.
In the revised SP (Palme et al. 2014), K is enriched by∼10% compared to the CI (Lodders 2003). It would compensate the deficit in K in ordinary chondrite types atleast in H and LL. On the other hand, it would cause
enrichment in K for the other four chondrites as they
are perfectly matched with the CI value, as described in
Section 3.2.
The analytical precision in determining concentrationsof elements are far better in the laboratory chemical analyses than those in the stellar spectrophotometry. Especiallythe abundances of minor and trace elements recommended for the solar system abundances depend on themeteorite (CI) analyses. On the other hand, the solar photosphere is no doubt representative of the solar systemelemental abundances. We rely on CI simply because its
elemental abundance is very similar to that of the solar
photosphere.
3.5 Comparison between Chondrites

We infer probable reasons from the fitted parameters
and the determined unknowns, why the chemical variations among the chondrites resulted from the same source
material, viz., CI-like primordial dust.
Figure 5 (upper panel) and Table 4 show the VD% forvarious chondrite types. Here the obtained VD indicates

Page 10 of 32

Fig. 5 Top panel: VD% of MLB predicted by the calculation for eachtype of chondrite, that obtains at the moment of ejection of thedroplets which would acquire the average chemical composition ofchondrules by subsequent incorporation of the vapor andcondensate. Bottom panel: the fs value of CIsil determined by thecalculation for each type of chondrite

the vaporization degree of MLB at the moment when
the chondrules with the average chondrule composition
are produced as jet-droplets from the MLB. Chondrules
have a wide range of VD value as already analyzed in
paper (I). Here the VD for a specified chondrite type
is the one that satisfies both its bulk composition andthe average composition of chondrules included in it.
The VD is ∼40% for CM and CO chondrites, ∼30%
for CV, E and LL and ∼25% for H and L. We haveassumed in the model calculation that the VD of theaverage chondrule is just a half of the final VD reached

Table 4 Results of the calculation
Molar proportion; total = 1
Chd

VD%

fs

fw

Cdls

Mtx

CAIs

Ghost CAIs

CV

32

0.03

0.1

0.84

0.11

0.0552

0

CM

42

0.04

0.1

0.25

0.68

0.0741

0

E

30

0.04

1

0.62

0.35

0.0226

0

CO

43

0.20

0.35

0.68

0.26

0.01560.0391

LL

32

0.21

0.65

0.74

0.25

0.00600.0009

H

24

0.22

1

0.80

0.20

0

0.0005

L

24

0.27

1

0.66

0.34

0

0.0007Note. Chd: Chondrite. Cdls: Chondrules. Mtx: Matrix

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

by MLB. Then the final VD reached would be twice aslarge as the VD, viz., 50-80%. These values are consistent
with the calculation made for individual chondrules inpaper (I).
Figure 5 (lower panel) and Table 4 show the fs values for various chondrite types. CV, CM and E chondrites have small fs values, 0.03-0.04, while CO, LL, H
and L have relatively high fs values, 0.20-0.27. The definition of fs is the molar fraction of oxidized Fe relative
to the total Fe contained in the primordial dust having the CI composition. Therefore, it is likely that thedetermined fs values reflect the original redox state of
the primordial dust before the chondrule formation. CV
and CM chondrites are usually considered as oxidized
types, but their fs values suggest that they were originallyreduced.
The fw values in Table 4 showing 0.1 for fitting CV and
CM chondrites suggest that they were aqueously alteredand oxidized after accumulation onto their parent bodies.
CO and LL chondrites showing fw < 1 also suggest theirpost-accretional aqueous alteration. E, H and L chondrites
having fw = 1, on the other hand, are considered free ofalteration.
Figure 6 and Table 5 show molar proportions of thefive components for the bulk composition and of thethree components for the average chondrule composition,
determined by the calculation. We can recognize four patterns in Fig. 6. CV is characterized by its high F1 andFig. 6 Top panel: Proportions of the five components, Fn ’s in the bulk
chondrite determined by the calculation for each chondrite type. F1 :jet-droplet. F2 : differential vapor. F3 : integrated vapor. F4 : final
integrated vapor. F5 : CI∗ dust. Bottom panel: Proportions of the threecomponents used for formation of the average chondrule

Page 11 of 32

Table 5 Molar fractions of components for the bulk chondriteand for the chondrules
Molar Fraction of Components
Chd

Bulk chondrite; total = 1

Ave. cdl; total = 1

F1

F2

F3

F4

F5

F1

F2

F3

CV

0.521

0.367

0.040

0.027

0.045

0.562

0.396

0.043

CM

0.126

0.200

0.001

0.584

0.089

0.386

0.611

0.002

E

0.276

0.357

0.089

0.273

0.005

0.382

0.495

0.123

CO

0.311

0.262

0.213

0.134

0.081

0.396

0.333

0.271

LL

0.392

0.210

0.178

0.069

0.151

0.503

0.269

0.228

H

0.549

0.154

0.150

0.000

0.147

0.644

0.180

0.175

L

0.428

0.158

0.108

0.015

0.291

0.617

0.227

0.156

Note. Chd: chondrite type
Ave. cdl: Chondrules having their average composition

F2 proportions as compared to low proportions in F3 , F4
and F5 . CM is relatively enriched in F2 and F4 . E resembles CM in its overall pattern. CO is characterized byits monotonous decrease from F1 through F5 . H and L
are enriched in F1 and F5 while very depleted in F4 . LL
may be recognized between the CO and the H and L
patterns.
Figure 7 shows the chemical compositions of the fivecomponents for three types of chondrites. The components have their own characteristic compositions, but they
are similar between different types of chondrites. Therefore, it is the difference in proportion among the fivecomponents that distinguishes and determines the bulk
composition and the average chondrule composition of a
specific type of chondrite. Specifically, E chondrites are
Si-rich for the reason that they contain more F2 (differential vapor) and F4 (final integrated vapor), which
are enriched in Si but depleted in Mg, as shown in
Figs. 6 and 7.
Figure 8 (top panel) shows the molar proportion1 ofchondrules in the bulk chondrite, determined by the calculation. The rest, (1 - chondrule), includes all othercomponents in the chondrite. The molar proportions ofchondrule, matrix, CAI and ghost CAI are shown in
Table 4. We have included metal and sulfide contributions to both chondrule and matrix with 1:4 proportions,
respectively, by considering their distributions in the realchondrites. The calculated molar proportions of eachpetrologic component (chondrule, matrix and CAI) are
generally consistent with those in the real chondrites, withexception of CV chondrite (Efremovka) where the calculated proportion of chondrule is too high. Possibly the Na
content of the average chondrule composition (average of
only eight chondrules) for CV used in the calculation is
not representative of the chondrules in Efremovka. If it is1

Here the molar proportion is defined as the total moles of theelements that constitute the mass of chondrules, divided by the
total moles of the elements that constitute the bulk of chondrite.

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

Page 12 of 32

Fig. 8 Molar proportion of chondrules (top panel), and CAIs + ghost
CAIs (bottom panel) in the bulk chondrite

Fig. 7 Chemical compositions of the components, Fn ’s determinedby the calculation, shown for CM, E and L chondrites, normalized to CI
and Si. Bulk: average composition of bulk chondrites (silicates) isshown for comparison

lower than the value used in the calculation, the chondrule
proportion is decreased down to 70%.
Figure 8 (bottom panel) shows molar proportions of
CAIs and ghost CAIs in the bulk chondrites calculated.
We identify three groups. CV, CM and E types contain
only CAIs, while CO and LL contain both CAIs and ghost
CAIs. H and L types are free of CAIs but contain small
amounts of ghost CAIs. A very simple interpretation of
the presence of CAIs and ghost CAIs in the chondrites
is that CAIs invaded the chondrite formation zone after
the chondrule forming process while ghost CAIs invaded
before the chondrule formation. The coexistence of both
CAIs and ghost CAIs in the same chondrite indicates theinvasion of CAIs during the chondrule formation.
We find a concomitant increase in fs value among thethree groups of chondrites. As shown in Fig. 5 (bottom
panel) and Table 4, CV, CM and E chondrites are very
low in fs , 0.03-0.04; CO and LL have similar and higher fs

values, 0.20; and H and L have the highest fs values, 0.220.27. Thus we suspect that the invasion of CAIs is relatedwith fs , directly or indirectly, for some reason. This aspect
will be focused in Section 4.1.
We come to the point what made the difference inchemical composition between different types of chondrites. The fs value most probably inherits the original
redox state of the primordial dust. Hence different typesof chondrites must have had different redox states in theirsource materials. This has a profound implication for thechemical evolution of PPD, as will be discussed in the next
section.
The different VD values reached by MLB and the different proportions Fn ’s for different types of chondrites,on the other hand, must have reflected different physicalconditions during the chondrule formation. Our current,
jet-droplet & vapor-cloud model is premature to give ita full consideration. We are developing a numerical codethat includes necessary physics and boundary conditions(Hashimoto and Nakano, in preparation).
3.6 Balance of the Elements Involved in the Chemical
Fractionation

We try to estimate the balance of the ten elements, ‘used’and ‘not used’, in forming various types of chondrites froma duston having the CIsil composition. For simplicity, wechoose CM, CV and E chondrites for this analysis, which
do not require an admixture of ghost CAIs to the duston
before the chondrule formation. L chondrite is also chosenbecause its minute amount of ghost CAI (a Ti-enriched,Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

Ca-Ti oxide) is negligibly small. The data used in the calculation are (i) the compositions of the four components
to be mixed and their proportions, Fn ’s (n =1-4), (ii) the
initial composition of duston, viz., CIsil that takes into
account the fs value of the chondrite, (iii) the VD% for
the average chondrule composition, (iv) the final VD%
reached by MLB, viz., a melted surface of the duston,which is taken twice as large as the VD% for the average chondrule, and (v) the composition of the evolved
MLB corresponding to the final VD% (called ‘evaporation residue’ here). Note that the calculation excludes
contribution of CAIs that later invaded into the chondrite
forming zones.
One unknown factor is the production efficiency of
jet-droplets ejected throughout the boiling process fromPage 13 of 32

VD = 0 to the final VD%. In our experiments (paper I),
the run# 138 and run# SZ6 produced jet-droplets with aproduction efficiency of their integrated mass relative tothe total mass lost (as a combined mass of jet-dropletsand vapor) by the sample, 11.0 and 11.9 wt.%, respectively.
Some other runs produced jet-droplets in a range of 5-10
wt.% relative to the initial masses of experimental charges.
In the following calculation, we adopt a round number, 10
mol% (mol% instead of wt.% because VD is also in mol%)for the jet-droplet mass percentage (JDMP), defined as
the molar fraction of total jet-droplets released during theboiling of a MLB relative to the initial MLB, for all typesof chondrites for simplicity.
Figure 9 shows the proportions of the ten elements relative to their initial abundances in CIsil , which reside in

Fig. 9 Proportions of each of the ten elements relative to its initial abundance in CIsil , which reside in (A-1) the chondrite forming material (a total of
F1 through F4 ), (A-2) the leftover residue of MLB that is not used in forming chondrules, and (A-3) the leftover vapor (or condensates) that is also not
used in chondrule formation. Used: A-1 component. Leftover (residue): A-2 component. Leftover (vapor): A-3 component. JDMP: jet-droplet masspercentage

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9(A-1) the chondrite forming material (a total of F1 throughF4 ), (A-2) the leftover residue of MLB that is not used informing chondrules, and (A-3) the leftover vapor (or condensates) that is also not used in chondrule formation. A
JDMP of 10 mol% relative to the initial MLB is assumed
for all four chondrites. Note that the purpose of thepresent calculation is to reveal whereabouts of the elements included in the initial MLB after the chondrule formation. As shown in Fig. 9, A-1 (‘Used’) takes the elements
in amounts necessary for forming the chondritic silicates,
but additional mixing of the unprocessed CI∗ (F5 : the fifthcomponent), CAI, metal and sulfide are required to form
final bulk chondrites. A-2 is particularly enriched in themost refractory Al, Ca and Ti, and Mg comes second.
A-3 is rich in Na and K, but also contains considerable
Si, Cr, Mn and Fe.
The CM chondrite is most efficient in forming a chondrite mass from the MLB, while L, CV and E chondrites must dump 70-80% of the initial mass as residue
and vapor. If the constraint of JDMP of 10 mol% isremoved, a maximum possible JDMP can be calculated;
11.3, 18.0, 42.4 and 47.0 mol% for CM, E, CV and L
chondrite, respectively. Above these percentages, massbalance is not maintained. On the other hand, a minimum JDMP is not limited down to 0%. Fig. 9 (bottom
panel) show the case for L chondrite with a JDMP of
47.0 mol% for example. However, such a presentation witha JDMP much larger than 10 mol% may not be strictly
valid because our calculation is based on the assumption that a mass loss of MLB by ejection of jet-droplets is
minimal.
The important point is that the two components, A-2
and A-3, described above need to be separated from thecomponent A-1 physically; otherwise chemical fractionations in chondrites are not completed. In Section 4.2,
we hypothesize a mechanism how the three components
were separated and where they were destined for.

4 Discussion
4.1 Constraints to the Chemical Evolution of PPD

Following the quantitative analyses in configuring bulk
chemistry of various types of chondrites (Section 3), we
distinguish chondrites between three generation groupsin accord with the order of events, CAI incorporation versus chondrule formation. G-1: CAIs were incorporated
into chondrite-forming components ‘after’ the chondrule
formation event, as represented by CV, CM and E chondrites. G-2: CAIs were incorporated ‘during’ the chondrule formation, like CO and LL. G-3: CAIs were incorporated ‘before’ the chondrule formation, like H and L.
If the CAIs formation and their subsequent migration tothe outer disk had occurred during a limited period in
the PPD evolution, it can be used as a time pivot for
whatever processes that are related to the CAIs. Thus

Page 14 of 32

the three generations of chondrites recognized above areinterpreted as reflecting a formation sequence in theorder, G-1 through G-3, as to their chondrule forming events , on condition that the chondrule forming
location, viz. its radial distance from the protostar, isfixed.
In Sections 4.2 and 4.4.3, we propose the snowline in
the disk as an ideal place for chondrule formation. Thus,
if the snowline moved radially in a time scale comparable to or shorter than the CAI migration timescale, theorder (G-1 through G-3) might not represent the formation sequence. Here, we continue our investigation by
assuming that the snowline was relatively stationary in theradial direction during the period of CAI migration.
As indicated in Section 3.5, fs (a redox indicator of primordial dust or duston) ascends in the order, CV, CM, E,
CO, LL, H and L chondrites. This is exactly the same orderas G-1→G-2→G-3.
With these facts and the assumption, together withother observational information of chondrites andcomets, we attempt to make a prediction about a possible
evolutionary sequence of primordial PPD materials.
4.1.1 Evolution in redox state

The increase in fs with the order G-1→G-2→G-3 suggeststhat the redox state of primordial dust or dustons evolved
towards oxidizing with time. We speculate when, where
and how it happened.
In their chemical network model of PPD, Walsh et al.
(2015) have indicated that gas phase reactions dominate
in the inner disk (≤10 au) because of high temperatures
and that the reaction of atomic O (produced by photodissociation of CO) with OH (produced by reaction O + H2 )proceeds to form molecular oxygen,
O + OH → O2 + H.

(2)

Furuya et al. (2013), in their reaction network modelof PPD, have suggested that at 10 au (∼60 K) ultra-fineice grains (∼0.1 μm) are continuously supplied to thedisk surface by turbulent vertical mixing and destroyed to
atoms by stellar UV photons and X-rays, which in turncome back to the disk midplane by turbulence. Atomic
oxygen is then converted to molecular oxygen by reaction 2, which becomes a predominant O-bearing species
in the disk, given enough time (>105 ys).
We propose that the molecular oxygen was radiallytransported by turbulent diffusion and made the disk
gradually oxidized inward as well as outward. This picture qualitatively matches the chronological order of thegeneration groups of chondrites, G-1 through G-3.
As an alternative, the cometary O2 can be a sourceof oxidizer in PPD. The comet 67P/ChuryumovGerasimenko is known to have kept producing a neutral
gas coma with unusually abundant O2 molecules

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9(O2 /H2 O = 0.01-0.1) (Bieler et al. 2015) during its periodof observation. In their model calculations of the chemical evolution of material from the pre-stellar core to the
midplane of PPD, Taquet et al. (2016) and Mousis et al.
(2016) have investigated the yield of O2 ice in cometary
ice inventories and concluded that the high abundanceof O2 in 67P, if produced solely as O2 ice by radiolysis, isonly adequately explained as having formed in the parent
cloud. Eistrup and Walsh (2019) have found a sweet spot
parameters for production of O2 ice in the pre-solar
nebula midplane at a level matching those in 67P and
1P/Halley, but preferred a primordial origin in the parent
cloud, having considered a sensitivity of such a result tothe assumed chemical parameters.
If true, the O2 -rich cometary materials such as 67P
and 1P might be a source for dustons that formed thegeneration group G-3 (viz., H and L chondrites), while
the O2 -free or -poor cometary materials like most othercomets could be a source for the generation group G-1(viz., CV, CM and E chondrites) and perhaps G-2.
Whichever mechanism of O2 enrichment in PPD istrue, the O2 molecules must have reacted with metal andsulfide embedded in the primordial dust to form ironoxides.
4.1.2 Evolution in D/H ratio

Figure 10 shows D/H ratios in various substances in oursolar system and extrasolar environments. CV and CM

Page 15 of 32

chondrites which have the lowest fs values and hence
are the most reduced types in our study, show the lowest D/H ratios (< 1 × 10−4 ) among the chondrites(Alexander et al. 2012). LL chondrites which have a higher
fs value in our study, show a high D/H ratio (∼ 3 ×
10−4 ) (Alexander et al. 2012). R chondrites, which are notincluded in our study due to the lack of composition data,
is known as the most oxidized type and have the highest
D/H ratio (7.26 × 10−4 ) (McCanta et al. 2008). The comet
67P/Churyumov-Gerasimenko, in spite of its being a J. F.
Comet, have the highest D/H ratio (5.3 × 10−4 ) among thecomets ever observed (Altwegg et al. 2015). This cometcontains unusually abundant O2 molecules as describedabove. All these evidence points to a strong correlation
between the high oxidation state and the high D/H ratio.
The water ice is mostly responsible for the D/H ratiosof chondrites and comets except some contribution of
the organic hydrogen (Alexander et al. 2012). Interstellar ices show the highest D/H ratio of ∼ 10−2 in thegalaxy (Fig. 10). It is postulated that H2 D+ is preferentially produced by ion-neutral reactions in a molecular
cloud core and is subsequently turned into ices in thecoldest (∼10 K) environment (Cleeves et al. 2014). All
matters including gas, ice, silicate and organics in PPD
come from a molecular cloud core (e.g., Williams andCieza 2011). In fact, the D/H ratios of all the solar system materials lie between 10−2 and 2 × 10−5 (that of theSun) as shown in Fig. 10. This implies that some amountFig. 10 D/H ratios of various solar system and extrasolar substances. Data and their references noted by numbers 1-37 are shown in Appendix B.
Blue-line represents the D/H ratio of Bulk Earth (15). Numbers 7-14 are chondrites. JFC: Jupiter family comets. OCC: Oort cloud comets. For otherdetails, see Appendix BHashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

of interstellar ice survived the formation of the solar
system and was incorporated into planetesimal bodies(Cleeves et al. 2014).
Furuya et al. (2013) proposed a model that explains thedecrease in D/H ratio of water ice in PPD. Depending on
the temperature in the midplane (either <40 K or >60 K),
atomic oxygen is either transformed into water ice (regeneration of water ice) by reaction with adsorbed hydrogenon the ice surface, or into molecular oxygen in the gas
phase reaction such as reaction 2. Given enough time(> 105 ys), the regeneration of water ice reduces the D/Hratio of water ice (Furuya et al. 2013). In the latter case,on the other hand, the initial D/H ratio of water ice tends
to be maintained in exchange for depletion of the water
ice, and the disk gas becomes gradually loaded with O2 as
described above.
The role of atomic oxygen, however, is not one-sided
since both ice-regeneration and O2 -formation should
concur (Furuya et al. 2013) and it is a matter ofbias depending on the midplane disk temperature. We
postulate that the disk conditions had changed with atimescale ∼ 105 years in such a way that the average
midplane temperature increased.
The reason why the increase in the D/H ratio of chondrites and comets has a good correlation with the increasein their oxidation states is easily understood because both
require the production of free oxygen in PPD.
4.1.3 Chronology of chondrules and CAIs

Here we examine whether the generation sequenceof chondrites, G-1→G-2→G-3, is consistent with thechronological information of chondrules and CAIs, on
condition that the chondrule forming location, viz., its
radial distance from the protostar, is fixed as explained in
Section 4.1.
CAIs typically have excess 26 Mg, a trace of extinct
radionuclide 26 Al at the canonical level of initial 26 Al/27 Al∼ 5 × 10−5 , while CAIs with less or no excess 26 Mg arealso abundant (see review by MacPherson et al. 1995).
Chondrules, on the other hand, generally have no excess
26 Mg, while some have initial 26 Al/27 Al ∼ 8 × 10−6 (e.g.,
Hutcheon and Hutchison 1989; Russell et al. 1996). With
the half-life of 26 Al = 7.3 × 105 yr, it has been interpreted that there is an age difference between CAIs andchondrules of ∼2.5 Myr or more. It looks like an immediate contradiction because the chondrule formation of
the generation group G-1 (viz., CV, CM and E) occurred
before the invasion of CAIs. The generation group G-3, on
the other hand, requires that it should have taken CAIs for>2.5 Myr to travel from its formation zone (perhaps theinner rim of the disk; e.g., Dullemond et al. 2007) to thezone of chondrule formation (∼3 au if it coincides withthe asteroid belt) because the chondrule formation of thegroup G-3 (viz., H and L) occurred after CAI invasion.

Page 16 of 32

Considering the mass accretion rate of T-Tauri stars typically of ∼ 10−8 M per year (Hartmann et al. 2016), suchan age difference is comparable to or longer than the timescale for dissipation of the gas disk, and thus unlikely.
Our result implies an irrefutable possibility that the
26 Al ages for chondrules (Davis and McKeegan 2014,references therein) are not real. In our investigation, chondrites except for CV, CM and E types contain ghost CAIs,
indicating that chondrules formed from silicate liquids
made from a mixture of primordial CI-like dust and invading CAIs. Even if the primordial dust contains no 26 Al,
chondrules should have 26 Al as a result of mixed CAIs
in the silicate liquid. In fact, CO and LL chondrites forwhich the invasion of abundant ghost CAIs are implied
from the present analysis contain many chondrules having
excess 26 Mg, and this is particularly so for their unmetamorphosed types (3.0 or 3.1) (Kita et al. 2000; Mostefaoui
et al. 2002; Kunihiro et al. 2004; Kurahashi et al. 2008).
Chondrules with high Al contents are preferentially analyzed because of their high precision in determinationof 26 Al/27 Al (e.g., Kita and Ushikubo 2012). As a matterof fact, the high-Al chondrules exhibit highest 26 Al/27 Al
values, ∼1/5 of the canonical CAI value (Davis and McKeegan 2014), reinforcing our prediction. We presume thatchondrules with high concentrations of live 26 Al simply
represent jet-droplets from portions of the silicate liquid
in MLB, that is inhomogeneously mixed with large CAIs.
We conclude that the 26 Al chronology for chondrules issubject to a serious problem in that their real ages areindeterminable because of the pre-mixing of CAIs which
are high in Al and 26 Al.
Connelly et al. (2012) and Bollard et al. (2017) haveshown that the ages of six among twenty-two chondrules
measured with the U-corrected Pb-Pb dating method
agree with the average age of four CAIs (4567.30±0.16Myr) within errors. With this result they claim that chondrules and CAIs are coeval, and that the assumption of theuniform distribution of 26 Al in PPD is wrong. If they arecoeval, the time interval for chondrule formation between
the group G-1, G-2 and G-3 could be as short as 0.16 Myr,although only six chondrules show such a sign and only
four data are available for CAIs ages. Their results, however, appear contradictory because the ages of thirteenchondrules from NWA 5697 (L3) span between 4563.64
and 4567.61 (±0.50) Myr, viz., ∼4 Myr interval. It seems
improbable that a single chondrite could reserve chondrules that had been continuously produced in PPD for as
long as 4 Myr.
The Pb-Pb chronology for chondrules appears to be freeof the problem of CAI mixing unlike 26 Al, but the wide
age span of chondrules in a single chondrite cast a doubt
on using it as a constraint on the timing of chondrule
formation. We explore a little more about the age data.
The four CAIs used for determination of their Pb-Pb ages

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9(Bollard et al. 2017) are limited to those in CV chondrites (three from Efremovka and one from Allende). In
our study, CV in the generation group G-1 is actually Efremovka itself. The U-corrected Pb-Pb method analyzed
only two chondrules that belong to CV chondrites (Connelly et al. 2012). They are Allende chondrules, one ofwhich shows 4567.32±0.42 Myr in good agreement with
the CAI age although another is a Myr younger. Thus thechondrules and CAIs in CV chondrites (viz., Efremovka
and Allende), as far as the existing data concerned, agree
in their ages within analytical errors except one chondrule.
This is consistent with our observation of the generation
G-1 in which chondrules formed prior to the invasion of
CAIs, as long as the time needed for CAIs to migrate to
the zone of chondrule formation is short. We therefore
suggest that a comparative chronology should be made on
chondrules and CAIs that belong to the same chondrite orat least to the same chemical type of chondrites.
4.2 Completion of the Chemical Fractionations

Chemical fractionations in chondrites are not completed
until the leftover refractory residue of MLB and the leftover volatile vapor (or condensates) are separated fromthe chondrite-forming ingredients, viz., chondrules andmatrix.
The physical separation is only possible through aerodynamic actions operating on objects with different sizes.
The leftover evaporation residue is a few-mm thick, oncemolten, surface layer of a large duston with the radius R >0.01 m. Bodies with R in the 0.01-10 m range lose theirangular momentum per unit mass much faster compared
to bodies of other sizes, due to their differential motions
against the gas. According to Weidenschilling (1977), abody with R = 1 m (solid ρ ∼3 g cm−3 , gas ρ ∼ 10−9 g
cm−3 and T ∼300 K) would migrate to the sun in ∼50 yr
per au, while it takes ∼5000 yr per au for R = 0.01 or 10
m (for the same parameters). On the other hand, grains
smaller than chondrules (R ≤0.001 m) take ≥ 105 yr per
au (ibid) and should remain in the chondrule formation
zone for a long time.
We propose that dustons were trapped in a large-scalevortex in the protoplanetary disk and that the chondrule
formation took place inside the vortex immediately after
their entrapment. There the Coriolis force is at work,
which pushes dustons of appropriate size, 0.01-10 m inradius, to the center of the vortex in a few rotation periods (e.g., Tanga et al. 1996; Chavanis 2000). The result
would be that small objects such as chondrules and finer
dust are left near the outer edge of the vortex. Small grains
with diameter <1 cm tend to bail out to the outside of thevortex due to turbulent diffusion (Chavanis 2000). Therefore chondrules must grow in size by attaching fine dust
rather efficiently (Beitz et al. 2012). Once chondrule-corednodules and their multiple clusters grow in size >1 cm,

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they would run after dustons but at a slower pace. In thisway we expect three populations being separated fromone another as a result of aerodynamic effects: (Pop-1)
the chondrule-cored nodules and their clusters that follow the dustons much later in time, (Pop-2) the dustonswith refractory residues that settle in the center of thevortex in a short time scale, and (Pop-3) the fine dust, a
mixture of the volatile-rich condensate and the primordial CI-like dust, which escape from the vortex. The three
populations correspond to the three components that are
produced in the chemical fractionation process during thechondrule formation, (A-1), (A-2) and (A-3) as describedin Section 3.6, except that Pop-2 consists of A-2 and a nonmelted portion of dustons, and Pop-3 is a mixture of A-3
and the primordial dust.
We discuss the two populations that remain in the vortex. The dustons (Pop-2) are so effectively trapped into thecenter of vortex (e.g., Barge and Sommeria 1995; Fromang
and Nelson 2005; Surville et al. 2016) that a gravitational
instability is triggered to generate a large planetesimal(e.g., Tanga et al. 1996). A swarm of the late-arriving,chondrule-cored nodules, viz., Pop-1, would be gravitationally attracted by the planetesimal and accumulate onto
its surface, forming a layer of ‘chondrite’. As a result thechemical fractionation is completed because the chondrite is spatially segregated from the dustons that form
the core of the planetesimal and represent most of its
mass. Vortices may not be only attractor of dustons. Anymechanism that attract dustons preferentially (e.g., a dustloaded ring: Surville et al. 2016) could provide a place
for forming planetesimals and late veneers of chondrites
around them.
As a logical consequence we cast doubt on a hypothetical, meteorite (or chondrite) parent body. The petrologic types (from 3.0 to 7) of chondrites have long been
believed as representing thermal metamorphic grades
which reflected depths of the sources where the chondrites came from after destruction of the parent body.
Rubin (2003, 2004) and Rubin and Wasson (2011) foundthat the common occurrence of shocked and annealed
ordinary and enstatite chondrites is consistent with collisional heating being a major mechanism responsible formetamorphosing those chondrites. Friedrich et al. (2014)
found that 26 Al was too depleted to have caused highdegrees of thermal metamorphism and partial melting of
LL7 chondrites and that heating due to impact is the most
likely heat source for the recrystallized chondrites. We’d
like to point out that the outermost layers of planetesimals
should have been most prone to shocks and disruption by
impacts of other bodies. Disrupted pieces may have accumulated on their original planetesimal surface or formed
independent rubble piles that were loosely tied with weakgravity, as seen in extant asteroid belts (Walsh 2018).
The third population (Pop-3) may have been further

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

mixed with a CI-like dust in the disk and diluted to
an insignificant concentration. Recent rendezvous missions to comets, however, revealed high concentrations ofcrystalline silicates in cometary comas, which are highly
enriched in Na and Si relative to Mg (Schulz et al. 2015;
Engrand et al. 2016; Bardyn et al. 2017). The enrichmentof volatile Na (and K), and Si relative to Mg is exactly afeature of the volatile condensates in the third population(Fig. 9). The third population may also give a hint to theorigin of GEMS (Keller and Messenger 2011), UCAMMs(Dobrica̧ et al. 2012) and CPMMs (Noguchi et al. 2015),
all of which are suspected to have genetic links to comets.
4.3 Comparison with the Equilibrium Condensation
Model

Having discussed our new ideas on the origin of thechemical fractionations in chondrites, we come to a point
where we could compare our model with those developed by Anders and his group. As described in Section 1,
their model basis, viz., the equilibrium condensation ofchondritic materials, has lost its reasoning. However, it
might be beneficial for us and all to do this since essential points would be clarified. In addition to the chemical
aspects which will be described below, there are several
physical difficulties attached to their model. 1) The grain
size of particles that condense from a gas of low density should be too small to be separated from the gas(Weidenschilling 1977), making the fractionation absolutely ineffective. 2) No reason is given for any particular temperatures at which they claim the fractionations
should occur. 3) Chondrules, the most abundant constituent of chondrites, is not taken into consideration.
4.3.1 Lithophile element fractionation

We refer to the major element or refractory lithophile element fractionations in chondrites (Larimer and Anders
1970; Larimer 1979). Larimer and Anders (1970) haveproposed that a partial loss of high-temperaturecondensation minerals at appropriate temperatures anda subsequent condensation of minerals which followedfrom the remaining gas reservoir could explain major
chemistry of ordinary and enstatite chondrites, starting from the CI-composition gas. They derived chemicalcompositions (for the five major elements, Si, Mg, Ca, Al
and Ti) similar to those of bulk ordinary (and enstatite)chondrites, by subtracting 15 (25), 23 (45) and 40 (60)
% of Si, Mg and Ca (same for Al and Ti), respectively,from the CI composition. Those minerals were identified
as typical CAI minerals and forsterite. As they pointed
out, these percentages are examples and other combinations are possible. Larimer (1979), based on his analysis
on the condensation track of major elements and averagecompositions of ordinary and enstatite chondrites, haveproposed that the bulk mineral chemistry to be subtracted

Page 18 of 32

from the CI composition was uniquely determined. His
estimates of mass subtraction are not so different fromthose by Larimer and Anders (1970).
In order to explain the bulk chemical compositions of
CII and CIII (now classified as CM for CII, and CO
and CV subtypes for CIII), Larimer and Anders (1970)
inexplicitly and Larimer (1979) explicitly suggested the
addition of CAI minerals in appropriate proportions to the
CI composition.
Larimer and Anders (1970) concluded that the chondrule formation had nothing to do with the lithophileelement fractionations, and that chondrules were simply
molten droplets of the existing solids.
An essential difference between our model and theirmodel is that we consider the chondrule formation andthe subsequent dynamical processes as a primary driving force for the lithophile element fractionation, while
they do not. Let us recapitulate our model for the sake ofcomparison.
As shown in Fig. 9, the initial CI-like material, duston, is
processed into three kinds of materials as a result of chondrule formation process in the vapor cloud that forms
around it. The chondrule- and matrix-forming components, F1 through F4 in the calculation, when combined,
are depleted in refractory elements such as Al, Ca andTi relative to Mg and Si (Fig. 9; ‘Used’). As a result, notonly enstatite and ordinary chondrites but also carbonaceous chondrites suffer from depletion in the refractoryelements once. The difference among these chondrites isthe amount of CAIs which invaded into a zone of chondrite formation. For carbonaceous chondrites, refractoryelements (in the form of CAIs) invaded and mixed withchondritic components in amounts more than compensating the lost fraction during the chondrule formation.
Enstatite chondrites incorporated Al-rich CAIs in quantity too small to compensate the largest depletion in therefractory elements caused during the chondrule formation. Ordinary chondrites (L and H types) incorporated
no CAI except for a trace of ghost CAI, thus remained
depleted in the refractory elements. Ordinary chondrites(LL type) incorporated both CAI and ghost CAI, but their
combined mass was too small to compensate the depletion in the refractory elements. Such is a brief explanationin our model for the lithophile element fractionations inchondrites.
To complete the chemical fractionation, however, theleftover residue which is enriched in the refractory elements (Fig. 9; ‘Residue’), must be removed from thechondrule-forming zone. This is automatic because theresidue is a once-molten surface layer of a large duston
which subsequently falls into the center of a large-scaled
vortex by the aerodynamic process. The equilibrium condensation model, on the other hand, has no means toremove the high-temperature condensates from theirHashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

formation zone since they are ultra-fine-grained particles
that strongly couple with the gas.
The removal of excess volatiles that are not incorporated into chondrite-forming materials (Fig. 9; ‘Vapor’)is also automatic in our model because the vapor
condensates, fine-grained in nature, would effectively
move away from the vortex by turbulent diffusion. The
removed volatiles in the form of low-temperature condensates must include not only Na and K but also
highly volatile elements (e.g., Pb, Bi, In, Tl). Therefore,
our model does not have to invoke any extra chemical fractionation process such as accretion-temperaturecontrolled fractionation of volatiles proposed by Keays
et al. (1971) and Laul et al. (1973) (viz., Chem. fract. inmeteorites-IV & -VI).
4.3.2 Redox state and metal-silicate fractionation

Different types of chondrites have different redox states ofFe and different total Fe contents (Urey and Craig 1953).
Fe exists in meteorites typically with three different states:oxides (mostly as FeO) in silicates, metals and sulfides. In
the latter two, Ni and Co are invariably included as minor
elements, which under most redox conditions are notoxidized. Larimer and Anders (1970) examined concentrations of Fe and Ni in various chondrites and ascribedthe depletion in total Fe in L and LL chondrites as opposed
to H and C chondrites, to the metal-silicate fractionationthat had occurred between ∼1050 K and 680 K (temperature for FeS formation) before accumulation of chondritic
materials into large bodies.
Larimer and Anders regarded the redox state of minerals in chondrites as reflecting their final equilibration
temperatures with the nebular gas. In the equilibrium
condensation model of high temperature nebular gas withthe solar elemental abundances, Fe metal condenses at∼1450 K at 10−3 bar in total pressure (Grossman 1972)
and at ∼1280 K at 10−5 bar (Wood and Hashimoto1993). No other Fe-bearing phase appears down to ∼900
K where a trace of Fe metal is oxidized and accommodated into Mg-silicates (forsterite and enstatite), but it is
not until 700 K (10−3 bar) or 600 K (10−5 bar) where
olivine takes FeO/(MgO + FeO) = 0.05, which is close
to the FeO concentration in enstatite in E-chondrites
and in forsterite in a reduced type of CV chondrite,
viz., Efremovka. In order to oxidize Fe to a level ofFeO/(MgO + FeO) ∼0.2 in olivine typically in ordinarychondrites, temperatures as low as 520 K is required(Wood and Hashimoto 1993).
We point out a contradiction between the above twoarguments. The Fe/Ni molar ratios of bulk chondrites
are 16.6 for H, 18.6 for L and 19.3 for LL (Jarosewich1990), while the Fe/Ni ratio in CI chondrites is 18.1 (Lodders 2003). Comparison of the temperature range for the
metal-silicate fractionation with those for oxidation of Fe

Page 19 of 32

metal, however, implies that the metal-silicate fractionation occurred before the oxidation. If so, the Fe/Ni ratioof chondrites should keep 18.1 if CI was their starting
composition. Hence their model with respect to the redox
states and metal-silicate fractionation bears an internal
inconsistency.
The Fe/Ni ratios of bulk chondrites higher than 18.1
indicates that the oxidation of Fe occurred before themetal-silicate fractionation. L and LL chondrites musthave lost a significant mass of metal before their accretion to large bodies. The lower Fe/Ni ratio of H chondrites
relative to CI, on the other hand, suggests a gain of excess
metal or a loss of silicate before their accretion.
In contrast with Larimer and Anders (1970), the discussions made in Sections 3 and 4.1.1 strongly argue
for the possibility that the redox state of Fe in the primordial dust was predetermined before the chondrule
formation process and that it evolved with time fromreducing to oxidizing, corresponding to the generation
sequence of chondrites, G-1 through G-3. This is consistent with the order of the events indicated by the Fe/Ni
ratios of chondrites, that the oxidation is followed by themetal-silicate fractionation, since the latter should haveoccurred during or after the chondrule formation in ourmodel.
4.4 In Search of Possible Heat Sources

Our model assumes that the surface of duston was heated
above their boiling temperature with some external sourceof heat. Let us scrutinize possible heating mechanisms in
PPD suggested for chondrule formation. Rubin (2000) has
considered ten constraints that are related with petrologic
and geochemical features of chondrules and made a checklist for sixteen heating mechanisms with these constraints(figure 5 in his paper). He has pointed out the three mechanisms being consistent with all the constraints: nebular
lightning, magnetic reconnection flares, and gas dynamic
shock waves.
We introduce two lines of evaluation procedures apartfrom his. The first line has to do with the coexistenceof chondrules with a matrix. In chondrites the finegrained matrix materials fill interstices between chondrules. Their abundance in volume ranges from 20 to 80%,depending on the type of chondrites. They are free ofmelting process and generally rich in volatiles includingorganic materials and water, being characteristic of lowtemperature origin. It means that any heating mechanism
which violates the presence and features of the matrix
materials is not appropriate for chondrule formation. The
second line is the consistency with our chondrule andchondrite formation model, and is considered after the
first line.
We apply our evaluation procedures to the following
heating mechanisms from Rubin (2000, table 5): nebular

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

lightning, supernova shock waves, magnetic reconnection
flares, gas dynamic (nebular) shock wave and planetesimal
bow shocks. We also evaluate the following mechanisms,
that were postulated since Rubin (2000): shocks in theenvelopes of giant protoplanets (Nelson and Ruffert 2005)
and current sheets in magnetically active nebula regions(Joung et al. 2004).
4.4.1 Constraints from the coexistence with the matrix, andscrutinization of various heat sources

The first line of evaluation considers the following five
constraints. With them, we attempt to scrutinize the heating mechanisms.
a)

b)

c)

d)

e)

The matrix materials are characterized by their veryfine-grained nature, typically subμm to μm in size.
Such fine dust move with gas and are unable to be
decoupled from the gas.
The matrix contains abundant materials and elements that are stable at low temperatures. Althoughrecondensation or regeneration (if such processes followed the destruction during chondrule
formation events) might partially restore their low-T
features, most indigenous materials such as IOMs
(e.g., Alexander et al. 2007) which are suggested
as having inherited their isotopic signatures fromthe low-T, outer disk environments or from themolecular cloud would not survive even a moderatetemperature rise.
The matrix contains presolar grains whose isotopic
compositions (e.g., Zinner 1998) are very distinct
from those of the common chondrite-forming minerals. Any event, thermal or shock, strong enough todestroy or alter the grains is prohibited.
The most stringent of all the constraints comes fromthe D/H ratios of water and organic materials inmatrices in various chondrites, which differ fromthose of the sun and the earth. As already describedin Section 4.1.2, different chondrite types appear
to possess characteristic ranges in the D/H ratio,
which are most likely attributed to the ion-molecule
reactions in the molecular cloud (e.g., Tielens 2013)
followed by modification in the low-T outer disk(e.g., Alexander et al. 2012; Cleeves et al. 2014). The
D/H ratio of water should be easily reset to that of
the nebular gas, ∼ 2 × 10−5 , if temperature exceeded
500 K (Lécluse and Robert 1994) in the presence ofthe nebular gas.
Complementary nature of the matrix to the chondrules. Two kinds of complementarity may be identified. 1) Chondrules and matrix show similar isotopic compositions and redox states, as in the caseof ordinary and enstatite chondrites. Carbonaceouschondrites, whose matrices are relatively H2 O-rich,

Page 20 of 32

possess oxidized matrices and reduced chondrules,
but the oxidation of the matrices are known to haveresulted from later hydrothermal actions after accumulation onto a large parent body (e.g., DuFresne
and Anders 1962; Clayton and Mayeda 1984). ‘Similarity’ rather than complementarity may be a better
term, but it indicates that both come from the same
source, not a chance mixture of different origins.
2) Excess or deficit in abundances of particular elements or isotopes in either of chondrules or matrix
cancels out to normal values when chondrules andmatrix are combined in their chondritic proportion, viz., the bulk chondrite. It is recognized thatchondrules are depleted in metallic elements, as
opposed to enrichment in these elements in thematrix, while the bulk chondrite have approximately
CI abundances in these elements (Bland et al. 2005).
This suggests that the metallic elements lost fromthe chondrules were mostly recovered by the matrix(e.g., Grossman and Wasson 1985). Isotopic complementarity is a very severe restriction, especiallyin non-mass-dependent isotopic fractionations, as
it suggests some sort of genetic link between them
Budde et al. (2016a, b ).
The above four constraints, viz., a, b, c and d disqualify theheat sources or heating mechanisms which raise temperatures of the gas on a large scale in the disk, where fine dust,a source of matrix materials, are immersed. They include
supernova and nebular shock waves, magnetic reconnection flares, current sheets, and shocks in the envelopes ofgiant protoplanets.
Planetesimal bow shock and lightning discharge should
involve only localized heating of the disk gas, thus most of
the fine dust in the disk would escape from heating. They
are scrutinized by the second line of evaluation method in
the followings.
4.4.2 Scrutinization of planetesimal bow shock model

As described in “Origin of Chondrule Chemistry” inpaper (I) and in Section 3.5 in the present paper, jetdroplets are postulated to have ejected from the boiling surface of dustons starting with vaporization degreeof MLB from less than 10% and ending with morethan 80%. In our experiments (paper I), the MLB completed evaporation (VD >90%) within several seconds. A
large size of duston would require more time, typically≥10 seconds for jet-droplets to be ejected with a wide
range of VD.
A high speed planetesimal moving in PPD (with a typical speed of 6 km s−1 relative to the gas) accompanies
a bow shock on its front side. According to Ciesla et al.
(2004), the thickness ofbow shocked zone is about threetimes of the radius Rp of the planetesimal. With Rp =10, 100 or 1000 km, its thickness is 30, 300 or 3000 km.

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

Then, large dust aggregates immersed in the gas would
be heated for duration of 5, 50 or 500 seconds, which islong enough in our criteria. The calculated temperatureof a compact dust aggregate of 0.1 cm in diameter in the
bow shock, however, reaches only 1600 K. Even with anassumed emissivity of dust being 0.1, which is unrealistically low, the maximum temperature reached is 2000 K,
which is still too low to make the dust aggregate boil.
Hood (1998) obtained a maximum temperature 2000 K fora dust aggregate by assuming a planetesimal of Rp = 70
km and the same values for size and emissivity of dust
grain as Ciesla et al. (2004).
Much larger dust aggregates like dustons (>3 cm) would
decouple from the gas more efficiently and hence would
be more strongly heated in bow shock, although we do
not have a quantitative estimate. Even if boiling occurred,however, the vapor cloud would be immediately destroyedby shock wave. Dustons would be also smashed into pieces
by impact with the planetesimal.
Miura et al. (2010) have proposed a possibility of liquid condensation for origin of chondrules that fine dust in
the bow shock once evaporate and then condense. They,
however, admitted that the condensed material shouldhave the same composition as that of the former dust.
Then it would not cause chemical fractionations in chondrules and chondrites from the dust.
We conclude that the bow shock is not a viable heatsource for our model of chondrule formation.
4.4.3 Lightning discharge: our last hope

In the terrestrial atmosphere, lightning discharge releases
its energy in an extremely confined path (a typical discharge path width is ∼2 mm; Pilipp et al. 1992). This
leaves most of the atmospheric volume free of heating
except for vicinity of the path which are heated withradiation (Whipple 1966). The path width of lightning
discharge postulated for PPD is ∼5000 times of the electron mean free path, viz., ∼5 km for gas density n(H2 )∼ 1020 m−3 (Pilipp et al. 1992), which is very narrow considering the spatial scale of PPD. Therefore, the lightning
discharge clears the first line of evaluation procedure, thecoexistence of the matrix.
Muranushi (2010) has raised three problems to be overcome for the lightning discharge to be a feasible heatsource for chondrule formation: energetics problem, neutralization problem, and destruction problem. We add
another constraint: charging-mechanism problem. In thefollowings we give preliminary but plausible solutions to
the four problems, and show that the lightning discharge
is compatible with our model of chondrule and chondrite
formation.

Charging mechanism The generally accepted concept
for the development of the thundercloud charge dipole

Page 21 of 32

in the terrestrial atmosphere is the physical separation of
oppositely charged particles within the cloud (Saunders
2008). The principal charge carriers are believed to be
H2 O ice particles and their charge separation mechanism
has been studied for a long time (reviewed by National
Research Council 1986). The H2 O ice is the most abundant solid substance in PPD and is naturally assumed as amain charge carrier for lightning discharge in space.
We postulate that the chondrule formation occurred inlarge vortices in PPD as described in Section 4.2. Theoretical works predict that a pressure bump near the snow-line(e.g., Kretke and Lin 2007) induces Rossby wave instability by which anticyclonic vortices develop (e.g., Lovelace
and Romanova 2014; Lin and Pierens 2018). If a large vortex (Huang et al. 2018) encompasses the snow-line, theicy dust trapped in it would experience evaporation andcondensation in its every rotation period.
According to Saunders (2008), the most promising of all
possible charging mechanisms of ice grains in the terrestrial atmosphere is a charging induced by condensation: If
the growth rate of ice grains is fast during condensation,
more defects (pairs of OH− and H3 O+ ) are created on theice surface. The H3 O+ diffuses into inside of the ice grains,
leaving OH− trapped on the surface. When small ice particles collide with the large ice grains, they remove OH−
and become negatively charged, while the large ice grains
having lost OH− become positively charged. Takahashi(1978) and Takahashi and Miyawaki (2002) conducted ice
charging experiments showing that an ice crystal (∼10
μm in diameter) removed a maximum charge of ∼ 3.3 ×
10−14 C per collision, which translates into a charge surface density of 10−4 C m−2 . This is more than enough to
explain activities of terrestrial thunderclouds (Takahashi1978). According to Takahashi (1978), however, the charge
surface density and its polarity depend strongly on temperature and density of H2 O molecules in the atmosphere.
Since there are no data available for the range of temperature and H2 O density in PPD, it may be premature toconclude the charging efficiency per collision for nebularice.
We find a similar situation in the vortex which by
anticyclonic rotation would bring trapped dustons fromwarm (inside the snow-line) to cold (outside) environment. If the mass function of stony dust is biased tolarge sizes, viz., dustons and their embryos rather thanfine dust, most of H2 O vapor would not immediately
condense but supersaturate up until homogeneous condensation generates a numerous number of ultra-fine ice
particles (probably sub-micron in size). Dustons and theirembryos, on the other hand, would be covered with an icy
layer or frost. Dustons gradually decouple from the gas(which also contains fine dust of ice and stone) and spiral down into the center of the vortex, while the fine dust
collide with the front and bottom sides of the dustons.

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

They are similar to the large ice grains in the terrestrial atmosphere, that grow by condensation of water in
updrafts of thunderclouds while small ice particles continuously collide with their bottoms. The separation of positively charged dustons and negatively charged ice particles
develops an electric field between the two populations.
Once the electric field is established, the dustons andtheir embryos are electrically polarized so that rebounding ice particles can deprive more negative charges fromthem, leaving them more positively charged. This results
in an enforcement of the field (Saunders 2008). If the vortex radius is comparable to the scale height of the diskgas, it would look like a cylindrical capacitor with electric charges of opposite polarities arranged in concentric
circles.

Energetics problem This problem has been recognized
as a most formidable one since Whipple (1966) suggested
a lightning discharge as a heat source of chondrules.
The ultimate energy source (gravitational potential of
the protoplanetary disk) is sufficient to melt the chondrules, but most of the energy earned by ingoing larger
dust go to the outgoing gas by the angular momentum exchange; little contribute to the random motion,
the energy source for the lightning (Muranushi 2010).
According to our new chondrule formation mechanism, however, the energy shortage seems easy to overcome because only the surface, a few mm in thickness,of dustons needs melting and evaporation to generatechondrules. The larger the duston’s average size, thesmaller the total energy would be required if the total
stony dust mass in the protoplanetary disk is assumed
constant.
The energy source of lightning discharge in the terrestrial atmosphere is the latent heat of water vapor during
its condensation in thunderclouds, partially transferred toturbulence and updraft in the developed cells, then partially to charge separation between icy grains (Rakov andUman 2003). We assume the latent heat of water vapor
as the source of the electric energy stored in the nebular
vortex, and calculate the minimum radius of the average
dustons, whose surface is exposed to lightning discharge
and boils to produce jet-droplets and vapor cloud.
For simplicity, the mass ratio of ice to stone in the vortex is assumed to be 3 : 1, and all the stone is used formaking dustons of single size (radius, R). It is assumed
that all ice once evaporates on a warm side of the vortex and then condense totally on a cold side, releasing thelatent heat. This latent heat is eventually used to heat the
dustons. We further assume that the duston’s surface witha thickness of R is kept molten at 2600 K, and that its
one-third thickness, (1/3)R evaporates. The initial temperature of the duston is assumed to be 100 K. A thermal
diffusion into the duston below the thickness R is not

Page 22 of 32

considered. The adopted duston’s thermodynamic properties are: Cp = 1.46 kJ kg−1 K−1 ; Hm = 6.27 × 102 kJ
kg−1 ; Hv = 8.37 × 103 kJ kg−1 (all data refer to enstatite
liquid; Chase et al. 1985). The water’s heat of vaporization is 2.45 × 103 kJ kg−1 . The radiative loss of energy(emissivity = 1) from the duston surface is assumed equal
to that for silicate vaporization, which is valid at 2600 K(Hashimoto and Nakano, in preparation).
We obtain R/R ∼4.0 −1
c , where c is the energy
conversion efficiency of the water latent heat to the totalenergy involved in lightning discharge, multiplied by theconversion efficiency of the latter to the heating of dustons. If R = 3 mm and c = 1, R = 12 mm. This
would be a minimum size of dustons, but c would besignificantly smaller than 1; if c = 0.001 (for the same
R = 3 mm), the duston’s radius should be as large as
12 m, which may be too large. Not all dustons would
be struck by thunderbolts, but only their small proportion would be, considering the rarity and unpredictable
nature of lightning on earth. This would reduce the optimum size of dustons significantly. If we presume c muchsmaller than 0.001, the productivity of chondrules shouldbe very low, but it would be more favorable from theenergy limitation.

Neutralization problem The protoplanetary disk is not
an ideal place for electric fields to build due to its low
gas density. If the gas is even slightly ionized, the field is
rapidly neutralized by Ohmic currents (Muranushi 2010).
Because of the large mean free path of electrons in PPD
compared to that in the earth atmosphere, the breakdown field is very small, of the order of ∼10 V m−1(Muranushi et al. 2015), while on earth it is ∼ 106 V
m−1 (Rakov 2013). This prevents a large electric field frombuilding up, as small discharges always wipe it out. Nevertheless, Pilipp et al. (1998) contended that global electricfields strong enough to induce lightning could have been
generated by gravitational sedimentation of dust particles and size sorting due to gas drag on these particles(Morfill et al. 1993), (1) only if charge transfer processes
operated in grain-grain collisions, (2) if the gas phase ionization rate were much lower than that usually assumed
for molecular clouds, almost as low as that resulting fromdecay of long-lived radioactive elements (40 K) trappedin the grains alone, (3) if precursors of chondrules werecompact with a specific mass density not much lower
than 1 g cm−3 , (4) and if the electrical energy was stored
in much larger structures. We agree to their assertions
except that the driving force for charge separation is the
Coriolis force in vortices rather than the disk gravity.
The vertical component of gravity in the disk midplane,
where much of dust are concentrated, is negligibly small;therefore an updraft with large velocities of unknown origin is needed to lift dust of various sizes to high altitudes,

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

e.g., a disk scale height, where the vertical component
becomes significant and causes separation of dust by size
difference.
The vortices must have formed in an MRI-inactive,‘dead zone’ (e.g., Kretke and Lin 2007), where the ionization source would be limited to radioactive elements
and cosmic rays. Pilipp et al. (1998) assumed only 40 K
for ionization source, which they found marginal to keep
a maximum allowable ionization from triggering global
discharges. They did not consider a decay of 26 Al, which
could be a strong source of ionization. As Desch andCuzzi (2000) pointed out, we may take it in a reversed
logic that the chondrule formation occurred because 26 Al
was already dead due to the time gap between chondrules and CAIs, or because 26 Al was not present in thechondrule formation zone due to its heterogeneous distribution (e.g., Larsen et al. 2011; Krot et al. 2012). We
consent to the latter possibility because some types ofchondrites (CO and LL chondrites) must have formed at
the same time as CAIs, and another types of chondrites(CV, CM and E chondrites) could have formed even before
the CAI formation. We also propose that any radioactive elements could not have been an effective ionization
source because of the large size of dustons and because of
the mass function biased to large aggregates. The electron(and perhaps positron) penetration depth is proportional
to their energy, ∼1.7 mm per MeV (Kanaya and Okayama
1972). Therefore, only a few mm surface layer of the
dustons may be liable to contribute to ionization of thegas; most of the mass which resides inside the dustons
would not.

Destruction problem Muranushi (2010), in his rebuttal argument to the experiment by Güttler et al. (2008),
pointed out that either the electron mean free path ismany orders of magnitude shorter or the electron kinetic
energy is much larger compared to the protoplanetary
disk environment.
We rather pay attention to the conclusion by Güttler
et al. (2008) that the fragmentation of experimental dust
aggregates is attributed to the expansion of the discharge
channel. In PPD the discharge channel is presumably very
wide (e.g., 5 km; Morfill et al. 1993) compared to that in
the experiment (Güttler et al. 2008; no description but
maybe ≤1 mm) and the discharge would continue formuch longer duration (e.g., 10-100 s; Morfill et al. 1993) ascompared to ∼60 μs in their experiment. Therefore, dust
aggregates in the discharge channel in PPD would be completely molten before the channel explosively expands as aresult of the vanishing magnetic fields around the channel.
4.4.4 Lightning discharge: consistency with our new model

We place three conditions on evaluating the lightning discharge as a possible heating mechanism for chondrule

Page 23 of 32

formation: (i) the temperature of the duston’s surface iskept above its boiling point for duration of 10 s or longer;(ii) the vapor cloud is kept for the same duration; and(iii) the matrix-forming fine dust coexist nearby at low
temperatures. We also add one more condition, (iv) thatthe chondrules that formed in the lightning bolt should
possess a large NRM (natural remnant magnetization)
because of the magnetic field formed around the discharge
path.
Morfill et al. (1993) estimated the energy available froma high temperature plasma of ∼30 eV for heating dust
grains in the discharge path, using a scaling of the typicalterrestrial bolt of lightning applied to a low density nebular gas. Due to a large mean free path of electrons, ∼1
m for n(H2 ) ∼ 1020 m−3 , the discharge path width is∼5000 m and the duration of a lightning pulse is of theorder 10-100 s (Morfill et al. 1993). Because of the widecross section of the path and the prolonged duration ofheating, the energy to impart to dust grains is diluted as
opposed to the terrestrial one (width ∼1 mm; duration<1 millisecond). This could be enough to melt grains as
small as chondrules (Morfill et al. 1993; Horányi et al.
1995), but is in no way sufficient for boiling the surface ofdustons.
We predict a new mechanism for heating dustons, a
direct strike by the lightning bolt. The allowable electric field in the nebula is restricted by the dielectricstrength of the molecular hydrogen. This limits the electric field inside vortices of the order of 10 V m−1 (0.14-30
V m−1 depending on the models of dielectric strength;
Muranushi et al. (2015). This field is so weak compared toa typical terrestrial thundercloud field of 1-2×105 V m−1(Rakov 2013) that a large scale charge separation, 106 -108m, is required to build an electric potential of 107 -109
V, typical of terrestrial thunderclouds. Therefore, the discharge path in the nebular gas might be a very long trail.
Our concern, however, is not the trail itself (which is usually assumed a heating scene of involved dust aggregates)
but its destination: how the discharge tip of the stepped
leader (e.g., Rakov and Uman 2003), a pathfinder so to
speak, finds its partner in opposite polarity. Our hypothetical dustons are the one, since their ‘point charge’ fields
stand out in the general field, like trees and lightning rods
as a terrestrial analogue. One unlucky duston struck by theleader is among a large number of dustons which we postulate distributing equally-spaced in a plane that extends
laterally more than thousands of km. A swarm of secondary electrons and ions from the attacked duston may
find another duston nearby, and the discharge process
should cascade.
Once the duston’s surface temperature rises highenough for evaporation of the icy layer and other volatiles,
the first vapor cloud forms whose density exceeds thatof the nebular gas by orders of magnitude. This would

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

make a mean free path shorter by the same magnitude and converge the wide discharge path into a narrow string similar to the terrestrial lightning. From
this on until discharge ends (for 10-100 s), the duston’s surface continues to boil and the vapor cloud ismaintained.
The cold fine dust exists outside of the discharge path.
If the path is more confined by being shepherded by dustons, rather than being spread over kilometers, a nearby
volume of the nebular gas around the vapor clouds may
be also free of heating and ready to mix its contained finedust with chondrules.
Wasilewski and Dickinson (2000) found that the
tetrataenite-bearing chondrules in Bjurbole (L/LL4) andChainpur (LL3) chondrites exhibited very high REM values (the ratio of NRM/SIRM) of > 100 × 10−3 , indicating that these chondrules were magnetized in a strong
magnetic field of the order of 100 mT (1000 G). According to their arguments, this high REM in the terrestrial
rocks is associated only with a direct strike by lightning discharge. In our new chondrule formation mechanism, supercooled liquid droplets solidify and cool below
the curie temperature (770 °C for tetrataenite; Herndon
and Rowe 1974) inside the vapor cloud that exists only
during the lightning discharge because the discharge
path expands explosively at the moment electric currents
vanish.
Our postulate, the lightning discharge as a heat sourceof boiling dustons, needs quantitative interrogation. We
do not deny a more plausible mechanism to be found in
future.

5 Conclusions
In paper (I), Nakano and Hashimoto have carried out
evaporation and condensation experiments and applied
the results to chondrules, explaining all the primaryfeatures of chondrules including their chemistry. On
this basis they proposed a new model of chondrule
formation that begins with dense and large aggregates of primordial CI-like dust, called ‘dustons’. Jetdroplets are ejected from the boiling surface of duston and react with the vapor and the condensate
while their traveling through the vapor cloud. Origin ofchondrules.
This paper started as a sequel to paper (I), in thatbasically the same model and calculation procedure areapplied to the bulk chemistry of chondrites, but having
seen entirely new results on the origin of chondrites, wehave expanded our view to the evolution of PPD materials to planetesimals. We highlight the following aspects inconclusions.
(i)

The duston-vapor cloud model include the five components: jet-droplets, differential vapor, integrated

Page 24 of 32

vapor, final integrated vapor and CI∗ dust. The first
three components make chondrules and the lasttwo components make the matrix of chondrites,
altogether forming the bulk chondrite. CAIs which
later mixed with the chondrite-forming components
is added as a sixth and foreign component to themodel to explain CAI-bearing chondrites. We havefound that in four types of chondrites CAIs had
mixed with the primordial dust before the chondrule formation. Ghost CAIs manifest themselves asunusual enrichment in refractory elements both inchondrules and in the bulk chondrite, and is added
as a seventh component to the model. Seven types ofchondrites, CV, CM, E, CO, LL, H and L, are appliedwith the numerical fitting procedures developed for
reproduction of bulk chondrite compositions withparameters, VD (vaporization degree) and fs (redox
indicator), to determine the compositions and molar
proportions of the (maximum) seven components.
We have obtained a single solution for each of thechondrite types.
(ii) The results of numerical fittings indicate that the
average chondrule compositions of seven types ofchondrites are achieved by significant evaporation
with 24-43% in VD, and that the maximum evaporation experienced by the molten surface of dustons reach as large as 50-85% in VD. It not only
proves that chondrules are not just melted dropsof pre-existing dust aggregates, but most importantly vindicates that the chondrule formation isthe driving force for the chemical fractionations inchondrites.
(iii) We have identified three groups of chondrites
according to the parameter fs determined. The most
reduced group, CV, CM and E, have fs = 0.03-0.04
and contain only CAIs; the middle group, CO and
LL, have fs = 0.20 and contain both CAIs and ghost
CAIs; and the most oxidized group, H and L, have
fs = 0.22-0.27 and contain a minor amount of ghost
CAIs only. From these results we have derived thechronological sequence of chondrule formation fordifferent types of chondrites: the chondrule formation for CV, CM and E occurred before the invasion of CAI into the chondrule formation zone; it
occurred during the CAI invasion for CO and LL;
and it occurred after the CAI invasion for H and
L. The concomitant increase in fs values with thischronological sequence indicates that the PPD environment changed from reducing to oxidizing in time.
We have found that this sequence is also related to
the D/H ratios of various solar system and extrasolar substances. We propose that the D/H ratio andthe concentration of O2 molecules in PPD increased
with time as PPD evolved.

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9(iv) The chronological order of the chondrule formation and the CAI invasion revealed in this study isin conflict with the 26 Al chronology of CAIs andchondrules. We have found that dating of chondrules with live 26 Al is an artifact due to invasion of
ghost CAIs before the chondrule formation, whichcontaminated the primordial dust with a live 26 Al.
The Pb-Pb dating of CAIs and chondrules seems
compatible with our result as long as CAIs andchondrules in the same chondrite are used.
(v) To complete the chemical fractionation, the chemically fractionated materials must be physically separated. Our model offers a natural selection according to the principle of aerodynamic friction in PPD
because as a result of chondrule formation, materials
are divided into three populations with different size
ranges. The chondrule-cored, dust-mantled nodules
and their clusters are supposed to be millimeters tocentimeter in size; the dustons with heat-scorchedsurfaces are more than 3 cm in diameter; and theleftover fine condensates and indigenous primordial dust, that fail to stick to chondrules, would be
typically less than μm in size.
(vi) We propose that the chondrule formation occurred
inside the large vortices which encompass the snowline in PPD. We envisage that the dustons, whether
heat-scorched or kept intact, fall faster into the center of the vortex and ultimately form a planetesimal
while the chondrule-cored nodules fall slower andform a veneer on the planetesimal, thus completing aphysical separation. The fine dust would not fall but
slowly bail out from the vortex.
(vii) Having discussed our new ideas on the origin of
the chemical fractionations in chondrites, we compare our model with those developed by Anders andhis group, viz. the equilibrium condensation model.
Our model provides a better explanation for thelithophile element fractionations in chondrites particularly because it explains the completion of thefractionation as a natural consequence of the chondrule formation from dustons, while the equilibrium
condensation model has no clue to this problem. The
condensation theory is in conflict with the metalsilicate fractionation observed in chondrites, while
our model can be compatible because the fractionation must have occurred during or after the chondrule formation.
(viii) We have scrutinized a dozen heat sources for chondrule formation based on our new measures. Only
one possible heat source is left compatible with ourchondrule and chondrite formation model: lightning
discharge. We propose that a large-scaled charge
separation, 10-100 thousand kilometers apart inside
the vortex, is possible between dustons and ice

Page 25 of 32

particles with opposite charges and induces directdischarge strikes on the surface of dustons formore than 10 seconds, energetic enough to makedustons boil and generate a swarm of chondrules. A
direct strike is also compatible with the large NRM
recorded in chondrules.
(ix) Chondrites are full of shocked records, which could
be explained by their formation history that during
the era of planet formation, violent planetesimalplanetesimal collisions should have caused theirchondritic veneers stripped off. Fragments were laterbound together with a weak self-gravity: rubble piled
asteroids, which are likely sources of chondritic
meteorites.
Finally, we have not positively included oxygen isotope
data in the argument since our model, as it stands now,
is not in need of those to construct it. A plethora of
the isotopic data on chondrules, chondrites, CAIs, andother solar system materials, including Earth and Moon
requires a full of consideration, which is difficult to do due
to space limitation. Tactically, however, it will be wise to
use the whole data not only for assessing our proposedmodel but also for guiding our coming works (Hashimoto
et al., in preparation).

APPENDIX(A) Data

All data in Table 1 are chemical compositions of silicatesin mol% on the ten element basis. The bulk chemicalcompositions of chondrites are mostly from the wetchemical analyses compiled by Jarosewich (1990). The
wet-chemical method has several advantages compared toothers, which are crucial in the present study. It usuallyuses a bulk of rock sample of 8-20 grams for each chondrite. Chondrites contain various petrographic units andmineral phases which are different in size, compositionand chemical state. They are not necessarily homogeneously distributed inside the bulk chondrite, so that a
few grams of rock sample may not represent its bulk
composition. According to Jarosewich (1990), 20 gramsof meteorite, whenever possible, is routinely allocated inorder to assure homogeneous and representative powders. The wet-chemical analysis distinguishes between Feoxides, metals and sulfides. This is also necessary in ourstudy.
The average composition of chondrules is a simple average of broad-beam EPMA data of individual chondrulesthat belong to a single chondrite or to a specified typeof chondrites. Precision and reliability of such analyses
are described in paper (I). Here the important fact isthat those EPMA data represents only silicate portionsof chondrules because metals and sulfides included inchondrules are routinely avoided in the analyses.

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

Data sources of the bulk chondrite compositions and theaverage chondrule compositions, as well as adjustments(whenever necessary) to the data, are explained in thefollowings.
Bulk chemical compositions
1 L chondrite: The average composition of 54
L-chondrites (falls) in Jarosewich (1990, table 5), after
normalization to 100 mol% on the ten element basis,is shown.
2 H chondrite: The average composition of 26
H-chondrites (falls) in Jarosewich (1990, table 5),
after normalization to 100 mol% on the ten element
basis, is shown.
3 LL chondrite: The average composition of 12
LL-chondrites (falls) in Jarosewich (1990, table 5),
after normalization to 100 mol% on the ten element
basis, is shown.
4 CV chondrite: The bulk composition of Efremovka(CV3) in Jarosewich (1990, table 2), after
normalization to 100 mol% on the ten element basis,is shown. We choose Efremovka simply because
Hezel and Palme (2010) have analyzed chondrules in
it. Allende and Bali are also CV3 chondrites listed in
Jarosewich (1990, table 2). There are many chondrule
analyses available for Allende (see paper (I)).
However, not only the matrix but also the chondrules
in Allende are heavily altered, making it unsuitable
for the present study.
5 E chondrite: The average composition of 10
E-chondrites, four in Jarosewich (1990, table 2) andsix from Yanai et al. (1995) is used after somemodification described below. In the wet-chemical
analysis, usually the FeO content is obtained bysubtraction of Fe metal and Fe sulfide from the total
Fe content. This makes it difficult to determine the
FeO content in good precision because the FeO
content in E chondrites is very low by nature. In
Jarosewich (1990, table 2), it is forced to zero becauseof this difficulty. According to Yanai et al. (1995),
however, the least altered E chondrites contain 1-4
wt.% FeO. Chondrules in the least altered Y-691 (E3)have their average FeO content 1.9 wt.% (Ikeda
1983). Considering these data, we adopt 2 wt.% for
the bulk FeO content in E chondrites. The
concentrations of other nine elements are simple
averages of 10 E-chondrites. The total is normalized
to 100 mol% just as for other types of chondrites.
6 CO chondrite: The average bulk composition of 3
CO-chondrites in Jarosewich (1990, table 2), after
normalization to 100 mol% on the ten element basis,is shown. They are ALH-77003 (CO3), ALH-82101(CO3) and Isna (CO3).

Page 26 of 32

7 CM chondrite: The average bulk composition of 3
CM-chondrites in Jarosewich (1990, table 2), after
normalization to 100 mol% on the ten element basis,is shown. They are Banten (CM2), Y-791824 (CM2)and Y-793321 (CM2). Murchison (CM2) in
Jarosewich (1990, table 2) is not included because of
its unusually low Na content compared to others.
8 CI chondrite: The weighted average bulk
composition of 3 CI-chondrites compiled by Lodders(2003, table 1 and 3) after normalization to 100 mol%on the ten element basis, is shown. They are Orgueil(CI), Alais (CI) and Ivuna (CI).
9 CI∗ : The composition after subtracting the half of
FeO from the CI composition (explained in 8) andbeing renormalized to 100 mol% is shown. See thetext (Section 2.1) for more detail.
Average composition of chondrules
1 L chondrules: Average composition of 437
chondrules from three L-chondrites. They are
Y-74191 (L3) (Ikeda and Takeda 1979; Kimura et al.
1979), ALH-77015 (L3) (Fujimaki et al. 1981;
Nagahara 1981; Ikeda 1983) and ALH-77249 (L3)
(Kimura 1983).
2 H chondrules: Average composition of 109
chondrules from two H-chondrites. They are
ALH-77299 (H3.7) and Y-790986 (H3-4), both in
Ikeda (1983). Ti and Mn data are transferred fromthose in the bulk H chondrite in Table 1 because thechondrule analyses frequently omitted theseelements from the list of analysis.
3 LL chondrite: Average composition of 74 chondrules
from ALH-764 (LL3) (Ikeda 1980). Ti and Mn data
are transferred from those in the bulk LL chondritein Table 1 because the chondrule analyses omitted
these elements from the list of analysis.
4 CV chondrules: Average composition of 8 chondrules
from Efremovka (CV3) (Hezel and Palme 2010).
5 E chondrules: Average composition of 88 chondrules
from Y-691 (E3) (Ikeda 1983).
6 CO chondrules: Average composition of 110
chondrules from three CO-chondrites. They are
ALH-77003 (CO3) (Ikeda 1982), Y-790992 (CO3)(Ikeda 1983) and Kainsaz (CO3) (Hezel and Palme
2010).
7 CM chondrules: Average composition of 10
chondrules from El-Quss Abu Said (CM) (Hezel andPalme 2010).
(B) D/H Ratios

The D/H ratios of various solar system and extrasolar substances are shown in Fig. 10. Data and their references areshown in Table 6.

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

Page 27 of 32

Table 6 D/H ratios and references#

Material or Source

D/H ratio

Reference

×10−4
1

Local interstellar medium (gas)0.15±0.01

Linsky (1998)

2

ProtoSolar

0.21±0.05

Geiss and Gloeckler (1998)

3

Saturn (atmosphere)

0.21±0.013

Pierel et al. (2017)

4

Jupiter (atmosphere)

0.295±0.055

Pierel et al. (2017)5

Uranus (atmosphere)

0.44±0.04

Feuchtgruber et al. (2013)6

Neptune (atmosphere)

0.41±0.04

Feuchtgruber et al. (2013)

7

Tagish lake-11i

0.164-1.14

Alexander et al. (2012)

8CV≤0.820Alexander et al. (2012)

9CI

0.643-0.976

Alexander et al. (2012)10CM

0.865±0.036

Alexander et al. (2012)11

CO

0.849-1.32

Alexander et al. (2012)12CR

1.71+0.17−0.1

Alexander et al. (2012)13

O

2.8-3.44

Alexander et al. (2012)14R

7.26±0.13

McCanta et al. (2008)15

Earth Bulk

1.49±0.03

Lécuyer et al. (1998)

16

Comet 103P/Hartley 2

1.61±0.24

Hartogh et al. (2011)17

Comet 45P/Honda-Mrkos-Pajdušáková

≤2

Lis et al. (2013)18

Comet 67P/Churymov-Gerasimenko

5.3±0.7

Altwegg et al. (2015)19

Comet C/2009 P1 (Garradd)

2.06±0.22

Bockelée-Morvan et al. (2012)20

Comet 153P/Ikeya-Zhang≤2.5

Biver et al. (2006)

21

Comet C/2002 T7 (Linear)2.5±0.7

Hutsemékers et al. (2008)

22

Comet C/1996 B2 Hyakutake

2.9±0.1

Bockelée-Morvan et al. (1998)

23

Comet C/1995 O1 Hale-Bopp

3.3±0.8

Meier et al. (1998)

24

Comet P/Halley

3.16±0.34

Eberhardt et al. (1995)

25

Comet 8P/Tuttle

4.09±1.45

Villanueva et al. (2009)26

NGC 1333 IRAS4B (Inner)

5.9±1.7

Persson et al. (2014)27

NGC 1333 IRAS4B (Inner)

1-37

Coutens et al. (2013)28

NGC 1333 IRAS4A (Inner)

10

Visser et al. (2013)29

NGC 1333 IRAS4A (Inner)

4-30

Coutens et al. (2013)29

NGC 1333 IRAS4A (Outer)≈100

Coutens et al. (2013)30

NGC 1333 IRAS4A (Inner)

19.1±5.4

Persson et al. (2014)31

NGC 1333 IRAS4A (Inner)

50-300

Taquet et al. (2013)

32

IRAS2A (Inner)

7.4±2.1

Persson et al. (2014)

33

IRAS2A (Inner)≥100

Liu et al. (2011)

33

IRAS2A (Outer)

900-1800

Liu et al. (2011)

34

IRAS2A (Inner)

30-800

Taquet et al. (2013)

35

IRAS 16293-2422 (Inner)

9.2±2.6

Persson et al. (2013)

36

IRAS 16293-2422 (Inner)

300

Parise et al. (2005)

36

IRAS 16293-2422 (Outer)≤20

Parise et al. (2005)

37

IRAS 16293-2422 (Inner)

140-580

Coutens et al. (2012)

37

IRAS 16293-2422 (Outer)

20-220

Coutens et al. (2012)‘Outer’ and ‘Inner’ in parentheses denote outer and inner regions of clouds

Hashimoto and Nakano Progress in Earth and Planetary Science(2021) 8:9

Abbreviations
VD: Vaporization degree; MLB: Mother liquid body; CROMs: C-rich refractoryorganic materials; JDMP: Jet-droplet mass percentage
Acknowledgements
We are greatly indebted to the members of the Planetary and Space Sciencegroup, Hokkaido University, for their valuable comments throughout this workand to Dr. A. Kouchi, Institute of Low Temperature Science, Hokkaido
University for useful discussion. We thank the anonymous reviewers for theircareful reading of our manuscript and their comments and suggestions.
Authors’ contributions
AH and YN conceived the study. AH devised the numerical model. YN
compiled the data base and surveyed astrophysical literature. AH and YN,
together, developed the new model of chemical evolution of PPD materials.
AH wrote the paper. All author(s) read and approved the final manuscript.
Funding
This research received no specific grant from any funding agency in the
public, commercial, or not-for-profit sectors.
Availability of data and materials
The datasets supporting the conclusions of this article are included within thearticle and its appendices.
Competing interests
The authors declare that they have no competing interest.
Author details
1 Suns & Fishermen Society, Sapporo, Japan. 2 Department of Cosmosciences,
Hokkaido University, N10 W8, 060-0810, Sapporo, Japan.
Received: 12 November 2019 Accepted: 21 October 2020

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