The Astrophysical Journal, 836:106 (6pp), 2017 February 10

https://doi.org/10.3847/1538-4357/aa5b8c© 2017. The American Astronomical Society. All rights reserved.

Diffusion of Oxygen Isotopes in Thermally Evolving Planetesimals
and Size Ranges of Presolar Silicate Grains1

Shigeru Wakita1, Takaya Nozawa2, and Yasuhiro Hasegawa3
Center for Computational Astrophysics, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan; shigeru@cfca.jp
2
Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan3
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
Received 2016 April 30; revised 2017 January 12; accepted 2017 January 19; published 2017 February 13

Abstract
Presolar grains are small particles found in meteorites through their isotopic compositions, which are considerably
different from those of materials in the solar system. If some isotopes in presolar grains diffused out beyond theirgrain sizes when they were embedded in parent bodies of meteorites, their isotopic compositions could be washedout, and hence the grains could no longer be identiﬁed as presolar grains. We explore this possibility for the ﬁrst
time by self-consistently simulating the thermal evolution of planetesimals and the diffusion length of 18O inpresolar silicate grains. Our results show that presolar silicate grains smaller than ∼0.03 μm cannot keep their
original isotopic compositions even if the host planetesimals experienced a maximum temperature as low as
600 °C. Since this temperature corresponds to that experienced by petrologic type 3 chondrites, isotopic diffusion
can constrain the size of presolar silicate grains discovered in such chondrites to be larger than ∼0.03 μm. We also
ﬁnd that the diffusion length of 18O reaches ∼0.3–2 μm in planetesimals that were heated up to 700–800°C. This
indicates that, if the original size of presolar grains spans a range from ∼0.001 μm to ∼0.3 μm like that in theinterstellar medium, then the isotopic records of the presolar grains may be almost completely lost in such highly
thermalized parent bodies. We propose that isotopic diffusion could be a key process to control the size distribution
and abundance of presolar grains in some types of chondrites.
Key words: diffusion – meteorites, meteors, meteoroids – planets and satellites: formation
The abundance of presolar grains varies among different
petrologic types of meteorites: in general, presolar grains aremost abundant in type 3, but their abundance decreases as thetype number increases from 3 to 6 (Huss 1990; Huss &Lewis 1995). These types are based on the degree ofmetamorphism experienced by meteorites when they wereembedded in planetesimals. Since the metamorphism depends
on the temperature, petrologic types are regarded as representing the peak temperature experienced by the planetesimals. For
instance, it is widely accepted that the ordinary chondrites of
petrologic type 3 experienced a peak temperature less than
700°C, that experienced by type 6 was higher than 800°C, andtypes 4 and 5 fall between them (Huss et al. 2006). Thus, thisclassiﬁcation suggests that the abundance of presolar grains
may be related to the thermal history of planetesimals.
It is implicitly presumed that metamorphism totally erases
the isotopic records of presolar grains. This may be because
metamorphism creates new minerals or crystalline structures bybreaking the original atomic bonds and forming new ones. If
metamorphism were the dominant process in washing out theisotopic compositions, more presolar grains would be discovered in unmetamorphosed (primitive) chondrites. While theleast metamorphosed type 3 chondrites have the highest
abundance of presolar grains among chondrites (Nguyen
et al. 2007, 2010; Floss & Stadermann 2009, 2012; Nittler
et al. 2013), it is still much lower than that in interplanetary
dust particles (IDPs), which are regarded as the most primitive
materials (Messenger et al. 2003; Floss et al. 2006; Busemannet al. 2009). Therefore, metamorphism would not explain the
difference in abundance of presolar grains between type 3chondrites and IDPs. On the other hand, even if the chemicalcompositions of minerals are not changed through metamorphism, the replacement of one atom by another—so-called atomic

1. Introduction
Primitive meteorites contain unique tiny materials called
presolar grains. The fundamental property of the presolar grainsis their isotopic compositions, which deviate signiﬁcantly fromextremely homogeneous values of materials in the solar system.
In particular, presolar silicate grains are identiﬁed via theoxygen isotopic ratios of 17O/16O and 18O/16O (e.g., Clayton& Nittler 2004). Since such isotopic anomalies must have beenpreserved over the entire history of the solar system (which is
why we can currently measure the differences in isotopic
composition), investigation of presolar grains can provide us
with important clues to understand the formation and evolutionof the solar system.
It is considered that the presolar grains originally formed in
nearby stars during post-main-sequence phases such as supernovae and/or asymptotic giant branch (AGB) stars. They werethen transported to the presolar nebular, which is a preliminary
stage to the formation of the Sun, and were ﬁnally incorporated
into planetesimals that are the parent bodies of meteorites.
Some theoretical studies suggest that dying stars could inject
relatively large grains with radii of 0.1–1 μm into theinterstellar medium (ISM, e.g., Nozawa et al. 2007; Yasuda& Kozasa 2012). On the other hand, while these grains weretraveling to the presolar nebula, many of them might fragment
into grains smaller than 0.1 μm as a result of shattering ininterstellar turbulence (Hirashita & Yan 2009). It is nonethelessimportant to point out that such small (<0.1 μm) presolar
grains have rarely been detected in the currently available
samples; the typical size distribution of presolar silicate grains
is from ∼0.1 to ∼1 μm (e.g., Zinner 2003; Hynes &Gyngard 2009; Nguyen et al. 2010; Leitner et al. 2012; Hoppeet al. 2015).
1

The Astrophysical Journal, 836:106 (6pp), 2017 February 10

Wakita, Nozawa, & Hasegawa

parameters of thermal conductivity K=2 [J s–1 m–1 K–1], densityρ=3300 [kg m−3], and speciﬁc heat c=910 [J kg–1 K–1]
(Yomogida & Matsui 1983; Opeil et al. 2010). We assume thatthese parameters do not depend on the temperature. The radiusand formation time of planetesimals, both of which are expected
to affect the maximum temperature they reach (see Figure8 in
Wakita et al. 2014), are parameterized; the formation time ofplanetesimals t0 is determined based on a formation time of Ca–
Al-rich inclusions (CAIs), 4567 Myr ago, when they had the initialratio of 26Al/27Al=5.25×10−5 in the solar nebula (e.g.,
Connelly et al. 2012). The radiogenic heat generation rate A falls
in direct proportion to the initial ratio of 26Al/27Al, which depends
on the formation time of planetesimals t0 (see Figure15 in Wakita& Sekiya 2011). Since the abundance of 26Al decreases with time(its half-life is 0.72 Myr), a planetesimal formed at a later time has
fewer heating sources than one formed earlier.
A diffusion length (L) is calculated as dL2=D(T)dt at eachtime step during the thermal evolution of planetesimals. It takes
about 103 yr to diffuse 18O entirely in particles with a size of
1 μm at 1000°C, and a much longer time (109 yr) is needed at
600°C. These times are long enough compared with the time
step for calculating the thermal evolution of planetesimals (dt),which is of the order of one year. We compute the accumulated
diffusion length of 18O given by L2 = å t dL2 . We assume thatplanetesimals do not experience any kind of disruption after
their formation.
Figure 1 shows the temperature evolution at the center ofplanetesimals (dashed lines) and the accumulated diffusion
length of 18O (solid lines) for planetesimals with different
radii (50 km and 100 km) and formation times (t0=1.9 Myr
and 2.4 Myr). The results show that the temperature evolution
controls how the diffusion length develops over time: as thetemperature increases, the diffusion length becomes longer.
When the temperature starts to decrease, the increase indiffusion length ceases (see the left panels of Figure 1). Since
we evaluate the accumulated diffusion length, it does notdecrease once the temperature starts to drop. This means thatthe maximum temperature governs the diffusion length of 18O
in grains.
Our results also indicate that for larger planetesimals (see theright panels of Figure 1), the diffusion length at the center
gradually increases even after the temperature reaches its
maximum value. This arises because larger planetesimals cankeep the maximum temperature for a longer time than smaller
ones (see Figures 1(b) and (d)). It should be noted that the
maximum temperature, and accordingly the diffusion length, ismore sensitive to the formation times of planetesimals thantheir radii. As seen from Figure 1, the diffusion lengths ofplanetesimals formed at earlier times (t0=1.9 Myr, top panelsof Figure 1) are much longer (10−4 m) than those (10−6 m)
formed at later times (t0=2.4 Myr, bottom panels of Figure 1).
This is because, if their sizes are the same, the planetesimals
formed at earlier epochs have more abundant 26Al and reach ahigher maximum temperature. Note that the above results are
obtained for the central region of planetesimals. The diffusion
lengths are different at different radii of the planetesimals. As
mentioned above, the resultant diffusion length is a function of
only the maximum temperature. Therefore, we can estimate a
diffusion length at every location in a planetesimal by simply
referring to the maximum temperature achieved there.

diffusion—could occur in slightly thermalized planetesimals.
Therefore, it can be anticipated that atomic diffusion can alsodelete the original isotopic composition possessed by presolar
grains in their parent bodies.
In this paper we explore this possibility for the ﬁrst time bycomputing the diffusion length of 18O in presolar silicate grains
in meteorites and by comparing it with the actually measured
size of presolar grains. Since the diffusion length is sensitive totemperature, we numerically simulate thermal evolution ofplanetesimals with different radii and formation times. We ﬁndthat the diffusion process of oxygen atoms can regulate the size
distribution of presolar silicate grains and that only grains
larger than ∼0.3 μm can keep their original isotopic properties
in chondrites of types 4–6. Our results also suggest that, even in
type 3 chondrites that experienced a peak temperature of only
600°C, atomic diffusion can entirely erode the isotopic records
of presolar silicate grains smaller than ∼0.03 μm. This may beviewed as a potential explanation of why the currently available
samples of presolar silicate grains in type 3 chondrites have asize larger than ∼0.05 μm. Thus, we conclude that isotopic
diffusion is one of the important processes governing thesurvival of presolar grains in thermally evolving planetesimals.
2. Isotopic Diffusion in Thermally Evolving Planetesimals
In order to compute the diffusion length of oxygen isotopes
in presolar silicate grains, we adopt a diffusion coefﬁcient of18
O in olivine from Dohmen et al. (2002). The diffusion
coefﬁcient D(T) [m2 s–1] is given as
D (T ) = 10-8.34 exp ( - 3.38 ´ 10 5 RT ) ,(1 )where R is the gas constant [J K–1 mol–1] and T is thetemperature [K]. Since the diffusion coefﬁcient is obtained fora temperature range of 1100°C<T<1500°C (Dohmen et al.
2002), we extrapolate the results down to lower temperatures.
Measurements with a transmission electron microscope showthat the chemical compositions of presolar silicate grains varyon the scale of a few tens of nanometers (Nguyen et al. 2007;
Busemann et al. 2009; Leitner et al. 2012). While it would beinteresting to see how the diffusion coefﬁcients depend on
stoichiometry of elements in silicate, there are no data forsilicate compositions with a variety of Mg/O, Fe/O, and Si/O
ratios. Thus, we assume that grains have a homogeneouscomposition of Mg-rich forsterite as used in Dohmen
et al. (2002).
As can be seen from Equation (1), the diffusion coefﬁcientdepends strongly on the temperature. Thus, we need tonumerically simulate the thermal evolution of planetesimals
to reliably estimate the diffusion length of 18O in silicate. We
assume that decay energy of the short-lived radioisotope 26Al
heats up materials within a planetesimal, as most thermal
modeling studies have done (e.g., Miyamoto et al. 1982). A
heat conduction equation,rc¶T
1 ¶ ⎛ 2 ¶T ⎞⎜r K
⎟ + A exp ( - lt ) ,= 2¶tr ¶r ⎝¶r ⎠(2 )is solved numerically based on Wakita et al. (2014), where t is
time measured from the formation time of planetesimals t0, r is
the distance from the center of the planetesimals, A is theradiogenic heat generation rate per unit volume, and λ is the
decay constant of the radionuclides. We adopt physical2The Astrophysical Journal, 836:106 (6pp), 2017 February 10

Wakita, Nozawa, & Hasegawa

Figure 1. Evolution of temperature at the center of planetesimals (dashed lines with left axes) and the corresponding evolution of diffusion lengths of 18O in olivine(solid lines with right axes) as a function of time after CAI formation. Panels give the result for planetesimals with radii of (a) 50 km and (b) 100 km formed 1.9 Myr
after CAI formation, and with radii of (c) 50 km and (d) 100 km formed 2.4 Myr after CAI formation.

We also ﬁnd that the diffusion length of 18O can beapproximately described by the following analytical formula:
L2 = D (Tmax) Dtmax,

While we adopt Δtmax=1 Myr in Equation (3), which is atypical duration for planetesimals of 50 km radius, it works
well for planetesimals with a radius of 100 km. Thus, ourresults demonstrate that our analytical formula (Equation (3))
reproduces the numerical results very well and the maximum
temperature can be used as an indicator to estimate thediffusion length of 18O.

(3 )where Δtmax is the duration of the maximum temperature Tmax.
Figure 2 represents the diffusion lengths obtained fromnumerical simulations and from Equation (3) with
Δtmax=1 Myr as a function of maximum temperature. It
should be emphasized that the dependence of the diffusion
length on the maximum temperature follows a simple relationand is reasonably described as a function of Tmax by
Equation (3). The maximum temperature achieved at eachlocation in a planetesimal decreases with increasing radius.
Thus, each curve in Figure 2 can be viewed as representing theradial dependence of diffusion length, where the greatest
diffusion length is achieved in the center of a planetesimal.

3. Discussion and Conclusions
Here we discuss the implications of our results for the size
distribution and abundances of presolar grains in various
petrologic types of meteorites. In Figure 2, we compare thecalculated diffusion lengths with the size ranges of presolar
silicate grains obtained from meteorites. For two data points on
grain sizes, the vertical error bars cover the maximum and theminimum sizes, and the horizontal ones are the suggested
3

The Astrophysical Journal, 836:106 (6pp), 2017 February 10

Wakita, Nozawa, & Hasegawapresolar silicate grains would be retained in such type 3.0 and
3.1 chondrites. In fact, it is interesting to notice that a type 3.0
chondrite, ALHA 77307, is considered to be a primitivechondrite with one of the highest abundances of presolar
silicate grains among type 3 chondrites (Nguyen et al. 2007).
Although the subtypes of type 3 chondrites cannot be clearly
distinguished by their peak metamorphic temperatures (e.g.,
Huss et al. 2006), it would be valuable to see how theabundance of presolar silicates changes in each subtype.
If the birthplace of presolar silicate grains is the outﬂowing
gas from supernovae and AGB stars, their initial sizes could bedominantly in the range from 0.1 to 1 μm (e.g., Nozawa
et al. 2007, 2015; Höfner 2008). As seen in Figure 2, the upperend (∼1 μm) of this range roughly corresponds to the
maximum size of grains that could form in supernovae and
AGB stars. This implies that the largest presolar grains thatmight be produced in stellar sources can survive any
destructive events (e.g., Hirashita et al. 2016) and they may
contain intact information that was recorded at the time of theirformation. On the other hand, many submicron-sized grains
collide with each other and fragment into nanometer-sizedgrains as a result of shattering in interstellar turbulence(Hirashita et al. 2010; Asano et al. 2014). Hence, presolar
grains should also include grains smaller than 0.1 μm. Nonetheless, the size (∼0.1 μm) of the smallest silicate grains
measured in type 3 chondrites is much larger than the minimum
size (∼0.001 μm) of interstellar dust. In fact, the critical valueof 0.1 μm coincides with the accumulated diffusion length
expected from our results. This may suggest that the smallest
size of presolar grains in type 3 chondrites might be determinedby the diffusion process triggered in thermally evolving
planetesimals.
For type 1 and 2 chondrites, which experienced peakmetamorphic temperatures of only ∼150°C or less, theexpected diffusion lengths of 18O are extremely short. Therefore, any size of presolar silicate grains can survive against theisotopic diffusion. However, the sizes of presolar grains
measured in these petrologic types are conﬁned to the range
0.1–1.7 μm, and no grains smaller than 0.1 μm have been
discovered so far. In general, in type 1 and 2 chondrites,aqueous alteration may have played an important role ineliminating the original isotopic information of grains smaller
than 0.1 μm. Leitner et al. (2012) suggest that the initialabundance of presolar silicate grains might be 10 times larger
than current values in a type 2 chondrite, and this reduction
may be due to destruction of the grains by aqueous alteration.
It should be kept in mind that there is a limitation to the size
measurement of presolar grains. Most of the data on the size ofpresolar grains are obtained from in situ measurements with asecondary ion mass spectrometer (SIMS), whose beam size iscomparable to 0.15 μm. This indicates that signiﬁcant amounts
of presolar grains of that size or smaller could be undetected.
An optimized setting of NanoSIMS makes it possible toidentify smaller (<0.1 μm) presolar grains (Hoppe et al. 2015).
However, measurements with a spatial resolution of 0.1μm
might suffer from instrumental biases in detecting smaller
grains (Nguyen et al. 2007, 2010). Thus, more sophisticatedtechniques are desired to ﬁnd presolar silicate grains smaller
than 0.1 μm in chondrites of types 1–3 and to check our
scenario in which isotopic diffusion (and aqueous alteration)
can affect the size distribution of presolar grains surviving inplanetesimals.

Figure 2. Diffusion length of 18O as a function of maximum temperature,
which can be translated to radial depth of the planetesimal. Numerical results
are denoted by colored lines, and the analytical result by the black one. We
adopt the same values as in Figure 1 for the radii and formation times ofplanetesimals, and the parameter set for each line is given in the legend of theﬁgure. The shaded region denotes a regime where diffusion can lead tocomplete erosion of presolar grains of a certain size. Symbols with bars plot theranges of size and peak temperature derived for presolar silicate grains ofchondrites of type 3 (green circle) and types 1 and 2 (black triangle). The
vertical magenta line with a rightward arrow indicates the lower value of thepeak temperatures expected for chondrites of types 4–6.

ranges of peak metamorphic temperatures. The sizes of presolar
silicate grains are 0.1–1.7 μm and 0.07–0.6 μm in petrologic
chondrites of types 1 and 2 and type 3, respectively(Zinner 2003; Hynes & Gyngard 2009; Nguyen et al. 2010;
Leitner et al. 2012; Hoppe et al. 2015). The metamorphic
temperature of type 3 chondrites is likely to be between 500°C
and 700°C (Huss et al. 2006; Krot et al. 2007), whereas that oftypes 1 and 2 carbonaceous chondrites might be around 100°C(Krot et al. 2015).
The maximum temperature governs the diffusion lengths.
The length is ∼0.001 μm when the maximum temperature is
500°C. If planetesimals reach a maximum temperature of
700°C, the diffusion length is ∼0.3 μm. Hence, the diffusion
length of 18O in silicate grains in type 3 chondrites ranges from∼0.001 μm to ∼0.3 μm, depending on the maximum temperature that they experienced. This indicates that, once we know
the minimum size of presolar silicate grains, we can estimate
the maximum temperature of their parent bodies. For example,
chondrites that contain the smallest presolar silicate grains of
0.07 μm would not have experienced a peak temperature higher
than 630°C when they were embedded in their parent bodies.
Our calculations imply that, even if typical type 3 chondrites
have undergone a peak temperature of 600°C, presolar grains
smaller than ∼0.03 μm can lose their oxygen isotopic anomaly
as a result of isotopic diffusion. This may be one of the reasons
why we do not ﬁnd such small presolar silicate grains in type 3chondrites.
Petrologic type 3 chondrites can be subdivided into types 3.0
to 3.9 based on their characteristics of thermoluminescence andcompositions of minerals (Sears et al. 1980; Scott & Jones
1990; Scott et al. 1994; Grossman & Brearley 2005; Bonalet al. 2006). It is suggested that type 3.0 and 3.1 chondrites
experienced lower peak temperatures of ∼200–400°C thantypical type 3 chondrites (Cody et al. 2008). If this would be
the case, our results imply that the original abundance of4

The Astrophysical Journal, 836:106 (6pp), 2017 February 10

Wakita, Nozawa, & Hasegawa

viewed as an important process to wash out the original
isotopic composition of presolar silicate grains in certain
meteorites. We show that isotopic diffusion can regulate thelower size limits of presolar silicate grains in various petrologic
types of chondrites, while the upper limits probably originate
from the formation processes of the grains in stellar envelopes.
For carbonaceous chondrites (usually types 1–3), measurements of grains <0.1 μm are needed to ﬁrmly address how
important the diffusion is in altering the size distribution ofpresolar grains in planetesimals. The methodology developedin this paper is applicable to any other isotopes in a variety ofminerals provided that their diffusion coefﬁcients are given.
The measured sizes of presolar grains, combined with thesimulations of diffusion lengths of the relevant isotopes, will
surely advance our understanding of presolar grains and theparent bodies of their host meteorites.

In chondrites of types 4, 5, and 6, which are considered tohave experienced a peak metamorphic temperature above
700°C (the vertical magenta line with a rightward arrow in
Figure 2), the expected diffusion length is comparable to oreven greater than ∼0.3 μm. Therefore, if the original size
distribution of presolar grains is limited to below ∼0.3 μm
following the grain size distribution in the ISM (Mathis
et al. 1977; Nozawa & Fukugita 2013), no presolar grains inthese chondrites can keep their original isotopic compositions,because of isotopic diffusion. Note that both isotopic diffusion
and thermal metamorphism may be able to delete the original
information of presolar grains in these highly thermalizedchondrites. Nonetheless, if the process of isotopic diffusion ismore efﬁcient in affecting their original isotopic composition
than thermal metamorphism, then there is a chance of ﬁnding alarge presolar grain of >1 μm in chondrites of types 4–6. As
demonstrated above, their minimum sizes give valuable hints tothe maximum temperatures experienced by the parent bodies.
Therefore, the search for presolar grains in such fully
metamorphosed meteorites is highly encouraged.
Finally, it would be worth discussing the abundances ofpresolar grains in chondrites and IDPs. The abundances ofpresolar grains in IDPs are higher than those in chondrites(Messenger et al. 2003; Floss et al. 2006; Busemannet al. 2009). It is very likely that IDPs, which have neverexperienced any kind of metamorphism, can retain the mostprimitive information about the chemical composition in thesolar nebula. Thus, it may be plausible to consider that theabundance of presolar grains in IDPs represents their original
abundance in meteorites. There should be some processes that
reduce the abundances of presolar grains in chondrites: aqueousalteration and thermal metamorphism. Although these processes can explain the abundances in chondrites of types 1 and
2 and types 4–6, respectively, they cannot be effective for type
3 chondrites. Hence, isotopic diffusion may be a primaryprocess to cause the difference in abundance of presolar grains
between primitive chondrites and IDPs.
As we examine the diffusion of 18O in thermally evolving
planetesimals, we can also apply the same approach to the
diffusion of other atoms. There are two interesting presolar
silicate grains (∼0.2 μm) that were found in an ungroupedcarbonaceous chondrite (type 2 or 3) and have a few
nanometers of iron-rich rims (Floss & Stadermann 2012).
This discovery suggests that these rims might be an outcomeof a kinetic process or a diffusion process. We estimate thediffusion length of iron using Equation (3) with the diffusion
coefﬁcient of iron in olivine, which is described in terms oftemperature, oxygen fugacity, and iron content (Miyamoto
et al. 2002; Dohmen & Chakraborty 2007). At any
temperature, the diffusion coefﬁcient of iron would be muchlarger than that of 18O. Thus, iron can easily diffuse into
whole grains while oxygen retains its original content. When
we assume an iron content of Fe/(Fe+Mg)=0.5, thediffusion length of iron would be of the order of a nanometer
when the maximum temperature is about 200°C. Hence, thediffusion process could explain a thin Fe-rich rim around thepresolar grains while they keep the original oxygen isotopic
composition that they had when they were in such a lightly
heated parent body.
In this paper, we have examined an isotopic diffusion
process in thermally evolving planetesimals, which has neverbeen investigated carefully. We ﬁnd that the diffusion can be

We thank an anonymous referee for helpful comments andsuggestions. Numerical computations were carried out on the
PC cluster at Center for Computational Astrophysics, National
Astronomical Observatory of Japan. S.W. thanks Hiroyuki R.
Takahashi for discussions about numerical simulations. T.N.
has been supported in part by a JSPS Grant-in-Aid for
Scientiﬁc Research (26400223). Part of this research was
carried out at JPL/Caltech under a contract with NASA. Y.H.
is supported by JPL/Caltech.
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