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

0.2 MB·

by  S. Wakita

Draftversion January25,2017
PreprinttypesetusingLATEXstyleAASTeX6v.1.0
DIFFUSION OF OXYGEN ISOTOPES IN THERMALLY EVOLVING PLANETESIMALS AND SIZE RANGES
OF PRESOLAR SILICATE GRAINS
Shigeru Wakita1, Takaya Nozawa2, and Yasuhiro Hasegawa3
1
CenterforComputational Astrophysics,NationalAstronomicalObservatoryofJapan,Mitaka,Tokyo181-8588,Japan; [email protected]
7 2
DivisionofTheoreticalAstronomy,NationalAstronomicalObservatoryofJapan,Mitaka,Tokyo181-8588, Japan
1
3
JetPropulsionLaboratory,CaliforniaInstitute ofTechnology, Pasadena, CA91109, USA
0
2
ABSTRACT
n
a Presolar grains are small particles found in meteorites through their isotopic compositions which are
J considerablydifferent from those of materials in the Solar System. If some isotopes in presolargrains

3 diffused out beyond their grain sizes when they were embedded in parent bodies of meteorites, their
2
isotopic compositions could be washed out, and hence the grains cannot be identified as presolar

grains any more. We explore this possibility for the first time by self-consistently simulating the
]
P thermal evolution of planetesimals and the diffusion length of 18O in presolar silicate grains. Our
E results show that presolar silicate grains smaller than ∼ 0.03µm cannot keep their original isotopic
. ◦
h compositionsevenifthehostplanetesimalsexperiencedmaximumtemperatureaslowas600 C.Since
p this temperature corresponds to the one experienced by petrologic type 3 chondrites, the isotopic
-
diffusion can constrain the size of presolar silicate grains discovered in such chondrites to be larger
o
r than ∼ 0.03µm. We also find that the diffusion lengths of 18O reach ∼ 0.3−2µm in planetesimals
t ◦
s that were heated up to 700-800 C. This indicates that, if the original size of presolar grains spans
a a range from ∼0.001µm to ∼0.3µm like that in the interstellar medium, the isotopic records of the
[
presolar grains may be almost completely lost in such highly thermalized parent bodies. We propose

1
thatisotopicdiffusioncouldbeakeyprocesstocontrolthesizedistributionandabundanceofpresolar
v
grains in some types of chondrites.
6
6 Keywords: meteorites, meteors, meteoroids – planets and satellites: formation – diffusion
6
6
0 1. INTRODUCTION withradiiof0.1-1µmintotheinterstellarmedium(ISM,
. e.g., Nozawa et al. 2007; Yasuda & Kozasa 2012). On
1 Primitive meteorites contain unique tiny materials
0 called presolar grains. The fundamental property of the the otherhand,while they weretravelingto the presolar
7 nebula, many of them might be fragmented into grains
presolar grains is their isotopic compositions, which are
1
smaller than 0.1µm due to shattering in the interstel-
: largely deviated from extremely homogeneous values of
v lar turbulences (Hirashita & Yan 2009). It is nonethe-
materialsintheSolarSystem. Inparticular,presolarsil-
i
X icate grains are identified via the oxygen isotopic ratios less important to point out that such small (< 0.1µm)
r of 17O/16O and 18O/16O (e.g., Clayton & Nittler 2004). presolargrainshavebeenrarelydetectedinthecurrently
a available samples; the typical size distribution of preso-
Since such isotopic anomalies have to be preserved over
lar silicate grains spans the range from ∼ 0.1 to ∼ 1 µm
the entire history of the Solar System (that’s why we
(e.g.,Zinner2003;Hynes & Gyngard2009;Nguyen et al.
can currently measure the differences in isotopic com-
2010; Leitner et al. 2012; Hoppe et al. 2015).
position), investigation of presolar grains can provide us
The abundance of presolar grains varies among differ-
with important clues to understand the formation and
ent petrologic types of meteorites: in general, presolar
evolution of the Solar System.
grains are the most abundant in type 3, and as the type
It is considered that the presolar grains originally
number increasesfrom 3 to 6, the abundance of presolar
formedinnearbystarsatthepost-mainsequencephases
grainsdecreases(Huss 1990;Huss & Lewis1995). These
such as supernovae and/or asymptotic giant branch
types are based on the degree of metamorphism experi-
(AGB)stars. Thentheyweretransportedtothepresolar
enced by meteorites when they were embedded in plan-
nebular that is a pre-stage of forming the Sun, and were
etesimals. Sincethemetamorphismdependsonthetem-
finally incorporated into planetesimals that are parent
perature, petrologic types are regarded as representing
bodies of meteorites. Some of theoretical studies sug-
a peak temperature experienced by the planetesimals.
gest that dying stars could inject relatively large grains
2
For instance, it is widely accepted that the petrologic 2. ISOTOPIC DIFFUSION IN THERMALLY
type 3 ordinary chondrites experienced a peak temper- EVOLVING PLANETESIMALS
◦ ◦
ature less than 700 C, type 6 did higher than 800 C,
Inorderto computethe diffusionlengthofoxygeniso-
and types 4 and 5 did between them (Huss et al. 2006).
topesinpresolarsilicategrains,weadoptadiffusioncoef-
Thus, this classification suggests that the abundance of ficient of 18O in olivine from Dohmen et al. (2002). The
presolar grains may be related to the thermal history of
diffusion coefficient D(T) is given as
planetesimals.
It is implicitly presumed that the metamorphism to- D(T)=10−8.34exp(−3.38×105/RT), (1)
tally erases the isotopic records of presolar grains. This whereRisthegasconstant[J/K/mol]andT isthe tem-
may be because the metamorphism creates new min- perature [K]. Since the diffusion coefficient is obtained
erals or crystalline structures by breaking the origi- for a temperature range of 1100 ◦C < T < 1500 ◦C
nal atomic bonds and forming new bonds. If the (Dohmen et al. 2002), we extrapolate the results down
metamorphism would be the dominant process to tolowertemperatures. Measurementswiththetransmis-
wash out the isotopic compositions, more presolar sionelectron microscope show that the chemical compo-
grains would be discovered in unmetamorphosed (prim- sitionsofpresolarsilicategrainsvaryonthescaleofafew
itive) chondrites. While the abundance of presolar tens nanometer (Nguyen et al. 2007; Busemann et al.
grains in the least metamorphosed type 3 chondrites 2009; Leitner et al. 2012). While it would be interesting
have the highest abundance of presolar grains among toseehowthediffusioncoefficientsdependonstoichiom-
chondrites (Nguyen et al. 2007; Floss & Stadermann etry of elements in silicate, there is no data for silicate
2009; Nguyen et al. 2010; Floss & Stadermann 2012; compositions with a variety of Mg/O, Fe/O and Si/O
Nittler et al.2013), itisstillmuchlowerthanthatinin- ratios. Thus, we assume that grains have homogeneous
terplanetary dust particles (IDPs) regarded as the most composition of Mg-rich forsterite used in Dohmen et al.
primitive materials (Messenger et al. 2003; Floss et al. (2002).
2006; Busemann et al. 2009). Therefore, the metamor- As can be seen from Equation (1), the diffusion co-
phism would not explain the difference in abundance of efficient strongly depends on the temperature. Thus,
presolargrains betweentype 3 chondrites andIDPs. On we need to numerically simulate thermal evolution of
theotherhand,evenifchemicalcompositionsofminerals planetesimals to reliably estimate the diffusion length of
arenotchangedthroughthemetamorphism,thereplace- 18O in silicate. We assume that decay energy of short-
ment of an atom with another one, so-called atomic dif- livedradioisotope26Alheatsupmaterialswithinaplan-
fusion,couldberealizedinslightlythermalizedplanetes- etesimal as most thermal modelling studies did (e.g.,
imals. Therefore, it can be anticipated that the atomic Miyamoto et al. 1982). A heat conduction equation,
diffusioncanalsodeletetheoriginalisotopiccomposition
∂T 1 ∂ ∂T
possessed by presolar grains in their parent bodies. ρc = r2K +Aexp(−λt), (2)
∂t r2∂r (cid:18) ∂r(cid:19)
In this paper we explore this possibility for the first
timebycomputingthediffusionlengthof18Oinpresolar is solved numerically based on Wakita et al. (2014),
silicategrainsinmeteoritesandbycomparingitwiththe where t is time measured from the formation time of
actually measured size of presolar grains. Since the dif- planetesimals t , r is the distance from the center of the
0
fusion length is sensitive to the temperature, we numer- planetesimals, A is the radiogenic heat generation rate
ically simulate thermal evolution of planetesimals with per unit volume, and λ is the decay constant of the ra-
different radii and formation times. We find that the dionuclides. We adopt physical parameters of thermal
diffusion process of oxygen atoms can regulate the size conductivity K= 2 [J/s/m/K],density ρ= 3300 [kg/m3]
distribution of presolar silicate grains and that only the andspecific heatc =910[J/kg/K](Yomogida & Matsui
grains larger than ∼ 0.3µm can keep their original iso- 1983; Opeil et al. 2010). We assume that these param-
topicpropertiesintypes4-6chondrites. Ourresultsalso eters do not depend on the temperature. Radius and
suggest that, even in type 3 chondrites that experienced formation time of planetesimals, both of which are ex-
◦
only a peak temperature of 600 C, the atomic diffusion pected to affect a maximum temperature achieved by
canentirely erode the isotope records of presolarsilicate planetesimals (see Figure 8 in Wakita et al. 2014), are
grains smaller than ∼0.03µm. This may be viewed as a parameterized; the formation time of planetesimals t
0
potentialexplanationofwhythecurrentlyavailablesam- is determined based on a formation time of Ca-Al-rich
ples of presolar silicate grains in type 3 chondrites have inclusions(CAIs), 4567Myr ago,when they hadthe ini-
asizelargerthan∼0.05µm. Thus,weconcludethatiso- tial ratio of 26Al/27Al =5.25×10−5 in the solar nebula
topic diffusion is one of the important processes to gov- (e.g., Connelly et al. 2012). The radiogenic heat gener-
ern the survival of presolar grains in thermally evolving ation rate A falls in direct proportion to the initial ra-
planetesimals. tio of26Al/27Al, whichdepends onthe formationtiming
3
of planetesimals t (see Figure 15 in Wakita & Sekiya Wealsofindthatthediffusionlengthof18Ocanbeap-
0
2011); since the abundance of 26Al decreases with time proximately described as a following analytical formula,
(half-life of 26Al is 0.72 Myr), a planetesimal formed at
L2 =D(T )∆t , (3)
max max
a later time has less heating sources than that formed
earlier. where ∆t is the duration time of the maximum tem-
max
A diffusion length (L) is calculated as dL2 = D(T)dt perature T . Figure 2 represents the diffusion lengths
max
at each time step during the thermal evolution of plan- obtained from numericalsimulations and from Equation
etesimals. Ittakesabout103yearstodiffuse18Oentirely (3) with ∆t = 1 Myr as a function of maximum
max
inparticleswiththe sizeof1µmat1000◦C andamuch temperature. It should be emphasized that the depen-
longertime (109 years)is neededat600◦C.These times dence of the diffusion length on the maximum tempera-
are long enough compared with the time step for calcu- turefollowsasimplerelationandisreasonablydescribed
lating the thermalevolutionofplanetesimals (dt), which as a function of T by Equation (3). The maximum
max
is an order of one year. We compute the cumulated dif- temperature achieved at each location of planetesimals
fusion length of 18O given by L2 = dL2. We assume decreases with increasing radius. Thus, each curve in
t
thatplanetesimals do notexperiencePany kindof disrup- Figure 2 can be viewed as representing the radial de-
tions after the formation. pendence of diffusion length, where the longest diffusion
Figure 1 shows the temperature evolutions at the cen- length is achieved at the center of planetesimals. While
ter of planetesimals (dashed lines) and the accumulated weadopt∆t =1MyrinEquation(3),whichisatyp-
max
diffusionlengthof18O(solidlines)forplanetesimalswith icaldurationtimeofplanetesimalswith50kminradius,
different radii (50 km and 100 km) and formation times it works well for planetesimals with the radius of 100
(t = 1.9 Myr and 2.4 Myr). The results show that the km. Thus, our results demonstrate that our analytical
0
temperature evolution controls the time development of formula (Equation (3)) reproduces the numerical results
diffusion length: as the temperature increases, the dif- very well and the maximum temperature can be used as
fusion length becomes longer. When the temperature an indicator to estimate the diffusion length of 18O.
starts to decrease,the increase in diffusion length ceases
3. DISCUSSION AND CONCLUSIONS
(see the left panels of Figure. 1). Since we evaluate
the cumulated diffusion length, it does not decrease af- Here we discuss the implications of our results for
ter temperature starts to drop. This means that the the size distribution and abundances of presolar grains
maximum temperature governs diffusion length of 18O in various petrologic types of meteorites. In Figure
in grains. 2, we compare the calculated diffusion lengths with
Our results also indicate that for larger planetesimals the size ranges of presolar silicate grains obtained from
(see the right panels of Figure 1), the diffusion length meteorites. For two data points on grain sizes, the
at the center gradually increases even after the temper- vertical error bars cover the maximum and the mini-
ature reaches the maximum value. This arises because mum sizes, and the horizontal ones are the suggested
largerplanetesimalscankeepthemaximumtemperature ranges of peak metamorphic temperatures. The sizes of
foralongertime thansmallerones(see Figure1(b)and presolar silicate grains are 0.1-1.7 µm and 0.07-0.6 µm
(d)). It should be noted that the maximum tempera- in petrologic types 1-2 and 3 chondrites, respectively
ture, accordingly diffusion length, is more sensitive to (Zinner 2003; Hynes & Gyngard 2009; Nguyen et al.
theformationtimesofplanetesimalsthantheirradii. As 2010; Leitner et al. 2012; Hoppe et al.2015). The meta-
seen from Figure 1, the diffusion lengths of planetesi- morphic temperature of type 3 chondrites is likely to be
mals formed at earlier times (t = 1.9 Myr, top panels between500◦Cand700◦C(Huss et al.2006;Krot et al.
0
of Figure 1) are much longer (>∼ 10−4 m) than those 2007),whereasthatoftypes1and2 carbonaceouschon-
(<∼ 10−6 m) formed at later times (t = 2.4 Myr, bot- drites might be around 100 ◦C (Krot et al. 2015).
0
tom panels of Figure 1). This is because, if their sizes The maximum temperature governs the diffusion
are the same, the planetesimals formed at earlierepochs lengths. The length is ∼ 0.001µm when the maximum
have more abundant 26Al and reach a higher maximum temperature is 500 ◦C. If planetesimals reach the max-
temperature. Notethattheaboveresultsareobtainedat imum temperature of 700 ◦C, the diffusion length is
thecentralregionofplanetesimals. Thediffusionlengths ∼ 0.3µm. Hence, the diffusion length of 18O in silicate
are different at different radii of planetesimals. As men- grains in type 3 chondrites ranges from ∼ 0.001µm to
tioned above,the resultant diffusion length is a function ∼0.3µm, depending on the maximum temperature that
of only the maximum temperature. Therefore, we can they experienced. This indicates that, once we know
estimate a diffusion length at every location of planetes- the minimum size of presolar silicate grains, we can es-
imals by simply referring to the maximum temperature timate the maximum temperature of their parent bod-
achieved there. ies. For example, chondrites which contain the smallest
4
Figure 1. Temperature evolutions at the center of planetesimals (dashed lines with left axes) and the corresponding
evolutions of diffusion lengths of 18O in olivine (solid lines with right axes) as a function of time after CAI formation.
Each panel gives the result for planetesimals with radii of (a) 50 km and (b) 100 km formed at 1.9 Myr after CAI
formation, and with radii of (c) 50 km and (d) 100 km formed at 2.4 Myr after CAI formation.
presolar silicate grains of 0.07 µm would not experience chondrites (Cody et al. 2008). If this is true, our results
◦
a peak temperature higher than 630 C when they were imply that the original abundance of presolar silicate
embedded in their parent bodies. Our calculations im- grainswouldbekeptinsuchtype3.0and3.1chondrites.
plythat,eveniftypicaltype3chondriteshaveundergone In fact, it is interesting to notice that a type 3.0 chon-
◦
the peak temperature of 600 C, presolar grains smaller drite, ALHA 77307 is placed as one of primitive chon-
than ∼ 0.03µm can lose their oxygen isotopic anomaly drites having the highest abundance of presolar silicate
duetotheisotopicdiffusion. Thismaybeoneoftherea- grains among type 3 chondrites (Nguyen et al. 2007).
sons why we cannot discover such small presolar silicate Although the subtypes of type 3 chondrites cannot be
grains in type 3 chondrites. clearlydistinguishedbytheirpeakmetamorphictemper-
Petrologic type 3 chondrites could be subdivided atures(e.g.,Huss et al.2006),itwouldbevaluabletosee
into types 3.0 to 3.9 based on their characteristics how the abundance of presolar silicates changes in each
of thermoluminescence and compositions of minerals subtype of type 3 chondrites.
(Sears et al.1980; Scott & Jones1990; Scott et al.1994; If the birth places of presolar silicate grains are the
Grossman & Brearley2005;Bonal et al.2006). Itissug- outflowing gas from supernovae and AGB stars, their
gestedthattype3.0and3.1chondritesexperiencedlower initial sizes could be dominantly in a range from 0.1 to
peaktemperaturesof∼200- 400◦Cthantypicaltype 3 1 µm (e.g., Ho¨fner 2008; Nozawa et al. 2007, 2015). As
5
Therefore, any size of presolar silicate grains can sur-
vive against the isotopic diffusion. However, the sizes
of presolargrains measuredin these petrologic types are
confinedtoarangefrom0.1to1.7µm,andgrainssmaller
than0.1 µm havenot beendiscoveredso far. Ingeneral,
intypes1and2chondrites,theaqueousalternationmay
have played an important role in eliminating the orig-
inal isotopic information of grains smaller than 0.1µm.
Leitner et al. (2012) suggests that an initial abundance
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 by aqueous alteration.
It should be kept in mind that there is a limitation
Figure 2. Diffusion length of 18O as a function of max- of the size measurement of presolar grains. Most of the
imum temperature, which can be translated to radial data on the size of presolar grains are obtained from in
depthoftheplanetesimal. Numericalresultsaredenoted situ measurements of a secondary ion mass spectrome-
by colored lines, while the analytical one by the black try (SIMS), whose beam size is comparable to a size of
one. For the radii and formation times of planetesimals, 0.15µm. Thisindicatesthatsignificantamountsofpreso-
we adopt the same values as in Figure 1 and the param- lar grains with that size or smaller could be undetected.
eter set for each line is given in the legend of the figure. An optimized setting of NanoSIMS makes it possible to
The shaded region denotes a regime where diffusion can identify smaller (<0.1µm) presolar grains (Hoppe et al.
leadtocompleteerosionofpresolargrainswithacertain 2015). However, the measurements with spatial resolu-
size. Symbols with bars plot the ranges of size and peak tionof0.1µmmightsufferfrominstrumentalbiasesinde-
temperature derivedfor presolarsilicate grainsin type 3 tecting smaller grains (Nguyen et al. 2007, 2010). Thus,
(green-cricle) and types 1-2 chondrites (black-triangle). moresophisticatedtechniquesaredesiredtofindpresolar
The vertical magenta line with a rightward arrow indi- silicategrainssmallerthan0.1µmintypes1-3chondrites
cates the lower value of the peak temperatures expected and to check our scenario in which the isotopic diffusion
for types 4-6 chondrites. (and aqueous alteration) can affect the size distribution
of presolar grains surviving in planetesimals.
In types 4, 5 and 6 chondrites, which are considered
seen in Figure 2, an upper end (∼ 1µm) for the size of to have experienced the peak metamorphic temperature
◦
presolar silicate grains roughly corresponds to the max- above 700 C (the vertical magenta line with a right-
imum size of grains that could form in supernovae and ward arrow in Figure 2), the expected diffusion length
AGB stars. This implies that the largest presolar grains is comparable to or even higher than ∼ 0.3µm. There-
thatmightbeproducedinstellarsourcescansurviveany fore, if the original size distribution of presolar grains is
destructive events (e.g., Hirashita et al. 2016) and they limited below ∼0.3µm following the grain size distribu-
may contain the intact information that was recorded tioninthe ISM (Mathis et al.1977; Nozawa & Fukugita
at the time of their formation. On the other hand, 2013), all of the presolar grains cannot keep their orig-
many of the submicron-sized grains collide with each inal isotopic compositions due to the isotopic diffusion.
other and fragment into nanometer-sized grains due to Note that both the isotopic diffusion and thermal meta-
shattering in the interstellar turbulence (Hirashita et al. morphismmaybe abletodeletethe originalinformation
2010; Asano et al. 2014). Hence, presolar grains should ofpresolargrainsinthesehighlythermalizedchondrites.
also include grains smaller than 0.1µm. Nontheless, the Nontheless,iftheisotopicdiffusionisamoreefficientpro-
size (∼ 0.1µm) of the smallest silicate grains measured cesstoaffecttheiroriginalisotopiccompositionthanthe
in type 3 chondrites is much larger than the minimum thermal metamorphism, then there is a chance to find a
size (∼ 0.001µm) of interstellar dust. In fact, the criti- largepresolargrainof>1µmintypes4-6chondrites. As
cal value of 0.1µm coincides with a cumulated diffusion demonstrated above, their minimum sizes have valuable
lengthexpected fromourresults. This may suggestthat hints to the maximum temperatures experienced by the
the smallest size of presolar grains in type 3 chondrites parent bodies. Therefore, the search for presolar grains
might be determined by the diffusion process triggered insuchfullymetamorphosedmeteoritesishighlyencour-
in thermally evolving planetesimals. aged.
For types 1 and 2 chondrites, which experienced only Finally,itwouldbeworthdiscussingtheabundancesof
the peak metamorphic temperatures of ∼150◦C or less, presolargrainsinchondritesandinterplanetarydustpar-
theexpecteddiffusionlengthsof18Oareextremelyshort. ticles(IDPs). TheabundancesofpresolargrainsinIDPs
6
are higher than those in chondrites (Messenger et al. isotopes in variety of minerals provided that their diffu-
2003;Floss et al.2006;Busemann et al.2009). Itisvery sioncoefficientsaregiven. Themeasuredsizesofpresolar
likelythatIDPs,whichhaveneverexperiencedanykinds grains,combinedwiththesimulationsofdiffusionlengths
ofmetamorphisms,cankeepthemostprimitiveinforma- of the relevant isotopes, will surely advance the under-
tionaboutthe chemicalcompositioninthe solarnebula. standing of presolar grains and parent bodies of their
Thus, it may be plausible to consider that the abun- host meteorites.
dance of presolar grains in IDPs represents the original
abundanceofpresolargrainsinmeteorites. Thereshould
We thank an anonymous referee for helpful comments
be some processes to reduce the abundances of preso-
and suggestions. Numerical computations were carried
lar grains in chondrites: aqueous alteration and thermal
out on PC cluster at Center for Computational Astro-
metamorphism. Although these processes can explain
physics,NationalAstronomicalObservatoryofJapan. S.
the abundances in types 1-2 and 4-6 chondrites, respec-
W. thanks Hiroyuki R. Takahashi for discussions about
tively, they cannot be effective for type 3 chondrites.
numerical simulations. T. N. has been supported in
Hence, the isotopic diffusion may be a primary process
part by a JSPS Grant-in-Aid for Scientific Research
to cause the difference in abundance of presolar grains
(26400223). The part of this research was carried out
between primitive chondrites and IDPs.
at JPL/Caltech under a contract with NASA. Y. H. is
Asweexaminethe diffusionof18Ointhermallyevolv-
supported by JPL/Caltech.
ing planetesimals, we can also apply the same approach
to the diffusion process of other atoms. There are two
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