Planetary and Space Science 133 (2016) 17–22

Contents lists available at ScienceDirect

Planetary and Space Sciencejournal homepage: www.elsevier.com/locate/pss

Revisiting the lifetime estimate of large presolar grainsin the interstellar medium
Hiroyuki Hirashita a,n, Takaya Nozawa b, Ryosuke S. Asano c, Typhoon Lee aa

Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141, Taipei 10617, Taiwan
National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japanc
Department of Particle and Astrophysical Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japanb

art ic l e i nf o

a b s t r a c t

Article history:
Received 10 November 2015
Received in revised form
5 February 2016
Accepted 11 February 2016
Available online 22 February 2016

Some very large ð 40:1 μmÞ presolar grains are sampled in meteorites. We reconsider the lifetime of verylarge grains (VLGs) in the interstellar medium focusing on interstellar shattering caused by turbulenceinduced large velocity dispersions. This path has never been noted as a dominant mechanism ofdestruction. We show that, if interstellar shattering is the main mechanism of destruction of VLGs, their
lifetime is estimated to be ≳108 yr; in particular, very large SiC grains can survive for  1 Gyr. The lifetimes obtained for VLGs are comparable to the longest residence time derived for some presolar grains
based on the cosmic-ray exposure time. However, most presolar SiC grains show residence times signiﬁcantly shorter than 1 Gyr, which may indicate that there is a more efﬁcient mechanism than shattering in destroying VLGs, or that VLGs have larger velocity dispersions than 10 km s  1. We also argue
that the enhanced lifetime of SiC relative to graphite can be the reason why we ﬁnd SiC among μm-sizedpresolar grains, while the abundance of SiC in the normal interstellar grains is much lower than graphite.
& 2016 Elsevier Ltd. All rights reserved.

Keywords:
Dust
Galaxy evolution
Meteorites
Milky Way
Presolar grains

1. Introduction
The elemental and isotopic compositions of presolar grains
found in primitive meteorites provide us with clues to their origins. The peculiar isotopic ratios obtained for presolar grains, suchas nanodiamonds, silicon carbide (SiC), and graphite, indicate thatthey are formed in the environments around particular types ofstars (Anders and Zinner, 1993; Zinner, 2014). SiC is the species
with the most detailed studies because it is relatively easy to be
separated from the other substances in meteorites and its hightrace element abundance allows us to perform isotope studies on amultitude of elements. Also, SiC is one of the most abundant μmsized (in this paper, sizes are given as radius)1 species identiﬁed inpresolar grains (Amari et al., 1994). Most of the SiC grains aredeﬁned as mainstream grains, which have 12C/13C isotope
ratio ¼10–100 (the solar ratio is 89) and enhanced 14N/15N ð 4 272¼ solarÞ (e.g., Amari et al., 2001). The isotopic abundances in themainstream SiC grains indicate an asymptotic giant branch (AGB)
star origin (e.g., Gallino et al., 1994; Lugaro et al., 2003). PresolarnCorresponding author.
E-mail address: hirashita@asiaa.sinica.edu.tw (H. Hirashita).
1
However, a factor 2 difference in size does not matter for most of the statements in the Introduction. Whenever precision is required, we use the word
“radius” or the notation a.
http://dx.doi.org/10.1016/j.pss.2016.02.006
0032-0633/& 2016 Elsevier Ltd. All rights reserved.

graphite grains are also identiﬁed: Amari et al. (2014) analyzed
presolar graphite grains extracted from the Murchison meteorite,and showed based on isotopic ratios of various elements that someof them originated from supernovae and others from AGB stars.
Theoretical studies of dust condensation in AGB star winds alsosuggest that large ð≳0:1 μmÞ SiC grains form (Yasuda and Kozasa,2012). In this paper, we refer to grains larger than 0.1 μm as verylarge grains (VLGs).2
After analysis of noble gas elements in SiC grains found inprimitive meteorites, Lewis et al. (1990) showed that their isotopic
and elemental ratios are consistent with the values theoretically
expected for AGB stars. They also derived their presolar cosmic-ray
exposure age (or residence time)  135 Myr based on the 21Ne
abundance. Heck et al. (2009) inferred interstellar residence times
of presolar SiC as 3–1100 Myr for large (diameter  5–50 μm)
presolar SiC grains. The residence times estimated may be uncertain because recoil losses of Ne from μm-sized grains are large. The
measurement of spallation xenon (Xe), which is much less affectedby recoil loss, suggested shorter cosmic-ray exposure ages o 200
2
The term ‘large grain’ or ‘big grain’ is often used to indicate the grain
population which dominates the far-infrared emission, and it refers to such a size
range as  0.01–0.25 μm (Désert et al., 1990; Li and Draine, 2001). To avoid confusion with this convention, we refer to large grains of interest in this paper
as VLGs.

18

H. Hirashita et al. / Planetary and Space Science 133 (2016) 17–22

Myr (Ott et al., 2005). Gyngard et al. (2009) estimated that theinterstellar exposure ages are 40 Myr–1 Gyr using 6Li excesses inpresolar SiC grains. These exposure ages give us clues to the lifetime (or residence time) of VLGs in the interstellar medium (ISM).
Since AGB stars are one of the most important sources of theinterstellar dust (Ferrarotti and Gail, 2006; Ventura et al., 2012),
the lifetime of dust grains formed in AGB stars is an important
quantity in considering the lifecycle of dust in the ISM.
There have been some attempts of direct sampling of interstellar dust using dust-detecting instruments on spacecraft such as
Ulysses (Grün et al., 1994; Baguhl et al., 1995; Krüger et al., 2015),
Galileo (Baguhl et al., 1996), Helios (Altobelli et al., 2006), Cassini(Altobelli et al., 2003), and Stardust (Westphal et al., 2014). They
indeed detected μm-sized grains whose velocities point to theirinterstellar origin. Interstellar grains smaller than  0.1 μm areexpelled by the solar radiation pressure and/or deﬂected by theinterplanetary magnetic ﬁeld (Levy and Jokipii, 1976; Sterken et al.,2013). Although the interpretation depends on the modeling of
the radiation pressure and gravity of the Sun and the magnetic
ﬁeld in the solar system (Sterken et al., 2013), the large abundanceof VLGs measured by the above spacecraft implies the existenceof a signiﬁcant abundance of grains larger than 0.1 μm in
the ISM.
The lifetime of dust grains in the ISM is governed by destructive
processes, among which the most violent one is believed to besupernova shocks. Assuming tight coupling between the motionsof gas and dust, Jones et al. (1996) argued that shattering insupernova shocks is the major destruction path for large ≳0:1 μm
grains and estimated the typical lifetime of the interstellar grains
to be  a few  108 yr. However, VLGs are not necessarily coupledwith the gas motion in the ISM. Indeed, Slavin et al. (2004)
showed, solving explicitly the grain trajectories in the presence ofmagnetic ﬁeld, that decoupling of the gas and dust is important for
grains with radii 4 0:1 μm in supernova shocks. Therefore, VLGs
may have lifetimes much longer than  108 yr, unless there isanother mechanism of limiting the lifetimes.
Although VLGs are decoupled from small-scale motions in the
ISM, they are coupled with a large-scale (  10–100 pc) turbulent
and magnetohydrodynamic motion in the ISM (Yan et al., 2004).
Based on an analytical kinetic theory of dust grains, Yan et al.
(2004) showed that grains larger than  0.1 μm can obtain random velocities as large as 10 km s  1 in the diffuse ISM. Using theirresults, Hirashita and Yan (2009) showed that VLGs are efﬁciently
disrupted by shattering in the diffuse ISM. Therefore, even if VLGs
escape from supernova shocks by being decoupled from thegas motion, shattering in the diffuse ISM is unavoidable. This
new destruction mechanism, not related to shocks, is worth
considering for the purpose of constraining the lifetime of
VLGs.
The existence of VLGs is also important in the following two
aspects. One is that the size range is around the upper mass cut-off
of grain radius of the grain size distribution in the ISM. A grain size
distribution nðaÞ p a  3:5 (a is the grain radius) with an upper cut ofgrain radius at 0.25 μm explains the Milky Way extinction curve(Mathis et al., 1977, hereafter MRN). More elaborate models for thegrain size distribution also show a fall-off just above a similar grainradius (  0.25 μm), although it is not a rigid cut-off (Weingartnerand Draine, 2001). The other important aspect of VLGs is that asigniﬁcant fraction of the total dust mass is occupied by grains
whose sizes are around the upper cut (fall)-off (  0.1 μm). If weassume that MRN grain size distribution in a grain radius range of
0.001–0.25 μm, the VLG regime ð 4 0:1 μmÞ contains 39 percent of
the dust mass. Therefore, the lifetime of VLGs has a large impact
on the total dust abundance in the ISM.
In this paper, we reconsider the lifetime of VLGs, focusing on
shattering in the diffuse ISM. This process has not been considered

to determine the VLG lifetime in previous studies. Moreover, as
mentioned above, VLGs may be decoupled from supernova shocks.
This means that the ‘classical' picture in which the lifetime of dust
grains is determined by the shock destruction may not bevalid for VLGs. Therefore, the new destruction mechanism of
VLGs proposed in this paper will give a new upper limit for
the lifetime of VLGs. The lifetime estimated in this paper iscompared with the residence time of presolar grains inferredfrom isotopic measurements. Here, the residence time indicates the time spent in the ISM before the formation of the solar
system.
The paper is organized as follows: we explain the formulation
adopted to estimate the lifetime of VLGs in Section 2. We show theresults in Section 3. We discuss the signiﬁcance of the results in
Section 4. Finally we conclude in Section 5.

2. Models for shattering
2.1. Collision rate
We consider a VLG once formed in stellar ejecta and injected
into the ISM. We denote the radius and root-mean-square (rms)velocity of a VLG as aVLG and vVLG , respectively. For simplicity, we
assume that all VLGs have the same velocity vVLG since the velocity
distribution function of grains in turbulent medium is unknown.3
The interstellar turbulence is a viable mechanism that causes therandom velocities of grains (e.g., Völk et al., 1980). Since largersized grains are coupled with larger-scale motions in the ISM andlarger-scale turbulent motions usually have larger velocity dispersions (e.g., Yan et al., 2004; Ormel and Cuzzi, 2007), we assume
that VLGs obtain the largest velocity dispersions, as large as 10 km s  1 (this value is taken from the velocity dispersion of the
diffuse neutral ISM in the solar vicinity; Spitzer, 1978; Mathis,2000). This means that we can approximate the collisional velocity
between a VLG and a grain in the ISM (referred to as an ISM grainin this paper) with vVLG  10 km s  1, which is treated as a constantparameter in this paper.
While a VLG travels in the ISM, it encounters the ISM grains.
The grain size distribution of the ISM grains, n(a), is deﬁned so thatnðaÞ da is the number density of grains whose sizes are between a
and a þ da. The rate at which a VLG traveling in the ISM encounters
the ISM grains with radii between a and a þ da is denoted as df colland estimated as
df coll ¼ π ðaVLG þ aÞ2 vVLG nðaÞ da:ð1Þ

2.2. Destroyed fraction
In collision with an ISM grain, a certain fraction of the VLG is
destroyed by shattering. In what follows, we adopt the formulation in Kobayashi and Tanaka (2010) to estimate the shattered fraction (the fraction of the volume fragmented into
smaller grains) of a VLG. They estimate the shattered fraction ofa grain as
F sh ¼

ϕ

;
1þϕ

ð2Þ

3
This assumption is not likely to affect the results signiﬁcantly. As shown in
Section 3, the destruction rate of a VLG is proportional to v3, where v is the velocityof the VLG. If the velocity distribution function, f(v), follows the Gaussian weighted
32
2
by the phase-space volume (f ðvÞ ¼ ðl =π 3=2 Þexpð  l v2 Þ  4π v2 , where l ¼ 3=ð2〈v2 〉Þ,we obtain 〈v3 〉 ¼ 1:23〈v2 〉3=2 , where 〈  〉 means the ensemble average. Thus, if we
represent the velocity vVLG with the rms velocity 〈v2 〉1=2 , v3VLG ¼ 〈v2 〉3=2 approximates〈v3 〉 well (unless we adopt a peculiar velocity distribution function).

H. Hirashita et al. / Planetary and Space Science 133 (2016) 17–22

19

Table 1Dust properties adopted (s, P1, and Q ⋆D ) and calculated (the others).
Speciess(g cm  3)

P1 (erg cm  3)

1)Q⋆
D (erg gητVLG a (yr)ητVLG (yr)M AGB
VLG ðM  Þ

frac.b (%)

Silicate

3.3

3  1011

4:5  1010

1:0  10  4

2:1  108

2:1  104

6:3  104

0.13

Graphite

2.2

4  1010

9:1  109

2:2  10  4

4:4  107

9:7  103

2:9  104

0.058

SiC

3.1

1:7  1012

2:7  1011

2:1  10  5

1:2  109

2:5  104

7:5  104

0.15

a
b

The lifetime is estimated at aVLG ¼ 1 μm.
Fraction to the total dust mass.

where ϕ is the impact energy normalized to the threshold
impact energy per mass for catastrophic disruption,4 Q ⋆
D:
v2
y
;
2Q D 1 þ y

ϕ ¼ VLG⋆ð3Þ

with y being the mass ratio, m=mVLG (m and mVLG are the massesof the ISM grain and the VLG, respectively).
The contribution of the ISM grains with radii between a anda þ da to the shattered fraction of a VLG per unit time is estimatedas F sh df coll . Therefore, the total shattered fraction of the VLG
increases at rate dΦ=dt estimated as
Z amaxZ amaxdΦdf
ϕ¼
F sh coll da ¼
π ðaVLG þ aÞ2 vVLG nðaÞ
da:
ð4Þ
dt
da
1þϕ
amin
amin
Note that ϕ is a function of a. If both the ISM grain and the VLG
have the same material density, y ¼ ða=aVLG Þ3 in Eq. (3). We hereafter assume this expression for y. The lifetime of the VLG isestimated as

dΦ
:
ð5Þ
τVLG ¼ 1
dt
2.3. Choice of parameter values
As mentioned in the Introduction, we are primarily interested
in SiC, which is well sampled for presolar grains, but we also
examine silicate and carbonaceous (graphite) dust as they are
known to be representative dust species in the ISM (e.g., Draineand Lee, 1984). Hirashita and Kobayashi (2013) showed that Q ⋆D isestimated using the critical pressure (P1), above which the solid
becomes plastic, as
Q⋆
DC

P1
;
2s

ð6Þ

where s is the grain material density. We list s and P1 as well as theobtained Q ⋆D for each grain species in Table 1.
Now we need to specify the grain size distribution of the ISM
grains, n(a) (Eq. (4)). We assume the MRN grain size distributionnðaÞ p a  3:5 with the minimum and maximum grain radii amin ¼
0:001 μm and amax ¼ 0:25 μm, respectively. This grain size distribution is consistent with the Milky Way extinction curve (MRN).
The results below do not change signiﬁcantly even if we adopt thegrain size distributions proposed for the Milky Way dust by
Weingartner and Draine (2001). The normalization of the grain
size distribution is determined by
Z amax
4 3
DμmH nH ¼
π a snðaÞ da;ð7Þamin 3where D is the dust-to-gas ratio, μ ¼ 1:4 is the gas mass perhydrogen nucleus, mH is the hydrogen atom mass, and nH is thenumber density of hydrogen nuclei. To ﬁx the number density of
ISM grains, we always adopt s ¼ sISM ¼ 3 g cm  3 in Eq. (7) with

Fig. 1. Lifetime of VLG against shattering as a function of radius aVLG . The solid,
dotted, and dashed lines show the results for SiC, silicate, and graphite,
respectively.

D ¼ 0:01 for the ISM grains. We adopt nH ¼ 0:25 cm  3 (Jones et al.,1996) for the typical density for the diffuse ISM, keeping in mind
that the grain lifetime is proportional to nH 1 . We also assume that
VLGs spend most of their lifetime in the diffuse ISM before being
incorporated into the molecular cloud from which the solar system
was formed.

3. Result and analysis
We calculate the lifetime of VLGs, τVLG , using the method
described in the previous section. In Fig. 1, we show τVLG as afunction of VLG radius aVLG for the three dust species. We observethat SiC VLGs have lifetimes longer than 108 yr, while silicate andgraphite VLGs have signiﬁcantly shorter lifetimes than SiC VLGs. In
particular, SiC grains with aVLG ≳1 μm (the radii appropriate for
actually sampled SiC VLGs) survive for more than 1 Gyr as long as
shattering in the ISM is the main mechanism of grain destruction.
The above result can be roughly reproduced by an analytic
argument as follows. As long as we consider VLGs, aVLG ⪢a or y⪡1
gives a good approximation for most of the collisions. Therefore,ϕ C v2VLG ða=aVLG Þ3 =ð2Q ⋆D Þ. Since a o 0:25 μm, ϕ≲1 holds for
aVLG ≳1 μm, which means that ϕ=ð1 þ ϕÞ C ϕ. With these approximations, Eq. (4), combined with Eq. (7), is reduced to the following expression for τVLG ¼ ðdΦ=dtÞ  1 :τVLG C

8aVLG Q ⋆D sISM
C 1:2
3v3VLG DμmH nH


4

Catastrophic disruption is deﬁned as a disruption event in which a signiﬁcant
fraction (half in the deﬁnition of Kobayashi and Tanaka, 2010) of the grain isshattered.

109 yr

aVLG
1 μm



Q⋆
D
2:7  1011 erg g  1

!

sISM
3 g cm  3

20

H. Hirashita et al. / Planetary and Space Science 133 (2016) 17–22  3 D   1
1
vVLG
nH
:

1

3
0:01
10 km s0:25 cm

ð8Þ

This explains the values of τVLG at aVLG ≳1 μm in Fig. 1. At
aVLG o1 μm, the proportionality ðτVLG p aVLG Þ does not hold primarily because the approximation of ϕ⪡1 does not hold. Yet, theabove expression gives a good approximation within a factor of
2 for the entire regime of VLG (i.e., aVLG 4 0:1 μm).
The above results indicate that SiC VLGs have long lifetimes
against interstellar shattering because of its high Q ⋆D value, andthat, as a grain becomes larger, its lifetime becomes longer. Thissuggests that SiC VLGs tend to preserve the memory of its formation site more than silicate and graphite, which have shorter
lifetimes.

4. Discussion
We discuss the implication of the lifetimes estimated above.
We focus on the comparison with presolar grains, whose residence
times in the ISM can actually be obtained. We also discuss the
expected abundance of VLGs in the ISM.
4.1. Comparison with presolar grains
The lifetime given above provides an upper limit for the residence time of presolar grains in the ISM. Experimentally, theresidence time of presolar grains in the ISM can be constrained byusing the excesses of spallogenic isotopes, from which one canderive the ﬂuence of cosmic rays, hence the exposure time.
Gyngard et al. (2009) estimated that the interstellar exposure
ages are 40 Myr–1 Gyr using 6Li excesses in presolar SiC grains
with radii 4 1 μm. The range is consistent with the lifetime estimated above (note that the lifetime gives an upper limit for the
residence time). Based on cosmogenic 3He and 21Ne, Heck et al.
(2009) derived the interstellar exposure ages as  3–200 Myr for
most of the sampled presolar SiC grains with radii 4 1 μm,
although a few grains show longer interstellar residence times of
400 Myr to 1 Gyr. It seems that most of the sampled SiC grainsshow much shorter residence times than the lifetime estimated inthis paper. Moreover, no trend of exposure ages with grain size isobserved in their sample, which is not in accordance with our
expectation that larger grains have longer lifetimes. Since theestimations of exposure age also have uncertainties in the correction for recoil losses of the elements and the poorly known
Galactic cosmic ray ﬂux at the formation epoch of the solar system,
it is still premature to judge whether or not we need to take these
discrepancies seriously.
It is worth mentioning that the estimated VLG lifetime is sensitive to the assumed velocity, vVLG (Eq. (8)). If we adopt a larger
value for the velocity, for example, vVLG ¼ 20 km s  1 as expectedby the acceleration by gyroresonance in the interstellar magnetic
ﬁeld (Yan et al., 2004), the lifetime of μm-sized SiC VLGs is 108 yr. Therefore, if an acceleration mechanism of VLGs, such as
gyroresonance, works in the ISM to make the velocity dispersion
of VLGs larger than that of gas, the grain lifetime can be moreconsistent with the residence times derived for a large part of theabove samples. A higher velocity dispersion of VLGs than
20 km s  1 is excluded since the lifetime of μm-sized SiC grains
becomes shorter than 100 Myr, which contradicts the residence
times measured.
We further discuss other possibilities of explaining the short
exposure ages in Section 4.3.

4.2. Expected abundance of VLGs in the ISM
We formulate the theoretically expected total mass of VLGs,
assuming that AGB stars are the major production sources and thatinterstellar shattering is the major destruction mechanism. We
consider the total dust budget in the Milky Way. The total mass of
VLGs originating from AGB stars in the Milky Way is denoted as
M AGB
VLG;i , where i stands for the grain species (silicate, carbonaceous
dust, and SiC). The time evolution of M AGB
VLG;i is described as
dM AGBM AGB
dM VLG;iVLG;i¼ VLG;i ;dtdtτVLG;iAGB

ð9Þwhere ½dM VLG;i =dtAGB is the production rate of VLGs of species i in
AGB star winds and τVLG;i is the shattering time-scale of VLGs intheir collisions with the ISM grains. We use the lifetime of VLGs
estimated in Eq. (5) for τVLG;i . The production rate of VLGs in AGB
stars is related to the star formation history, the statistics of stellar
mass (speciﬁed by the initial mass function), and the total dust
produced by individual stars (e.g., Asano et al., 2013):

Z 8 M
dM VLG;i¼ψ ðt  τm Þmi ðmÞϕðmÞ dm C ψ η;
ð10Þ
dt
mt
AGB
where ψ ðt  τm Þ is the star formation rate (SFR) in the Galaxy att  τ m (t is the current age, and τm is the lifetime of a star withmass m; note that the dust production occurs at the end of stellarlife), mt is the turn-off mass (the mass of a star whose lifetime isequal to the age of the Galaxy; assumed to be 1 M  in this paper),mi(m) is the total mass of dust species i produced by the starwith mass m, ϕðmÞ is the stellar initial mass function, andR η  m8M
mi ðmÞϕðmÞ dm. From the ﬁrst to the second line in Eq.
t(10), we approximate the SFR with the time-averaged SFR ðψ Þ
assuming that the SFR does not vary drastically as a function oftime. We do not consider a strong enhancement of SFR at a particular time as discussed in Clayton (2003) (see also Section 4.3).
For mi(m) we adopt the calculation of dust condensation in AGB
star winds in Zhukovska et al. (2008) for silicate, carbonaceous
dust, and SiC. Silicate in our calculation includes all the species
other than carbonaceous dust and SiC, so that the total dust mass
is equal to the sum of the mass of SiC, graphite, and silicate.
Now we are only interested in equilibrium states since thegrain lifetime is signiﬁcantly shorter than the age of the Galaxy.
Even if this does not hold (i.e., τVLG;i ≳t), the equilibrium value gives
the maximum VLG mass expected in the Milky Way since dM AGB
VLG;i=dt 40 holds (i.e., the VLG mass originating from AGB stars still
continues to increase until it reaches the equilibrium value
because the ﬁrst term on the right-hand side in Eq. (9) dominates
over the second term). Considering the equilibrium dM AGB
VLG;i =dt ¼ 0
in Eq. (9), combined with Eq. (10), we obtain
M AGB
VLG;i C ψ ητ VLG;i :ð11Þ

In Table 1, we show η, τVLG (estimated for aVLG ¼ 1 μm) and ητVLG for each dust species. We observe that ητVLG of SiC is as large
as that of silicate because the long lifetime of SiC VLGs compensates the small yield of SiC in AGB stars. This explains the fact that
SiC is found in presolar grains although SiC is a minor dust species
in the ISM compared with silicate and graphite; that is, if wesample only μm-sized grains originating from AGB stars, SiC VLGs
are found as easily as other species because of their long lifetime.
The SFR in the Galactic disk has been rather constant: indeed,
the current SFR is estimated as  3 M  yr  1 , and this level of SFR
explains the total stellar mass in the disk if the disk age is
C10 Gyr (Trimble, 2000). Therefore, we assume that ψ C ψ C
3 M  yr  1 . Multiplying this value with η obtained above (foraVLG ¼ 1 μm), we get M AGB
VLG;i for each species as listed in Table 1.

H. Hirashita et al. / Planetary and Space Science 133 (2016) 17–22

The total dust mass in the Milky Way is estimated to be  5 
107 M  (Hirashita et al., 2014). We also list the ratio of M AGB
VLG ofeach species to the total dust mass in Table 1. The fractions are on
the order of 0.1 percent. Therefore, the existence of VLGs in the
ISM does not contradict the observational properties reﬂecting theinterstellar grains such as extinction curves and infrared emission
because of the negligible fractions.
However, these fractional abundances of VLGs cannot bedirectly compared with the fraction in primitive meteorites. The
actual fraction of sampled SiC grains in meteorites (up to 150 ppm;
Zinner, 2014) is much smaller than those values estimated above
probably because additional processing in the solar system may
have destroyed SiC grains by exposure to hot ð≳1000 KÞ gas(Mendybaev et al., 2002). It is also interesting to compare thecalculated and measured silicate/SiC ratios. We predict a silicate/
SiC ratio of 0:13=0:15  1 (Table 1) while measurements of presolar grains indicate a ratio of  5 (Leitner et al., 2012). Althoughprocessing of SiC and silicate grains in the solar system makes the
direct comparison difﬁcult, it is encouraging that both theory
and measurement show silicate/SiC ratio of the same order ofmagnitude.
4.3. Grain processing mechanisms other than shattering
Sputtering in SN shocks is the dominant mechanism of dust
destruction for the ISM grains (Dwek and Scalo, 1980; McKee,
1989; Jones et al., 1994; Nozawa et al., 2006). However, Jones andNuth (2011) pointed out that the destruction rate of dust by
supernova shocks is highly uncertain. Moreover, as mentioned in
the Introduction, the motion of VLGs tends to be decoupled fromthe shocks, which indicates that some VLGs are likely to escapedestruction by sputtering in shocks. In this paper, we have considered shattering in the diffuse ISM, not associated with supernova shocks, and have given another constraint on the lifetimeof VLGs.
VLGs may also form as a result of coagulation in the dense ISM(Ormel et al., 2009; Hirashita et al., 2014). The anomalous isotopic
compositions of presolar grains (Introduction) often support theformation in speciﬁc types of stars. VLGs formed as a result of
coagulation are expected to be compounds, which do not show
uniformity of composition. Thus, it is expected that VLGs of coagulation origin, even if they are contained in a meteorite, are hard
to be identiﬁed as single presolar grains. At the same time, VLGs of
coagulation origin would be less isotopically anomalous because
coagulation of many grains dilutes the peculiarity of isotopic
compositions. Although dust can also grow through the accretionof gas-phase metals (e.g., Draine, 2009), VLGs cannot have been
formed through accretion: as shown by Hirashita and Kuo (2011),
accretion only modiﬁes a few nm of the dust surface, which is too
thin compared with the radii of VLGs.
Bernatowicz et al. (2003) studied 81 μm-sized pristine presolar
SiC grains. They found that a large fraction of the SiC grains arecoated with an apparently amorphous, possibly organic phase.
This may indicate that the surface of SiC is affected by accretion in
the ISM or in the solar system. On the other hand, their SiC grainsurface studies did not show strong evidence for cratering or
sputtering. They suggested that surface coatings protected the SiC
grains from destructive processing in the ISM.
As mentioned in Section 4.1, most of the sampled SiC presolar
grains have lifetimes much shorter than the theoretically estimated shattering time-scale ( 1 Gyr). Ott et al. (2005) suggested,based on efﬁcient amorphization in the ISM inferred from the highamorphous fraction (or low crystalline fraction) of silicate by
Kemper et al. (2004), that a large part of interstellar SiC grains areamorphized. Provided that amorphous SiC is easily destroyed in
the early solar system, the amorphization time-scale is more

21

relevant than the shattering time-scale for the lifetime in the ISM
since the amorphized SiC grains are not sampled as presolar
grains.
Another solution for the short residence time of presolar grains
is to consider an enhancement of AGB star dust production justbefore the solar system was formed. This means that anenhancement of SFR (or a starburst) occurred 1–2 Gyr before theformation of the solar system (Ott et al., 2005). In this star formation history, AGB stars originating from stars with m  2 M form SiC dust grains just before the formation of the solar system,so that their residence times are observed to be short. Clayton(2003) also explained the isotopic ratios of the mainstream SiC
presolar grains by considering a starburst activated by a merger ofa metal-poor satellite galaxy with the Milky Way.

5. Conclusion
We have investigated interstellar shattering as a mechanism ofdetermining the lifetime of very large grains (VLGs with radii
aVLG 4 0:1 μm) in the interstellar medium (ISM). Sputtering insupernova shocks, which is considered to be the main destruction
mechanism for the interstellar dust, may not work for VLGs
because such large grains are decoupled from the gas motion on
the spatial scale of shocked regions (Slavin et al., 2004). On theother hand, VLGs are coupled with a large-scale turbulent motionin the ISM and attain random velocities as high as  10 km s  1.
Therefore, we have considered shattering of VLGs under successive
collisions with the grains present in the ISM (ISM grains). Estimating the shattering time-scale for VLGs, we have shown that SiC
VLGs have lifetimes as long as  1 Gyr.
We have also compared the destruction time-scale obtained
above with the residence time of presolar SiC grains sampled inmeteorites. We referred to laboratory studies in the literature forthe residence time estimated from the cosmic ray exposure time in
the ISM using the excesses of isotopes caused by Galactic cosmic
ray spallation. Indeed, some presolar SiC grains show residence
times as long as 1 Gyr, which is consistent with our estimate oflifetime above. However, most presolar grains have residence
times signiﬁcantly shorter than 1 Gyr, which may indicate that
there is a more efﬁcient mechanism than shattering in destroying
VLGs, that a large abundance of dust was produced by AGB stars
shortly before the birth of the solar system, or that VLGs havelarger velocity dispersions than assumed in this paper (i.e.,
4 10 km s  1 ).
SiC VLGs have a longer shattering time than VLGs composed ofsilicate and carbon. The long lifetime of SiC VLGs may serve toenhance the abundance of SiC in presolar μm-sized grains.

Acknowledgment
We are grateful to S. Tachibana and the anonymous referees for
useful comments. H.H. is supported by the Ministry of Science andTechnology (MoST) Grant 102-2119-M-001-006-MY3. T.N. is supported in part by the JSPS Grant-in-Aid for Scientiﬁc Research(26400223).

References
Altobelli, N., Grün, E., Landgraf, M., 2006. A new look into the Helios dust experiment data: presence of interstellar dust inside the Earth's orbit. Astron.
Astrophys. 448, 243–252.
Altobelli, N., Kempf, S., Landgraf, M., Srama, R., Dikarev, V., Krüger, H., MoragasKlostermeyer, G., Grün, E., 2003. Cassini between Venus and Earth: detection ofinterstellar dust. J. Geophys. Res. (Space Phys.) 108, 8032.

22

H. Hirashita et al. / Planetary and Space Science 133 (2016) 17–22

Amari, S., Lewis, R.S., Anders, E., 1994. Interstellar grains in meteorites: I. Isolationof SiC, graphite and diamond; size distributions of SiC and graphite. Geochim.
Cosmochim. Acta 58, 459–470.
Amari, S., Zinner, E., Gallino, R., 2014. Presolar graphite from the Murchison
meteorite: an isotopic study. Geochim. Cosmochim. Acta 133, 479–522.
Amari, S., Nittler, L.R., Zinner, E., Lodders, K., Lewis, R.S., 2001. Presolar SiC grains ofType A and B: their isotopic compositions and stellar origins. Astrophys. J. 559,
463–483.
Anders, E., Zinner, E., 1993. Interstellar grains in primitive meteorites: diamond,silicon carbide, and graphite. Meteoritics 28, 490–514.
Asano, R.S., Takeuchi, T.T., Hirashita, H., Inoue, A.K., 2013. Dust formation history ofgalaxies: a critical role of metallicity for the dust mass growth by accreting
materials in the interstellar medium. Earth Planets Space 65, 213–222.
Baguhl, M., Grün, E., Hamilton, D.P., Linkert, G., Riemann, R., Staubach, P., 1995. The
ﬂux of interstellar dust observed by ULYSSES and Galileo. Space Sci. Rev. 72,
471–476.
Baguhl, M., Grün, E., Landgraf, M., 1996. In situ measurements of interstellar dustwith the ULYSSES and Galileo spaceprobes. Space Sci. Rev. 78, 165–172.
Bernatowicz, T.J., Messenger, S., Pravdivtseva, O., Swan, P., Walker, R.M., 2003.
Pristine presolar silicon carbide. Geochim. Cosmochim. Acta 67, 4679–4691.
Clayton, D.D., 2003. A presolar Galactic merger spawned the SiC-grain mainstream.
Astrophys. J. 598, 313–324.
Désert, F.-X., Boulanger, F., Puget, J.L., 1990. Interstellar dust models for extinctionand emission. Astron. Astrophys. 237, 215–236.
Draine, B.T., 2009. Interstellar dust models and evolutionary implications. In:
Henning, Th., Grün, E., Steinacker, J. (Eds.), Cosmic Dust—Near and Far. ASP
Conference Series, vol. 414. Astronomical Society of Paciﬁc, San Francisco, USA,
pp. 453–472.
Draine, B.T., Lee, H.M., 1984. Optical properties of interstellar graphite and silicate
grains. Astrophys. J. 285, 89.
Dwek, E., Scalo, J.M., 1980. The evolution of refractory interstellar grains in the solar
neighborhood. Astrophys. J. 239, 193–211.
Ferrarotti, A.S., Gail, H.-P., 2006. Composition and quantities of dust produced by
AGB-stars and returned to the interstellar medium. Astron. Astrophys. 447,
553–576.
Gallino, R., Raiteri, C.M., Busso, M., Matteucci, F., 1994. The puzzle of silicon, titanium, and magnesium anomalies in meteoritic silicon carbide grains. Astrophys. J. 430, 858–869.
Grün, E., Gustafson, B., Mann, I., Baguhl, M., Morﬁll, G.E., Staubach, P., Taylor, A.,
Zook, H.A., 1994. Interstellar dust in the heliosphere. Astron. Astrophys. 286,
915–924.
Gyngard, F., Amari, S., Zinner, E., Ott, U., 2009. Interstellar exposure ages of largepresolar SiC grains from the Murchison meteorite. Astrophys. J. 694, 359–366.
Heck, P.R., Gyngard, F., Ott, U., Meier, M.M. Matthias, Ávila, J.N., Amari, S., Zinner, E.
K., Lewis, R.S., Baur, H., Wieler, R., 2009. Interstellar residence times of presolar
SiC dust grains from the Murchison carbonaceous meteorite. Astrophys. J. 698,
1155–1164.
Hirashita, H., Asano, R.S., Nozawa, T., Li, Z.-Y., Liu, M.-C., 2014. Dense molecular
cloud cores as a source of micrometer-sized grains in galaxies. Planet. Space Sci.
100, 40–45.
Hirashita, H., Kobayashi, H., 2013. Evolution of dust grain size distribution by
shattering in the interstellar medium: robustness and uncertainty. Earth Planets Space 65, 1083–1094.
Hirashita, H., Kuo, T.-M., 2011. Effects of grain size distribution on the interstellar
dust mass growth. Mon. Not. R. Astron. Soc. 416, 1340–1353.
Hirashita, H., Yan, H., 2009. Shattering and coagulation of dust grains in interstellar
turbulence. Mon. Not. R. Astron. Soc. 394, 1061–1074.
Jones, A.P., Nuth III, J.A., 2011. Dust destruction in the ISM: a re-evaluation of dust
lifetimes. Astron. Astrophys. 530, A44.
Jones, A.P., Tielens, A.G.G.M., Hollenbach, D.J., 1996. Grain shattering in shocks: theinterstellar grain size distribution. Astrophys. J. 469, 740–764.
Jones, A.P., Tielens, A.G.G.M., Hollenbach, D.J., McKee, C.F., 1994. Grain destruction
in shocks in the interstellar medium. Astrophys. J. 433, 797–810.
Kemper, F., Vriend, W.J., Tielens, A.G.G.M., 2004. The absence of crystalline silicatesin the diffuse interstellar medium. Astrophys. J. 609, 826–837.
Kobayashi, H., Tanaka, H., 2010. Fragmentation model dependence of collisioncascades. Icarus 206, 735–746.

Krüger, H., Strub, P., Grün, E., Sterken, V.J., 2015. Sixteen years of Ulysses interstellar
dust measurements in the solar system. I. Mass distribution and gas-to-dust
mass ratio. Astrophys. J. 812, 139.
Leitner, J., Vollmer, C., Hoppe, P., Zipfel, J., 2012. Characterization of presolarmaterial in the CR Chondrite Northwest Africa 852. Astrophys. J. 745, 38.
Levy, E.H., Jokipii, J.R., 1976. Penetration of interstellar dust into the solar system.
Nature 264, 423–424.
Lewis, R.S., Amari, S., Anders, E., 1990. Meteoritic silicon carbide: pristine material
from carbon stars. Nature 348, 293–298.
Li, A., Draine, B.T., 2001. Infrared emission from interstellar dust. II. the diffuse
interstellar medium. Astrophys. J. 554, 778–802.
Lugaro, M., Davis, A.M., Gallino, R., Pellin, M.J., Straniero, O., Käppeler, F., 2003.
Isotopic compositions of strontium, zirconium, molybdenum, and barium insingle presolar SiC grains and asymptotic giant branch stars. Astrophys. J. 593,
486–508.
Mathis, J.S., 2000. Circumstellar and interstellar material. In: Cox, A.N. (Ed.), Allen's
Astrophysical Quantities, 4th edition Springer, New York, USA, pp. 523–541.
Mathis, J.S., Rumpl, W., Nordsieck, K.H., 1977. The size distribution of interstellar
grains. Astrophys. J. 217, 425–433 (MRN).
McKee, C.F., 1989. Dust destruction in the interstellar medium. In: Allamandola, L.J.,
Tielens, A.G.G.M. (Eds.), Interstellar Dust, IAU Symposium, vol. 135. Kluwer,
Dordrecht, pp. 431–443.
Mendybaev, R.A., Beckett, J.R., Grossman, L., Stolper, E., Cooper, R.F., Bradley, J.P.,
2002. Volatilization kinetics of silicon carbide in reducing gases: an experimental study with applications to the survival of presolar grains in the solar
nebula. Geochim. Cosmochim. Acta 66, 661–682.
Nozawa, T., Kozasa, T., Habe, A., 2006. Dust destruction in the high-velocity shocks
driven by supernovae in the early Universe. Astrophys. J. 648, 435–451.
Ormel, C.W., Cuzzi, J.N., 2007. Closed-form expressions for particle relative velocities induced by turbulence. Astron. Astrophys. 466, 413–420.
Ormel, C.W., Paszun, D., Dominik, C., Tielens, A.G.G.M., 2009. Dust coagulation andfragmentation in molecular clouds. I. How collisions between dust aggregatesalter the dust size distribution. Astron. Astrophys. 502, 845–869.
Ott, U., Altmaier, M., Herpers, U., Kuhnhenn, J., Merchel, S., Michel, R., Mohapatra, R.
K., 2005. Spallation recoil II: xenon evidence for young SiC grains. Meteorit.
Planet. Sci. 40, 1635–1652.
Slavin, J.D., Jones, A.P., Tielens, A.G.G.M., 2004. Shock processing of large grains in
the interstellar medium. Astrophys. J. 614, 796–806.
Spitzer, L., 1978. Physical Processes in the Interstellar Medium. Wiley, New York,USA.
Sterken, V.J., Altobelli, N., Kempf, S., Krüger, H., Srama, R., Strub, P., Grün, E., 2013.
The ﬁltering of interstellar dust in the solar system. Astron. Astrophys. 552,
A130.
Trimble, V., 2000. Milky Way and galaxies. In: Cox, A.N. (Ed.), Allen's AstrophysicalQuantities, 4th edition Springer, New York, USA, pp. 569–584.
Ventura, P., di Criscienzo, M., Schneider, R., Carini, R., Valiante, R., D'Antona, F.,
Gallerani, S., Maiolino, R., Tornambé, A., 2012. Dust formation around AGB and
SAGB stars: a trend with metallicity?. Mon. Not. R. Astron. Soc. 424, 2345–2357.
Völk, H.J., Jones, F.C., Morﬁll, G.E., Röser, S., 1980. Collisions between grains in aturbulent gas. Astron. Astrophys. 85, 316–325.
Weingartner, J.C., Draine, B.T., 2001. Dust grain-size distributions and extinction in
the Milky Way, Large Magellanic Cloud, and Small Magellanic Cloud. Astrophys.
J. 548, 296–309.
Westphal, A.J., et al., 2014. Evidence for interstellar origin of seven dust particles
collected by the Stardust spacecraft. Science 345, 786–791.
Yan, H., Lazarian, A., Draine, B.T., 2004. Dust dynamics in compressible magnetohydrodynamic turbulence. Astrophys. J. 616, 895–911.
Yasuda, Y., Kozasa, T., 2012. Formation of SiC grains in pulsation-enhanced dustdriven wind around carbon-rich asymptotic giant branch stars. Astrophys. J.
745, 159.
Zhukovska, S., Gail, H.-P., Trieloff, M., 2008. Evolution of interstellar dust andstardust in the solar neighbourhood. Astron. Astrophys. 479, 453–480.
Zinner, E., 2014. Presolar grains. In: Davis, A.M. (Ed.), Meteorites and Cosmochemical Processes. Treatise on Geochemistry, vol. 1. Elsevier, Amsterdam,
pp. 181–213.