Planetary and Space Science 100 (2014) 40–45

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Dense molecular cloud cores as a source of micrometer-sizedgrains in galaxies
Hiroyuki Hirashita a,n, Ryosuke S. Asano b, Takaya Nozawa c, Zhi-Yun Li d, Ming-Chang Liu aaInstitute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141, Taipei 10617, Taiwan
Department of Particle and Astrophysical Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japanc
Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba 277-8583, Japand
Astronomy Department, University of Virginia, Charlottesville, VA 22904, USAb

art ic l e i nf o

a b s t r a c t

Article history:
Received 5 October 2013
Received in revised form
17 January 2014
Accepted 17 January 2014
Available online 31 January 2014

Coreshine in dense molecular cloud cores (dense cores) is interpreted as evidence for micrometer-sized grains(referred to as very large grains, VLGs). VLGs may have a signiﬁcant inﬂuence on the total dust amount and theextinction curve. We estimate the total abundance of VLGs in the Galaxy, assuming that dense cores are the siteof VLG formation. We ﬁnd that the VLG abundance relative to the total dust mass is roughly ϕVLG 
0:01ð1  εÞ=εðτSF =5  109 yearÞ  1 ðf VLG =0:5Þðt shat =108 yearÞ, where ε is the star formation efﬁciency in dense
cores, τSF is the timescale of gas consumption by star formation, f VLG is the fraction of dust mass eventuallycoagulated into VLGs in dense cores, and t shat is the lifetime of VLGs (determined by shattering). Adopting their
typical values for the Galaxy, we obtain ϕVLG  0:02–0:09. This abundance is well below the value detected in
the heliosphere by Ulysses and Galileo, which means that local enhancement of VLG abundance in the solar
neighborhood is required if the VLGs originate from dense cores. We also show that the effects of VLGs on theextinction curve are negligible even with the upper value of the above range, ϕVLG  0:09. If we adopt an
extreme value, ϕVLG  0:5, close to that inferred from the above spacecraft data, the extinction curve is still in
the range of the variation in Galactic extinction curves, but is not typical of the diffuse ISM.
& 2014 Elsevier Ltd. All rights reserved.

Keywords:
Dust
Galaxy evolution
Grain size distribution
Milky WayInterstellar medium

1. Introduction
Dust grains play an essential role in some fundamental physicalprocesses in the interstellar medium (ISM). First, they dominate
the radiative transfer of stellar light in the ISM. In particular, theextinction curve, that is, the wavelength dependence of opticaldepth for dust absorption plus scattering is known to reﬂect the
dust materials (e.g., Hoyle and Wickramasinghe, 1969) and grain
size distribution (e.g., Mathis et al., 1977, hereafter MRN; Draine,
2003). Second, the dust surface is the main site for the formationof some molecular species, especially H2 (e.g., Gould and Salpeter,
1963; Cazaux and Tielens, 2002). The rate of dust surface reaction
is proportional to the total surface area of dust grains (e.g.,
Hollenbach and Salpeter, 1971; Yamasawa et al., 2011). Since theextinction curve and the total grain surface area both depend
strongly on the grain size distribution, clarifying the regulating
mechanism of grain size distribution is of particular importance inunderstanding those important roles of dust in the ISM.
MRN showed that a mixture of silicate and graphite with agrain size distribution (number of grains per grain radius) proportional to a  3:5 , where a is the grain radius ða ¼ 0:001 –0:25 μmÞ,
reproduces the Milky Way extinction curve. This size distributionnCorresponding author.
E-mail address: hirashita@asiaa.sinica.edu.tw (H. Hirashita).

0032-0633/$ - see front matter & 2014 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.pss.2014.01.013

is referred to as the MRN size distribution. Kim et al. (1994) andWeingartner and Draine (2001) made more detailed models of the
Milky Way extinction curve. In both these models, the abundanceof grains whose radii are beyond the maximum in the MRN size
distribution (0.25 μm) is so low that the contribution of such large
grains to the total dust mass is negligible.
The existence of micrometer (μm)-sized grains is suggested indense molecular cloud cores (called dense cores in this paper). The
so-called “coreshine” refers to emission in the mid-infrared(especially the 3.6-μm Spitzer Infrared Array Camera (IRAC) band)from deep inside dense cores of molecular clouds (Steinacker et al.,2010; Pagani et al., 2010). It is detected in about half of the coresstudied by Pagani et al. (2010). The emission is interpreted as lightscattered by dust grains with typical sizes of  1 μm, which ismuch larger than the maximum grain radius in the diffuse
interstellar medium (  0:25 μm; MRN). We refer to μm-sizedgrains as “very large grains (VLGs)” in this paper.
Formation of VLGs by coagulation in dense cores has beentheoretically investigated by Hirashita and Li (2013) (see also
Ormel et al., 2009, 2011). Based on the timescale on which grains
grow up to μm sizes by coagulation, they argued that dense cores
are sustained over several free-fall times. Since their main aim wasto constrain the lifetime of dense cores, the impact of VLG
formation on the grain size distribution in the entire ISM wasbeyond their scope. A certain fraction of VLGs formed in dense
cores may be injected into the diffuse ISM when the dense coresH. Hirashita et al. / Planetary and Space Science 100 (2014) 40–45

disperse. Efﬁcient formation of VLGs would contradict the MRN
grain size distribution in which the maximum grain radius is 0:25 μm. Thus, based on an estimation of the total abundance of
VLGs in the Milky Way, we examine the consistency between theformation of VLGs suggested by coreshine and the Galactic
extinction curve (or the MRN grain size distribution). In this paper,
the abundance of VLGs stands for the ratio of the total VLG mass tothe total dust mass (including VLGs), and is denoted as ϕVLG (seeSection 2). By deﬁnition, 0 r ϕVLG r 1.
There are some indications that VLGs exist in the ISM. One of
the indications of interstellar VLGs is provided by meteorites.
Large interstellar grains ð 4 1 μmÞ are known to exist in chondritic
meteorites. Such grains were identiﬁed based on their extremely
anomalous (way off from the average solar system isotope ratios)
isotopic compositions (Clayton and Nittler, 2004). This implies thatinterstellar dust grains must have resided and survived in a dense
core that ended up forming the solar system.
Another indication of interstellar VLGs comes from direct detection of interstellar grains in the heliosphere by Ulysses and Galileo.
These experiments have shown that the volume mass density of
VLGs is comparable to the total dust volume mass density derived
from the typical dust-to-gas ratio in the diffuse ISM in the Galaxy(Landgraf et al., 2000; Krüger et al., 2007; Frisch and Slavin, 2013).
This seems contradictory to the above grain size distribution derived
by MRN, who found that most of the dust grains have radii less than
0.25 μm. Thus, it has been argued that the density of VLGs isenhanced in the solar neighborhood (Draine, 2009; Frisch andSlavin, 2013). Nevertheless, it is still interesting to compare the VLG
abundance expected from the formation in dense cores with themeasurements, in order to quantify what fraction of the observed
VLGs can be explained by the formation in dense cores.
We may also need to consider stellar sources of dust grains,
especially asymptotic giant branch (AGB) stars and supernovae(SNe) for the production of VLGs. Indeed, the size distribution ofgrains produced by AGB stars is suggested to be biased toward
large ð≳0:1 μmÞ sizes from the observations of spectral energy
distributions (Groenewegen, 1997; Gauger et al., 1999; Norris et al.,2012), although Hofmann et al. (2001) showed that the grains are
not single-sized. Theoretical studies have also shown that the dust
grains formed in the winds of AGB stars have typical sizes ≳0:1 μm(Winters et al., 1997; Yasuda and Kozasa, 2012). SNe (Type II SNe)are also considered to produce relatively large ð 40:01 μmÞ grains
because small grains are destroyed by reverse shocks before they
are ejected into the ISM (Nozawa et al., 2007; Bianchi andSchneider, 2007). However, the timescale of dust supply fromstars is longer than the shattering timescale (Hirashita, 2010) by anorder of magnitude. Therefore, even if VLGs are supplied fromstars, they probably fail to survive in the ISM. In this paper, we donot treat the stellar production of VLGs because of the difﬁculty intheir survival, but focus on their formation in dense cores,
motivated by the new evidence of VLGs – coreshine.
In this paper, we estimate the abundance of VLGs in the Galaxy,
assuming that dense cores are the main sites for the formation of
VLGs. This paper is organized as follows. In Section 2, we formulate
and estimate the abundance of VLGs in the Galaxy. In Section 3, wecompare our estimates with some observations. In Section 4, we
discuss our results and implications for the dust evolution ingalaxies. In Section 5, we give our conclusions.

2. Estimation of the total VLG mass
2.1. Formation rate of VLGs in the Galaxy
We estimate the supply rate of VLGs (μm-sized grains) in the
Galaxy. Motivated by coreshine as evidence of VLGs in dense cores,

41

we examine the hypothesis that dense cores are the main sites forthe formation of VLGs in the Galaxy (see also Introduction). We
assume that all dense molecular cloud cores (dense cores) eventually convert a signiﬁcant fraction of dust grains into VLGs bycoagulation after their lifetimes. The formation rate of VLGs (thetotal mass of VLGs is denoted as M VLG ) in dense cores in the
Galaxy, ½dM VLG =dtform , is estimated as
dM VLGX core M dust ð1  ϕVLG Þf VLG ð1  εÞ

;
ð1Þ
τcore
dt
form
where X core is the mass fraction of dense cores to the total gas
mass, M dust is the total dust mass in the Galaxy (X core M dust is thetotal dust mass contained in the dense cores), ϕVLG  M VLG =M dust is
the ratio of the VLG mass to the total dust mass (the factor 1  ϕVLG
means that we need to subtract the dust that has already become
VLGs), f VLG is the fraction of dust that is eventually coagulated toμm sizes in the dense cores, ε is the star formation efﬁciency in thedense cores (the factor 1  ε means that the gas that is not included
in stars is assumed to be dispersed into the ISM), and τcore is the
lifetime of dense core (i.e., the timescale of VLG formation). Notethat Eq. (1) should not be regarded as an ordinary differential
equation, but just gives an estimate for the VLG formation rate.
Since dense cores are also the sites of star formation, the starformation rate of the Galaxy is estimated by dividing the total gas
mass contained in the dense cores with their lifetime (i.e., thetimescale of star formation):
ψ¼

εX core M gas
;
τcore

ð2Þ

where M gas is the total gas mass in the Galaxy (X core M gas is thetotal gas mass in dense cores). This equation converts the coreformation rate ðX core M gas =τcore Þ into the star formation rate, andserves to eliminate the core formation rate, which is unknown
observationally compared with the star formation rate. By introducing the dust-to-gas ratio, D  M dust =M gas and using Eq. (2), we
obtain
X coreDψ¼:
τcore εM dust

ð3Þ

Inserting Eq. (3) into Eq. (1), we ﬁnally get the following estimate
for the VLG formation rate:dM VLG1εDð1  ϕVLG Þψf VLG :
¼
ð4Þ
ε
dt
form
This VLG formation rate could be implemented in a larger framework of dust enrichment, which is capable of calculating theevolution of the total dust mass in the Galaxy, to calculate theevolution of M VLG in a consistent way with M dust or D. However,this is not necessary for the purpose of estimating the total VLG
mass in the Galaxy. The timescale of dust enrichment (i.e., thetimescale of the variation of M dust or D) in the Galaxy is roughly
the metal-enrichment timescale (  several Gyr) (e.g., Dwek,
1998; Zhukovska et al., 2008; Inoue, 2011; Asano et al., 2013a),which is much longer than the lifetime of VLGs (typically determined by the shattering timescale  108 year; Hirashita, 2010).
Therefore, we can assume that M dust and D are constant within the
lifetime of VLGs. In such a case, the total mass of VLGs can beapproximately estimated as follows.
It is shown that μm-sized grains are shattered in the diffuse ISM
by grain–grain collisions under the grain motion induced byturbulence (Yan et al., 2004; Hirashita, 2010). Shattering also
occurs in supernova shocks (Jones et al., 1996). Thus, we assume
that the lifetime of VLGs is determined by the shattering timescale,t shat (  108 year; Hirashita, 2010). The destruction rate of VLGs canthus be approximately estimated as M VLG =t shat , and the equilibrium between the VLG formation and destruction is achieved on

42

H. Hirashita et al. / Planetary and Space Science 100 (2014) 40–45

a timescale of  t shat . Since, as mentioned above, t shat is much
shorter than the evolution timescale of the dust mass, thevariation of D in t shat can be neglected. Therefore, the total massof VLGs in the Galaxy is estimated by the equilibrium between theformation and the destruction under a ﬁxed D:dM VLG1εDð1  ϕVLG Þψf VLG t shat :M VLG  t shat ¼
ð5Þ
ε
dt
form
2.2. Estimations of various quantities
We adopt dust-to-gas ratio D ¼ 0:01, the same value as adopted
in our previous calculations of coagulation in dense cores(Hirashita and Li, 2013). The star formation rate in the Galaxy
can be estimated from the total luminosity of OB stars. Hirashita
et al. (2007) obtained a star formation rate of 1:3 M  year  1 basedon the total OB star luminosity derived observationally by Mathis
et al. (1983). According to Hirashita and Li (2013), almost all thedust mass is in VLGs after coagulation in dense cores. Here we
conservatively assume that half of the dust mass is converted into
VLGs after coagulation in dense cores (i.e., f VLG ¼ 0:5). For t shat , weadopt 108 year according to Hirashita (2010), who consideredshattering under the grain motion driven by interstellar turbulence. As calculated by Jones et al. (1996), shattering can also takeplace in supernova shocks. Even if the supernova shocks are themain site of shattering (Jones et al., 1996), a similar timescale isobtained for shattering (Section 4.3).
Using the above values, we obtain


1ε D
M VLG  5  105 ð1  ϕVLG Þ
ε
0:01
!



ψ
f VLG
t shat

ð6Þ
M :
0:5
1M  year  1
108 yearFor comparison, we also estimate the total dust mass. The total gas
mass in the Milky Way is M gas  5  109 M  (Mathis, 2000;
Tielens, 2005). By multiplying the dust-to-gas ratio, the dust massis estimated as
!


M gas
D
7
M dust ¼ M gas D  5  10
ð7Þ
M :
0:01
5  109 M 
Dividing Eq. (6) with Eq. (7), we obtain the following expression byrecalling that ϕVLG ¼ M VLG =M dust :!  1
!

ϕVLG
1ε
τSF
f VLG
t shat¼ 0:01;ð8Þ
ε1  ϕVLG
0:5
5  109 year
108 year
where τSF  M gas =ψ is the star formation (gas consumption) time.
The star formation efﬁciency ε in molecular cloud cores is around
0.1–0.3 (Alves et al., 2007; Curtis and Richer, 2010; Lada et al.,2010). Thus, we can assume that ϕVLG ⪡1 in the Galaxy. In this case,we simply replace the left-hand side of Eq. (8) with ϕVLG .
3. Comparison with observational data
3.1. Direct detection
Interstellar dust grains with radii a≳0:1 μm can be detected
directly in space (Mann, 2009). In Fig. 1, we show the grain mass
distribution for interstellar grains in the heliosphere observed by
the Ulysses and Galileo spacecraft (Frisch and Slavin, 2013). Small
grains with typically a o 0:1 μm are excluded from the heliospheric plasma because of large charge-to-mass ratios. Thus, weare only interested in the data at a 4 0:1 μm.
In Fig. 1, we also plot the grain mass distribution calculated byHirashita and Li (2013) but scaled so that the total mass density ofFig. 1. Grain mass distributions. The solid and dashed lines show the grain mass
distributions calculated by Hirashita and Li (2013), but scaled with the total VLG
abundance appropriate for ε ¼ 0:1 and 0.3, respectively. The dotted line shows the
MRN distribution, which is considered to be representative of the grain size
distribution in the diffuse ISM. The data taken by the Ulysses and Galileo spacecraft
are represented by the shaded area, the width of which shows the typical error(Frisch and Slavin, 2013). The corresponding grain radii are also shown on theupper axis with grain material density 3.3 g cm  3.

VLGs is ϕVLG DμmH nH , where μ is the gas mass per hydrogen atom
(1.4), mH is the mass of hydrogen atom, nH ¼ 0:1 cm  3 is thenumber density of hydrogen nuclei in the local ISM (Frisch andSlavin, 2013). Draine (2009) adopted nH ¼ 0:22 cm  3 , but thedifference by a factor of 2 does not affect the conclusions. The
functional form of the distribution is taken from the maximal
coagulation model with a number density of hydrogen nuclei of
105 cm  3 at t ¼ 5:5t ff (t ff is the free-fall time), when the peak islocated at a ¼ 1 μm. The peak roughly reﬂects the mass density of
VLGs, and is not sensitive to the choice of t in any case. From
Eq. (8), we adopt VLG-to-total-dust mass ratio ϕVLG ¼ 0:01ð1  εÞ=εwith star formation efﬁciency ε ¼0.1–0.3 (Section 2.2). Note thatthe grain mass distribution is expressed as m2 nðmÞ ¼ ð4πρgr =9Þn0ðaÞa4 , where ρgr is the grain material density, and n0 ðaÞ is the grain
size distribution,1 which is related to n(m) by nðmÞ dm ¼ n0 ðaÞda.
We adopt the same grain material density, ρgr ¼ 3:3 g cm  3, as inHirashita and Li (2013).
As we observe in Fig. 1, the mass density of VLGs expected with
ϕVLG  0:02–0:09 (for ε ¼ 0.3–0.1) is much lower than observed inspace. This means that the large mass density observed in the
heliosphere cannot be explained by the abundance of VLGs formed
in dense cores. From the analysis of their velocities, the VLGs
detected in space are not likely to be the remains of the large
grains that were produced by coagulation in the dense core insidewhich the Solar System formed (Howe and Raﬁkov, 2013). If dense
cores are the site of VLG formation, we need some mechanism forenhancing the VLG abundance locally to explain the spacecraft
data. The physical mechanism of such an enhancement is still
unknown (Draine, 2009).
For comparison, we also show the MRN (Mathis et al., 1977)
grain size distribution (n0 ðaÞ p a  3:5 , with the upper and lower
limits of grain radius, 0.001 μm and 0.25 μm, respectively). The
normalization of the MRN grain size distribution is determined sothat the total dust mass density is DμmH nH with dust-to-gas ratio
D ¼ 0:01. This MRN size distribution is representative of the grain
size distribution in the diffuse ISM of the Galaxy. The abundance of

1
The grain size distribution is deﬁned so that n0 ðaÞ da is the number density of
dust grains with radii between a and a þ da.

H. Hirashita et al. / Planetary and Space Science 100 (2014) 40–45

43

VLGs expected from star formation efﬁciency ε ¼ 0.1–0.3 is well
below the extrapolation of the MRN grain size distribution toa  1 μm. This is consistent with a small VLG-to-total-dust mass
ratio, ϕVLG ⪡1; that is, VLGs make only a small contribution to thetotal dust mass in the Galaxy.
3.2. Extinction curves
The wavelength dependence of interstellar extinction, the socalled extinction curve, is a viable tool to derive the grain size
distribution. The MRN size distribution was derived by ﬁtting the
averaged interstellar extinction curve in the Milky Way. For the
MRN size distribution, the upper limit of the grain radius is0.25 μm. Here we examine if the inclusion of VLGs is consistent
with the Galactic extinction curve or not.
A possible caveat of extinction curve ﬁtting is that the solution
is not unique. For example, MRN adopted graphite for the
carbonaceous material because of the strong 2175 Å bump, while
Jones (2012) proposed hydrogenated amorphous carbon.
Compiègne et al. (2011) used the latter species for the carbonaceous dust component and reproduced both the extinction andemission of dust in the Galaxy. The relative contribution between
silicate and carbonaceous dust also depends on the material
properties adopted. Therefore, strictly speaking, adopting a speciﬁc model reproducing the extinction curve means that thefollowing result only serves as an example of the effects of VLGs.
However, our results below are valid at least qualitatively as longas large grains tend to show ﬂat extinction curves in the opticaland the 2175 Å bump is produced by small grains.
We assume that grains are composed of two species: silicate
and graphite. Extinction curves are calculated by using the same
optical properties of silicates and graphites as in Hirashita and Yan(2009). That is, we adopt the optical constants from Draine and Lee(1984) and calculate extinction cross-sections by the Mie theory(Bohren and Huffman, 1983). The cross-sections are weighted by
the grain size distributions, and summed up for silicate andgraphite. The fraction of silicates to the total dust mass is assumed
to be 0.54, and the rest is assumed to be graphite (Takagi et al.,
2003; Hirashita and Yan, 2009). The contributions from the MRN
size distribution and from the VLGs to the total extinction areproportional to ð1  ϕVLG Þ and ϕVLG , respectively.
In Fig. 2, we show the results. The extinction is normalized to the
V band (0.55 μm), and the normalized extinction at wavelength λ isdenoted as Aλ =AV . We ﬁnd that, even for star formation efﬁciency
ε ¼ 0:1 (equivalent to VLG-to-total-dust mass ratio ϕVLG ¼ 0:09),
there is only a slight difference from the extinction curve for the
MRN model2 with a little enhancement in infrared extinction, andslightly lower carbon bump and ultraviolet extinction. All thesedifferences can be explained by the contribution from VLGs, as isclear from the extinction curve of the VLG component (dashed line in
Fig. 2). However, the difference is negligible compared with thetypical variation in the Milky Way (Nozawa and Fukugita, 2013).
RV  AV =ðAV  AB Þ, which is an indicator of the ﬂatness of extinction
curve, is 3.6 and 3.7 for MRN and ε ¼ 0:1, respectively. For ε ¼ 0:3, thedifference is even smaller. Therefore, our estimate of the VLG
abundance is within the acceptable range as far as the variation of
extinction curve is concerned.
We also show an extreme case where ϕVLG ¼ 0:5, consideringthat the above Ulysses and Galileo data show a mass density of
2
The extinction curve calculated by the MRN model has some deviations fromthe observational data taken from Pei (1992): one is seen around 1=λ  6 μm  1 andanother is the different value of RV (note that the mean value of RV is 3.1 (Pei,
1992)). However, the overall shape of the observed mean extinction curve (shownby ﬁlled squares in Fig. 2) is well reproduced by the MRN grain size distribution,and further ﬁne-tuning does not affect the discussions and conclusion in this paper.

Fig. 2. Extinction curves. The solid and dot-dashed lines show the extinction
curves calculated for ϕVLG ¼ 0:09 (corresponding to ε ¼ 0:1) and ϕVLG ¼ 0:5 (as anextreme case, based on the Ulysses and Galileo data), respectively. The dotted anddashed lines show the extinction curves for the MRN and VLG components,
respectively. The ﬁlled squares show the observed Galactic extinction curve takenfrom Pei (1992).

VLGs comparable to the total dust mass density in the diffuse ISM(i.e., the MRN component in Fig. 1). The deviation from the mean
Galactic extinction curve is clear in this case. For this extinction
curve, we obtain RV ¼ 4.6, which is still in the range of the variationin the Milky Way extinction curve, but is not typical of the diffuse
ISM (Cardelli et al., 1989; Fitzpatrick and Massa, 2007). This again
supports the view that the high VLG abundance is due to local
enhancement. Draine (2009) also calculated the extinction curve
based on Weingartner and Draine (2001)'s model modiﬁed for the
Ulysses and Galileo measurements. They obtained RV ¼5.8, thedifference from our models being due to their higher abundanceof VLGs. They also conclude that the large excess of μm-sizedinterstellar grains in the heliosphere is not representing the typicaldiffuse medium in the Milky Way but is probably due to local
enhancement of VLG abundance.

4. Discussion
4.1. In the context of galaxy evolution
The above estimate of ϕVLG (the VLG-to-total-dust mass ratio) is
applicable to the Milky Way. Galaxies in general are expected to havea variety in ϕVLG . The central hypothesis in this paper is that VLGs
form in dense cores. This is probably true in solar-metallicity
environments where dust-to-gas ratio is large enough for coagulation to occur efﬁciently in dense cores. In contrast, in a galaxy whose
dust-to-gas ration is lower, coagulation in dense cores may not be
efﬁcient enough to produce VLGs; in other words, f VLG is smaller if
dust-to-gas ratio (or metallicity) is lower. Since dust-to-gas ratio has
a positive correlation with metallicity (Schmidt and Boller, 1993), we
expect that ϕVLG is smaller in lower-metallicity galaxies.
Asano et al. (2013b) showed that the major source of grains
with a 4 0:1 μm is stars (SNe and AGB stars) in low-metallicity (orlow-dust-to-gas-ratio) environments. Therefore, if coagulation is
not efﬁcient, we expect that most of the VLGs (if they exist) are ofstellar origin. As mentioned in Introduction, the size distributionsof grains produced by AGB stars and SNe are suggested to bebiased toward large ð≳0:1 μmÞ sizes. However, there is still an
uncertainty in the size distribution of dust grains formed in stellar
ejecta. For more quantitative estimates of relative importance44

H. Hirashita et al. / Planetary and Space Science 100 (2014) 40–45

between stellar VLGs and dense-core VLGs, we need to construct aframework that takes into account all dust formation and destruction mechanisms as done by Asano et al. (2013b). Since they did
not include VLG formation in dense cores, it is necessary to
implement it into their framework in the future.
The stellar origin of VLGs is worth considering further.
As mentioned in Introduction, large interstellar grains ð 4 1 μmÞ exist
in chondritic meteorites. Given their large isotope anomalies that are
reﬂective of stellar nucleosynthesis processes (Clayton and Nittler,
2004), the grains may have formed in stellar ejecta. However, it isunlikely that grains formed in stellar ejecta have such a highabundance as observed by the spacecraft, since the timescale of dust
supply from stellar sources is likely to be longer than the destruction
timescale by shattering (Hirashita, 2010) and sputtering (McKee,
1989; Jones et al., 1996). Recently, Jones and Nuth (2011) havesuggested that the lifetime of silicate dust is comparable to thedestruction timescale, which means that the possibility of VLG
formation in stellar ejecta is still worth investigating.
The existence of VLGs can have a signiﬁcant inﬂuence on theextinction curve if there is local enhancement of VLG abundance as
indicated by the spacecraft missions (see the case of ϕVLG ¼ 0:5 in
Fig. 2). Thus, if we are concerned with the local variation of extinction
curves, the contribution from VLGs should be taken into account. On
global scales of a galaxy, in contrast, the abundance of VLGs is nothigh enough to affect the extinction curve, as long as the values ofthe parameters in Eq. (8) are similar to the Galactic values.
The far-infrared spectral energy distribution is also affected by
the existence of VLGs. The equilibrium temperature ðT eq Þ of a dust
grain depends on the grain radius as T eq p a1=ðβ þ 4Þ , where βð  2Þ isthe power-law index of the mass absorption coefﬁcient κ ν as afunction of frequency ν, κ ν p νβ (Evans, 1994). Because of thisdependence, VLGs tend to be colder than “normal” grains witha≲0:1 μm. If the abundance of VLGs is high, we should consider asigniﬁcant contribution from such a “cold” dust component.
4.2. Star formation efﬁciency in dense cores
The star formation efﬁciency in dense cores, ε, is a key factor for
the VLG-to-total-dust mass ratio ϕVLG . It enters our formulation in
two ways. The ﬁrst is through Eq. (1), in which the factor ð1  εÞexpresses the fraction of dust that is not included in stars formed indense cores. The second is through Eq. (2), which connects the coreformation rate to the star formation rate. As a result, ϕVLG p ð1  εÞ=ε(as long as ϕVLG ⪡1). If ε is nearly unity, ϕVLG  0, which means that all
VLGs once formed in dense cores are eventually included in stars. In
contrast, if ε≲0:01, ϕVLG  1. This corresponds to a case in which thetotal mass of dense cores is large.
The volume density of VLGs measured by Ulysses and Galileo iscomparable to that of the entire dust population expected fromthe dust-to-gas ratio in the ISM, D ¼ 0:01 (MRN in Fig. 1). For
example, ϕ ¼ 0:5 corresponds to ε ¼ 0:01, indicating an extremely
low star formation efﬁciency. Considering that star formation
efﬁciencies observationally estimated for dense cores are 0:1–0:3 (Section 2.2), the high VLG abundance is probably due
to local enhancement (see also Section 3.2).
4.3. Variation of other parameters
In galaxies, τSF and t shat may also change. The gas consumption
time τSF ranges from  108 year to  1011 year for nearby galaxies(Kennicutt, 1998). In a starburst galaxy with τSF  108 year, if we
adopt ε ¼ 0:1, f VLG ¼ 0:5 and t shat ¼ 108 year, we obtain ϕVLG C 0:8.
This large value is due to the enhanced formation rate of dense cores.
Therefore, the abundance of VLGs can be enhanced in starburst
galaxies.

If the typical dust size in starburst galaxies is really large and VLGs
are continuously supplied there, it may have important consequence
for the dust destruction efﬁciency by sputtering. Since the timescaleof dust destruction by thermal sputtering is proportional to the grain
size (Draine and Salpeter, 1979), the VLGs survive longer than smaller
grains. In particular, extreme starbursts at high redshift seem to havemore dust than can be produced by stars with a dust lifetime
expected for the “normal-sized” grains (Valiante et al., 2011;
Mattsson, 2011). The discrepancy is explained by grain growththrough accretion of gas-phase metals in the ISM (Michałowski
et al., 2010; Mattsson, 2011; Valiante et al., 2011; Kuo andHirashita, 2012). However, if the VLGs dominate the total dust mass,
their longer survival would make the discrepancy smaller, requiring
less grain growth than is thought in previous studies. This is also true
for nearby starburst galaxies.
However, in starburst galaxies, shattering may also be efﬁcient.
Grains acquire larger velocities in the ionized medium than in theneutral medium because less dissipative magnetohydrodynamic
nature of the ionized medium leads to more efﬁcient gyroresonance (resonance between the magnetohyrodynamical waves
with the gyromotion of a grain) acceleration of grains (Yan et al.,
2004; Hirashita and Yan, 2009). As a result, t shat is shorter in theionized medium. Therefore, if the ISM is highly ionized as a resultof high star formation activities in starburst galaxies, t shat may
decrease, compensating the decrease of τSF in Eq. (8).
In this paper, we have considered turbulence as the source of grain
motion for shattering. Shattering also occurs in supernova shocks(Jones et al., 1996). Hirashita et al. (2010) showed that shattering insupernova shocks is as efﬁcient as shattering in turbulence. They
derived the timescale of shattering in supernova shocks  0:01τSF ,which gives the same order of magnitude as t shat above. If we adopt
this expression, the dependence of ϕVLG on τSF cancels out (Eq. 8).
Therefore, if supernova shocks are the main site of shattering, the VLG
abundance is insensitive to the star formation activity.
In summary, it is not clear if the abundance of VLGs increases
or decreases in starburst galaxies. Nevertheless, the expression in
Eq. (8) is useful to understand the dependence of the VLG
abundance on star formation activity and shattering timescale.

5. Conclusion
We have estimated the abundance of very large grains (VLGs),
whose radii are typically ≳1 μm, in the Galaxy. Coreshine in dense
molecular cloud cores (dense cores) is taken as evidence for such
VLGs. Assuming that VLGs are formed in dense cores, we haveestimated the abundance of VLGs in the Galaxy. The VLG abundance relative to the total dust mass is estimated as ϕVLG 
0:01ð1 εÞ=εðτSF =5  109 yearÞ  1 ðf VLG =0:5Þðt shat =108 yearÞ, where εis the star formation efﬁciency in dense cores, τSF is the timescaleof gas consumption by star formation, f VLG is the fraction of dust
mass eventually coagulated into VLGs in dense clouds, and t shat is
the lifetime of VLGs (determined by shattering). Adopting typicalstar formation efﬁciencies ε  0:1–0:3, we obtain ϕVLG  0:02–0:09
for the Galaxy. This abundance is well below the value detected by
Ulysses and Galileo. Thus, if the VLGs originate from dense cores,
local enhancement of VLG abundance in the solar neighborhood isnecessary. We have also examined the effect of VLGs on theextinction curve, ﬁnding that the effect is negligible even withthe upper value of the above range, ϕVLG  0:09. With ϕVLG  0:5,
which is near the value of the above spacecraft data, the extinction
curve is still in the range of the variation in Galactic extinction
curves, but is not typical of the diffuse ISM. This again supports theidea that the high VLG abundance in the heliosphere is due to local
enhancement. Finally, it is worth noting that the explicit

H. Hirashita et al. / Planetary and Space Science 100 (2014) 40–45

dependence of ϕVLG on τSF , f VLG , and t shat , can be used to estimate
the VLG abundance in galaxies as well as in the Milky Way.
Acknowledgments
We are grateful to B.T. Draine and the anonymous referees forhelpful discussions and comments. HH is supported from NSC grant
NSC102-2119-M-001-006-MY3. RSA is supported from the Grant-inAid for JSPS Research under Grant no. 23-5514. TN is supported by
the Grant-in-Aid for Scientiﬁc Research of the Japan Society for the
Promotion of Science (22684004 and 23224004). ZYL is supported inpart by NSF AST-1313083 and NASA NNX10AH30G grants.
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