The Astrophysical Journal Letters, 811:L39 (5pp), 2015 October 1

doi:10.1088/2041-8205/811/2/L39© 2015. The American Astronomical Society. All rights reserved.

PROBING THE PHYSICAL CONDITIONS OF SUPERNOVA EJECTAWITH THE MEASURED SIZES OF PRESOLAR Al2O3 GRAINS
Takaya Nozawa1, Shigeru Wakita2, Yasuhiro Hasegawa1,4, and Takashi Kozasa3
1

Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan; takaya.nozawa@nao.ac.jp
2
Center for Computational Astrophysics, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan3
Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan
Received 2015 August 14; accepted 2015 September 4; published 2015 September 30

ABSTRACTA few particles of presolar Al2O3 grains with sizes above 0.5 μm are believed to have been produced in the ejecta
of core-collapse supernovae (SNe). In order to clarify the formation condition of such large Al2O3 grains, weinvestigate the condensation of Al2O3 grains for wide ranges of the gas density and cooling rate. We ﬁrst show thatthe average radius and condensation efﬁciency of newly formed Al2O3 grains are successfully described by a nondimensional quantity Lon , deﬁned as the ratio of the timescale with which the supersaturation ratio increases to thecollision timescale of reactant gas species at dust formation. Then we ﬁnd that the formation of submicron-sized
Al2O3 grains requires at least 10 times higher gas densities than those presented by one-dimensional SN models.
This indicates that presolar Al2O3 grains identiﬁed as having their origin in SNe might be formed in dense gas
clumps, allowing us to propose that the measured sizes of presolar grains can be a powerful tool for constraining
the physical conditions in which they formed. We also brieﬂy discuss the survival of newly formed Al2O3 grains
against destruction in the shocked gas within SN remnants.
Key words: dust, extinction – Galaxy: evolution – ISM: supernova remnants – meteorites, meteors, meteoroids –stars: massive – supernovae: generalcomponents in the Cassiopeia A (Cas A) SNR (Douvion
et al. 2001; Rho et al. 2008). Furthermore, most of the dust
formation calculations have predicted the formation of Al2O3
grains in the ejecta of SNe as the ﬁrst condensate among oxide
grains (Kozasa et al. 1989, 1991; Todini & Ferrara 2001;
Nozawa et al. 2003, 2008, 2010; Bianchi & Schneider 2007;
Kozasa et al. 2009; Sarangi & Cherchneff 2015). However, thecalculated sizes of Al2O3 grains are below 0.03 m m , which ismuch smaller than the measured sizes of presolar Al2O3 grains
with 0.5–1.5 μm in diameter (Choi et al. 1998; Nittler et al.
1998), and such small Al2O3 grains are found to be almost
completely destroyed in the hot gas within the SNRs before
being ejected into the ISM (Nozawa et al. 2007; Silvia
et al. 2010, 2012). This seems to contradict the fact that we areobserving Al2O3 grains of an SN origin on the Earth.
One of the main reasons why only small Al2O3 grains areproduced in simulations is the low number density of Al atoms
in the ejecta, led by the relatively homogeneous ejecta ofspherically symmetric SN models (hereafter referred to as 1D
SN models). In reality, the SN ejecta should be much more
inhomogeneous and complicated, as is suggested from multidimensional hydrodynamic simulations (e.g., Kifonidis
et al. 2003; Hammer et al. 2010; Joggerst et al. 2010) andvarious observations of SN 1987A (e.g., Kjær et al. 2010;
Larsson et al. 2013). This implies that the formation ofdust grains would proceed in the gases with a variety ofdensities and that large grains could be formed in high-density
clumps.
In this Letter, we investigate the formation of Al2O3 grains
for wide ranges of density and cooling rates of gas to explore
the formation condition of presolar Al2O3 grains as large as
those measured in meteorites. We show that submicron-sized
Al2O3 grains can be produced only in gas with more than 10times higher densities than those predicted by 1D SN models,suggestive of the presence of dense gas clumps in the ejecta.

1. INTRODUCTION
The role of core-collapse supernovae (SNe) as dust
producers is a fundamental issue for understanding theevolution history of dust in the universe. Recent far-infraredobservations of young supernova remnants (SNRs) revealed
that 0.1–1 Me of dust had formed in the metal-rich inner ejecta(Barlow et al. 2010; Sibthorpe et al. 2010; Matsuura et al. 2011,2015; Gomez et al. 2012; Indebetouw et al. 2014). However, itremains to be clariﬁed what fraction of these newly formed
grains can survive destruction in the shock-heated gas within
SNRs and be injected into the interstellar medium (ISM). The
destruction efﬁciency of dust grains depends on their chemicalcompositions and size distributions (e.g., Nozawa et al. 2007),
which are determined by the density and temperature evolutionof the gas out of which they form (Nozawa & Kozasa 2013) aswell as the degree of mixing and clumpiness of the ejecta(Nozawa et al. 2003; Sarangi & Cherchneff 2015). Therefore,
the physical condition and structure of the SN ejecta must be
fully appreciated through various approaches to unravel theproperties of dust that is formed in the ejecta and is ﬁnallyejected into the ISM.
Presolar grains, which are identiﬁed in meteorites due totheir highly anomalous isotopic compositions, are invaluablefossils that enable us to directly observe the detailed chemicalcompositions and sizes of stellar dust (Clayton & Nittler 2004
and references therein). Their isotopic signatures give clues
about nucleosynthesis in stars and mixing of elements in the
SN ejecta. In addition, the measured sizes of presolar grains
could offer key information on the physical conditions at theirformation sites.
Among the presolar grains that are considered to haveoriginated in SNe, Al2O3 grains are of great importancebecause Al2O3 is believed to be one of the major dust
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The Astrophysical Journal Letters, 811:L39 (5pp), 2015 October 1

Nozawa et al.
Table 1
Numerical Constants Used for Dust Formation Calculations

We also examine the survival of Al2O3 grains against thedestruction process in SNRs. We propose that the comparison
between the calculated sizes and the measured sizes of presolar
grains can be a novel and valuable approach that gives insight
into the physical conditions and structure of the SN ejecta.

The formation of Al2O3 grains is calculated by applying theformula of non-steady-state dust formation in Nozawa &Kozasa (2013). In this formula, the formation of small clusters
and the growth of grains are self-consistently followed under
the consideration that the kinetics of the dust formation process
is controlled by collisions of key species, deﬁned as the gas
species that have the lowest collisional frequency among
reactants. The formula leads us to derive the size distribution
and condensation efﬁciency of newly formed grains, given
chemical reactions for the formation of clusters, abundances of
the relevant gas species, and time evolutions of gas density andtemperature. The detailed prescription of the calculations of
non-steady dust formation is given in Nozawa &Kozasa (2013).
In the ejecta of SNe, the most likely formation site of Al2O3
grains is the O-rich layer, where Al atoms as well as O atoms
abundantly exist. We consider as a chemical reaction at cluster
formation 2Al + 3O  Al2O3 (Kozasa et al. 1989). The initial
number ratio of Al to O atoms is taken as cAl,0 cO,0 = 1 200,
where cAl,0 and cO,0 are, respectively, the number densities of Al
and O atoms at a given initial time t = t0, so that the key
species are Al atoms. This abundance ratio approximately
corresponds to that in the Al-rich region of solar-metallicity
SNe (see, e.g., Kozasa et al. 2009; Nozawa et al. 2010). Notethat the results of calculations are little affected by the Al/O
ratio as long as cAl,0 cO,0  1.
The ejecta of SNe freely expands after ∼1 day postexplosion, and the gas density is inversely proportional tothe cube of time t. Thus, the number density of a gas
species c˜i (t ) (where i is Al or O), without the depletion of thegas-phase atoms due to the formation of clusters and grains, isgiven by

a0a
(Å)

σb
(erg cm−2)

18.4788

45.3542

1.718

690

determine T0 for a given cAl,0 and cO,0 from the equationln S = -⎛ cAl,0 kT0 ⎞Dg+ ln ⎜⎟
kT0⎝ ps ⎠+

3 ⎛ cO,0 kT0 ⎞ln ⎜⎟ = 0,
2 ⎝ ps ⎠(3 )where Dg is the change of the chemical potential at thestandardpressureandisapproximatedaspsD
g kT = -A T + B with the numerical values A and B
taken from Nozawa et al. (2003) (see Table 1).
In this study, we regard the clusters containing more than
100 Al atoms as grains. This corresponds to the minimum grainradius of a* = 8.0 Å (Al2O3 grains are assumed to be
spherical). The sticking probability of gas species is assumed to
be unity for any sizes of clusters and grains. In the calculations,
we take t0 = 300 days, so the free parameters are cAl,0 and γ, forwhich we consider the ranges of cAl,0 = 104–1011 cm−3 andγ = 1.1–1.7. The calculations are performed until the gas
density becomes so low that grain growth is negligible. In what
follows, we mainly examine the resultant behavior of the ﬁnal
average radius aave,¥ and condensation efﬁciency fcon,¥ which
are obtained at the end of the calculations. The condensation
efﬁciency is deﬁned as the fraction of Al atoms locked up in
Al2O3 grains.
3. RESULTS OF DUST FORMATION CALCULATIONS
Figure 1 shows the size distributions of newly formed Al2O3
grains calculated for γ = 1.25, adopting cAl,0 = 107, 108, and109 cm−3. For these cases, all Al atoms are ﬁnally locked up in
Al2O3 grains (that is, fcon, ¥ = 1). As seen from the ﬁgure, thesize distribution is lognormal-like for any of cAl,0 considered
here, with a narrower width for a higher cAl,0 . More importantly,
the average radius increases with increasing cAl,0 :aave, ¥ = 0.0067, 0.047, and 0.36 μm for cAl,0 = 107, 108, and109 cm−3, respectively. This is because a higher gas density
leads to more efﬁcient growth of grains. The results in Figure 1
point out that, for γ = 1.25, the number density of Al atoms at
dust formation must be higher than ∼5 × 108 cm−3 in order for
Al2O3 grains with radii larger than 0.25 μm (0.5 μm in
diameter) to form.
Nozawa & Kozasa (2013) demonstrated that the formation
process of dust grains is described in terms of the timescales of
two physical quantities: the timescale with which the supersaturation ratio S increases tsat and the collision timescale ofkey species tcoll . They found that, for C and MgSiO3 grains, theaverage radius and condensation efﬁciency are universallyscaled by one non-dimensional quantity Lon º tsat (ton )tcoll (ton ), where ton is the onset time of dust formation(ton  t0 ) and is taken as a time at which the condensation(1 )As in Nozawa & Kozasa (2013), the gas temperature T(t) is
assumed to decrease as⎛ t ⎞-3 (g - 1)
T (t ) = T0 ⎜ ⎟,⎝ t0 ⎠

B

Notes.
aHypothetical radius of the condensate per key molecule.
b
Surface tension of bulk condensate (Overbury et al. 1975).

2. MODEL OF DUST FORMATION⎛ t ⎞-3c˜i (t ) = ci,0 ⎜ ⎟ .
⎝ t0 ⎠

A/104 K(2 )where T0 is the gas temperature at t0 and γ is a free parameterthat prescribes the cooling rate.
As the gas cools down, the formation of dust from gas can berealized in a supersaturated state (S > 1); S is the supersaturation ratio deﬁned as ln S = -Dg kT with k being theBoltzmann constant and Δg the change of the chemical
potential per key species for the formation of bulk condensate
from the reactants, as is formulated in Equation (30) in Nozawa& Kozasa (2013). Here we take t0 as a time at which S = 1 and
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Nozawa et al.

Figure 1. Final size distribution spectrum of newly formed Al2O3 grains
calculated for γ = 1.25 and t0 = 300 days. The size distributions are plotted as
a4 n(a) so as to represent the mass distribution per logarithmic grain radius,
where n(a) is the arbitrarily normalized number density of grains with radii
between a and a + da. Three cases are considered for the number density of Al
atoms at t = t0; cAl,0 = 107 (dotted), 108 (solid), and 109 cm−3 (dashed).

Figure 2. Dependence of the ﬁnal average radii aave,¥ and condensation
efﬁciencies fcon,¥ of newly formed Al2O3 grains on L on . The results for four
different γ (γ = 1.1, 1.3, 1.5, and 1.7) are shown in each color but they areplotted as almost the same curve. The hatched regions depict the expected
ranges of L on for the formation of Al2O3 grains in the Al-rich region, referring
to 1D models of a Type II-P SN (cyan; Kozasa et al. 2009) and a Type IIb SN(Nozawa et al. 2010). The solid vertical line denotes the minimum value of L on(=3 ´ 10 4 ) necessary for explaining the measured sizes (radius of
0.25 μm) of presolar Al2O3 grains.

efﬁciency reaches 10−10. According to their study, it would beinteresting to see if such a scaling relation holds for Al2O3
grains.
Figure 2 depicts the average grain radii aave,¥ andcondensation efﬁciencies fcon,¥ obtained from the calculations
with a variety of cAl,0 for each of γ = 1.1, 1.3, 1.5, and 1.7, as afunction of Lon . In the present study, Lon is approximately
written as (Nozawa & Kozasa 2013)
L on 

⎞ ⎡ c˜Al ( ton ) ⎤ ⎡ T ( ton ) ⎤ 32
1082 ⎛
ton
⎟⎢
⎜
⎥⎢
⎥ .
g - 1 ⎝ 300 days ⎠ ⎣ 108 cm-3 ⎦ ⎣ 2000 K ⎦Our calculations show that, in order to produce Al2O3 grains
larger than 0.25 μm (diameter of 0.5μm) as measured forpresolar grains, Lon should be higher than 3 × 104. Given thatγ and T (ton ) do not change largely, such a high Lon could beachieved by considering the gas densities that are more than
one order of magnitude higher than those presented by 1D SN
models (namely, c˜Al (ton )  7 ´ 108 cm-3 at ton = 300
days; see Equation (4)). This strongly suggests that thediscovered presolar Al2O3 grains were formed in dense clumps
within the ejecta. Equation (4) tells us that the formation oflarge Al2O3 grains may also be possible if the formation time ofdust is later than ton = 3000 days. However, it is too hard to
keep the gas density as high as c˜Al  108 cm-3 in such lateepochs because the gas density rapidly decreases with time (seeEquation (2)).

(4 )Figure 2 clearly shows that the results for different γ are well
overplotted, indicating that both aave,¥ and fcon,¥ are uniquelydetermined by Lon even for Al2O3 grains. As is the case for C
and MgSiO3 grains, the formation of Al2O3 grains can berealized at Lon  1–2, and fcon, ¥ = 1 at Lon  20 . In
addition, aave,¥ becomes large as Lon increases, which meansthat the ﬁnal average radius is larger for a higher gas density
and/or a slower gas cooling because Lon is roughly proportional to the product of gas density and cooling timescale that is
reﬂected by ton .
In Figure 2, we also plot the ranges of Lon expected in theejecta of Type II-P and IIb SNe, referring to 1D SN models
used in Kozasa et al. (2009) and Nozawa et al. (2010),
respectively. For a Type II-P SN with the massive hydrogenenvelope, the number density of Al atoms in the Al-rich regionis estimated to be c˜Al (ton )  (0.2–8) ´ 107 cm-3 at ton = 300
days. For g  1.25 and T (ton )  2000 K, this corresponds to
Lon  70–3000, for which aave,¥  0.002–0.03 μm. On theother hand, for a Type IIb SN with a small mass envelope,c˜Al (ton )  (0.3–5)´ 10 4 cm-3 at ton = 300 days, resulting in
Lon  0.1–2. Hence, Al2O3 grains are not expected to form inType IIb SNe. Nozawa et al. (2010) reported the formation of
Al2O3 grains in Type IIb SNe but their average radii are lessthan ;8 Å, which is regarded as being small clusters in thisstudy.

4. DISCUSSION AND CONCLUSIONS
We have systematically investigated the formation of Al2O3
grains, adopting a wide variety of gas densities and coolingrates. We show that, as in the cases of C and MgSiO3 grains,
the average radius and condensation efﬁciency of Al2O3 grains
are nicely scaled by a non-dimensional quantity Lon , deﬁned as
the ratio between the timescale of the supersaturation ratio andthe collision timescale of key species at dust formation. We
also ﬁnd that large Al2O3 grains with radii 0.25 μm can beformed only in dense gas regions that have more than 10 times
higher densities than those estimated from 1D SN models. This
points out the presence of dense clumps in the ejecta of corecollapse SNe.
The formation of dust in dense clumps was deduced fromvarious early-phase (1000 days after explosion) observationsof SN 1987A (e.g., Lucy et al. 1991; Meikle et al. 1993;
Colgan et al. 1994), which can be classiﬁed as a Type II-P SN.
The recent radiative transfer models of dust emission andabsoption also suggested the necessity of optically thick clumps
to account for the evolution of optical to infrared emission from3

The Astrophysical Journal Letters, 811:L39 (5pp), 2015 October 1

Nozawa et al.

in the ISM, for which we take reasonable values of 1.8 × 1051
erg and 1.0 cm−3, respectively.
The result of the calculation is given in Figure 3, whichshows that small grains with initial radii of a ini  0.01 m m arecompletely destroyed in the shocked gas. Grains with
0.02 m m  a ini < 0.1 m m are eroded in the hot gas and are
ﬁnally destroyed as soon as they encounter the cool dense shellthat is formed behind the forward shock after 5 ´ 10 4
years. On the other hand, Al2O3 grains with a ini  0.2 m m canbe ejected from SNe without reducing their size signiﬁcantly.
This simple calculation illustrates that, once large Al2O3 grains
are produced in dense clumps, they are likely to survive thedestruction in SNRs and to be easily transported to the ISM.5
Thus, we suggest that the formation of submicron-sized Al2O3
grains in dense clumps is also indispensable in order that newly
formed Al2O3 grains can endure destruction by shocks and beincorporated into nearby molecular clouds and protoplanetarydisks.
The identiﬁcation of Al2O3 grains as SN in origin comesfrom their relatively high 18O/16O ratio (so-called Group 4
grains, Nittler et al. 1997; Choi et al. 1998) or large enrichmentof 16O (represented by Grain T84, Nittler et al. 1998). Since weconsider the formation of Al2O3 grains in the O-rich layer
where 16O is rich, they may be categorized as T84-like grains(or Group 3 grains with the moderate enhancement of 16O). On
the other hand, to explain the 18O-enriched composition ofGroup 4 grains, the extensive mixing between different layers
in the ejecta is invoked with the relatively 18O-rich hydrogenenvelope being the dominant component (Nittler et al. 2008).
However, even if large-scale mixing takes place, the molecular
diffusion lengths are much smaller than the typical size of gas
clumps so that the microscopic mixing of elements may be very
ineffective (Deneault et al. 2003). Therefore, the origin of theoxygen isotopic composition of the Group 4 Al2O3 grains, aswell as their formation process, is still a challenging problem.
We conclude that dense gas clumps are necessary for theformation of submicron-sized Al2O3 grains as discovered inmeteorites. The presence of such dense clumps in the O-richlayer may also cause silicate grains to be formed with verylarge radii compared to those based on 1D SN models. Given
that the radii of silicate grains are generally larger than those of
Al2O3 grains by a factor of about 10 (e.g., Nozawa et al. 2003),
the discovery of 16O-enriched micron-sized (;1–10 μm)
silicate grains in meteorites will serve as further evidence fordense clumps in the SN ejecta.

Figure 3. Time evolutions of the positions (upper) and the ratios of radii to theinitial ones (lower) of Al2O3 grains in an SNR. The results are plotted for the
initial grain radii of 0.01, 0.02, 0.05, 0.1, and 0.25 μm. In the upper panel, thethick solid curves depict the trajectories of the forward shock (FS) and reverse
shock (RS).

SN 1987A over ;600–9000 days (Ercolano et al. 2007; Bevan& Barlow 2015; Dwek & Arendt 2015; Wesson et al. 2015).
The density contrast between the clumps and interclumps
considered by these works is ;10–100, which is in good
agreement with the density enhancement needed for theformation of large Al2O3 grains (i.e., more than 10 times thatof 1D SN models). This allows us to conclude that themeasured size of presolar grains is an independent and usefulprobe for constraining the clump density in ejecta.
Our calculations show that Al2O3 grains cannot form in TypeIIb SNe as a result of the too low ejecta density in the 1D SN
model. However, the analyses of the infrared emission spectraof Cas A, which was identiﬁed as Type IIb through a light echo
(Krause et al. 2008), have suggested the presense of newly
formed Al2O3 grains (Douvion et al. 2001; Rho et al. 2008).
This contradiction can also be resolved by considering thedense gas clumps in the ejecta; from Figure 2, we can estimatethat the density of gas clumps required for the formation of
Al2O3 grains (that is, Lon  2) is more than 10 times that of the
1D Type IIb SN model. We also note that the recent
observation of near-infrared extinction implies the existenceof large (0.1 m m ) Si grains in Cas A, providing anotherindication of dust formation in dense clumps (Lee et al. 2015).
Next we discuss the survival of Al2O3 grains formed in theejecta against the destruction by SN shocks on the basis of adust evolution model in SNRs (Nozawa et al. 2007). Thismodel assumes a spherically symmetric shock, but it has beenshown that the destruction efﬁciency of dust is not greatly
different from those by multi-dimensional hydrodynamic
simulations (Silvia et al. 2010, 2012). As the initial conditionof the ejecta, we here consider the core-envelope structure of
3 + 12 M (implicitly assuming Type II-P SNe). The other
input parameters are the explosion energy and the gas density

We thank Masaomi Tanaka for useful comments. We are
grateful to the anonymous referee for critical comments that
improved the manuscript. This work has been supported in partby a JSPS Grant-in-Aid for Scientiﬁc Research (23224004,
26400223).
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