The Astrophysical Journal, 736:45 (13pp), 2011 July 20

doi:10.1088/0004-637X/736/1/45


C 2011. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

FORMATION OF DUST IN THE EJECTA OF TYPE Ia SUPERNOVAE
Takaya Nozawa1 , Keiichi Maeda1 , Takashi Kozasa2 , Masaomi Tanaka1 , Ken’ichi Nomoto1 , and Hideyuki Umeda3
1 Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba 277-8583, Japan; takaya.nozawa@ipmu.jp
2 Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan
3 Department of Astronomy, School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan

Received 2011 February 2; accepted 2011 May 3; published 2011 July 5

ABSTRACT
We investigate the formation of dust grains in the ejecta of Type Ia supernovae (SNe Ia), adopting the carbondeflagration W7 model. In the calculations of dust formation, we apply the nucleation and grain growth theory andconsider the two extreme cases of the formation of CO and SiO molecules: complete formation and no formation.
The results of the calculations show that for the sticking probability of αj = 1, C, silicate, Si, and FeS grains cancondense at early times of ∼100–300 days after the explosion, whereas Fe and SiC grains cannot form substantially.
Due to the low gas density in SNe Ia with no H-envelope, the average radii of the newly formed grains are generally
below 0.01 μm, being much smaller than those in Type II-P SNe. This supports our previous conclusion that theradius of dust formed in the ejecta is smaller in SNe with less massive envelopes. The total dust mass ranges from3 × 10−4 M to 0.2 M for αj = 0.1–1, depending on whether or not CO and SiO molecules are formed. We
also estimate the optical depths and thermal emission by the newly formed dust and compare them to the relevant
observations of SNe Ia. We find that the formation of C grains in SNe Ia must be suppressed to be consistent withobservational constraints. This implies that energetic photons and electrons heavily depress the formation efficiency
of C grains or that the outermost C–O layer of SNe Ia is almost fully burned. Finally, we calculate dust destructionin the SN remnants and find that dust grains formed in the ejecta of SNe Ia are almost completely destroyed in theshocked gas before being injected into the interstellar medium. This indicates that SNe Ia are unlikely to be themajor sources of interstellar dust.
Key words: dust, extinction – galaxies: abundances – infrared: stars – ISM: supernova remnants – supernovae:
general – white dwarfs
Online-only material: color figures
isotopic signatures of type X silicon carbide (SiC) particles canbe explained if SiC grains condense out of the explosive heliumburning layer in SNe Ia. However, the composition, size, andamount of dust grains formed in the ejecta of SNe Ia and injected
into the interstellar medium (ISM) have not been fully exploredto date.
It should be mentioned that systematic studies of SN Ia rates
have proposed the presence of a prompt component of SNe Ia
exploding in a timescale as short as 0.1 Gyr after the stellar
birth (Mannucci et al. 2005, 2006; Della Valle et al. 2005;
Scannapieco & Bildsten 2005). The increasing testimonies ofsuch short-lived SNe Ia have been thereafter given by many
theoretical and observational works (Totani et al. 2008; Aubourg
et al. 2008; Hachisu et al. 2008a, 2008b; Matteucci et al. 2009;
Brandt et al. 2010; Maoz et al. 2010). Although in a single
degenerate scenario SNe Ia are not expected to generate inmetal-poor environments as low as [Fe/H] < −1.1 (Kobayashi
et al. 1998), prompt SNe Ia might have occurred in the early
universe at redshifts higher than z = 4, where most of theobserved quasar systems have already reached solar- and supersolar metallicities (Juarez et al. 2009). Hence, if prompt SNe
Ia could actually produce dust grains, they would have made alarge contribution to dust budgets not only in our Galaxy but
also in high-redshift dusty galaxies (e.g., Valiante et al. 2009).
On the other hand, no observation of normal SNe Ia hasreported convincing evidence for the ongoing formation of dustin the ejecta as indicated by an increase in the infrared (IR)continuum, a rapid decline in optical luminosity, and blueshifts
of atomic line emissions; Gerardy et al. (2007) observed two
SNe Ia, SN 2003hv and SN 2005df, at t ∼100–400 days since
the explosion with the Spitzer Space Telescope. However, the

1. INTRODUCTION
Type Ia supernovae (SNe Ia) are considered to be thermonuclear explosions of carbon–oxygen white dwarfs (WDs). In asingle degenerate scenario, the progenitor of an exploding WD
grows up to a mass close to the Chandrasekhar limit throughmass transfer from the binary companion and finally undergoes
carbon ignition near the center (e.g., Nomoto 1982). However,it has been a matter of controversy whether the nuclear burning
front propagates as a subsonic deflagration wave (Nomoto et al.
1976, 1984b) or as a supersonic detonation wave growing fromthe deflagration (Khokhlov 1991a, 1991b). Although there aresome differences in the resulting elemental distributions, bothpropagation modes can synthesize a significant amount of ironpeak elements as well as intermediate-mass elements such as
Si, S, and Ca (Höflich et al. 1995; Iwamoto et al. 1999). Thus,
SNe Ia are major sources of heavy elements and play a critical role in the chemical enrichment history of the universe (e.g.,
Nomoto et al. 1984a; Timmes et al. 1995; Kobayashi & Nomoto2009).
It has also been supposed that SNe Ia can be possible
producers of dust grains, especially Fe grains (Tielens 1998),
and would have important consequences for the evolution andinventory of interstellar dust (Dwek 1998). This presumption
is mainly based on their metal-rich compositions of coolinggas in the ejecta similar to those in core-collapse supernovae(CCSNe) for which several pieces of observational evidence
for dust formation have been reported (see Kozasa et al. 2009
for review). In addition, the formation of dust in SNe Ia has
been suggested from the analysis of presolar grains extracted
from meteorites; Clayton et al. (1997) pointed out that the1

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Nozawa et al.

observed mid-IR spectral energy distributions (SEDs) did notshow any evolution, allowing the authors to conclude that themid-IR fluxes are dominated by strong atomic line emission
rather than thermal emission from newly formed dust. Maeda
et al. (2009) discovered an accelerated fading of the opticallight curve for the peculiar SN Ia 2006gz, but it remains unclear
whether this is responsible for dust formation. Furthermore, noIR emission from dust formed in the ejecta has been seen in the
Tycho supernova remnant (SNR; Douvion et al. 2001) identified
as a standard SN Ia (Krause et al. 2008), although recently
Ishihara et al. (2010) suggested the possible detection of thermal
emission from ejecta-origin dust, based on IR observations withAKARI.
The fact that the existence of newly formed dust has notbeen distinctly confirmed so far implies that formation of dustin SNe Ia is likely to be inefficient or impossible because ofsome physical conditions in the ejecta that are different fromCCSNe; SNe Ia have much higher expansion velocities of ejecta
and produce much more radioactive element 56 Ni than typical
CCSNe. A higher expansion velocity leads to a lower gas density
in the ejecta, which prevents dust grains from growing to radiilarger than 0.01 μm or even makes the condensation of dust
unsuccessful (Nozawa et al. 2008, 2010). In addition, energetic
photons and electrons generated from the decay of radioactive
elements can inhibit the formation of dust grains (Nozawa
et al. 2008) and can also disturb the formation of SiO and CO
molecules which affects the dust formation processes (Höflichet al. 1995). Thus, it is essential to examine how the formation
process of dust in the ejecta depends on the type of SNe, by
taking into account the time evolution of gas temperature anddensity, the formation of CO and SiO molecules, and the impactof high-energy photons and electrons.
In this paper, we investigate the formation of dust in the
expanding ejecta of SNe Ia, with the aim of revealing the rolesof SNe Ia in the dust enrichment in the universe. In Section 2,
we describe the models of SNe Ia and the method of calculationof dust formation. In the calculations, we adopt the carbondeflagration W7 model (Nomoto et al. 1984b; Thielemann et al.
1986) as a model of SNe Ia and apply the nucleation and grain
growth theory to estimate the composition, size, and mass of dustthat can condense in the ejecta. The results of the calculations arepresented in Section 3 for the cases with and without formationof CO and SiO molecules. In Section 4, we calculate the opticaldepths by the newly formed grains and their thermal emission
and apply them to the observational constraints. Then we discuss
the formation process of dust in SNe Ia and the elemental
composition in the outermost layer of SNe Ia. In Section 5,
we calculate the destruction of the newly formed grains that iscaused by the propagation of the reverse shock into the ejecta
and examine whether they can survive to be injected from SNe
Ia into the ISM. A summary is given in Section 6.

Figure 1. Relative number abundances of elements taking part in dust formationin the ejecta of the SN Ia (W7 model) at 300 days after the explosion as afunction of enclosed mass. The decay of radioactive elements is taken into
account, and the abundance of each element is summed up over the isotopes.
In the calculations of dust formation, the original onion-like composition isassumed to be preserved with no mixing of elements.
(A color version of this figure is available in the online journal.)

1984b; Thielemann et al. 1986). The W7 model can account for
many of the observed characteristics of normal SNe Ia, so it has
been extensively used as one of the most standard SN Ia models.
In the W7 model, the ejecta mass is Meje = 1.38 M and the
kinetic energy of the explosion is Ekin /1051 erg = E51 = 1.3.
The mass of synthesized 56 Ni is M(56 Ni) = 0.6 M , which isone order of magnitude larger than those (M(56 Ni)  0.06 M )produced in typical CCSNe.
Figure 1 shows the number abundances of elements relevant
to dust formation in the ejecta of the W7 model at 300 days
after the explosion as a function of enclosed mass Mr . In
Type II-P SNe (SNe II-P) with massive H-envelopes, dust grains
can only form in the metal-rich gas inside the He core (Kozasa
et al. 1989). However, SNe Ia do not have H-rich envelopes,
and dust formation would be possible in the entire region of
the ejecta. We divide the ejecta of the W7 model into four
layers, according to the elemental composition of interest to dust
formation: the Fe–Ni layer (Mr = 0–0.91 M ), the Si–S layer(Mr = 0.91–1.14 M ), the O-rich layer (Mr = 1.14–1.28 M ),and the C–O layer (Mr = 1.28–1.38 M ).
In the deflagration W7 model, 0.1 M of C and O remains
unburned in the outermost layer. In W7, the initial C+O
white dwarf is assumed to be composed of X(12 C) = 0.475,
X(16 O) = 0.50, and X(22 Ne) = 0.025 (where X denotes themass fraction) with a number ratio of C/O = 1.27. Therefore, we
can expect the formation of C grains in the outermost C–O layer,
although the C/O ratio in the outermost layer is determined bymany cycles of recurrent He-shell flashes, thus being highly
uncertain. On the other hand, in the delayed detonation model,
pre-existing C atoms can be completely burned, except for thosein the very outer layers with expansion velocities higher than
∼20,000 km s−1 (Iwamoto et al. 1999), which prohibits thecondensation of large amounts of C grains. The formation of C
grains and the elemental composition in the outer layer of SNe
Ia will be discussed in Section 4.4.
In the calculations, we consider the onion-like elemental composition as shown in Figure 1, assuming that any microscopic
and macroscopic mixing of elements does not occur before the

2. CALCULATION OF DUST FORMATION IN THE
EJECTA OF SNe Ia
2.1. Model of SNe Ia
The composition, size, and number density of dust formedin SNe depend on the elemental composition in the ejecta
as well as the time evolution of the density and temperatureof the gas (Kozasa et al. 1989, 1991; Nozawa et al. 2003).
In the calculations of dust formation in SNe Ia, we adopt
the nucleosynthesis and hydrodynamic results of the onedimensional carbon-deflagration W7 model (Nomoto et al.
2The Astrophysical Journal, 736:45 (13pp), 2011 July 20

Nozawa et al.

condensation of dust grains. This assumption is supported by avariety of studies; the spectrum synthesis calculations of a timeseries of spectra obtained during t = 5–377 days for SN 2002bo,
SN 2004eo, and SN 2003du demonstrated that the abundance
distributions in the ejecta of these SNe Ia are fully stratified
with some degree of macroscopic mixing (Stehle et al. 2005;
Mazzali et al. 2008; Tanaka et al. 2011). Based on the analysisof the emission profiles in the mid-IR spectrum at t  135 days,
Gerardy et al. (2007) have also shown that the ejecta structurein SN Ia 2005df is chemically stratified. Furthermore, X-ray
observations of the Tycho SNR indicate that the layered composition has been retained in the ejecta even at ∼450 yr after
the explosion (Badenes et al. 2006; Hayato et al. 2010; see also
Kosenko et al. 2010 for Type Ia SNR 0519–69.0).
The time evolution of the gas density in the freely expanding
ejecta is calculated as ρ ∝ t −3 , based on the density structureof the W7 model. The time evolution of the gas temperature isevaluated by solving the radiative transfer equation simultaneously with the energy equation of the radiation plus gas under
the assumption of local thermodynamic equilibrium (Iwamoto
et al. 2000). The energy deposition through the decay of radioactive isotopes is calculated by giving a constant γ -ray absorption
opacity that can reproduce the behavior of the bolometric light
curves observed for standard SNe Ia. The kinetic energies of
positrons are assumed to be deposited instantaneously in situ.
The energy loss by positron escape becomes more important atlater times when the density in the ejecta is low enough. However, at the epochs relevant to this study (t  300 days), thiseffect can be negligible (Milne et al. 2001).
Figures 2(a) and (b) show the structures of the gas temperatureand density in the ejecta of the W7 model, respectively, at
100 days (thick solid lines) and 300 days (thick dashed lines)
after the explosion. Figure 2(c) displays the velocity distributionof the W7 model. For comparison, we also show those in the
He core of the SN II-P model with Meje = 17 M , E51 = 1,
and a massive H-envelope of MHenv = 13.2 M (thin lines;
Umeda & Nomoto 2002). As can be seen from Figure 2(c),the expansion velocity of the metal-rich ejecta is much higher
in the SN Ia than in the SN II-P, despite the almost identical
explosion energy of both SNe; in the SN Ia all of the explosion
energy is deposited into the low-mass ejecta with no H-envelope,
whereas in the SN II-P most of the explosion energy is used toblow off the massive H-envelope. As a result, the gas density
in the SN Ia is more than three orders of magnitude lower thanthat in the SN II-P. In addition, the gas temperature in the SN
Ia decreases more quickly than that in the SN II-P and drops
to ∼2000 K at 100 days. This is because the lower gas density
causes absorption of γ -ray in the ejecta to be less efficient andbecause the thermal energy produced at the explosion is quickly
lost by the adiabatic expansion unlike SNe II-P.

Figure 2. (a) Temperature and (b) density distributions of the gas in the ejectaof the SN Ia (W7 model) at day 100 (thick solid lines) and day 300 (thickdashed lines) after the explosion, and (c) the velocity structure for the W7model (thick lines). The enclosed mass is normalized to the ejecta mass of the
SN Ia (Mc = Meje = 1.38 M ). For comparison, those for the SN II-P model(thin lines) with Mpr = 20 M and E51 = 1 (Umeda & Nomoto 2002) are
shown. The mass coordinate for the SN II-P is normalized to the mass of themetal-rich ejecta (Mc = MHecore − Mmasscut = 3.34 M ) within which dust
formation is realized (Nozawa et al. 2003).
(A color version of this figure is available in the online journal.)

dust formation calculations, we refer readers to Nozawa et al.
(2003). We also note that there is another approach to evaluate
the amount of dust formed in SN ejecta, which follows theabundances of dust precursor molecules by solving a complex
chemical reaction network (Cherchneff & Dwek 2009, 2010).
The nucleation rate, taking account of chemical reactions atcondensation, is evaluated by introducing the concept of the key
species defined as the least abundant gaseous species among
the reactants. By assuming that the key species controls the
kinetics of nucleation and grain growth (Kozasa & Hasegawa
1987; Hasegawa & Kozasa 1988) and taking into account thedifference between the temperatures of gas and condensation
nuclei (Kozasa et al. 1996), the steady-state nucleation rate Jjs
for a given grain species j is written as4 12 
 12
4μ3j
2σj
T
s
2
Jj = αj Ωjc1,j exp −, (1)π m1,jTd,j27(ln Sj )22.2. Nucleation Rate
One of the main aims of this paper is to clarify how the size
and mass of dust formed in the ejecta depend on the type of
SNe. In order to achieve this goal, we apply a non-steady state
nucleation and grain growth theory, which has been utilized
for investigating the dust formation in various types of CCSNe
in our previous studies (Nozawa et al. 2003, 2008, 2010). The
theory enables us to estimate the size distribution and mass of
newly formed dust, given the elemental composition and thetime evolution of density and temperature of the gas. Here we
present the formula for the nucleation rate, which will be usefulfor discussion in Section 4. For a comprehensive description ofwhere αj is the probability that the key species stick to the2
surface of grains, μj = 4π a0,j
σj /kTd,j is the energy barrier
for nucleation, k is the Boltzmann constant, σj is the surface
energy, T is the gas temperature, Td,j is the temperature of
the condensation nuclei, and Ωj and a0,j = (3Ωj /4π )1/3
are, respectively, the volume and hypothetical radius of the
4 There is a typographical error in Equation (3) for the nucleation rate in
2 as seen in Equation (1).
Nozawa et al. (2003); c1,j should be replaced with c1,j3

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Nozawa et al.

Table 1
Chemical Reactions for Silicate Grains Considered in This Paper
No.

Dust Species

Key Species

Chemical Reaction

A/104 K

B

Model A
(1)
(2)

MgSiO3(s)Mg2 SiO4(s)Mg(g) /SiO(g)Mg(g)
SiO(g)
SiO(g)

Mg(g) + SiO(g) + 2O(g) → MgSiO3(s)2Mg(g) + SiO(g) + 3O(g) → Mg2 SiO4(s)2Mg(g) + SiO(g) + 3O(g) → Mg2 SiO4(s)SiO(g) + O(g) → SiO2(s)25.012918.6200
37.2400
12.602872.001552.4336104.8672
38.1507

Mg(g) /Si(g)
Mg(g)
Si(g)
Si(g)

Mg(g) + Si(g) + 3O(g) → MgSiO3(s)2Mg(g) + Si(g) + 4O(g) → Mg2 SiO4(s)2Mg(g) + Si(g) + 4O(g) → Mg2 SiO4(s)Si(g) + 2O(g) → SiO2(s)34.721423.474246.9484
22.311387.7178
60.2918120.5836
53.8670(3)

SiO2(s)Model B
(4)
(5)
(6)

MgSiO3(s)Mg2 SiO4(s)SiO2(s)

Notes. The key species is defined as the gas species whose collisional frequency is the lowest among reactants. The subscripts (s) and (g) denote solidcondensate and gas species, respectively. The Gibbs free energy ΔG0j for the formation of a condensate from reactants per molecule of the key species
is approximated by ΔG0j /kTd,j = −A/Td,j + B, where the numerical values A and B are derived by least-square fittings of the thermodynamics data
(Chase et al. 1985) in the range of temperature of interests.

(O-bearing) grains, and SiO molecules lock up silicon atoms
available to form Si and SiC. On the other hand, SiO molecules,
whose rapid depletion was observed concurrently with the onsetof dust formation in SN 1987A (Roche et al. 1991) and SN
2004et (Kotak et al. 2009), are considered to be precursors ofsilicate grains such as MgSiO3 , Mg2 SiO4 , and SiO2 (Kozasa
et al. 1989) as represented by reactions (1)–(3) in Table 1.
In astronomical environments hospitable to dust formationsuch as in mass-loss winds of evolved late-type stars, it isusually assumed that the formation of CO and SiO molecules
is complete. However, in the ejecta of SNe, these molecules aredestroyed by impacts with energetic electrons and/or chargetransfer reactions with the ionized inert gas. For SN 1987A,
the masses of CO and SiO molecules were estimated to be5 × 10−3 M (Liu et al. 1992; Liu & Dalgarno 1995; Gearhart
et al. 1999) and 10−3 M (Liu & Dalgarno 1994, 1996),
respectively. These masses correspond to formation efficienciesof less than a few percent, where the formation efficiency isdefined as the mass fraction of carbon and silicon locked in CO
and SiO molecules. The disruption of CO molecules may enablecarbon grains to condense out of the oxygen-rich gas in the SN
ejecta (Clayton et al. 1999, 2001; Deneault et al. 2006; Todini& Ferrara 2001; Bianchi & Schneider 2007).
In the ejecta of SNe Ia that produce much more 56 Ni thantypical CCSNe, destruction of CO and SiO molecules canbe more effective as a result of more vigorous radioactivity(Liu 1997). Höflich et al. (1995) argued that CO and SiO
molecules can form more or less in subluminous SNe Ia
with M(56 Ni)  0.3M but cannot form in normal SNe Ia
with M(56 Ni)  0.6 M . Indeed, neither the fundamental nor
overtone emissions of CO molecules have been detected inordinary SNe Ia, although Taubenberger et al. (2011) havereported probable detection of CO emission at ∼85 days after
the peak brightness in superluminous SN Ia 2009dc. We also
note that the possible formation of SiO molecules is supposed for
SN Ia 2005df, but the formation efficiency would be extremely
low (0.01%; Gerardy et al. 2007).
In the present calculations, we consider two extreme cases forthe formation of CO and SiO molecules. One is the complete
formation of CO and SiO molecules, in which case the lesser ofcarbon (silicon) and oxygen is locked up in CO (SiO) molecules
and SiO molecules act as precursors of silicate grains. Thisis the assumption made in a series of our previous works.
Although CO and SiO molecules can be the dominant coolants

condensate per molecule of the key species. The concentrationand mass of the key species are represented as c1,j and m1,j ,respectively. Note that a factor Πj , which depends on the partialpressures of reactant and product gas species except for the key
species (Chigai et al. 1999), is omitted from the equation since
we set Πj = 1 in the calculations (see Nozawa et al. 2003). The
supersaturation ratio Sj is calculated byln Sj = −

ΔG0j
kTd,j

+


i

νi ln Pi +



T
1
,
ln
2
Td,j

(2)

where ΔG0j is the Gibbs free energy at the standard pressure for condensation of the jth dust species from the reactants per molecule of the key species and Pi are thepartial gas pressures of the reactants and products. The
stoichiometric coefficients νi , which are normalized to the
key species, are positive for a reactant and negative for a
product.
In the following calculations, we assume Td,j = T so as
to be consistent with a treatment in our earlier studies; dust
formation in the case where the temperature of the condensation
nuclei is not equal to the gas temperature is examined in
Section 4.2. We take αj = 1 and 0.1 as the sticking probability,
assuming that it is the same for all grain species; for αj 
0.01, dust formation does not occur substantially for the SN
model considered here. The Gibbs free energy for formation ofa grain species is approximated as ΔG0j /kTd,j = −A/Td,j + B
through the least-squares fitting of the thermodynamic data
(Chase et al. 1985). The formation of all possible condensates
is calculated simultaneously. The grain species considered andthe data needed for the dust formation calculations are given in
Table 2 in Nozawa et al. (2003).
2.3. Formation of CO and SiO Molecules
Since the first detection in SN 1987A (Spyromilio et al. 1988;
Aitken et al. 1988), the formation of CO and SiO molecules has
been observed in several CCSNe (Spyromilio & Leibundgut
1996; Spyromilio et al. 2001; Gerardy et al. 2000, 2002; Kotak
et al. 2006, 2009; Hunter et al. 2009). Formation of thesemolecules prior to dust formation can affect the composition,size, and mass of dust grains that condense in the ejecta(e.g., Nozawa et al. 2003); carbon (oxygen) atoms bound in
CO molecules are not available for formation of C-bearing
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Nozawa et al.

Table 2Mass of Each Dust Species Formed in the Ejecta of the SNe Ia (W7 Model)
Dust Species

A1

A0.1

B1

B0.1

C
MgO
MgSiO3Mg2 SiO4
SiO2
Al2 O3
FeS
Si
Fe
Ni

5.66 × 10−3

3.17 × 10−6
7.59 × 10−3
7.01 × 10−3
1.47 × 10−2
8.18 × 10−7
1.78 × 10−2
6.30 × 10−2
9.52 × 10−5
1.48 × 10−6

2.84 × 10−4

3.73 × 10−2
9.26 × 10−8
1.95 × 10−2
6.08 × 10−3
4.91 × 10−2
8.53 × 10−6
1.78 × 10−2
6.40 × 10−2
9.52 × 10−5
1.48 × 10−6

2.40 × 10−2
1.93 × 10−9
1.11 × 10−5
6.49 × 10−6
2.21 × 10−3
7.71 × 10−10
1.53 × 10−5
3.21 × 10−5
1.09 × 10−8
2.22 × 10−10

Total

1.16 × 10−1

3.44 × 10−4

1.94 × 10−1

2.63 × 10−2

1.85 × 10−9
1.31 × 10−6
1.50 × 10−6
9.94 × 10−6
7.48 × 10−10
1.53 × 10−5
3.15 × 10−5
1.09 × 10−8
2.22 × 10−10

Notes. The dust mass is given in units of M . Models A1 and A0.1 are the cases where the formation of CO and SiO
molecules is assumed to be complete, with sticking probabilities of αj = 1 and 0.1, respectively. In model B1 with αj =1 and model B0.1 with αj = 0.1, it is assumed that any molecule never forms in the ejecta.

in SNe (Liu & Dalgarno 1995), we do not take into account theeffects of cooling by these molecules on the thermal structureof the ejecta.5 The other case is no formation of CO and SiO
molecules, where carbon, silicon, and oxygen take part in dust
formation as free atoms. It should be mentioned here that even
if SiO molecules cannot form in the ejecta, silicate grains may
condense via chemical reaction paths different from reactions(1)–(3) given in Table 1. Here we calculate the formation ofsilicates by considering reactions (4)–(6) in Table 1.

form at 160–250 days in the Si–S layer. Despite the presenceof the extended Fe–Ni layer, Fe and Ni grains are not produced
at Mr = 0.15–0.8 M ; the gas density in this region becomes
too low for them to nucleate before the gas cools down to theircondensation temperatures (800 K). Fe and Ni grains cancondense at 250–300 days only in the innermost region (Mr =0–0.15 M ) with the highest gas density (see Figure 2), though
their masses are very small (see below).
The above results indicate that a variety of dust grains canform in SNe Ia according to the elemental abundances in the
different layers, given that the stratified elemental composition
is retained with no mixing. The resulting composition of newly
formed grains and the order of their condensation are almost
the same as those in any type of CCSNe (Nozawa et al. 2003,
2008, 2010). This means that the condensation sequence of dust
does not depend on the type of SNe, reflecting the fact thatthe elemental composition of the metal-rich gas in the ejecta is
not greatly different among different types of SNe. However,the condensation times of dust in SNe Ia are much earlier(tc 100–300 days) than those (tc  300 days) in SNe II-P
(Nozawa et al. 2003). Such early condensation of dust is causedby the rapid decrease of the gas temperature resulting from low
gas density in the ejecta (see Figure 2).
The low gas density in SNe Ia also leads to an importantconsequence for the size of dust formed in the ejecta. Figure 3(b)exhibits the average radii aave of newly formed grains as afunction of enclosed mass. We can see that the average radiiof all dust species except Fe and Ni grains are under 0.01 μm,
being considerably smaller than those (aave  0.01 μm) in
SNe II-P (Nozawa et al. 2003). As demonstrated by Nozawa
et al. (2010), the condensation of dust grains in less dense gas
demands a larger supercooling, and the resulting formation andgrowth of a huge number of condensation nuclei makes theaverage radius of grains small due to the conservation of massof materials available for dust formation. On the other hand, ingas with an even lower density, formation of the seed nuclei
itself is significantly depressed. In this case, the final radius isdetermined by the competition between the collision timescaleof the key species onto the grain surfaces and the expansion
timescale of the gas. This is the case for Fe and Ni grains, which
can acquire average radii of aave ∼ 0.01 μm
It should be emphasized that the masses of Fe and Ni grains
are quite low (10−4 M ), although their radii are relatively
large. This indicates that SNe Ia cannot be major sources of

3. RESULTS OF DUST FORMATION CALCULATIONSIn this section, we present the results obtained from themodels of calculations outlined in Section 2. In what follows,
we refer to the cases with and without formation of CO andSiO molecules as model A and model B, respectively, with thevalues of sticking probabilities αj attached to the model names.
For example, A1 represents the model taking complete CO andSiO formation with αj = 1. For each of the models consideredin this paper, the mass of each dust species formed in the ejecta
is summarized in Table 2. In the following, we focus on the
results in the most optimistic cases of αj = 1 for dust formation(i.e., models A1 and B1) to make a direct comparison with ourprevious studies where αj = 1 was assumed.
3.1. Cases with Molecular Formation
Figure 3(a) shows the condensation time tc of dust grains
formed in the ejecta of SNe Ia for model A1, where tc is definedas the time when the nucleation rate reaches the maximum(see Nozawa et al. 2003). In the outermost C–O layer, C
grains are formed at 80–110 days from the remaining carbon
atoms that are not locked in CO molecules. In the O-richlayer, Al2 O3 grains first condense around 100 days, and silicate(Mg2 SiO4 , MgSiO3 , SiO2 ) grains condense at 120–150 days
via the reactions involving SiO molecules. Then MgO grains
form at 150–160 days in the O-rich layer, and FeS and Si grains
5

The cooling by CO and SiO molecules causes rapid decreases in the gas
temperatures in the C–O layer and the O-rich layer. This would lead to theearlier condensation of silicate and C grains and their larger average radii thanthose given in this paper. However, the temperature decrease by molecularcooling cannot cause the mass of these dust grains to increase appreciably inthe case of αj = 1, where most of the metals available for dust formation areincorporated into dust grains (see Section 3.1). We also note that if the ejecta
were optically thick for CO and SiO emissions, the cooling could not operate
effectively (Gearhart et al. 1999).

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Nozawa et al.

Figure 3. (a) Condensation times and (b) average radii of dust grains formed in
the ejecta of the W7 model as a function of enclosed mass for model A1 taking
complete formation of CO and SiO molecules with αj = 1.

Figure 4. (a) Condensation times and (b) average radii of dust grains formed at
Mr = 0.8–1.38 M in the W7 model for model B1 taking no formation of COand SiO molecules with αj = 1.

Fe and Ni grains, contrary to the presupposition made in somestudies. In model A1, the total mass of newly formed dust is
0.116 M and the main dust species in mass are Si (0.063 M ),FeS (0.018 M ), and SiO2 grains (0.015 M ). The total massof silicate (Mg2 SiO4 , MgSiO3 , SiO2 ) grains is 0.03 M andoccupies 25% of the total dust mass. C grains are produced with
5.7×10−3 M . In model A0.1 with αj = 0.1, the total dust massis 3.4 × 10−4 M and is dominated by C grains (see Table 2).
The average grain radii are a factor of 5–10 smaller in modelA0.1 than in model A1. However, the condensation times ofdust grains for model A0.1 are not significantly different fromthose for model A1.

factor of 2–3 and 6.6, respectively, compared with those in model
A1. Furthermore, because of the absence of formation of SiO
molecules, more free silicon atoms are available for formationof Si grains at Mr = 1.10–1.15 M , leading to a slightly higher
mass of Si grains than in model A1.
The difference in the results between models A1 and B1
also appears in the formation of silicate grains. In model B1,
Mg2 SiO4 , MgSiO3 , and SiO2 grains can condense a few
tens of days earlier than those in model A1. Moreover, thecondensation time of SiO2 grains is earlier than those of
Mg2 SiO4 and MgSiO3 , in contrast to the case in model A1.
These differences come from the difference in the Gibbs freeenergies for their condensation; reactions (4)–(6) in Table 1
provide lower Gibbs free energies than reactions (1)–(3). Since
the lower Gibbs free energy allows the supersaturation ratio torise above unity more rapidly (see Equation (2)) for a given
temperature evolution of cooling gas, the earlier formation ofsilicate, especially SiO2 grains, is realized in model B. The
average radii and the masses are enhanced for SiO2 and MgSiO3 ,as a result of their formation in the denser gas (at earlier times).
However, both the average radius and mass are slightly reducedfor Mg2 SiO4 , compared with those in model A1; the earlier
condensation of SiO2 and MgSiO3 significantly reduces Si

3.2. Cases with No Molecular Formation
Figures 4(a) and (b) show the condensation times and theaverage radii of newly formed grains in model B1, where nomolecular formation and αj = 1 are assumed. Since dust
formation in the inner Fe–Ni layer (Mr < 0.8 M ) is not affectedby the formation of CO and SiO molecules, only the results in theregion of Mr = 0.8–1.38 M are shown in Figure 4. In model B1
with no CO formation, nucleation and growth of C grains in theoutermost C–O layer can advance in more carbon-rich gas. As
a result, the average radii and the mass of C grains increase by a6

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Nozawa et al.

atoms available for the later formation of Mg2 SiO4 . The total
mass of silicate is 0.075 M , which is 2.5 times higher than thatin model A1.
Our calculations demonstrate that SiC grains never condensein SNe Ia, regardless of the formation of CO and SiO molecules.
The main reason for this is that in the ejecta of the W7 model
there is no layer where carbon and silicon coexist abundantly.
However, even if both elements are abundant in some layer,
as appeared to be the case in CCSNe, theoretical calculations(Nozawa et al. 2003; Cherchneff & Dwek 2009, 2010) do
not predict the condensation of SiC grains with radii morethan 0.1 μm as discovered in presolar grains. Thus, it remains
unexplained whether presolar SiC grains originated from SNe
Ia (Clayton et al. 1997) or CCSNe (Amari et al. 1992; Nittler
et al. 1996, see also Deneault et al. 2003; Deneault 2009).
In summary, the formation of CO and SiO molecules as wellas the sticking probability have substantial impact on the massof dust grains formed in SNe Ia; the total dust mass for model
B1 (B0.1) without molecular formation is 0.194 M (0.026 M )and is much higher than 0.116 M (3 × 10−4 M ) for model A1(A0.1) with molecular formation. In particular, the difference indust mass is more than two orders of magnitude between models
A0.1 and B0.1 for which the total dust masses are dominatedby C grains. In model B0.1 without CO formation, the number
density of C atoms available for dust formation is about fivetimes higher than in model A0.1. Thus, even if αj = 0.1,
condensation of C grains can still proceed efficiently, and aconsiderable amount of C grains can form in model B0.1.
On the other hand, in all of the models considered here, thecondensation times of dust are significantly early (<300 days),and the average grain radii are small (0.01 μm). These
conclusions are not influenced by CO and SiO formation andarise from the low density of the gas in the ejecta of SNe Ia with
no H-envelope. Our preceding studies demonstrated that a tiny
size of dust grains with aave  0.01 μm condenses in envelopestripped Type Ib SN 2006jc (Nozawa et al. 2008) and Type IIb
SNe (Nozawa et al. 2010), while relatively large grains withaave  0.01 μm form in envelope-retaining SNe II-P (Nozawa
et al. 2003). Thus, we conclude that the radius of dust formedin the ejecta depends on the type of SNe and that smaller dust
grains are produced as the envelope masses of SNe become
lower.

radius R of the ejecta is calculated as follows,τλ (r, t) =τλ,j (r, t)

j

=

 r
j

R

dr



 amax,j
amin,jext
mj (a)κλ,j(a)fj (a, r  , t)da,(3)

where fj (a, r, t) is the size distribution function of the jth dust
species per volume at a position r, mj (a) = 4π a 3 ρj /3 is themass of a grain with a radius a and a bulk density ρj , andextκλ,j(a) is the mass extinction coefficient. The maximum andminimum radii of dust (amax,j and amin,j , respectively), as well
as fj (a, r, t), are obtained from the dust formation calculationsin Section 3. Here we assume that dust grains formed at a given
position distribute homogeneously within the corresponding
mesh. The bulk density ρj of each dust species is taken from
Table 2 in Nozawa et al. (2006), and the optical constants forext
calculating κλ,jare taken from the references summarized in
Section 4.1 in Nozawa et al. (2010).6 Note that the optical depths
scale as τλ ∝ t −2 for the free expansion of the ejecta.
The results of calculations show that the total optical depths
in the V band (λ = 0.55 μm) are τ0.55 = 163 (279) at 300 days
for model A1 (B1); C, Si, FeS, and Fe grains are the major
donors of the opacity with τ0.55,j = 22 (137), 78 (79), 14 (14),and 49 (49), respectively. At 300 days, silicate grains only have
τ0.55,sil = 0.01 (0.02) because of their low extinction efficiencies
at λ = 0.55μm, while they provide large optical depths ofτ10,j = 5.4 (11.7) at λ = 10 μm. Note that even for model A0.1
(B0.1) with αj = 0.1, the V-band optical depths by C grains
reach τ0.55 = 2.5 (93) at 200 days, which are large enoughto affect the optical light curve of the SN. The calculation by
Sugerman et al. (2006) suggested that the clumpy structure of theejecta can make the opacity by dust smaller by about one orderof magnitude than a homogeneous distribution with the same
dust mass (see also Ercolano et al. 2007). However, even if we
consider the effect of dust clump, the V-band opacities calculated
here are still too high to be consistent with observations. This
indicates that the mass of dust formed in SNe Ia must be smaller
than our calculations predict.
SNe Ia produce approximately 10 times more 56 Ni thannormal CCSNe and thus may have stronger radiation fields inthe ejecta. Moreover, dust formation in SNe Ia is realized within
the first year, during which energetic photons and electrons arelikely to be abundant inside the ejecta. In such an environment,
small clusters that are composed of several to a few tens ofatoms are heated by impacts with UV–optical photons andfast electrons, and their temperature could be higher than thetemperature of the gas, depending on their optical properties.
The heating of small clusters can lead to detachment of atoms
from the clusters and thus can inhibit the formation of dust. In
the next subsection, we evaluate the temperature of condensate
nuclei and examine how the formation process of dust can beaffected by the effect of non-local thermal equilibrium between
the nucleated dust and the gas.

4. DISCUSSIONAs shown in the previous section, dust grains of 3 ×
10−4 –0.2 M can form in the ejecta of SNe Ia for sticking
probabilities of αj = 0.1–1. The formation of such an amountof dust grains may show some observational signatures suchas a fading of optical luminosity and a rising of IR luminosity.
However, these events suggestive of dust formation have notbeen confirmed by any observation of ordinary SNe Ia. In thissection, we calculate the opacity and thermal emission by the
newly formed dust and apply the results to the observational
constraints. Then we discuss the composition and mass of dust
formed in the ejecta as well as the elemental composition of theoutermost layer in SNe Ia.

6

The bulk density and the source of optical constants for Ni grains have notbeen given in Nozawa et al. (2006, 2010). We adopt ρNi = 8.87 g cm−3 as abulk density of Ni grains, which is evaluated by using the hypothetical radius
a0,j = 1.377 Å of the condensate (Nozawa et al. 2003). For the opticalconstants, we assume that the optical properties of Ni grains are the same as
those of Fe grains. Since the mass of Ni grains formed in the ejecta is
negligible, this assumption has no impact on the results in the rest of this paper.

4.1. Optical Depth by Newly Formed Dust
We begin with estimating the optical depths by dust formed in
the ejecta. The optical depth τλ as measured from the outermost
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Nozawa et al.

4.2. Dust Formation in a Non-local Thermal
Equilibrium Condition
In the calculations of dust formation in Section 3, we assumed
that the temperature of condensation nuclei Td,j is the same as
the temperature of the gas T. However, Td,j is not generally equal
to T, and the resulting temperature difference can influence thecondensation process of dust (Kozasa et al. 1996). In particular,
if T < Td,j in the cooling gas, the supersaturation ratio(ln Sj ) increases more slowly than the case of the local thermal
equilibrium with T = Td,j (see Equation (2)), which retards
the formation of dust. Furthermore, the effects of the enhanced
detachment of monomers from a heated small cluster can be−1seen in Equation (1) via the factors (T /Td,j )1/2 and μj ∝ Td,j.
The temperature of a condensate is determined by the balance
between the heating and cooling. In the ejecta of SNe, thepossible heating processes of small clusters are the absorptionof UV-optical radiation and collisions with energetic electrons,
while the cooling of dust takes place via thermal emission
and collisions with cooler gaseous atoms. However, the energy
transferred through collisions with the gas is found to be much
lower than that transferred through radiative processes. Thus,
we neglect the heating and cooling by collisions with electrons
and gaseous atoms. Also, for simplicity, we do not consider
the effect of stochastic heating in evaluating the temperatureof small clusters; in the SN ejecta with a relatively strong
radiation field, the temperature of a stochastically heated grain
distributes symmetrically around the equilibrium temperature(Nozawa et al. 2008), which therefore does not significantly
affect the IR emission spectra calculated in the next subsection
as well.
By balancing the heating by photon absorption and the cooling by thermal radiation of dust, the equilibrium temperatureof dust Td,j (r, t) at a given time t and at a given position r is
calculated from the equation
4(r, t)KP ,j (a, Td,j ),F (r, t)KF,j (a, T∗ ) = 4σB Td,jFigure 5. Time evolutions of the square root of the ratio of the gas temperature
to the dust temperature (T /Td,j )1/2 for the main dust species: Fe grains at Mr =0.001 M ; Si and FeS grains at Mr = 0.98 M ; MgSiO3 , Mg2 SiO4 , and SiO2
grains at Mr = 1.18 M ; and C grains at Mr = 1.33 M .
(A color version of this figure is available in the online journal.)

or lower than the gas temperature, depending on position andtime.
Using the calculated time evolution of dust temperature andtaking into account the effect of non-local thermal equilibrium,
we performed dust formation calculations for C, Fe, FeS,
and Si grains with T /Td,j < 1. As a result, we find thatthe condensation of Fe, FeS, and Si grains is delayed by
50–350 days, and their condensation times are 300–400 days
for Fe and FeS grains, and 450–500 days for Si grains. At suchlate times, the gas density is too low for dust grains to form
efficiently, so the resulting grain masses are heavily reduced:∼5 × 10−6 M for Fe grains; ∼4 × 10−4 M for FeS grains;and ∼1 × 10−6 M for Si grains in both models A1 and B1.
Thus, apart from Fe grains formed in the innermost ejecta,
FeS and Si grains make a negligible contribution to the opacity(τ0.55,j  0.1) after  300 days. On the other hand, the massof C grains, whose condensation times are 5–20 days later thanthose for the case of the local thermal equilibrium, decreases
only by less than ∼10% for all of the models considered inthis paper. Namely, an optical depth (τ0.55,C  10) endowed by
C grains that is too high cannot be mitigated by the effects of
non-local thermal equilibrium.
It should be mentioned here that, using a kinetic approachto nucleation, Lazzati (2008) pointed out that the nucleationof small clusters with a temperature lower than that of the gas
can proceed faster in the absence of a strong radiation field.
However, to examine the stability of small clusters in the SN
ejecta with a strong radiation field, the nanoscale effect suchas thermal fluctuations and the finite energy of small clusters
needs to be treated properly. Such a computation is too timeconsuming (Keith & Lazzati 2011) and is beyond the scope of
this paper.

(4)

where F(r,t) is the flux, σB is the Stefan–Boltzmann constant,
and KF,j (a, T ) and KP ,j (a, T ) are, respectively, the flux-mean
and the Planck-mean of the absorption coefficient Qλ,j (a);here we assume that the optical properties of small clusters
are the same as those of the small dust grains. The flux ofthe radiation field F(r, t) in the ejecta has been obtained fromthe radiative transfer calculation in deriving the time evolutionof the gas temperature. In the SN model considered here, theflux at day 400 ranges from F = 1.7 × 105 erg s−1 cm−2 toF = 8.2 × 105 erg s−1 cm−2 over most parts of the ejecta. Notethat the SED of the radiation field in the ejecta at late nebulaphases has not been known very well either observationally or
theoretically. In the calculations, we assume that the radiation
field has a blackbody spectrum with a temperature of T∗ =TBB = 5000 K, independent of position and time.
In Figure 5, we present the time evolutions of the squareroot of the ratio between the gas temperature and the dust
temperature for the main grain species. Note that the calculated
dust temperature is not sensitive to grain radius for the size range(a  0.01 μm) of dust formed in SNe Ia. The temperatures of
MgSiO3 , Mg2 SiO4 , and SiO2 grains have been lower than thegas temperature (T /Td,j > 1) since their formation and are as
low as Td,j = 90–150 K at 400 days. However, Fe, FeS, andSi grains hold Td,j ∼600 K, 720 K, and 1000 K at 400 days,
respectively, and have maintained higher temperatures than thegas (T /Td,j < 1). The temperature of C grains becomes higher

4.3. Thermal Emission from Newly Formed Dust
In this subsection, we assess the thermal emission spectrafrom dust formed in the ejecta by employing the equilibrium
temperature of dust given in the last subsection. Then, we
compare the results with the observed mid-IR SEDs and discuss
the mass and composition of newly formed dust. The derived IR
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Nozawa et al.

(dashed) lines are the thermal emission spectra in the casewhere the contribution of C grains is included for model A1-non(B1-non). In both models and at both dates, the thermal emission
from C grains formed in the inner part of the C–O layer, as well
as from silicate grains in the inner ejecta, is mostly absorbed,
and the total IR SEDs are dominated by that from C grains in theoutermost part of the C–O layer. (As a result, the difference in
the IR SEDs between model A1-non and B1-non is small, even
if the mass of C grains for model B1-non is about one order ofmagnitude larger than for model A1-non.) It should be noted thatthe calculated flux densities are a few orders of magnitude higher
than the observed values; if C grains had actually condensed in
SNe Ia 2005df, the IR observations would have detected theircontinuum emission. This outcome, as well as the very highoptical depths, contradicts the observations, implying that theformation of C grains in SNe Ia should be extremely inefficientor unsuccessful.
In order to gain further insight into the composition andmass of dust formed in SNe Ia, we also calculated the midIR spectra in the case where the contribution of C grains isarbitrarily removed. The results are shown by the thick lines in
Figures 6(a) and (b). In models A1-non (solid lines) and B1-non(dashed lines), the IR SEDs at 200 days are produced by silicate
grains with masses of 0.03 M and 0.075 M , respectively. At
400 days, in addition to the contribution of silicate grains at λ 
8 μm, FeS grains of ∼4 ×10−4 M contribute to the IR fluxes
at λ < 8 μm. As can be seen from these figures, the calculated
SEDs do not conflict with the observational data at both day
200 and day 400. Therefore, from this comparison, we cannot
impose any constraints on the composition and mass of grains
species other than C grains. In other words, ∼0.03–0.075 M ofsilicate grains can be allowed as a mass of dust formed in SNe
Ia within the present observational constraints.
4.4. C Grain Formation and the Outermost
C–O Layer of SNe Ia

Figure 6. SEDs by thermal emission from newly formed dust for models
A1-non (solid lines) and B1-non (dashed lines) at (a) 200 days and (b) 400 days
after the explosion. The thin lines are the thermal emission spectra summed up
over all of the grain species formed in the ejecta before 200 days or 400 days.
The thick lines are the mid-IR spectra obtained by assuming an absence ofC grains. The observational data are the photometric results of SN 2005df by
Spitzer and are taken from Gerardy et al. (2007).
(A color version of this figure is available in the online journal.)

The discussion in the previous subsection indicates thatthe formation of appreciable amounts of C grains in SNe Ia
is incompatible with the existing observational results. Thus,
the condensation of C grains must be suppressed much morethan the present calculations predict. In our model, one of thefactors that produces massive C grains is relatively high sticking
probabilities of αj  0.1; if we take αj  0.01, neither C grains
nor other grains can substantially condense. Such low sticking
probabilities are suggested for the formation of C grains in thepeculiar Type Ib SN 2006jc; Nozawa et al. (2008) showed thatαj  3 × 10−3 is required for C grains to obtain the dust massneeded to reproduce the IR observations of SN 2006jc. They
argued that in SN 2006jc C grains can form at very early timesof ∼50 days, when energetic photons and electrons are expected
to be abundant, so the low sticking probability may reflect theeffective destruction of small clusters by collisions with photons
and electrons. Given that the formation of C grains in SNe Ia
can also occur at an early epoch of ∼100 days, it can be possible
for precursor clusters of C grains to be significantly destroyed.
Another reason for the formation of a large quantity of C
grains is the presence of massive (0.05 M ) unburned carbon
in the outer layer. In the W7 model adopted in this paper, thedeflagration wave halts on the way, and the original compositionof WDs with a number ratio of C/O = 1.27 is retained in theoutermost ejecta. However, whether the C/O ratio exceeds unity
is not conclusive, and the composition of the outer layer ofaccreting WDs is unclear because of many uncertain processes

spectra will also be useful as a guide to future IR observationsof SNe Ia.
The flux densities of thermal emission from newly formed
dust are calculated with Equations (2) and (3) in Nozawa
et al. (2008) by taking into account the self-absorption of dust
emission. In this calculation, we adopt the mass of each dust
species resulting from the dust formation calculations under
the non-local thermal equilibrium condition for models A1 andB1 (hereafter models A1-non and B1-non, respectively). The
observational data are taken from the photometric results of SN
at 200 days and 400 days by Gerardy et al. (2007), which
may be the only mid-IR measurements of normal SNe Ia atlate times. Gerardy et al. (2007) claimed that the observed midIR spectra are not due to thermal emission from dust but are
dominated due to line emissions. Here, we regard the observed
flux densities as the upper limits for thermal emission from dust.
We take D = 18.7 Mpc as a distance to SN 2005df (Hamuy
2003).
Figures 6(a) and (b) present the calculated total mid-IR
SEDs at day 200 and day 400, respectively; the thin solid
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Nozawa et al.

than those in normal SNe Ia, which may make dust formation
more feasible. On the other hand, energy deposition from a large
amount of 56 Ni (>1 M ) produced in super-Chandrasekhar SNe
Ia prevents the gas temperature from quickly decreasing down
to the dust condensation temperature (2000 K), which may
make the condensation of dust unfeasible. In order to clarify
how these competing processes affect the condensation time andmass of dust, the formation of dust in super-Chandrasekhar SNe
Ia should be explored both theoretically and observationally.

such as the 12 C(α, γ )16 O reaction rate, convective overshooting,dredge-up from the core, accretion rate from the companion
star, and strength of He-shell flashes (e.g., Shen & Bildsten
2009; Y. Kamiya et al. 2011, in preparation); if the C/O number
ratio is less than unity in the surface layer of a WD and if
a majority of C atoms should be locked in CO molecules, C
grains may be unable to form efficiently in the cooling ejecta.
Thus, observations of CO molecules in SNe Ia can provide
meaningful clues to the formation process of C grains as well as
the pre-explosion composition of WDs, although the existenceof CO molecules has never been reported for normal SNe Ia todate.
On the other hand, the mass of carbon deduced from theobservations is much smaller than in the W7 model. From
the analyses of the spectra before the maximum of the light
curves (Marion et al. 2006; Tanaka et al. 2008), the mass ofcarbon in normal SNe Ia is estimated to be at most 0.01 M .
If, as mentioned in these studies, the abundance of carbon is10–100 times less than oxygen, the mass of newly formed
C grains may be too low for observational signatures of dust
formation to be detected. Therefore, from a point of view of
dust formation, we assert that the composition of the outermost
ejecta is very carbon-poor. Such a small carbon abundance might
result from strong He-shell flashes in accreting high-mass WDs(Y. Kamiya et al. 2011, in preparation), or be the results of thedelayed detonation which burns almost all carbon.
Apart from the outermost layer, the one-dimensional delayed
detonation models predict the temperature and density structures and the elemental composition that are similar to those in
the one-dimensional deflagration models (Iwamoto et al. 1999).
This implies that in the delayed detonation models the averageradii and masses of newly formed grains except for C grains cannot be significantly different from those obtained in this paper.
The remaining amount of unburned carbon in the delayed detonation models is smaller (∼0.005–0.03 M ) than 0.0475 M
in the deflagration model W7, but it heavily depends on the still
uncertain transition density at which the deflagration turns into
detonation. Thus, in order to investigate how the mass of newly
formed C grains can be changed by the underlying explosion
models, it will be necessary that comprehensive calculations ofdust formation are performed for the delayed detonation models
with different transition densities.
Here it would be worth mentioning dust formation in theextremely luminous SNe Ia. Recently, four over-luminous
SNe Ia have been discovered and suggested to originate fromthe progenitors with super-Chandrasekhar masses: SN 2003fg(Howell et al. 2006), SN 2006gz (Hicken et al. 2007), SN
2007if (Scalzo et al. 2010; Yuan et al. 2010), and SN 2009dc(Yamanaka et al. 2009; Tanaka et al. 2010; Silverman et al.
2011). Interestingly, these bright SNe Ia show much stronger
C lines in their spectra near the maximum brightness than any
other normal SNe Ia. This implies that thick unburned C-richlayers are left in their outermost ejecta. Since the formation of
C grains accompanies the presence of the C layer as shownin this paper, C grains may be able to condense in these superChandrasekhar SNe Ia. Indeed, Maeda et al. (2009) reported thatafter one year SN 2006gz is quite fainter than expected from thepeak luminosity, suggesting that such a fading might be causedby dust formation. Taubenberger et al. (2011) also discovered
an enhanced fading of the light curve around 200 days for SN
2009dc.
The super-Chandrasekhar SNe Ia have high ejecta masses andlow expansion velocities. Thus, the density of the ejecta is higher

5. INJECTION OF NEWLY FORMED
DUST INTO THE ISM
The composition, size, and amount of dust grains injectedfrom SNe into the ISM are determined by conflicting processes
between the formation of dust in the expanding SN ejecta andthe subsequent destruction of dust in the hot gas swept up by
the reverse and forward shocks propagating within the SNRs
(Nozawa et al. 2007, 2010; Bianchi & Schneider 2007; Nathet al. 2008; Silvia et al. 2010). In this section, in order toreveal the mass of dust ejected from SNe Ia, we investigate
the evolution of dust in the shocked gas inside SNRs, applying
the results of dust formation calculations.
The calculations of dust evolution in SNRs are based on
the model by Nozawa et al. (2007, 2010). In the models, thetransport and destruction of dust within SNRs are pursued
simultaneously with time evolution of the gas temperature anddensity in spherical symmetry shocks; by treating dust grains
as test particles, the deceleration by gas drag and erosion by
sputtering are self-consistently calculated, according to theinitial radius and the initial position of each dust species. The
sputtering yield of each dust species is taken from Nozawa et al.
(2006).
Note that the destruction efficiency of dust heavily depends
on the ambient gas density as well as the initial grain radius. In
the present calculations, we assume that the ISM around SNe Ia
is uniform, and consider the hydrogen number density of nH,0 =0.01, 0.1, and 1 cm−3 as the gas density in the ISM, whose gas
composition is set as the solar abundance. As for the model of
dust formed in the ejecta of SNe Ia, we adopt the results formodels A1 and B1 given in Section 3; the adoption of thesemodels is intended to estimate the maximum possible mass ofeach dust species supplied to the ISM. Assuming that the ejecta
interact with the ambient medium at 30 yr after the explosion,
we follow the calculations up to a few ×106 yr.
Figure 7(a) shows the time evolutions of the total mass of dustin SNRs for models A1 (solid lines) and B1 (dashed line). We cansee that for nH,0  0.1 cm−3 the dust grains formed in the ejectaof SNe Ia are completely (10−5 M ) destroyed before 106 yr.
Such effective destruction of dust arises from the following two
reasons. (1) Since SNe Ia do not have a H-envelope, the reverse
shock can sweep up the dust formation region much earlier(<500 yr) than in envelope-retaining SNe II-P (>1000 yr). At
such early times, the gas density in the shocked ejecta is highenough that dust grains are efficiently decelerated and eroded
due to frequent collisions with the gaseous ions. (2) Since theradii of newly formed grains are small (0.01 μm), they arequickly decelerated by the gas drag soon after encountering
the reverse shock. Thus, these small grains are finally trappedin the postshock gas and are destroyed by thermal sputtering
without being injected into the ISM.
On the other hand, for an ISM density as low as nH,0 =0.01 cm−3 , the deceleration and destruction of dust in the
hot plasma are quite inefficient, and dust of (1–2)×10−2 M
10The Astrophysical Journal, 736:45 (13pp), 2011 July 20

Nozawa et al.

that are too extended and whose sizes are incompatible with theobserved ones of nearby Type Ia SNRs (Badenes et al. 2007).
It should be mentioned that, as discussed in Nozawa et al.
(2010), if SNRs expand non-spherically, a part of the newly
formed grains may be able to evade the destruction and to be
injected in directions that do not strongly interact with theambient medium. Recently, a variation of late-time nebular
spectra of SNe Ia has been successfully explained by taking
into account the global asymmetry in the innermost ejecta that is
produced by deflagration developing from the off-center ignition(Maeda et al. 2010a, 2010b; see also Motohara et al. 2006).
Aside from the global asymmetry issue, the deflagration flameis also expected to create a small-scale mixing structure (e.g.,Röpke et al. 2007). In addition, given that SNe Ia are the endproducts of the binary interaction, an aspherical circumstellar
medium might have been formed around exploding WDs, which
may have resulted in the non-spherical evolution of SNRs.
However, analyses of X-ray morphology of young SNRs (Lopezet al. 2009, 2011) have shown that the remnants of SNe Ia do
not seem to be far from spherical symmetry. Although the effectof the degree of non-sphericity and small-scale structure on dust
survival is uncertain, we propose here that these effects are notenough to make SNe Ia dominant sources of interstellar dust.
6. SUMMARY
We investigate the formation of dust in the ejecta of SNe Ia,
adopting the carbon-deflagration W7 model. In our calculations,
we apply the nucleation and grain growth theory to compare ourfindings with the results for dust formation in different types
of CCSNe in our earlier studies. We find that for the sticking
probability of αj = 1, various grain species can condense in
the stratified ejecta of SNe Ia, although Fe grains cannot form
appreciably, contrary to the expectation. The composition ofdust grains formed in SNe Ia reflects the elemental compositionof the gas in the ejecta and is basically the same as those in any
other CCSNe.
On the other hand, the condensation times of dust in SNe
Ia are much earlier (tc = 100–300 days), and the average radiiof newly formed dust are much smaller (aave  0.01 μm) thanthose in SNe II-P. This is due to the low gas density in the ejectaof SNe Ia that do not have H-rich envelopes. We conclude thatthe radius of newly formed dust depends on the type of SNe andthat smaller grains condense in SNe with less massive envelopes.
The total mass of dust that can condense in the ejecta of SNe Ia
is significantly affected by the sticking probability αj and theformation efficiency of CO and SiO molecules, ranging from3 × 10−4 M to 0.2 M for αj = 0.1–1.
Furthermore, we estimate the temperature of small clusters
and evaluate the effect of the non-local thermal equilibrium on
the formation process of dust. We find that the non-local thermal
equilibrium effect can suppress the condensation of FeS, Si, andFe grains that are otherwise the main donors for optical depths.
We also calculate the IR emission spectra from the newly formed
dust, which will be helpful in discussing the possibility of dust
formation in future observations of SNe Ia. On the other hand,from the present observational constraints, we note that theformation of massive C grains is suppressed in SNe Ia. Thisimplies that the nucleation of C grains fails due to the destruction
by energetic photons and electrons, or that the outermost C–O
layer of SNe Ia is burned by the delayed detonation wave, orthat the pre-supernova C/O ratio is exceedingly small as a resultof strong recurrent He-shell flashes.

Figure 7. (a) Time evolutions of the total mass of the newly formed dust within
the Type Ia SNRs expanding into the uniform ISM with a hydrogen number
density of nH,0 = 0.01, 0.1, and 1 cm−3 . The solid lines are for model A1, andthe dashed lines are for model B1. (b) Time evolutions of the mass of each dust
species for model A1 and for nH,0 = 0.01 cm−3 .
(A color version of this figure is available in the online journal.)

survives in the models of A1 and B1; C, FeS, and Mg2 SiO4
grains with smaller average radii (aave  30 Å) are trappedin the shocked gas to be completely destroyed, whereas afraction of Si, SiO2 , MgSiO3 , and Fe grains with larger averageradii (aave  30 Å) are injected into the ISM. However, thetotal mass of surviving dust is dominated by Si grains (seeFigure 7(b) for model A1), whose formation has been expected
to be greatly suppressed by the effect of the non-local thermal
equilibrium (see Section 4.2). Thus, neglecting the contributionof Si grains, we regard ∼10−3 M (∼5 × 10−3 M ) of silicate
grains as a more realistic mass estimate of surviving dust for
nH,0 = 0.01 cm−3 in model A1 (B1).7 These results indicate
that, even if the ambient gas density is very low, the amount of
dust ejected from SNe Ia into the ISM is considerably small. We
also note that typical ISM densities around SNe Ia are estimatedto be nH,0 = 1–5 cm−3 (e.g., Borkowski et al. 2006) and that an
ambient density lower than nH,0 ∼ 0.01 cm−3 results in SNRs
In model B1, in addition to silicate grains of ∼5 × 10−3 M , C grains of
4 × 10−3 M can survive for nH,0 = 0.01 cm−3 . However, as discussed in
Section 4, the formation of C grains is problematic, judging from thecomparison with the observational constraints. Therefore, we do not include
here the mass of C grains as an estimate of the total mass of surviving dust.

7

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The Astrophysical Journal, 736:45 (13pp), 2011 July 20

Nozawa et al.

Finally, we examine the survival of dust grains formed in theejecta against their destruction in the SNRs. We find that, unlessthe gas density around SNe Ia is too low (nH,0  0.01 cm−3 ),the newly formed grains are almost completely destroyed in theshocked gas in the course of their injection into the ISM. Even
if the asymmetric effect of explosion is taken into account, SNe
Ia are likely to be poor producers of interstellar dust. However,SNe Ia are major production factories of heavy elements which
will be available for the subsequent growth of the pre-existinggrains through accretion onto their surface in dense molecular
clouds.

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