COSMIC DUST—NEAR AND FAR
ASP Conference Series, Vol. 414, 2009
Th. Henning, E. Grün, and J. Steinacker, eds.

Dust in Supernovae: Formation and Evolution
T. Kozasa1 , T. Nozawa2 , N. Tominaga3 , H. Umeda4 , K. Maeda2 , K.
Nomoto2,4
1 Department of Cosmosciences, Graduate School of Science, Hokkaido

University, Sapporo 060–0810, Japan
2 Institute for the Physics and Mathematics of the Universe, Universityof Tokyo, Kashiwa 277-8568, Japan
3 Optical and Infrared Astronomy Division, National Astronomical
Observatory of Japan, Mitaka 181-8588, Japan
4 Department of Astronomy, School of Science, University of Tokyo,
Tokyo 113-0033, Japan
Abstract.
Core–collapsed supernovae (CCSNe) have been considered to be
one of sources of dust in the universe. What kind and how much mass of dust areformed in the ejecta and are injected into the interstellar medium (ISM) dependon the type of CCSNe, through the difference in the thickness (mass) of outerenvelope. In this review, after summarizing the existing results of observations
on dust formation in CCSNe, we investigate formation of dust in the ejecta andits evolution in the supernova remnants (SNRs) of Type II–P and Type IIb SNe.
Then, the time evolution of thermal emission from dust in the SNR of Type IIb
SN is demonstrated and compared with the observation of Cas A. We find thatthe total dust mass formed in the ejecta does not so much depend on the type;∼ 0.3 − 0.7M⊙ in Type II–P SNe and ∼ 0.13M⊙ in Type IIb SN. However thesize of dust sensitively depends on the type, being affected by the difference inthe gas density in the ejecta: the dust mass is dominated by grains with radiilarger than 0.03 µm in Type II-P, and less than 0.006 µm in Type IIb, which
decides the fate of dust in the SNR. The surviving dust mass is ∼ 0.04−0.2M⊙ inthe SNRs of Type II–P SNe for the ambient hydrogen density of nH = 10.0 − 1.0
cm−3 , while almost all dust grains are destroyed in the SNR of Type IIb. The
spectral energy distribution (SED) of thermal emission from dust in SNR wellreflects the evolution of dust grains in SNR through erosion by sputtering andstochastic heating. The observed SED of Cas A SNR is reasonably reproducedby the model of dust formation and evolution for Type IIb SN.

1.

Introduction

Dust is one of important ingredients in space to control the physical and chemical conditions in interstellar medium (ISM) and the formation process of stars
in molecular clouds via the interactions with radiation and gas as well as theformation of H2 molecule on the surface. In astrophysical environments, dust
grains form in a cooling gas outflowing from star to interstellar space such as in
the stellar winds from asymptotic giant branch (AGB) stars and in the ejecta
of novae and supernovae (SNe) where gas density is high enough to proceed theformation and growth of seed nuclei through collisions of relevant gas species.
43

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Kozasa et al.

Formation of dust in the ejecta of SNe had been invoked to explain the originof interstellar dust (Cernuschi, Marsicano, & Codina 1967), and the microscopic
analysis of individual grains in meteorites has identified the dust grains formed in
SNe from their isotopic compositions (see Clayton & Nittler 2004 for a review).
Dust formation in the ejecta of SNe had been directly observed for the firsttime in SN 1987A (see McCray 1993 for a review), after then dust formationin the ejecta was reported in a handful of core–collapsed SNe (CCSNe). Basedon the observations of nearby SNe, the mass of dust formed in the ejecta has
been considered to be less than 10−3 M⊙ per SN, which is more than two to
three orders of magnitude smaller than the dust mass predicted by theoreticalinvestigations (Kozasa, Hasegawa, & Nomoto 1989, 1991; Todini & Ferrara 2001;
Nozawa et al. 2003). Furthermore the observed dust mass is too small to explain
the amount of dust observed in the host galaxies of quasars at redshift of z > 5(e.g. Bertoldi et al. 2003) where CCSNe are considered to be a major source ofdust because the cosmic age is too young for AGB stars to supply the dust. So
how much mass of dust forms in the ejecta has been still controversial.
In the ejecta of SNe, dust formation proceeds within the He–core wherecondensible elements are more abundant and the gas density is higher enoughdue to the smaller expansion velocity than in the outer envelope. How much
mass and what kind of dust are injected from a SN into ISM depend not only on
the formation in the ejecta but also on the destruction in the supernova remnant(SNR) where dust grains are injected into and eroded by sputtering in the hot
gas swept up by the reverse and forward shocks produced by the interactionof ejecta with interstellar/circumstellar medium. Both processes depend on thetype of SNe through the thickness (mass) of outer envelope: With the samekinetic energy of explosion, the thicker outer envelope makes the expansion
velocity slower and results in the gas density within He–core being high enoughto form large–sized dust. Furthermore, the lower gas density in the shocked
region caused by the delayed arrival of the reverse shock at the dust forming
region decreases the erosion rate of dust by sputtering.
In this review we show how the formation and destruction of dust in SNe
depend on the type, comparing the results of calculations for Type II–P andType IIb SNe; Type II–P SN is a typical type among CCSNe, and the wellstudied Cas A was recently identified as Type IIb SN (Krause et al. 2008).
Then, we demonstrate the time evolution of thermal emission from dust residing
in SNR of Type IIb SN, based on the results of calculations of dust formationand destruction. In § 2, we summarize the observations of dust formation in
SNe after briefly introducing the classification of SNe. We present the resultsof calculations of dust formation in the ejecta of Type II–P and IIb SNe in § 3.
Focusing on Type IIb SN, in § 4 we calculate the evolution of dust in the SNRs
and the time evolution of thermal emission from dust, and compare with theobservation of Cas A. Summary and concluding remarks are presented in § 5.
2.

Observations of Dust Formation in Supernovae

In this section we summarize the observations of dust formation in SNe. First we
briefly introduce the classification of SNe for your information, and then review
the observations of dust forming SNe. Massive stars whose main sequence mass

Dust in Supernovae

45

is larger than 8 M⊙ end up their lives as CCSNe, but the details depend on theinitial metallicity (Heger et al. 2003 for details). Here we shall confine to SNeevolved from stars with solar metallicity.
2.1.

Classification of Supernovae

Supernova is the most energetic explosion in the universe. Physically the supernovae are classified by the explosion mechanism; Core–collapsed supernovae
which are triggered by the gravitational collapse of the central core, and thermonuclear supernovae in which the explosion energy is supplied by explosive
thermonuclear burning (e.g. Hillebrandt & Niemeyer 2000).
Observationally SNe are classified by the spectral features at the early phaseand the behavior of the light curve (e.g. Wheeler & Harkness 1990; Filippenko
1997; Leibundgut 2008). According to the presence of the H feature, SNe are
divided into Type I and Type II; Type I without H, and Type II with H. Type I
SNe are classified by the strength of the Si feature (Si II absorption at 6150 Å);Type Ia SNe showing the strong Si absorption feature are thermonuclear SNe
whose progenitors are white dwarfs in binary systems. H–deficient Type I SNe
with weak Si feature are subdivided by the content of He. He–rich is Type Ib
and He–poor is Ic. The progenitors are Wolf–Rayet stars; H–envelope, and both
H– and He–envelopes are removed before explosion for Type Ib SN and Type Ic
SN, respectively, by stellar wind and/or interaction in binary system.
Type II SNe, whose progenitors are red supergiants, are divided by thecontent of H; H–poor are IIb SNe in which almost all of the H–envelope is removed during the evolution. H–rich Type II SNe are classified by the behaviorof the light curves; the light curve linearly decays in Type II–L SNe, and havea plateau in Type II–P SNe. Type II SNe showing narrow emission lines originating in circumstellar medium are labelled as IIn. Type II, Ib and Ic SNe arecore–collapsed supernovae.
2.2.

Observations of Dust Formation in Core–Collapsed Supernovae

Dust formation in the ejecta has been observed so far in the ejecta of CCSNe
except for Type Ic SNe. No evidence of dust formation is reported in the ejecta
of Type Ia SNe. Table 1 summarizes the observations of dust formation in theejecta of CCSNe. Formation of dust in the ejecta had been confirmed observationally for the first time in SN 1987A which is a peculiar Type II SN because
the progenitor is not a red supergiant but a blue supergiant (West el al. 1987).
The evidences of dust formation in the ejecta of SN 1987A (see McCray
1993; Wooden 1997; the references in Table 1) are the following; (1) the enhancement of infrared flux at ∼ 10 µm starting from day 450 followed by the
decline of U to M bolometric luminosity from ∼ day 500, and (2) the appearanceof blue–shifted profiles of [Mg I], [O I], [C I] lines starting from ∼ day 530. The
behavior of bolometric luminosity obtained by combining the observed U to M,
infrared (thermal emission from dust), X-ray and γ–ray luminosities satisfies
the energy budget expected from the decay of radioactive element 56 Co. The
appearance of blue–shifted lines was interpreted as the result of the attenuation of emission from the far (receding) side of the ejecta caused by dust grains
formed in clumps within the ejecta, and in addition the intensities of [Mg I], [OI] and [Si I] lines concurrently decreased (Lucy et al. 1991). It should be noted

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Kozasa et al.

that, in prelude to the dust formation, formation of CO and SiO molecules wasobserved as early as day 112 and 165, respectively. The emission of SiO was nolonger recognized at day 517 around which dust formation was confirmed by theobservation of blue–shifted lines (Roche et al. 1991). The dust mass estimatedfrom the observation was at least 1 × 10−4 M⊙ at day 775, and no informationon the dust composition was available since the thermal emission was well fitted
by a grey body (Wooden et al. 1993).
Taking the appearances of the blue–shifted lines, infrared excess and/or
decline of optical luminosity as the diagnostics, so far dust formation in theejecta has been reported in four SNe excluding SN 1987A (see the referencesin Table 1); three are Type II–P SNe which is the most common type among
CCSNe (e.g. Smartt et al. 2009), and one is Type Ib. The evidence of dust
formation in SN 2005af is based only on the mid–infrared (MIR) excess observedby Spitzer, but the detection of CO and SiO molecules supports the formation
since CO and/or SiO molecules are detected prior to dust formation in Type
II–P SNe. The molecules could play an important role in formation of dust
because CO acts as a coolant in the ejecta (e.g. Liu & Dalgarno 1995), and SiO
is considered to be a precursor of dust grains (Kozasa et al. 1989). The onsetof dust formation ranges from ∼ 300 to ∼ 600 days after the explosion in Type
II–P SNe. In SN 1990I, which is Type Ib, the onset seems to be earlier, as canbe expected, because the escape of γ-rays with less effective deposition causes
the gas in the ejecta to cool down faster without an H–envelope. The dust massderived from the observations is less than 10−3 M⊙ , although the observation of
SN 1999em suggested that dust much more than 10−4 M⊙ was produced in theejecta (Elmhamdi et al. 2003).
Recently formation of dust in cool dense shells (CDSs) generated by theinteraction of ejecta with a circumstellar medium (CSM) has been reported inthree SNe summarized in Table 2 (see the references in Table 2); two are TypeIIn and one is Type Ib, where the presence of dense circumstellar envelopes isconfirmed by the X–ray observations (e.g. Smith et al. 2008a). The evidences
come from the NIR/MIR excess and the concurrent appearance of the blueshift of
the narrow lines in CSM and/or the intermediate–width components originatingin shocked gas. Onset of dust formation depends on when the ejecta encounterswith dense CSM. The early formation of dust at day ∼ 50 in SN 2006jc isconsistent with the LBV–like outburst ∼ 2 yr prior to the explosion. The dust
mass estimates are > 2 × 10−3 M⊙ in SN 1998S, and 3 × 10−4 by day 230 in
SN 2006jc, assuming carbon dust. It should be noted that in addition to theformation of dust in CDSs, we cannot deny the possibility that dust also forms in
the expanding ejecta; see Smith et al. (2008b) for SN 2005ip; Sakon et al. (2009),
Tominaga et al. (2008), and Nozawa et al. (2008) for SN 2006jc. Although thefrequency of Type IIn SNe is rare among CCSNe (Gal–Yam et al. 2007; Smartt
et al. 2009), these observations on dust formation in CDS provide a new window
to investigate the formation process of dust in astrophysical environments.
Nowadays, based on the observations, the mass of dust formed in the ejecta
has been claimed to be less than 10−3 M⊙ and to be too small to contributeto the inventory of dust in our Galaxy. However, we should keep in mind thatthe conclusion is not necessarily definite, based on the limited number of theobservations and the assumption that thermal radiation from dust is opticallyTable 1.
Formation of dust in the ejecta. References; 1) Lucy et al. (1991), 2) Meikle et al. (1993), 3) Roche et al. (1989),
4) Whitelock et al. (1989), 5) Suntzeff & Bouchet (1990), 6) Lucy et al. (1989), 7) Catchpole & Glass (1987), 8) Aitken et al.
(1988), 9) Ercolano et al. (2007), 10) Elmhamdi et al. (2004), 11) Elmhamdi et al. (2003), 12) Spyromilio et al. (2001), 13)
Sugerman et al. (2006), 14) Hendry et al. (2005), 15) Meikle et al. (2007), 16) Kotak (2008), 17) Kotak et al. (2006). Note;
The optical depth of the dust core derived from [O I] line profile τd ≫ 10 at day 510 in SN 1999em (Elmhamdi. et al. 2003),
which is much larger than τd ∼ 1 in SN 1987A (Lucy et al. 1991).

name

Type

onset of dust
formation tc [day]IR excess(NIR/MIR)

decline of
opt. lum.

blue–shiftedlines

molecules

Md
[M⊙ ]

SN 1987A
SN 1990I
SN 1999em
SN 2003gd
SN 2005af

II–pec.
Ib
II–P
II–P
II–P

∼ 350–530 1),2)∼ 250 10)465< tc <510 11)
250< tc <493 13)
214< tc <571 16)

MIR 3)––MIR 13)
MIR 16)

yes 4),5)
yes 10)
yes 11)
yes 13)–[Mg I],[O I] etc. 6)[O I], [Ca II] 10)[O I],[Mg I],etc. 11)[O I], Hα 13),14)–

CO 7) , SiO 8)–
CO 12)
CO,SiO ? 15)
CO,SiO 17)

7.5 × 10−4 9)–≥ 10−4 11)
4 × 10−5 15)∼ 4 × 10−4 16)

name

Type

onset of dust
formation tc [day]IR excess(NIR/MIR)

decline of
optical lum.

blue–shiftedlines

molecules

Md
[M⊙ ]

SN 1998S
SN 2005ip
SN 2006jc

IIn
IIn
Ib

∼ 250 1)
∼ 730 3)∼ 50 5,6)

NIR 1)NIR 3,4)
NIR–MIR 5,6)

–
–
yes

Hα , He I 1)
He I 3)He I 5,6)

CO 2)
–
–

> 2 × 10−3 1)–
3 × 10−4 6)Dust in Supernovae

Table 2.
Formation of dust in a cool dense shell produced by the interaction with dense circumstellar medium. References; 1)
Pozzo et al. (2004), 2) Gerardy et al. (2000), 3) Smith et al. (2008b), 4) Fox et al. (2009), 5) Smith et al. (2008a), 6)Mattila
et al. (2008). Note: For SN 2005ip, Fox et al. (2009) suggested the early formation of dust at day ∼ 50, but the spectroscopic
observation (Smith et al.2008b) suggested the later formation. It should be noted that Smith et al. (2008b) have suggested
formation of dust in the ejecta at earlier time.

47

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Kozasa et al.

thin in some cases; as pointed out by Meikle et al. (2007), the dust may reside in
optically thick clumps in the ejecta. Also, the NIR–MIR observations could missthe cool dust, since dust grains might cool down quickly after the formation as
is demonstrated by Nozawa et al. (2008). Therefore, the monitorings of various
types of SNe after the explosions, covering the temporal and wavelength ranges
as wide as possible, are necessary to reveal the mass of dust formed in theejecta and its dependence on the type of SNe. In addition the sophisticatedradiative transfer calculations such as those carried out by Sugerman et al.
(2006) and Ercolano et al. (2007) are inevitable to derive the dust mass from theobservations relevant to dust formation, taking into account the more realistic
spatial distribution and chemical composition of dust in the ejecta.
3.

Formation of Dust in the Ejecta

In this section we investigate how the formation process of dust in the ejecta
depends on the type of SNe, focusing on Type II–P and Type IIb SNe whose
progenitors are evolved from massive stars with solar metallicity. The calculationof dust formation is based on the theory of nucleation and growth developed by
Nozawa et al (2003), taking into account chemical reaction at the condensationby considering that the key species, defined as a gas species with the least
collisional frequency among the reactants, controls the kinetics of nucleation andgrain growth (Kozasa & Hasegawa 1987, Hasegawa & Kozasa 1988) 1 . Given
the time evolution of gas density and temperature together with the elemental
composition, we can determine when, where, what kind, what size, and how
much mass of dust condenses in the ejecta.
3.1.

Models of Supernovae and Dust Formation Calculation

Formation process of dust grains in the ejecta of SNe is controlled by the time
evolution of gas density and temperature as well as the elemental compositionin the ejecta as demonstrated by Kozasa et al. (1989). Thus, we apply thehydrodynamic model of a SN explosion for the time evolution of the gas density
and the nucleosynthesis calculation for the elemental composition in the ejecta.
The time evolution of the gas temperature is calculated by solving the radiativetransfer equation taking into account the energy deposition from radioactive
elements. Table 3 summarizes the models of SNe used for the calculations.
In the calculations we consider that dust forms within the He–core because
the large expansion velocity in the outer envelope causes the density of condensible elements to be too low to form dust grains. For the elemental composition,
we do not consider any mixing since the mixing driven by the Rayleigh–Taylor
instability in the ejecta at the explosion is not microscopic but macroscopic as
have been revealed by the observation of Cas A (Douvion et al. 1999; Ennis etal. 2006). We assume that formation of CO and SiO molecules is complete; allcarbon (silicon) atoms are locked into CO (SiO) molecules in the locations where
C/O (Si/O) is less than 1. This implies that C–bearing dust condenses only in
1

There was a typo in the nucleation rate J in Kozasa & Hasegawa (1987) and Nozawa et al.
(2003); replace c1 with c21 , where c1 is the number density of key species.

49

Dust in Supernovae
Table 3.
Models of SNe; Mpr is the progenitor mass, Eexp the kinetic energyof the explosion, M (56 Ni) the mass of 56 Ni in the ejecta, Meje the mass ofthe ejecta, MH−env the mass of the hydrogen envelope, MHe−core the mass ofthe He–core in the ejecta, and Mmatal the mass of metal inside the He–core.
Model A is taken from Nomoto et al. (2006), and model B from Umeda andNomoto (2002).
model

Type

Mpr
[M⊙ ]

Eexp
[erg]

M (56 Ni)
[M⊙ ]

Meje
[M⊙ ]

MH−env[M⊙ ]MHe−core[M⊙ ]Mmetal
[M⊙ ]

A
B
C

II–P
II–P
IIb

15.0
20.0
18.0

1051
1051
1051

0.134
0.07
0.07

12.2
15.7
2.94

10.4
10.9
0.08

1.80
4.77
2.86

0.482
3.35
1.297

the region of C/O> 1; see Todini & Ferrara (2001) and Bianchi & Schneider(2007) for the calculation of dust formation assuming the uniform mixing ofelements and considering formation processes of CO and SiO in the ejecta.
Figure 1 shows the elemental composition within the He-core for a Type
II–P SN (model A; upper panel) and for a Type IIb SN (model C; lower panel).
From the view point of dust formation, the He-core is roughly divided into four
layers; the outer C-rich layer, the O-rich layer, the Si–S–Fe layer and the Fe–
S–Si layer. What kind of dust grain really condenses depends on the detailsof elemental composition. Thus, in the calculation we simultaneously solve theequations of nucleation and grain growth for 19 possible condensates (see Nozawa
et al. 2003 for details).
Figure 2 shows the time evolution of the gas density and temperature in
the ejecta; Left panel for Type II–P SN (model A) and right panel for Type IIb
SN (model C). It should be noted that the gas density in the ejecta of TypeIIb SN is more than three orders of magnitude smaller than that of type II–P
SN, because the expansion velocity in the ejecta is much higher in Type IIb SN
without thick H–envelope. The time evolution of the gas temperature depends
on the model through the mass of H–envelope and M (56 Ni) in the ejecta.
3.2.

Results of Dust Formation Calculations

Figure 3 shows the condensation time of each grain species formed in the ejecta;
Left for Type II–P SN (model A) and right for Type IIb SN (model C). As thegas in the ejecta cools down with time, C grains start to condense first in the
C–rich layer around day 300 after the explosion. Afterwards, in the oxygen–richlayer, Al2 O3 , Mg2 SiO4 , MgSiO3 and SiO2 condense in this order from day 350
to day 450. In the Si–S–Fe rich layer, FeS and Si condense around day 450 in
Type II–P SN and around day 630 in Type IIb SN. After then, in the innermost
Fe–S–Si layer, Si, FeS and Fe condense in Type II–P SN, but Si and FeS in TypeIIb SN. The condensation sequence of MgO and Fe3 O4 in the O–rich layer isdifferent between Type II–P SN and Type IIb SN, depending on the detailed
density structure and elemental composition in the ejecta. Also small amount

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Kozasa et al.

Figure 1.
Elemental composition within He–core: Upper panel for Type
II–P SN (model A) and lower panel for Type IIb SN (model C). Note thatthe position in the ejecta is indicated by the mass coordinate that is definedas the enclosed mass from the center.

Dust in Supernovae

51

Figure 2.
Time evolution of gas density and temperature in the ejecta; Leftpanel for Type II–P(model A) and right panel for Type IIb (model C)

Figure 3.
Condensation times of dust species formed in the ejecta; Leftfor Type II–P SN (model A) and right for Type IIb SN (model C). The
condensation time is defined as the time at which the nucleation rate reaches
the maximum. The condensation times of dust species in the C and O–richlayers are a little earlier in Type II–P than in Type IIb, except for FeS and
Si in C–rich layer of Type II–P SN, and FeS in Type IIbof FeS and Si condenses from 450 to 500 days in the C–rich layer of Type II–P
SN, and so does FeS around day 580 in the O–rich layer of Type IIb SN.

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Kozasa et al.

Figure 4.
Average radii of dust species formed in the ejecta: Left for Type
II–P SN (model A) and right for Type IIb SN (model C)

Figure 5.
Cumulative size distributions of dust species by mass summed up
over the ejecta. The mass is dominated by dust grains with radii larger than
0.03 µm for Type II–P SN (model A; left), but with radii less than 0.006 µm
for Type IIb SN (model C; right)

Figure 4 shows the average radius of each dust species formed in the ejecta.
In Type IIb SN (right panel), the average radii of all grain species are smaller
than 0.01 µm due to the low gas density in the ejecta. On the other hand, theaverage radii of dust grains are larger than 0.01 µm in Type II–P (left panel),
except for Si and FeS in the C–rich layer, and Al2 O3 , MgO and Fe3 O4 in theO–rich layer. The difference in the size of dust grains between Type II-P SN andType IIb SN is much more clearly represented by the cumulative size distributionof dust by mass summed up over the ejecta, which is given in Figure 5. Except
for Al2 O3 , the dust mass is dominated by grains with radii larger than 0.03µm
in Type II–P SN (model A; left panel), while the dust mass of all species isdominated by the grains whose radii are less than 0.006 µm in Type IIb (model
C; right panel). This leads to the big difference in the fate of dust grains in
SNRs as is presented in the next section.
Table 4 summarizes the mass of dust formed in the ejecta of Type II–P
SNe (model A and B) and Type IIb SN (model C). The masses of C, Mg–
silicates (Mg2 SiO4 and MgSiO3 ), SiO2 , Si and FeS do not depend so much on

Dust in Supernovae
Table 4.

53

Dust mass formed in the the ejecta
model
Type
Mpr [M⊙ ]dust speciesC
Al2 O3Mg2 SiO4
MgSiO3MgO
SiO2
Fe3 O4FeS
Si
Fe
total mass
Md /Mmetal

A
II-P
15
4.30 × 10−2
1.76 × 10−3
2.95 × 10−2
1.91 × 10−3
3.19 × 10−7
2.06 × 10−2
5.60 × 10−5
3.79 × 10−2
6.65 × 10−2
0.134
0.327
0.695

B
II-P
20
Md,j [M⊙ ]4.00 × 10−2
4.33 × 10−2
0.133
5.68 × 10−3
0.159
8.21 × 10−2
1.55 × 10−3
5.66 × 10−2
9.04 × 10−2
6.46 × 10−2
0.676
0.202

C
IIb
18
7.08 × 10−2
6.19 × 10−5
1.74 × 10−2
5.46 × 10−2
2.36 × 10−3
1.57 × 10−2
1.47 × 10−3
5.07 × 10−3
0.167
0.129

Figure 6.
Optical depth of the ejecta at 1000 days after explosion as afunction of mass coordinate; Left for Type II–P SN (model A) and right forType IIb SN (model C).

the model, while masses of Al2 O3 , MgO, Fe3 O4 and Fe are different from model
to model, depending on the detailed elemental composition and density structurein the ejecta. Generally the total dust mass increases with increasing progenitor
mass. The total dust mass Md ranging from ∼ 0.17 to 0.68 M⊙ is two to threeorders of magnitude larger than the mass inferred from the observations. The
condensation efficiencies defined by Md /Mmetal ranges from 0.13 (model C) to
0.7 (model A). The condensation efficiency of model A is significantly higher
than in the other models, because the metal mass within the He–core is smaller
due to the thin O–rich layer (see Table 1 and Figure 1). Thus, being different
from the total dust mass, the condensation efficiency strongly depends on thedetailed density structure and elemental composition in the ejecta.

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Kozasa et al.

Finally we present the optical depth of the ejecta at day 1000 after the
explosion in Figure 6. The optical depth of the ejecta after dust formation
decreases proportional to t−2 since the ejecta expands homologously. Thus,around day 500 after the onset of dust formation, the ejecta is optically thickeven at 24 µm except for the outer ∼ 0.3 M⊙ (1.5 M⊙ ) region for model A(model C). This result suggests that it could be inappropriate to estimate dust
mass from the thermal emission by assuming the ejecta to be optically thin at
MIR. It takes about 800 (60) yr at 0.5 µm for the entire ejecta to be opticallythin, and about 50 (10) yr at 24 µm for model A (model C).

4.

Evolution of Dust in Supernova Remnant

Dust grains formed in the ejecta suffer from erosion and destruction by sputtering in the hot gas between the reverse and forward shocks produced by theinteraction of the ejecta with the surrounding medium. This process determines
how much mass and what kind of dust can survive and be injected into ISM. In
this section we demonstrate the evolution of dust in SNRs, focusing on type IIb
SN (model C). Then, we calculate the time evolution of thermal emission fromdust in the SNR and compare with the observation of Cas A.
4.1.

Motion and Destruction of Dust in SNRs

At the time when the ejecta encounters the ISM surrounding the SN, the forward shock propagating into the ISM and the reverse shock into the ejecta are
generated (e.g. Truelove and McKee 1999), and the gas swept up by the shocks
is heated up and ionized. The dust grains hit by the reverse shock are injected
into the shocked gas with a velocity relative to the gas; gas is decelerated by
the shock, while dust grains decoupling from gas penetrate into the hot gas withthe same velocity just before the encounter. Then dust grains are decelerated
and eroded by collision with gas. The deceleration of dust by the gas drag is inversely proportional to ρd a, and the erosion rate of dust by sputtering is almost
independent of a (e.g. Dwek & Arendt 1992), where a and ρd is the radius andthe bulk density of dust, respectively. As a result, the small sized/low density
dust is easily trapped into gas, and is eroded by non–kinetic (thermal) sputtering, while larger sized/high density dust moves through the gas, suffering kinetic
sputtering.
We calculate the motion and destruction of dust in the SNR, adapting themodel for the SN explosion as the initial conditions for gas velocity and density,and applying the results of dust formation calculations as the initial spatial andsize distributions of dust grains in the ejecta. The method of calculation andthe underlying assumptions are the same as those by Nozawa et al. (2007). In
the calculations, we assume that the ejecta expands into a uniform medium withsolar metallicity. We consider the two cases for the ambient hydrogen number
density; nH =1.0 and 10.0 cm −3 . We assume the gas temperature in the ambient
medium Tg,amb = 104 K, and that the ejecta hits the ISM at tenc = 10 yr after
the explosion. Note that the assumptions on Tg,amb and tenc do not significantly
affect the result of calculations. The sputtering yield of each grain species istaken from Nozawa et al. (2006).

Dust in Supernovae

55

Figure 7.
Time evolution of gas density and temperature (left panel), andthe motion and destruction of dust grains (right panel) in the Type IIb SNR
for nH = 10.0 cm−3

The left panel of Figure 7 shows the time evolution of gas density andtemperature in the SNR of type IIb SN (Type IIb SNR) for nH = 10 cm−3 ; thepositions of the reverse (forward) shock at given times are indicated by upward(downward) arrows. The temperature of gas hit by the shocks quickly rises up
to 107 to 109 K, and is kept to be > 105 K until the cool dense shell forms behindthe forward shock at t ∼ 106 yr after the explosion. The reverse shock encounters
the C–rich layer at ∼ 80 yr, the O–rich layer at ∼ 440 yr, the Si–S–Fe rich layerat ∼ 800 yr, and the Fe-Si–S rich layer at ∼ 880 yr after the explosion, and theejecta are completely swept up by the reverse shock in ∼ 1400 yr. The right–
upper panel shows the trajectories of dust species with radii of 0.001 µm (dashedcurves) and 0.003 µm (solid curves) together with the positions of the forward
and reverse shocks and the outer boundary of He–core. The time evolution of
the radius of each grain species is depicted in the right–lower panel. As can beseen, grains with radii of 0.003 µm are quickly trapped into the hot gas behind
the reverse shocks and are completely destroyed by thermal sputtering within∼ 3 × 103 yr. How long dust grains remain in SNR depends not only on theinitial position but also on the chemical composition.
The time evolution of the mass of each dust species in the hot gas of TypeIIb SNR is displayed in Figure 8; Left for nH = 1.0 cm−3 , and right for nH = 10.0
cm−3 . Except for C grains for nH = 1.0 cm−3 , all dust grains are destroyed int < 3×104 (4×103 ) yr for nH = 1.0 (10.0) cm−3 . Although the time necessary forthe reverse shock to reach the dust forming layer is almost two times longer for
nH = 1.0 cm−3 than for nH = 10.0 cm−3 , it takes much longer for dust grains
to be destroyed for nH = 1.0 cm−3 because the lower density in the hot gas
caused by the delayed encounter reduces the erosion rate of dust by sputteringsignificantly. It should be noted that C grains dominate the dust mass almost
over all times for nH = 1.0 cm−3 , while for nH = 10.0 cm−3 the mass of C grains
quickly decreases at t > 300 yr, and then MgSiO3 and SiO2 grains dominate the56

Kozasa et al.

dust mass in the SNR. Thus, the ambient gas density strongly affects not only
the mass but also the composition of dust grains remaining in the SNR.

Figure 8.
Time evolution of dust mass in the shocked gas of the Type IIb
SNR:Left for nH = 1.0 cm−3 and right for nH = 10.0 cm−3 .

Table 5.
Mass of dust surviving in the SNRs Msurv at t=10 5 yr and theefficiency of survival defined by η = Msurv /MdnH [cm−3 ]

1.0

10.0

model (type)Msurv [M⊙ ]ηMsurv [M⊙ ]ηA (Type II–P)
B (Type II–P)
C (Type IIb )˙

0.190
5.66 × 10−2
7.83 × 10−5

0.581
8.37 × 10−2
6.07 ×10−4

0.104
3.91 × 10−2
0.00

0.318
5.78 × 10−2
0.00

Table 5 presents the surviving dust mass Msurv at t = 105 yr for the models.
Although Msurv decreases with increasing nH , how much mass of dust survives
strongly depends on the type of SNe through the thickness of outer H–envelopethat influences the size of dust formed in the ejecta as well as the time when
the reverse shock reaches the dust forming layers. In the Type IIb SNR, dust isdestroyed quickly partly because the small sized dust grains with radii < 0.006µm populate the remnant region. In addition, the earlier arrival of reverse shockat the dust–forming layer causes the gas density behind the reverse shock to behigher, and enhances the erosion rate of dust grains; for example, the 35 times
earlier arrival to the C–rich layer compared to the Type II–P SNR (model A)
results in the 10 times higher gas density behind the reverse shock in the TypeIIb SNR. However, it should be noted that, contrary to the expectation, dust
grains are more destroyed in model B than in model A, despite that the massof H–envelope is almost same. One of the reasons is that MgO grains with asputtering rate somewhat larger than others grains (Nozawa et al. 2006) are
more abundant in model B (see Table 4), and another is that the sizes of Fe and
Si grains in model A are significantly larger than those in model B. Thus, thesurvival of dust grains in SNR depends on not only the thickness of H–envelopes

Dust in Supernovae

57

but also on the detailed chemical composition, size distribution, and the amountof dust grains formed in the ejecta.
The efficiency of survival η defined as Msurv /Md is larger than ∼ 0.06 in
the Type II–P SNR, but less than 6 ×10−4 in the Type IIb SNR. Dust grains
surviving at t = 105 yr are almost free from the destruction by sputtering, andare trapped into the dense cool shell formed behind the forward shock or injected
into the ISM. Thus, the injection efficiency strongly depends on the type, whichshould be incorporated into chemical evolution models of dust in the ISM. In
addition, it should be mentioned here that the survival in SNRs and the injection
into the ISM of newly formed dust depend on the density structure in the ISM
as well as the inhomogeneity in the ejecta. For the ambient medium whose gas
density decreases as r−n with distance r, the time evolution of the density of gas
swept up by the reverse shock is different from that for a constant density as
shown by Chevalier & Oishi (2003), which affects the evolution of dust in SNRs.
If dust grains reside in dense clumps (knots) as suggested by the observations(e.g. Arendt, Dwek, & Moseley 1999), the dust grains could survive, since thereverse shock encountering dense clumps could indeed be radiative so that thegas temperature could stay cool enough for dust grains to be rescued from thedestruction by sputtering. These aspects should be explored to reveal how much
mass of dust grain can survive in SNRs and be injected into the ISM.
4.2.

Thermal Emission from Dust in Type IIb SNR

Dust grains formed in the ejecta and injected into the hot plasma between thereverse and forward shocks are heated up by collision with gas, and emit thermalradiation. The equilibrium temperature of dust grain is determined by balancing
the collisional heating with the radiative cooling. However, in a rarefied hot
plasma such as in SNRs, small sized dust grains undergo stochastic heating which
affects the emissivity and the resulting spectral energy distribution (SED); see
Dwek (1986) and Dwek et al. (2008) for details. For example, Figure 9 shows

Figure 9.
Temperature distribution functions of small astronomical silicate
in the hot plasma with ne = 10cm−3 and Te = 107 K (left) and the emissivities(right) for given radii, where the radius is in units of µm.

the temperature distribution function and the emissivity of astronomical silicate(Draine and Lee 1984) embedded in a hot plasma with the electron temperatureof Te = 107 K and number density of ne = 10.0 cm−3 , which is calculated by a

58

Kozasa et al.

Monte–Carlo method. The fraction of incident energy that is deposited in a grain
is calculated by fitting the experimental data of the stopping ranges of electrons
tabulated by Iskef et al. (1983), according to the method by Dwek (1987b).
With decreasing radius, the temperature distribution function becomes broader
and the resulting emissivity deviates strongly from the emissivity calculated by
the equilibrium temperature; the deviation becomes significant for the radius ofa < 0.02µm.

Figure 10.
The time evolution of SEDs of Type IIb SNR for nH = 1.0 cm−3with (solid curve) and without (dotted curves) stochastic heating. Closed
circles are the flux densities subtracting the synchrotron radiation from theobserved ones of Cas A (Hines et al. 2004)

Taking into account the stochastic heating, we demonstrate the time evolution of thermal emission from dust grains embedded in the shocked gas in
the Type IIb SNR, based on the results of dust formation and evolution calculations for Type IIb SN presented in § 3 and § 4.1. In the calculations, theheat capacities of grain species are taken from Takeuchi et al. (2005), and we
use the same optical constants as those of Hirashita et al. (2005), except foramorphous Al2 O3 (Begemann et al. 1997 for the wavelength λ > 8 µm), SiO2
(Phillip 1985) and Si (Pillar 1985). We consider only collision with electrons
for heating, because the radii of dust grains formed in the ejecta are so smallthat dust grains injected into the hot gas are quickly trapped and comove withthe gas, and the heating is dominated by collision with electrons. In order tocompare with the observations of Cas A, we put the SNR at the distance of 3.4
kpc. Figure 10 and 11 show the time evolution of SED ranging from 200 toDust in Supernovae

59

1800 yr after the explosion for nH =1.0 and 10.0 cm−3 , respectively, where thesolid (dotted) curve denotes the SED with (without) stochastic heating. The
solid circles are the flux densities subtracting the synchrotron radiation from theobserved ones tabulated by Hines et al. (2004).
The SEDs taking into account the stochastic heating is completely different
from those with the equilibrium temperatures, especially in the wavelengths
shorter than 20 µm. After the revere shock encounters the C–rich layer at ∼180 (80) yr for nH =1.0 (10.0) cm−3 , the thermal emission from the stochasticallyheated C grains contribute to the SED until the reverse shock encounters theO–rich layer. In the case of nH = 1.0 cm−3 , the thermal emission from C
grains dominates the SED over the entire simulation period considered in thecalculation, because the mass of dust in the SNR is almost dominated by C
grains as can be seen from Figure 8. The emission features of MgO appearing at
λ ∼ 16 µm from t = 800 to 1200 yr, Mg–silicates at λ ∼ 10 µm after t = 1200 yr
and SiO2 at λ ∼ 20 µm after t = 1600 yr are not prominent, being overwhelmedby thermal emission from C grains. On the other hand, in the case of nH = 10.0
cm−3 , with C grains being more efficiently destroyed by sputtering, the emission
features from other dust grains get prominent with time, after the reverse shock
encounters the O–rich layer at t ∼ 400 yr; although the feature of MgO isweak, the emission feature of Mg–silicates around 10 µm becomes noticeable
at t = 600 yr, after then the 20 µm feature of SiO2 is prominent at t = 800
yr. With increasing time, the SED is dominated by the emission features fromstochastically heated dust grains.

Figure 11.

The same as Figure 10, but for nH = 10.0 cm−3

60

Kozasa et al.

The result of calculations clearly demonstrates that the time evolution of the
SED is very sensitive to the evolution of dust in SNRs through the destruction
by sputtering and the stochastic heating, which strongly depends on the density
in the ambient medium. It should be noted that the calculated SED cannot be
reproduced by a single dust component with multiple temperatures.

Figure 12.
Comparison with the observation of Cas A. The symbols denotethe flux densities of Cas A. The solid curve is the total flux density, and thedotted curves denote the contributions of each grain species.

4.3.

Comparison with the Observation of Cas A

Cas A is the nearby Galactic SNR well–studied at various wavelengths and wasrecently identified as Type IIb SN from the spectrum of the scattered lightecho (Krause et al. 2008). The presence of dust formed in the ejecta has been
confirmed by the infrared and submillimeter observations (Lagage et al. 1996;
Arendt et al. 1999; Dunne et al. 2003). However, the dust mass derived fromthe observations has been controversial, ranging from < 1 × 10−3 to ∼ 1.0M⊙(Dwek et al. 1987a; Douvion, Lagage, & Pantin 2001; Dunne et al. 2003; Hines
et al. 2004; Rho et al. 2008). The comparison of the calculated SED with theobservations of Cas A could provide some insights on dust and its evolution in
the Cas A SNR, although the models of Type IIb SN and the evolution of the
SNR are not necessarily applicable to the Cas A SNR.
As shown in Figures 10 and 11, the calculated SEDs for n = 1.0 cm−3 ,being dominated by thermal emission from small C grains, cannot reproduce theobservations at the wavelengths λ < 20 µm at t ≤ 1000 yr, and are significantly
smaller than the observed flux densities at λ ≥ 20 µm. On the other hand, fornH = 10.0 cm−3 , the calculated SED at t = 800 around which the reverse shock
encounters the Si–rich layer seems to reproduce the observed SED.

Dust in Supernovae

61

Figure 12 shows the detailed comparison of the SED calculated at t = 800
yr with the observation and the contribution of each dust grains. Although thediscrepancy around λ ∼ 12 µm is remarkable and the 20 µm feature of SiO2 is
too sharp, the calculated SED can reasonably reproduce the overall shape of theobserved SED without any tuning. The SED is dominated by Mg-silicates and
SiO2 at λ > 15 µm, and by C and Mg-silicates at λ < 10 µm. The dominant
dust species (the mass in unit of solar mass) are MgSiO3 (1.72 × 10−2 ), SiO2
(1.08 × 10−2 ), MgSiO4 (6.46 × 10−3 ), Si (3.62 × 10−3 ), C (1.6 × 10−3 ), and FeS(1.04 × 10−3 ). The total dust mass is ∼ 0.04 M⊙ , which is consistent withthe dust mass of 0.02–0.054 M⊙ evaluated by Rho et al. (2008), apart fromthe details. The presence of Si grains in the model indicates that the reverse
shock already reaches a part of the inner Si–S–Fe layer, which is also not incontradiction with the observation of Cas A by Spitzer showing that the deeperSi–rich layer has been hit by the reverse shock in the region associated with thejet arising from the asymmetric explosion (Ennis et al. 2006).
5.

Summary and Concluding Remarks

We calculate dust formation in the ejecta and evolution in the SNRs of Type
II–P and IIb SNe in order to clarify how these precesses depend on the type of
CCSNe through the difference in the thickness (mass) of the outer envelope. We
show that the mass of newly formed dust ranging from ∼ 0.1 to 0.7 M⊙ does not
so much depend on, but the size of dust grains is sensitive to the thickness of
H–envelope. The radii of dust grains are less than 0.006 µm in Type IIb SN with
MH−env = 0.08 M⊙ , while the dust mass is dominated by the grains with radiilarger than 0.03 µm in Type II–P SNe with MH−env ∼ 10M⊙ . The difference inthe size of the dust formed in the ejecta plays a crucial role in the evolution ofdust in SNRs because the smaller sized grains are quickly trapped into the hot
gas behind the reverse shock and are destroyed by sputtering. The surviving
dust mass ranges from 0.19 to 3.9 × 10−2 M⊙ in the SNR of Type II–P SN for
the ambient H number density of nH = 1.0–10.0 cm−3 , but the dust grains arealmost completely destroyed in the SNR of Type IIb SN.
The SED of the thermal emission from dust embedded in SNRs can beapplied as a diagnosis of the evolution of dust, reflecting the destruction by
sputtering and the stochastic heating. The comparison of the calculated SED of
Type IIb SNRs with the observation of Cas A suggests that the mass of dust in
the SNR is 0.04 M⊙ , which implies that the mass of dust formed in the ejecta is
not less than 1.0 × 10−3 M⊙ , being different from the dust mass estimated fromthe dust forming CCSNe. In addition, Mg–silicates and SiO2 with mass reaching
up to 3.0 × 10−2 M⊙ dominate the SED at λ > 15µm, in contrast to the observed
dust forming SNe that so far show no signature of silicates. This may indicatethat these dust grains formed in the O–rich layer cool down quickly and evade
being detected by the observations as is discussed by Nozawa et al. (2008).
It has been claimed that the mass of dust formed per CCSN is less than
1.0 × 10−3 M⊙ and is too small to contribute to the inventory of dust in ISM,
based on the observations. However, it should bear in mind that the conclusion
comes from a small number of observations. In order to clarify when how much
mass and what kind of dust condenses in the ejecta of various types of SNe, it62

Kozasa et al.

is inevitable to monitor SNe with temporal and wavelength coverages as wide
as possible. In addition, the dedicated radiation transfer calculations such as
those by Sugerman et al. (2006) and Ercolano et al (2007) are promising inevaluating the dust mass compared with the observations, taking into accountthe distribution and chemical composition of dust grains in the ejecta.
Acknowledgments. This work is partly supported by the Grant–in–Aid
for Scientific Research of the Japan Society for the Promotion of Science(18104003, 20340038).
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