The Astrophysical Journal, 713:356–373, 2010 April 10

doi:10.1088/0004-637X/713/1/356


C 2010. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

FORMATION AND EVOLUTION OF DUST IN TYPE IIb SUPERNOVAE WITH APPLICATION TO THECASSIOPEIA A SUPERNOVA REMNANT
Takaya Nozawa1 , Takashi Kozasa2 , Nozomu Tominaga1,3 , Keiichi Maeda1 , Hideyuki Umeda4 , Ken’ichi Nomoto1,4 ,and Oliver Krause5
1 Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa, Chiba 277-8583, Japan; tnozawa@mail.sci.hokudai.ac.jp
2 Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan
3 Department of Physics, Faculty of Science and Engineering, Konan University, Okamoto, Kobe 658-8501, Japan
4 Department of Astronomy, School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
5 Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
Received 2009 September 21; accepted 2010 February 23; published 2010 March 22

ABSTRACTThe amount and size of dust formed in the ejecta of core-collapse supernovae (CCSNe) and injected into theinterstellar medium (ISM) depend on the type of CCSNe through the varying thicknesses of their outer envelopes.
Recently Cas A was identified as a Type IIb SN (SN IIb) that is characterized by a small-mass hydrogen envelope.
In order to clarify how the amount of dust formed in the ejecta and supplied into the ISM depends on the type of
CCSNe, we investigate the formation of dust grains in the ejecta of an SN IIb and their evolution in the shocked gas
in the SN remnant (SNR) by considering two sets of density structures (uniform and power-law profiles) for thecircumstellar medium (CSM). Based on these calculations, we also simulate the time evolution of thermal emission
from the shock-heated dust in the SNR and compare the results with the observations of Cas A SNR. We find thatthe total mass of dust formed in the ejecta of an SN IIb is as large as 0.167 M but the average radius of dust issmaller than 0.01 μm and is significantly different from those in SNe II-P with massive hydrogen envelopes; in the
explosion with the small-mass hydrogen envelope, the expanding He core undergoes little deceleration, so that thegas density in the He core is too low for large-sized grains to form. In addition, the low-mass hydrogen envelopeof the SN IIb leads to the early arrival of the reverse shock at the dust-forming region. If the CSM is more or lessspherical, then the newly formed small grains would be completely destroyed in the relatively dense shocked gas
for the CSM hydrogen density of nH > 0.1 cm−3 without being injected into the ISM. However, the actual CSM is
likely to be non-spherical, so a portion of the dust grains could be ejected into the ISM without being shocked. We
demonstrate that the temporal evolution of the spectral energy distribution (SED) by thermal emission from dust issensitive to the ambient gas density and structure that affects the passage of the reverse shock into the ejecta. Thus,
the SED evolution reflects the evolution of dust through erosion by sputtering and stochastic heating. For Cas A,
we consider the CSM produced by the steady mass loss of Ṁ  8 × 10−5 M yr−1 during the supergiant phase.
Then we find that the observed infrared SED of Cas A is reasonably reproduced by thermal emission from the
newly formed dust of 0.08 M , which consists of the 0.008 M shock-heated warm dust and 0.072 M unshocked
cold dust.
Key words: dust, extinction – infrared: ISM – ISM: supernova remnants – shock waves – supernovae: general –supernovae: individual (Cassiopeia A)
Online-only material: color figures

Observations of nearby CCSNe have reported increasing
evidence for dust formation in the ejecta (see Kozasa et al.
2009, for review). Nevertheless, the composition and size of
newly formed dust have not been specified except in two cases:
SN 2004et (Kotak et al. 2009) and SN 2006jc (Sakon et al.
2009; Smith et al. 2008; Mattila et al. 2008). The masses ofdust formed in the SN ejecta are estimated to be less than
10−3 M from the observations by assuming usually that theejecta is optically thin for thermal emission of dust. However,
newly formed dust may reside in optically thick clumps (e.g.,
Meikle et al. 2007). Moreover, some species of dust grains cancool down quickly after the formation (Nozawa et al. 2008), sothat near- to mid-infrared (IR) observations could miss the cold
dust. Hence, the derived mass of dust could be the lower limit
in some cases, and sophisticated radiative transfer calculations(e.g., Sugerman et al. 2006; Ercolano et al. 2007) referring to theobservational data at UV/optical to far-IR wavelengths would
be required to deduce the properties and mass of dust formed in
the ejecta from observations.

1. INTRODUCTION
Core-collapse supernovae (CCSNe) are considered to beimportant sources of interstellar dust. They eject a large amountof heavy elements synthesized during their stellar evolution andexplosive burning, and form dust grains inside the dense, metalrich He core in the expanding ejecta. Meanwhile, the reverse andforward shocks driven by the encounter of the ejecta materials
with the surrounding medium propagate into the supernova(SN) ejecta and the interstellar medium (ISM), respectively,
producing the hot gas plasma within the supernova remnant(SNR). The dust grains formed in the He core, before being
dispersed into interstellar space, pass through the shock-heatedgas and suffer from erosion and destruction by sputtering due
to collisions with the energetic ions. Since the efficiency ofdestruction of dust grains depends heavily on their compositionand size, the composition and size of dust that condenses in theejecta should be clarified for understanding the properties andamount of dust finally injected from CCSNe into the ISM.
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Theoretical studies have shown that various species of dust
grains with a radius of 0.001–1 μm and a total mass of 0.1–1 M
can condense in the ejecta of Type II-P SNe (SNe II-P)
retaining a massive hydrogen envelope (Kozasa et al. 1989,
1991; Todini & Ferrara 2001; Nozawa et al. 2003). Adopting
the results of dust formation calculations, a semi-analyticalmodel (Bianchi & Schneider 2007) and a numerical simulation(Nozawa et al. 2007) investigated the survival of dust in the
SNRs and found that the dust mass injected into the uniform ISM
is ∼0.01–0.8 M for the ambient hydrogen density of nH,0 =10–0.1 cm−3 . This mass of dust supplied by SNe II-P is stilllarge enough to explain a huge quantity of dust in excess of
108 M observed for the host galaxies of quasars at redshiftz > 5 (Morgan & Edmunds 2003; Maiolino et al. 2006; Dwek
et al. 2007), though it is proposed that asymptotic giant branchstars can also contribute to dust enrichment even at such an early
epoch (Valiante et al. 2009).
Recently Kozasa et al. (2009) have suggested that the amountand size of dust formed in the ejecta and injected into the ISM
depend on the type of CCSNe, reflecting the thickness of the
H-rich envelope. A less massive outer envelope leads to extremely high expansion velocity of the He core unless the kinetic
energy of the explosion is very low, and makes the gas density
in the expanding ejecta of the He core too low for large-sizedgrains to be produced. Furthermore, a low-mass outer envelope
can allow the reverse shock to arrive early at the dust-forming
region and result in efficient destruction of newly formed dustin the shock-heated gas with high density. Because a significant
fraction of CCSNe (∼0.3) explode as hydrogen/helium-poor
CCSNe such as SNe Ib/Ic and SNe IIb (Prieto et al. 2008;
Smartt et al. 2009; Boissier & Prantzos 2009), it is essential toinvestigate how the formation and destruction processes of dust
depend on the type of CCSNe, in order to clarify the role of
CCSNe as sources of interstellar dust.
It should be mentioned here that dust grains embedded in thepostshock gas are eroded by sputtering and are heated up by
collisions with the hot gas, radiating their thermal emission at
IR wavelengths. Since the destruction efficiency and the heating
rate of dust are sensitive to grain size as well as gas density, theIR spectral energy distributions (SEDs) by thermal emission
from dust in SNRs can be a diagnostic feature of the size andtemperature of dust, and therefore provide key information on
the nature of dust formed in the ejecta, density structure in theambient medium, and destruction and heating processes of dust.
In particular, young SNRs that originated from SNe with lowmass envelopes are ideal for comparing the observed IR SEDs
with calculated ones; the reverse shock can quickly arrive at the
He core and heat up newly formed dust before the forward shock
sweeps up a considerable amount of circumstellar/interstellar
dust, so that we mainly see the IR emission from dust grainscondensed in the ejecta. Cassiopeia A (Cas A) SNR is one of
the best targets for this study because the Cas A SN has been
recently identified as Type IIb by a striking similarity between
the optical spectrum of its scattered light echo and the timeaveraged spectrum of SN IIb 1993J (Krause et al. 2008), and thepresence of dust freshly formed in the ejecta has been confirmed
by IR observations (e.g., Rho et al. 2008).
In this paper, we explore the formation of dust in an SN IIb
and the evolution of the dust inside the SNR, with the aim of
revealing the composition, size, and mass of dust ejected fromhydrogen-deficient CCSNe. In addition, the time evolution ofthermal emission from dust within SNRs is calculated and iscompared with observations of Cas A to discuss the composition357

and amount of dust. In Section 2, we perform a calculation ofdust formation in the ejecta of an SN IIb whose progenitor
has lost most of its hydrogen envelope during the evolution(Nomoto et al. 1993; Podsiadlowski et al. 1993). In Section 3,
we investigate the evolution of the newly formed dust in the gas
heated by the reverse and forward shocks and its dependence
on the ambient gas density and structure. Then, following the
calculations of dust evolution in SNRs, we present the temporal
evolution of IR emission from collisionally heated dust in the
hot gas in Section 4, and compare the results with observationsof Cas A in Section 5. We summarize our results in Section 6.
2. FORMATION OF DUST IN THE EJECTA OF SN IIb
In the ejecta of SNe, dust formation takes place within the
He core where the densities of condensible elements are highenough to advance the formation and growth of seed nuclei
through collisions with the relevant gas species. Formation
processes of dust grains are influenced by the time evolution of
the density and temperature of the gas as well as the elemental
composition in the ejecta (Kozasa et al. 1989). In this section,
we describe a model of the dust formation calculation for an SN
IIb and present the results of the calculations.
2.1. Model of SN IIb and Calculation of Dust Formation
The calculation of dust formation is carried out by applying
the theory of non-steady state nucleation and grain growthdeveloped by Nozawa et al. (2003). The theory takes into
account chemical reactions at condensation, considering thatthe kinetics of nucleation and grain growth is controlled by the
key species defined as the gas species with the least collisionalfrequency among the reactants (Kozasa & Hasegawa 1987;
Hasegawa & Kozasa 1988). Given the elemental compositionof the gas in the ejecta as well as the time evolution of the gas
density and temperature, the theory allows us to determine thecondensation time, chemical composition, size distribution, andmass of dust that condenses in the ejecta (see Nozawa et al. 2003
for details).
In the calculation of dust formation, we adopt the model ofthe SN IIb with a zero-age main-sequence mass of 18 M and a
metallicity of Z = 0.02. The ejecta mass is Meje = 2.94 M , themass of the hydrogen envelope is Menv = 0.08 M , the kinetic
energy of the explosion is Ekin = 1051 erg, and the synthesized56
Ni mass is M(56 Ni) = 0.07 M . These model parameters are
invoked to reproduce the light curve of SN 1993J by referring to
the SN model in Shigeyama et al. (1994). Note that the mass ofejecta in this model is in good agreement with the ejecta mass of
Cas A (=2–4 M ) estimated from the studies of shock dynamics(Borkowski et al. 1996; Chevalier & Oishi 2003; Laming &Hwang 2003) and from X-ray observations (Vink et al. 1996;
Favata et al. 1997; Willingale et al. 2003).
In Figure 1, we show the elemental composition in the ejectaof the SN IIb model at 600 days after the explosion, taking
into account the decay of radioactive elements. In Table 1, we
also present the mass of the dust-forming elements i in theejecta. We assume that the elemental distribution in the ejecta
remains an onion-like structure without any mixing, which isconsistent with the theoretical model of mixing in SN 1993J;
Iwamoto et al. (1997) have shown with a two-dimensional
simulation that the deceleration of the He core by the thin
H-rich envelope is so weak that the growth of theRayleigh–Taylor instability is too slow to cause substantial mixing in the ejecta, in contrast to SN 1987A which has a thick

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Figure 1. Relative number abundance of elements in the ejecta of the SN IIb
model at 600 days after the explosion as a function of enclosed mass. The
decay of radioactive elements is taken into account, and the original onionlike structure is assumed to be preserved without any mixing of elements. The
progenitor mass of the SN IIb is 18 M , and the mass at the explosion is4.52 M . The mass cut is 1.58 M , which results in the ejecta mass of 2.94 M .
The mass of the hydrogen envelope is 0.08 M .

H-rich envelope (e.g., Hachisu et al. 1990, 1992). Although thejet formation in the explosion suggested from the observationsof Cas A can lead to macroscopic mixing (e.g., Tominaga 2009),
a simple argument of molecular diffusion has shown that mixing
at the atomic level is extremely ineffective before the condensation of dust grains in the ejecta (Deneault et al. 2003). Indeed,
the observations of Cas A at various wavelengths have suggested
that the mixing in the ejecta should not be at atomic level butat the macroscopic level (e.g., Willingale et al. 2002; Fesen et al.
2006b; Ennis et al. 2006). From Figure 1, we can see the layered
structure of elemental composition with the very thin hydrogen envelope at the outermost ejecta, which is followed by the
C-rich (C/O > 1) He layer, the O-rich layer, the Si–S–Fe layer,
and the Fe–Ni layer inwardly.
The distributions of gas temperature and density in theejecta of the SN IIb at 300 days and 600 days are shown in
Figures 2(a) and (b), compared with those for the SN II-P
model of Meje = 17 M and Menv = 13.2 M with the same
Ekin and M(56 Ni) as those of the SN IIb model (Umeda &Nomoto 2002). The gas density scales as t −3 with the time t after
the explosion, and the time evolution of the gas temperature
is mainly regulated by the energy deposited from radioactive
elements (i.e., M(56 Ni)). It should be noted that the gas density
in the He core of the SN IIb is about three orders of magnitude
lower than that in the SN II-P. The reason for this is that, sincealmost all of the explosion energy is deposited into the He core
without the thick hydrogen envelope, the resulting expansion
velocity of the gas in the He core of the SN IIb is much higher
than that of the SN II-P, as shown in Figure 2(c).
Based on the hydrodynamic and nucleosynthesis models
for the SN IIb, we calculate dust formation. Dust formation
proceeds through the formation and growth of seed nuclei as
the gas cools down. The number of seed nuclei is evaluated by
calculating the non-steady state nucleation rate (Equation (5)in Nozawa et al. 2003) coupled with the time evolution of thegas temperature and the number density of the key species. In
the calculations, it is assumed that without coagulation the seed
nuclei grow homogeneously at a rate controlled by the collisionsof the key species with the sticking probability of unity. We also
assume that the formation of CO and SiO molecules is complete;Figure 2. Structures of (a) temperature and (b) density of the gas within
the He core at day 300 (solid lines) and day 600 (dashed lines) after the
explosion, and (c) the velocity distribution for the SN IIb model (thick lines).
For comparison, those for the SN II-P model (thin lines) with Meje = 17 M
and Menv = 13.2 M (Umeda & Nomoto 2002) are also shown. The mass
coordinate is normalized by the mass of the He core. Note that both SN models
have Ekin = 1051 erg and M(56 Ni) = 0.07 M .

all C (Si) atoms are locked in CO (SiO) molecules in the casewhere the number density of C (Si) atoms is lower than that of O
atoms. Under this assumption, C-bearing grains can condense
only in the He layer with C/O > 1. Depletion or rarefactionof the key species due to grain growth or the expansion of theejecta, respectively, causes the process of nucleation and growthof dust grains to cease in less than a few tens of days from theonset of nucleation.
2.2. Results of Dust Formation Calculation
The simulation results of dust formation in SN IIb are
illustrated in Figures 3(a) and (b), where the mass distribution
and average radius of each dust species formed in the ejecta are
given as a function of enclosed mass Mr , respectively. Without
any mixing of elements, different species of dust condense
according to the elemental composition of the gas in each layer:
C grains in the He layer, silicates (MgSiO3 , Mg2 SiO4 , and SiO2 )and oxides (Al2 O3 and MgO) in the O-rich layer, and FeS and Si
grains in the Si–S–Fe layer. The typical times (gas temperatures)at which dust grains condense in the ejecta are 300–350 days
(1400–1700 K) for C grains, 350–500 days (1100–1400 K) for
silicate and oxide grains, and 600–700 days (800–900 K) for
Si and FeS grains. In the innermost Fe–Ni layer, neither Fe nor
Ni grains can be formed because the gas density becomes too
low before the gas cools down to the temperatures (800 K) at
which these grains can condense. Fe atoms residing in both the
O-rich and He layers are not abundant enough to be locked ingrains as Fe-bearing dust (see Figure 1). Except for Fe grains,the major species of dust formed in the SN IIb are the same as
those for the unmixed cases in SNe II-P with Z = 0 in Nozawa
et al. (2003).

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Table 1Mass of the Main Refractory Species in the Ejecta of the SN IIb
Species(1)

MA,i (M )(2)dust (M )
MA,i

(3)

dust /M
MA,i
A,i
(4)

C
O
Mg
Al
Si
S
Fe
Others1.14 × 10−1
6.86 × 10−1
1.07 × 10−1
9.31 × 10−3
1.07 × 10−1
3.33 × 10−2
7.92 × 10−2
1.61 × 10−1

7.08 × 10−2
4.35 × 10−2
2.05 × 10−2
3.28 × 10−5
3.12 × 10−2
5.35 × 10−4
9.35 × 10−4
0

0.621
0.063
0.192
0.004
0.292
0.016
0.012
0

Total

1.30

0.167

···

Notes. Column 1: species of the main heavy element in the ejecta of the SN IIb.
Column 2: mass of each heavy element (MA,i ). Column 3: mass of each element
dust ). Columnthat is locked up in dust grains at the time of dust formation (MA,i4: mass fraction of each element that is locked up in dust grains at the time ofdust /M
dust formation (MA,iA,i ).
Table 2Mass of Each Dust Species Formed in the Ejecta of the SN IIb
Dust Species(1)

Md,j (M )(2)

Md,j /Md(3)

Md,j /MA(4)C
Al2 O3
MgSiO3Mg2 SiO4
SiO2
MgO
FeS
Si

7.08 × 10−2
6.19 × 10−5
5.46 × 10−2
1.74 × 10−2
1.57 × 10−2
2.36 × 10−3
1.47 × 10−3
5.07 × 10−3

0.423
3.7 × 10−4
0.326
0.104
0.094
0.014
0.009
0.030

0.054
4.8 × 10−4
0.042
0.013
0.012
1.8 × 10−3
1.1 × 10−3
3.9 × 10−3

0.167

1

0.128

Total

Figure 3. (a) Mass distribution and (b) average radius of each dust species
formed in the ejecta of the SN IIb model as a function of enclosed mass.

The mass of each dust species formed in the ejecta of SN IIb
is presented in Table 2, together with the ratio of its mass to thetotal dust mass (see Table 1 for the mass and mass fraction ofmajor elements locked in dust grains). The total mass of newly
formed dust is 0.167 M , which is more than two orders ofmagnitude larger than the dust mass estimated from a handful ofobservations of nearby dust-forming SNe. C grains are the mostdominant species in mass, with the mass of 0.07 M , and thebulk of them is in the innermost He layer at Mr = 2.7–2.9 M(see Figure 3(a)), where the mass fraction of available C atoms
locked in C grains is fC = 0.4–1. The masses of MgSiO3 ,Mg2 SiO4 , and SiO2 are 0.055 M , 0.017 M , and 0.016 M ,respectively, and these silicate grains account for more than 50%of the total dust mass. The mass distributions of silicate grains
are influenced by the abundance of SiO molecules (namely Si
atoms, see Figure 1), and concentrate at Mr = 1.7–1.9 M
with the mass fraction of the preexisting SiO molecules lockedin silicate grains fSi = 0.4–0.8. The condensation efficiency,
defined as the ratio of the total dust mass to the total metal mass,is 0.13 for the SN IIb and lies in the range of those estimatedfor SNe II-P (0.05–0.25; Nozawa et al. 2003).
It should be emphasized here that, as can be seen from
Figure 3(b), the average radii of all grain species formed in
the SN IIb are below 0.01 μm and are much smaller than those

Notes. Column 1: species of dust formed in the ejecta of the SN IIb. Column 2:
mass of each grain species (Md,j ). Column 3: ratio of mass of each dust species
to the total dust mass (Md,j /Md ). Column 4: ratio of mass of each dust species
to the total metal mass (Md,j /MA ).

(aave > 0.01 μm) of dust grains formed in SNe II-P (Nozawa
et al. 2003). This difference is caused by the difference in the gas
density within the expanding ejecta of the He core. In general,a larger supercooling necessary for dust grains to condense in agas with lower density leads to the formation of a large numberof seed nuclei and results in smaller average radii even if allavailable gaseous atoms are used up for the growth of seed
nuclei (fj = 1, where fj is the mass fraction of key species j
locked in a given grain species). As was discussed in Kozasa
et al. (1989), under the condition that the number density of
key species is so low that the collision timescale of key species
is longer than the expansion timescale of the gas, neither asignificant number of seed nuclei can condense nor nucleatedgrains can grow to sufficiently large radii via accretion onto thesurface of the grains.
2.3. Dependence of Grain Radius on SN Parameters
Here we briefly discuss how our results on dust formation
are affected by the model parameters for an SN explosion, inparticular focusing on the kinetic energy of the explosion Ekin .
A lower Ekin leads to a higher He core density, thus making it
possible for more dust grains with larger radii to condense if
the time evolution of the gas temperature could not be affectedby the explosion energy. At a fixed time t1 , the gas density−3
is scaled by the expansion velocity v eje as ρeje (t1 ) ∝ veje

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NOZAWA ET AL.

for a given mass and density structure of the ejecta. Since
1/3
veje ∝ (Ekin /Meje )1/2 and roughly aave ∝ ρeje (Nozawa et al.
2003), we find aave ∝ 1/veje ∝ (Meje /Ekin )1/2 . Thus, even for
the extremely low explosion energy of Ekin = 1050 erg, theincrease in the average grain radii is as small as a factor of  3.
In addition, if we consider Ekin = (1–4)×1051 erg estimated for
Cas A (Willingale et al. 2003; Chevalier & Oishi 2003; Laming& Hwang 2003; Young et al. 2006), grain radii only reduce bya factor of  2, compared with those given in Figure 3(b).
In reality, however, the assessed variation of the grain radius
is suppressed by the dependence of the time evolution of gas
temperature on Ekin ; with the same amount of 56 Ni in theejecta, the lower (higher) explosion energy can cause the gas
temperature to decrease more slowly (more quickly) becauseof more (less) efficient energy deposition in the ejecta withthe higher (lower) gas density. This leads to the later (earlier)condensation of dust, which compensates for the increase(decrease) in the gas density. Consequently, the condensationof dust occurs at a similar gas density, and not only the radius
but also the mass of dust formed in the ejecta is almost thesame, regardless of the explosion energy (see Appendix A in
Nozawa et al. 2003), as long as the range of variation of Ekin is
not extremely large. The qualitative analysis indicates that thegrain radius is insensitive to the explosion energy, and that our
results on dust formation are robust for the expected variationof model parameters for Cas A SN.
On the other hand, it should be noted that the grain radius isgreatly affected by the structure of the progenitor star resulting
from the presence or absence of a massive outer envelope; asseen from Figure 2(c), the He-core velocity of the SN IIb withthe thin hydrogen envelope is 5–10 times higher than that of
the SN II-P with the thick envelope. The higher velocity of the
SN IIb leads to a few orders of magnitude lower gas density
and thus produces about one order of magnitude smaller dust
grains than the SN II-P. Nozawa et al. (2008) have also pointed
out the effect of the lack of the outer envelope on the size of
newly formed dust in Type Ib SN 2006jc, applying the SN
model by Tominaga et al. (2008). They found that too low
gas density in the He core, which is caused by the absence ofthe outer envelope, prevents dust grains with radii larger than
0.01 μm from forming within the He core. These results indicatethat the radii of dust grains formed in SNe IIb and SNe Ib/Ic
are generally smaller than those in SNe II-P with thick outerenvelopes.
Our results demonstrate that the composition and mass of dust
grains formed in the ejecta are almost independent of the typeof CCSNe and the initial metallicity of the progenitors because
the distribution and yield of metals in the He core are similar.
On the other hand, their radii strongly depend on the type of
CCSNe; SNe with lower-mass envelopes produce much smaller
dust grains (aave < 0.01 μm) than SNe II-P with much more
massive envelopes. As shown in the next section, the small sizesof newly formed dust grains will determine their subsequent
fates within the SNR.
3. EVOLUTION OF DUST IN TYPE IIb SNR
Dust grains formed in the He core initially move with thegas without suffering from any processings. Upon encountering
the reverse shock, the gas is quickly decelerated, while the dust
grains decouple from the gas with high velocities relative to thegas, and intrude into the hot plasma region created by the passageof the reverse and forward shocks. These shocked dust grains

Vol. 713

are decelerated by the drag force, eroded by thermal and/or
kinetic sputtering, and heated up by collisions with the hot gas.
The motion, destruction, and heating of dust depend not only on
the properties of dust but also on the density and temperature in
the postshock gas. In this section, applying the result of the dust
formation calculation, we examine the evolution of the dust in
the hot gas within SNRs and its dependence on the gas density
and structure in the circumstellar medium (CSM).
3.1. Model of Calculations for Destruction and Motion of Dust
in SNRs
The calculations of dust evolution within SNRs follow themethod described by Nozawa et al. (2007); dust grains aretreated as test particles, and the motion and destruction of dust
are pursued by self-consistently calculating the erosion due tosputtering and the deceleration caused by the gas drag together
with the time evolution of gas temperature and density in thespherical symmetry shock. We use the size distribution andspatial distribution of each dust species obtained in the lastsection as the initial conditions, and adopt the model of the SN
IIb used in Section 2 for the velocity and density structure in theejecta.
For the structure of CSM, which affects the evolution of SNRs
and thus critically impacts the evolution of dust, we consider
two sets of the density profile. One is the uniform CSM withthe hydrogen number densities of nH,0 = 0.1, 1, and 10 cm−3 ,assuming that the gas in the CSM has the solar composition andis fully ionized. For the other CSM density profile, we consider
the density structure produced by the steady stellar wind during
the evolution of the progenitor; the density profile is represented
in terms of hydrogen number density as −2rnH (r) = nH,1
cm−3 for r < r2
r1
= 1 cm−3forr  r2 ,(1)

where r1 = 1.2 × 1018 cm is the radius of the freely expanding
outermost ejecta at t = 10 yr after the explosion in the present
model, and r2 is the radius such that nH,1 (r2 /r1 )−2 = 1 cm−3 .
The coefficient nH,1 is given as
nH,1 = nH (r1 ) =ṀAH,
4π r12 vw μmH(2)

where Ṁ is the mass-loss rate, vw is the stellar wind velocity,
μ is the mean molecular weight, and mH and AH are the massand the number abundance of the hydrogen atom, respectively.
In the calculations, we consider three cases of nH,1 = 30, 120,and 200 cm−3 ; for example, the case of nH,1 = 30 cm−3 with
vw = 10 km s−1 corresponds to Ṁ = 2 × 10−5 M yr−1 , whichis the mass-loss rate of Cas A’s progenitor suggested from theanalysis of shock dynamics by Chevalier & Oishi (2003).
The CSM models used in the calculations are listed in Table 3,
and the uniform CSM and the stellar wind CSM (ρ ∝ r −2 ) arereferred to as models A and B, respectively, with the valueof nH,0 or nH,1 attached for each case. In the calculations, thespatial bin for hydrodynamic calculation is linearly divided into
2510 bins, and the size bin of dust is logarithmically divided into
80 bins for the range of 1 Å to 1 μm. We assume that the gas in
the CSM has a temperature of 104 K and that the ejecta collidewith the CSM at t = 10 yr after the SN explosion. We haveconfirmed that moderate changes in the CSM gas temperature

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Table 3Results of the Dust Evolution Calculation for Each CSM Model
He
tcoll
(yr)
(2)

O
tcoll
(yr)
(3)

Si
tcoll
(yr)
(4)

Msurv
(M )
(5)

η
(Msurv /Md )
(6)

330
Rrev
(pc)
(7)

330
Rforw
(pc)
(8)

330
Mwarm
(M )
(9)

330
Mcool
(M )
(10)

A0.1
A1
A10

335
155
75

1300
590
270

3400
1550
700

1.3 × 10−4
0.0
0.0

7.8 × 10−4
0.0
0.0

2.76
1.98
1.32

3.46
2.52
1.83

0.0
1.0 × 10−4
0.038

0.167
0.167
0.094

B30
B120
B200

63
48
45

340
150
120

1850
560
370

0.0
0.0
0.0

0.0
0.0
0.0

1.51
0.93
0.70

2.20
1.67
1.50

0.048
0.008
0.028

0.111
0.072
0.011

CSM model(1)

Notes. Column 1: name of the CSM models considered in this paper. Labels A and B represent the uniform CSM and the stellar
wind CSM (ρ ∝ r −2 ), respectively, and the attached number denotes the value of nH,0 for model A and nH,1 model B (see the text).
Columns 2–4: times at which the reverse shock encounters the He core, O-rich layer, and Si-rich layer, respectively. Column 5: massof surviving dust at t = 106 yr. Column 6: ratio of surviving dust mass Msurv to the initial dust mass Md . Columns 7 and 8: radii ofthe reverse and forward shocks at t = 330 yr. Column 9: mass of warm dust heated up by the shock at t = 330 yr. Column 10: massof unshocked cold dust at t = 330 yr.

Figure 4. Time evolution of radius (upper panel) and velocity (lower panel) of
the reverse shock for the uniform CSM models A0.1 (dotted), A1 (solid), andA10 (dashed) with nH,0 = 0.1, 1, and 10 cm−3 , respectively. The trajectory of
the boundary between the He core and the hydrogen envelope is depicted by
the thin solid line in the upper panel, where the boundary is assumed not to be
decelerated after the collision with the reverse shock for illustration.
(A color version of this figure is available in the online journal.)(∼103 –105 K) do not influence the results of the calculations.
The calculations are performed up to t = 105 –106 yr, dependingon the CSM density.
3.2. Results of Dust Evolution Calculation
3.2.1. Penetration of the Reverse Shock into the Ejecta

We first describe how the penetration of the reverse shock
depends on the gas density in the CSM. Figure 4 exhibits thetime evolution of the radius and the velocity of the reverse shock
for the uniform CSM models A0.1, A1, and A10 with nH,0 =0.1, 1, and 10 cm−3 , respectively. In the upper panel, we also
show the trajectory of the boundary between the He core and thehydrogen envelope for a reference, assuming that the boundary
is not decelerated even after the collision with the reverse shock.
The interaction of the SN ejecta with the ambient medium
generates the forward shock running into the CSM to compress
the ambient medium. The shocked hot ambient gas thrusts theejecta in turn, driving the reverse shock that propagates into theejecta but initially expands outward in the Eulerian coordinate.
For the higher CSM density, the forward shock acquires a lower
velocity, and the denser shocked gas is produced behind theforward shock. Accordingly, the reverse shock travels throughthe ejecta with a smaller outward velocity so that the unshocked
ejecta can catch up with the reverse shock at earlier times (seeFigure 4). Thus, the time at which the reverse shock collides
with the He core is earlier for the higher gas density in the CSM:
tcoll = 355 yr, 155 yr, and 75 yr for the models A0.1, A1, andA10, respectively. For the stellar wind CSM, the collision times
are earlier than for the uniform CSM models because of higher
ambient density at the time of the ejecta–CSM interaction: tcoll =63 yr, 48 yr, and 45 yr for the models B30, B120, and B200
respectively with nH,1 = 30, 120, and 200 cm−3 (see Table 3).
Note that these collision times for the remnant of Type IIb
SN (hereafter Type IIb SNR) are a few tens times earlier thanthose for Type II-P SNRs, for which tcoll = (1.5–10) ×103 yr
for the CSM densities of nH,0 = 10–0.1 cm−3 (Nozawa et al.
2007). The earlier arrival of the reverse shock at the He core in
Type IIb SNRs is due to their much thinner hydrogen envelopeand higher expansion velocity of the He core (see Figure 2(c))
than those of Type II-P SNRs. As shown below, the thicknessof the hydrogen envelope has great effects on the evolution ofdust in SNRs.
3.2.2. Destruction of Dust for the Uniform CSM

Figure 5 shows the time evolution of gas density (upper
panel) and temperature (lower panel) within Type IIb SNR
for the model A10 (uniform CSM with nH,0 = 10 cm−3 ). The
gas densities behind the reverse and forward shocks, whose
positions are depicted by the downward- and upward-pointing
arrows in the lower panel, respectively, increase by a factor of
about 4, compared with the unshocked ones. The temperatureof the gas swept up by both the shocks rises to >107 K andremains over 106 K by t  105 yr. Dust grains staying in thishot gas are subject to destruction by sputtering.
Figure 6 presents the time evolution of positions (upper
panel) and radii (lower panel) of dust grains with initial radii

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Figure 5. Structures of density (upper panel) and temperature (lower panel)of the gas at given times within the Type IIb SNR for the model A10 with
nH,0 = 10 cm−3 . The positions of the forward and reverse shocks are indicatedby the upward- and downward-pointing arrows in the lower panel, respectively.

of 0.001 μm (for Al2 O3 and FeS) and 0.003 μm (for the othergrains) for the model A10, together with the trajectories of thereverse and forward shocks in the upper panel. In this model, thereverse shock encounters the He layer at t = 75 yr, the O-richlayer at t = 270 yr, and the Si-rich layer at t = 700 yr. Once
newly formed dust grains intrude into the shocked gas, they are
efficiently decelerated by the gas drag and are quickly trapped in
the hot plasma. These grains are completely destroyed and are
not injected into the ISM. Actually, all newly formed grains aredestroyed in the postshock gas for most of the models consideredin this paper. One of the reasons for this is that the radii of newly
formed grains are very small; since the deceleration rate of dust
is inversely proportional to the grain radius (e.g., Nozawa et al.
2007), dust grains with radii of <0.01 μm are easily captured by
the shock-heated gas and are destroyed by thermal sputtering.
Another reason is that the reverse shock can reach the He core
more than 20 times earlier for SNe IIb than for SNe II-P as
mentioned above; although the initial gas density in the ejectaof the SN IIb is three orders of magnitude lower than those in
SNe II-P (see Figure 2(b)), at such an early time, the gas density
in the He core of the SN IIb is still higher by a factor of ∼10than those in SNe II-P at several thousand years. This leads tofrequent collisions between dust and gas and causes the efficient
deceleration and destruction of dust.
In Figure 7(a), we compare the time evolution of the total dust
mass for the uniform CSM with nH,0 = 0.1, 1, and 10 cm−3 .
We can see that dust grains are destroyed more efficiently andquickly at higher CSM density. This is because the increaseof the gas density in the CSM leads to the earlier arrival of
the reverse shock at the dust-forming region, which keeps thegas density in the He core high enough for dust grains to beeroded by sputtering efficiently. For nH,0 = 0.1 cm−3 , C grainsof ∼10−4 M can survive for t = 106 yr, while all dust grains

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Figure 6. Time evolutions of the positions (upper panel) and radii (lower panel)of dust grains within the Type II SNR for the model A10. The initial radii ofgrains shown in the figures are 0.001 μm for Al2 O3 and FeS (dashed lines)
and 0.003 μm for C, MgSiO3 , Mg2 SiO4 , SiO2 , MgO, and Si (solid lines).
The trajectories of the reverse and forward shocks as well as the position of theboundary between the He core and the hydrogen envelope are depicted by the
thick curves in the upper panel.

are destroyed within t = 4 × 105 yr for nH,0 = 1 cm−3 andt = 5 × 103 yr for nH,0 = 10 cm−3 .
3.2.3. Destruction of Dust for the Stellar Wind CSM

Figure 7(b) shows the evolution of the total dust mass in
SNRs for the stellar wind CSM (ρ ∝ r −2 ) models. For thesemodels, dust grains are completely destroyed before t = 105 yr.
However, the evolution of dust in SNRs shows the different
behaviors as shown in Figures 8(a) and (b), where the time
evolutions of mass of each dust species for the models B30 and
B120 are presented. For model B30 with nH,1 = 30 cm−3 , asmall amount of C grains survive after t = 104 yr, whereas theother grain species are completely destroyed before t ∼ 104 yr.
In the case of model B120 with the CSM gas density four times
higher than that for B30, C grains are destroyed quickly after thecollision with the reverse shock, whereas the masses of somedust species such as SiO2 and Si grains decrease more slowly
than those for B30.
In order to explain these different behaviors of dust evolution,
we show the time evolutions of density structure within SNRs
for B30 and B120 in Figures 9(a) and (b), respectively. Since thedeceleration and erosion rates are dependent on the ion number
density, the time evolutions of the total ion number density, n,
are given in the lower panel in Figure 9, along with the positionsof C, SiO2 , and Si grains with the initial radii of 0.003 μm. We
also present the time evolutions of positions and radii of theseC, SiO2 , and Si grains in Figure 10.
For model B30 (Figures 9(a) and 10(a)), the SNR expands
into the CSM with the density profile of ρ ∝ r −2 during only
340 yr, and then propagates into the ISM with a constant densityof nH = 1 cm−3 . Thus, one might guess that the evolution ofdust in the SNR would be quite similar to that for model A1 with

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Figure 7. Time evolutions of the total dust mass inside the Type IIb SNRs
running into (a) the uniform CSM with nH,0 = 0.1 cm−3 (dotted), 1 cm−3(solid), and 10 cm−3 (dashed), and (b) the stellar wind CSM with nH,1 =30 cm−3 (dotted), 120 cm−3 (solid), and 200 cm−3 (dashed).

the uniform CSM of nH,0 = 1 cm−3 . However, as presented in
Figure 7, dust grains in the ejecta are completely destroyed about
10 times earlier for B30 than for A1, because the gas density
behind the reverse shock for B30 is about 8 times higher thanfor A1 at t  340 yr due to the fast passage of the reverse shock
into the ejecta (see Table 3). In addition, the density of gas in
the region swept up by the reverse shock at the initial phaseremains quite high (n  0.3 cm−3 ) even after t = 3000 yr (seeFigure 9(a); hereafter, such a region is referred to as the dense gas
region). As can be seen in Figure 10(a), dust grains are trapped in
the dense gas region shortly after their collisions with the reverse
shock and are completely destroyed by thermal sputtering. C
grains formed in the inner C-rich region of the He layer collidewith the reverse shock at an early epoch (t  330 yr) and areeroded by sputtering in the denser gas than those for SiO2 andSi grains formed inside the O-rich layer. However, C grains cansurvive for a relatively long period, compared with SiO2 and Si
grains (see Figure 8(a)), because the erosion rate of C grains
is smaller than the other grain species by a factor of about 5(Nozawa et al. 2006).
In the case of model B120 (Figures 9(b) and 10(b)), thereverse shock more quickly penetrates into the ejecta than B30,
which results in an extended shocked region between the reverse
shock front and the dense gas region (see Figure 9(b)). C grains

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Figure 8. Time evolution of the mass of each dust species inside the Type IIb
SNRs running into the stellar wind CSM with the density profile of ρ ∝ r −2for (a) nH,1 = 30 cm−3 and (b) nH,1 = 120 cm−3 . The thick solid line indicates
the time evolution of the total dust mass.

collide with the reverse shock at t  140 yr and are immediately
destroyed in the shocked gas with (330/140)3  13 times higher
density than that for B30. SiO2 and Si grains, which encounterthe reverse shock at t  400 yr and t  700 yr, respectively,
intrude into the 30–40 times denser postshock gas than the cases
for B30. However, the gas density is not high enough for the
SiO2 and Si grains to be trapped and completely destroyed.
Instead, upon collisions with the reverse shock, these grainsare greatly decelerated by the gas behind the reverse shock,which prevents them from reaching the dense gas region ina short time; SiO2 grains are finally trapped in the extended
shocked region and are destroyed without arriving at the dense
gas region. Si grains are eroded slowly passing through theextended shocked region until they reach the dense gas region
at 104 yr.
For model B200, the reverse shock can propagate into theejecta even earlier than B120. Hence, the gas density behind thereverse shock is so high that all grain species are trapped and arequickly destroyed once they are swept up by the reverse shock.
These results demonstrate that the evolution of dust within SNRs
strongly depends on the gas density and structure in the CSM,
as well as on the composition of dust grains and their initial
position in the ejecta.
In Table 3, we summarize the total mass Msurv of surviving
dust in Type IIb SNRs at t = 106 yr for the CSM models

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Figure 9. Time evolutions of the gas density (upper panel) and the corresponding total ion number density (lower panel) as a function of distance from the center for(a) nH,1 = 30 cm−3 and (b) nH,1 = 120 cm−3 . The positions of the reverse shock are indicated by the arrows in the upper panels. In the lower panels, the positions ofC (circles), SiO2 (squares), and Si grains (triangles) are plotted where the filled and opened symbols denote the unshocked and shocked ones, respectively.

Figure 10. Time evolutions of the positions (upper panel) and radii (lower panel) of C, SiO2 , and Si grains with the initial radii of 0.003 μm in the Type IIb SNR for(a) nH,1 = 30 cm−3 and (b) nH,1 = 120 cm−3 . The trajectories of the reverse and forward shocks as well as the position of the surface of the He core are depicted by
the thick curves in the upper panel.

considered in this paper. For all CSM models except for model
A0.1, dust grains formed in the ejecta are completely destroyed
before t = 106 yr. Even for model A0.1, the destruction
efficiency η, defined as the ratio of Msurv to the initial dust mass
Md , is less than 10−3 , in contrast to the case of SNe II-P withthick hydrogen envelopes, for which 2%–80% of dust grains
can survive for the ISM with nH,0 = 10–0.1 cm−3 (Nozawa
et al. 2007). As shown above, the difference in the evolutionof dust between Type IIb and Type II-P SNRs is caused by
the thickness of the outer envelope; for SNe II-P retaining a

massive hydrogen envelope, the radii of newly formed grains
are larger than 0.01 μm, and the arrival time of the reverse shockat the dust-forming region inside the He core is retarded, bothof which act against the destruction of dust grains by sputtering.
Therefore, the amount of dust injected into the ISM strongly
depends on the type of SNe through the varying thicknesses of
their outer envelopes, even if a large amount of dust grains canform in the ejecta of CCSNe. From the results of the present
calculations, we conclude that low-mass envelope SNe such as
SNe IIb and SNe Ib/c cannot be major contributors of interstellar

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dust as long as the gas density in the CSM is not too low(nH  0.1 cm−3 ).
4. IR THERMAL EMISSION FROM DUST IN TYPE IIb
SNRs
Dust grains bathed in the shocked gas inside SNRs areheated up by collisions with the hot gas and emit their thermalradiation at IR wavelengths. If the collisional heating rate andradiative cooling rate of dust are balanced, the dust can reachequilibrium temperature. However, in a rarefied hot plasma suchas SNRs, small-sized dust grains undergo stochastic heating,which influences the emissivity and the resulting SED (e.g.,
Dwek 1986). In this section, based on the results of thesimulations of dust evolution presented in Section 3 and taking
into account stochastic heating, we calculate the SED by thermal
emission from shock-heated dust within SNRs. The SNRs areplaced at a distance of 3.4 kpc in order to compare with theobservations of Cas A SNR in the next section.
4.1. Calculation of Stochastic Heating
The heating and thermal emission of dust are calculated byusing the output of the dust evolution simulations: density andtemperature of the gas as well as size, velocity relative to thegas, and number density of each dust species in each spatial
bin as a function of time. We employ a Monte Carlo method to
calculate the temperature distribution functions of dust grains
by stochastic heating. In the calculations, we consider only
collisions with electrons for the heating of dust; under thepresent situation in which dust grains are quickly trapped in
the hot gas, collisions with ions are much less frequent, and theheating of dust is dominated by collisions with electrons.
The fraction of incident energy that is deposited into a grain is
calculated following the prescription by Dwek (1987), and thestopping range of an electron for each grain species is calculatedby the approximation formula derived on the basis of those by
Tabata et al. (1972) and Iskef et al. (1983). The heat capacity ofeach grain species is taken from Takeuchi et al. (2005), and theoptical constants are taken from the following sources: C (Edoh1983), Al2 O3 (Toon et al. 1976 for λ  8 μm and Begemannet al. 1997 for λ > 8 μm), MgSiO3 (Dorschner et al. 1995;
but the optical constants of Mg2 SiO4 are used for λ  0.3 μm,
see Hirashita et al. 2008), Mg2 SiO4 (Semenov et al. 2003),
SiO2 (Philipp 1985), MgO (Roessler & Huffman 1991), FeS(Semenov et al. 2003), and Si (Piller 1985). We re-bin the sizesof dust into 12 bins from 1 Å to 0.1 μm and divide the shocked
region into 20 spatial bins weighted by the mass of the gas,because the calculation is too time-consuming. We have verified
that even if the number of re-binned size (spatial) bins increases
to 20 (50), the resulting SEDs are virtually the same.
4.2. Time Evolution of Thermal Emission from Dust
Figures 11–14 show the time evolution of SEDs by thermal
emission from shocked dust for different CSM models every
200 yr in the range from 200 yr to 1800 yr after the explosion.
In these figures, the solid curves display the SEDs taking
into account stochastic heating, and the dashed curves theSEDs calculated by assuming the equilibrium without stochastic
heating. We can see that the SEDs taking account of stochastic
heating are strongly different from those with the equilibrium
temperatures, especially at wavelengths shorter than λ =20 μm. This implies that the effect of stochastic heating is very

365

important in modeling the IR SED by dust emission within
SNRs, as demonstrated by Dwek (1986).
For model A1 with uniform gas density (Figure 11), thereverse shock hits the He core at t = 155 yr after the explosion.
The mass of C grains formed in the outer C-rich region of
the He layer is too small (<5 × 10−4 M ) to emit the thermal
emission significantly during t = 200–400 yr. At t > 400 yr,
thermal emission from a large amount of C grains formed in
the inner C-rich part of the He layer always dominates theSED, because the gas density in the SNR is not high enough todestroy C grains efficiently. The reverse shock reaches the Orich layer at t  600 yr, but the emission features of silicate andoxide grains are inconspicuous, being overwhelmed by thermal
emission from C grains.
For the higher CSM density of model A10 (Figure 12), C
grains are more efficiently destroyed by sputtering than thosein model A1, and the emission features from other dust species
grow prominent with time. The reverse shock encounters the
O-rich layer at t = 270 yr, and the emission feature of Mgsilicates (MgSiO3 and Mg2 SiO4 ) around λ = 10 μm begins to
be noticeable at t = 600 yr. The feature of SiO2 at λ = 20 μm is
outstanding after t = 800 yr, and the emission features from Si
and FeS grains appear after t = 1200 yr. Because of the efficient
destruction of dust, the thermal emission continues to decrease
with time.
In the case of model B30 with the stellar wind’s density profile(Figure 13), the reverse shock collides with the He core at t =63 yr, which is earlier than in model A10. Thermal emission
from C grains dominates the SED by t ∼ 1000 yr, and afterthat the contributions from Mg-silicates become recognizable.
However, stochastic heating of small C grains still contributes to
the SED at λ  10 μm, because some C grains can survive evenafter t = 1000 yr owing to the low gas density (nH = 1 cm−3 )at a large distance in comparison with model A10. We can seethat the flux densities significantly increase between 1200 yr and1400 yr in this model. This is due to the fact that during this timeinterval, the reverse shock has swept up the ejecta region wherea large amount of silicate grains are formed (Mr  1.8 M ,see Figure 3(a)). The dust grains swept up by the shocks continue
to be eroded by sputtering, while the reverse shock continues to
intrude into the inner He core and to supply newly formed dust
grains to the shocked gas. Thus, the time evolution of SEDs isdetermined by the balance between the amount of dust destroyedin the hot gas and the amount of dust swept up by the reverse
shock.
For model B120 (Figure 14), the reverse shock can quickly
propagate into the ejecta, and arrives at the He core, O-rich layer,
and Si-rich layers at t = 48 yr, 150 yr, and 560 yr, respectively.
Thus, we can see the quick evolution of the SED characterized
by the features of various grain species. Since the gas density
is significantly high, especially at an early phase, C grains arequickly destroyed as can be seen from the evolution of SED at
λ  8 μm, and the emission from stochastically heated small C
grains disappears at t  600 yr.
The results of these calculations clearly demonstrate that thetime evolutions of IR emission from dust heated up in SNRs
are sensitive to the density of gas as well as the density profilein the surrounding medium. The ambient gas density controls
the passage of the reverse shock into the ejecta and affects thedestruction by sputtering and stochastic heating of dust in the hotgas. Hence, the resulting IR SED reflects the evolution of dustin SNRs and also holds key information on the density structurein the ambient medium. In other words, the temporal evolution

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Figure 11. Time evolution of SEDs by thermal emission from shocked-heated dust within the Type IIb SNR for the uniform CSM model A1 (nH,0 = 1 cm−3 )every 200 yr after the explosion. The solid and dashed lines show the IR thermal emission with and without stochastic heating, respectively. The data points are thesyncrotron-subtracted flux densities observed for Cas A and are taken from Hines et al. (2004).
(A color version of this figure is available in the online journal.)of SED from dust in shock-heated gas can be a very useful toolfor investigating the properties of dust in SNRs as well as thedensity structure in the CSM and thus the mass-loss history of
the progenitor star during the late phase of its evolution.
5. APPLICATIONS TO THE Cas A SNR
In this section, we apply the results of our calculations fordust evolution and the resulting SEDs presented in Sections 3
and 4 to Cas A SNR, to gain insight into the composition andmass of dust residing in Cas A SNR as well as the mass-loss
rate of the progenitor. After briefly summarizing the observed
characteristics of Cas A relevant to this study, we present thecomparison of the calculated SEDs with the observed one.
5.1. Cas A SNR
Cas A is one of the best studied Galactic SNRs at a broad
range of wavelengths spanning from radio to γ -ray. Its estimatedage is ∼330 yr (Fesen et al. 2006a; Thorstensen et al. 2001),

and the distance to Cas A is determined to be 3.4 kpc fromthe proper motion of fast moving knots (FMKs; Reed et al.
1995). The X-ray observations with Chandra have resolved theradii of the reverse and forward shocks to be 95 ± 10 and153 ±12 , respectively (Gotthelf et al. 2001), which correspond330
330
to Rrev= 1.57 ± 0.17 pc and Rforw= 2.52 ± 0.19 pc at a
distance of 3.4 kpc.
Recently Krause et al. (2008) obtained an optical spectrum of
the Cas A SN around the maximum brightness via the scattered
light echo, and concluded that the Cas A SN was of Type IIb,
originating from a supergiant that had lost most of its hydrogenenvelope prior to the explosion as has been suggested by theclose binary scenario for SNe IIb (e.g., Nomoto et al. 1995). The
numerical simulations (Chevalier & Oishi 2003; Young et al.
2006) and the discovery of FMKs containing some hydrogen(Fesen & Becker 1991; Fesen 2001) also seem to strongly
support this conclusion.
The presence of dust formed in the ejecta has been confirmed
by IR observations with the IRAS (Dwek et al. 1987), the ISO

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DUST FORMATION AND EVOLUTION IN SN IIb

367

Figure 12. Same as Figure 11, but for model A10 (nH,0 = 10 cm−3 ).
(A color version of this figure is available in the online journal.)(Lagage et al. 1996), and Spitzer (Hines et al. 2004). The IR
spectra of FMKs taken by the ISO allowed us to examine thecomposition of dust, leading to the conclusion that the main
species of newly formed dust in Cas A are silicate and/or oxide
grains (Arendt et al. 1999; Douvion et al. 2001).
There has been a continuing controversy about the amountof dust residing in Cas A SNR; the dust mass derived from theobservations described above was smaller than 3 × 10−3 M .
Rho et al. (2008) estimated the mass of dust to be 0.02–0.054 M
from the spectral mapping covering the entire region of Cas A by
the Spitzer. Based on submillimeter (submm) observation with
the SCUBA, Dunne et al. (2003) have reported the detectionof 2–4 M of cold dust in Cas A. Dwek (2004) ascribed thiscold dust emission to metallic needles of <10−3 M formedin the ejecta. On the other hand, the MIPS 160 μm map of
Cas A, complemented by CO and OH line observations, havedemonstrated that the detected submm emission originated frominterstellar dust in the foreground molecular clouds (Krause
et al. 2004), and the mass of cold dust associated with Cas A isestimated at most to be 0.2 M (Krause et al. 2004) and 1.5 M
(Wilson & Batrla 2005).

Although the existence of a peculiar species of cold dust with
∼1 M is also proposed from submm polarization (Dunne et al.
2009), we do not consider here the measurements at wavelengths
longer than 160 μm. In what follows, we compare the calculated
SEDs with the synchrotron-subtracted IR flux densities at λ =8–100 μm taken from the photometric observations tabulated in
Hines et al. (2004).
5.2. Comparison with the Observations of Cas A
5.2.1. IR Emission from Shock-heated Newly Formed Dust

We first compare the results for the uniform CSM with theobservations of Cas A. For nH,0 = 1 cm−3 , IR emission isdominated by stochastically heated small C grains throughout
the age of the remnant, as shown in Section 4.2. This causes
the excess emission over the observed SED at λ  15 μm untilt = 1000 yr, and the calculated SED cannot reproduce theobservational data. The fact that the C grain-dominated IR SED
does not match with the IR measurements of Cas A is also
pointed out by Bianchi & Schneider (2007).

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Figure 13. Same as Figure 11, but for the stellar wind CSM model B30 (nH,1 = 30 cm−3 ).
(A color version of this figure is available in the online journal.)

For the case of nH,0 = 10 cm−3 , the calculated SED at
t = 800 yr is in good agreement with the IR observationsof Cas A (see Figure 12). The mass of shock-heated dust at
t = 800 yr is 0.048 M , which is consistent with the dust mass of
0.02–0.054 M in Cas A estimated from the Spitzer observations(Rho et al. 2008). The comparison strongly suggests that thedominant species of dust responsible for the observed SED aresilicate grains and that the reverse shock has already reached
the inner O-rich layer in the ejecta. However, the remnant ageof 800 yr is much older than the age of Cas A, and the SED
at t = 330 yr does not agree with the observations. We also
found that any uniform CSM models with gas density higher
than nH,0 = 10 cm−3 cannot reproduce the observed SED, partly
because the dust grains are quickly destroyed and partly because
the temperature of the dust is too high. Thus, we conclude that
thermal emission of dust grains heated up in SNRs expanding
into the uniform CSM cannot explain the observed IR SED of
Cas A.
Next, we move to the comparison of the results for the CSM
density structure of ρ ∝ r −2 . Figures 15(a)–(c) present thecalculated SEDs at t = 330 yr for nH,1 = 30, 120, and 200 cm−3 .
In these figures, we also show the contribution of each dust
species to the total flux densities. Note that the SEDs calculated
without stochastic heating are not shown in these figures, since
they can never reproduce the observations of Cas A for any CSM
models.
The case of nH,1 = 30 cm−3 corresponds to Ṁ = 2 ×−5
10 M yr−1 for vw = 10 km s−1 , and Chevalier & Oishi(2003) have suggested that the density structure reproduces theobserved radii of the reverse and forward shocks derived fromthe X-ray observations (Gotthelf et al. 2001). Our simulation
also approximately reproduces the observed shock radii for Cas
A: 1.5 pc for the reverse shock and 2.2 pc for the forward shock.
However, in this case, the reverse shock has not yet reached
the O-rich layer at t = 330 yr (see Table 3). The calculated flux
densities from the shock-heated C grains of ∼0.05 M are muchhigher than the observations at the whole mid-IR wavelengths.
With nH,1 = 120 cm−3 , the calculated SED reasonably
reproduces the observed SED at λ  30 μm, although there
is some discrepancy at λ  12 μm. The SED also predicts

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369

Figure 14. Same as Figure 11, but for model B120 (nH,1 = 120 cm−3 ).
(A color version of this figure is available in the online journal.)

the considerably lower flux densities at λ  50 μm, which
can be recovered by considering the unshocked dust as will be
discussed later. The dust species most contributing to the SED
is MgSiO3 , which is one of the major grain species in Cas A
presumed from the IR spectra (Douvion et al. 2001; Rho et al.
2008). Mg2 SiO4 , SiO2 , and MgO grains more or less contributeto the SED, and C grains partly contribute at λ  15 μm as
well. The total mass of shocked dust grains is 0.008 M , whichis smaller than the estimate by Rho et al. (2008) but is larger
than those from the other IR observations.
For nH,1 = 200 cm−3 , the calculated SED does not matchwith the observations, especially at λ = 20–60 μm. In thiscase, the reverse shock invades deeper layers in the ejecta andsweeps up a larger mass (0.028 M ) of silicate grains, comparedwith the case of nH,1 = 120 cm−3 . Therefore, the derived SED
produces much higher flux densities than the observations. We
also calculate the thermal emission from shocked dust for the
CSM denser than nH,1 = 200 cm−3 , but the outcomes sufferfrom much lower flux densities at λ  30 μm because of theefficient destruction of dust and the relatively high temperatureof dust. In addition, in such dense cases, the shock radii are muchsmaller than the observations. Hence, we conceive that the casesof nH,1  200 cm−3 are unlikely as the density structure around
Cas A.
In summary, our results indicate that the stellar wind’s density
profile with nH,1  120 cm−3 is most favorable to account forthe observed IR emission at the age of Cas A. The corresponding
mass-loss rate 8 × 10−5 M yr−1 is at most a factor of 4
higher than the mass-loss rates estimated for SNe IIb: (3–4)
×10−5 M yr−1 (Suzuki & Nomoto 1995; Fransson et al.
1996) deduced for SN 1993J (at r  1 × 1015 cm) and2 × 10−5 M yr−1 for Cas A (Chevalier & Oishi 2003). In
view of the uncertainties involved in the density gradient andclumpiness in the CSM, these estimated mass-loss rates can be
regarded as being consistent. On the other hand, the result for
nH,1 = 120 cm−3 predicts quite smaller shock radii than those
for Cas A (see Table 3). The discrepancy in the shock radii aswell as the mass-loss rate could be considered to be partly causedby the difference in the explosion energy and the thickness ofthe hydrogen envelope of the SN model used in this study.
It should be emphasized that the IR emission from newly
formed dust grains that are heated up in the hot plasma inside

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Vol. 713

sources to the observed SED at λ  50 μm: (1) the circumstellar(CS) dust grains that were formed in the mass-loss wind during
the evolution of the progenitor star and then were swept up
by the forward shock and (2) the newly formed dust that wereformed in the ejecta but have not been yet swept up by thereverse shock.
5.2.2. Contribution from Pre-existing CS Dust

Figure 15. Comparison between the IR observations of Cas A and the calculated
SEDs by thermal emission from shocked dust at 330 yr for (a) nH,1 = 30 cm−3 ,(b) 120 cm−3 , and (c) 200 cm−3 . The dashed lines indicate the contribution ofeach dust species. The IR flux densities in (a) are produced only by C grains.
The data points are the same as in Figure 11.
(A color version of this figure is available in the online journal.)

SNRs can reproduce the mid-IR (λ = 8–30 μm) SED of Cas A
without any fine-tuning. On the other hand, the obtained results
for nH,1 = 120 cm−3 significantly underestimate the flux
densities at longer wavelengths (λ  50 μm). Although thethermal emission from cooler dust in the dense optically emitting
knots is expected to mitigate this difference, modeling of sucha dust emission may need a sophisticated radiative transfer
simulation and is beyond the scope of this paper. Hereafter,
we discuss the contributions from the following two potential

In order to examine the contribution from the preexisting CS
dust, we simulate the destruction and heating of the shocked
CS dust for the density structure of the CSM corresponding to
the mass-loss rate of 8 × 10−5 M yr−1 . The composition of
the CS dust is considered to be either carbonaceous or silicate
depending on the C/O ratio in the stellar wind. Carbonaceous
grains condense in C/O > 1, which is realized in the windsof carbon-rich Wolf–Rayet stars. Silicate grains are expected
to form in the wind of a supergiant, where the abundance ratioof heavy elements is nearly solar with C/O < 1. Although asupergiant is a more likely progenitor of Cas A (Section 5.1),
we consider here, as the dust composition in the CSM, both
amorphous carbon and astronomical silicate, for which theoptical constants are taken from Edo (1983) and Draine & Lee(1984), respectively. For the size distribution of the dust, we
adopt the MRN size distribution (n(a)da ∝ a −3.5 da; Mathis
et al. 1977) with upper and lower limits of a = 0.001 μm and0.5 μm, respectively. The dust-to-gas mass ratio in the CSM isassumed to be constant and is taken as a free parameter.
Figure 16 illustrates the contribution from CS carbon(Figure 16(a)) and astronomical silicates (Figure 16(b)) for thecase of nH,1 = 120 cm−3 , where the ejecta-dust and CS dust
components are depicted by the dotted and dashed lines, respectively. The dust-to-gas mass ratios adopted here are 1.6 × 10−4for carbon and 2.8 × 10−4 for silicate because higher dustto-gas mass ratios cause excess emission over the observed
SED at λ  50 μm. At t = 330 yr, the masses of shockheated CS carbon and silicate grains are 1.4 × 10−3 M and1.8 × 10−3 M , respectively, and both grain species have typical temperatures of 100 K. Thus, we can see that both grain
species can only contribute to the SED at λ  50 μm withthe peaks around λ = 30 μm, and cannot compensate the flux
densities at λ  50 μm. This means that the observed SED
cannot be improved by the contributions from CS grains evenif we consider any mixtures of these CS grains and dust-to-gas
mass ratios different from those considered here. Therefore, we
suppose that the IR emissions from shocked CS grains should
not significantly contribute to the IR SED of Cas A and thata small content of CS dust may be due to low condensation
efficiency of dust in the mass-loss wind and/or to partial destruction of CS dust by the strong radiation associated with theshock breakout at the explosion (e.g., Blinnikov et al. 1998).
We emphasize that the thermal emission from CS dust alone
can never reproduce the observations of Cas A for any models
considered in this paper.
5.2.3. Contribution from Unshocked Ejecta-dust

As shown in Section 5.2.1, in the case of nH,1 = 120 cm−3 ,only 0.008 M of newly formed dust grains is heated in theshocked gas at t = 330 yr, and 0.072 M of dust grains remains
cold without being swept up by the reverse shock (see Table 3).
These unshocked dust grains are expected to be heated up by
absorbing the X-ray and UV/optical photons generated from theshock-heated plasma and dense knots, and they may radiate their
thermal emission with a higher temperature than that (∼20 K) inNo. 1, 2010

DUST FORMATION AND EVOLUTION IN SN IIb

371

Figure 16. Contributions from (a) CS amorphous carbon and (b) CS astronomical silicate to the IR SED calculated for nH,1 = 120 cm−3 . The dashed anddotted lines denote the thermal emissions from the shocked CS dust and shocked
newly formed dust, respectively, and the solid lines represent the total SED. The
observation data for Cas A are the same as in Figure 11.
(A color version of this figure is available in the online journal.)

Figure 17. Contributions from the unshocked ejecta-dust to the IR SED
calculated for nH,1 = 120 cm−3 at (a) 330 yr and (b) 340 yr. The dashedand dotted lines denote the thermal emissions from the unshocked and shocked
newly formed dust, respectively, and the solid lines represent the total SED. The
temperature of cold dust is 43 K in (a) and 40 K in (b). The observation data for
Cas A are the same as in Figure 11.
(A color version of this figure is available in the online journal.)

the diffuse ISM and contribute to the SED at IR wavelengths. In
fact, the presence of cold dust in the unshocked ejecta of Cas A
SNR has been suggested from the association of a “featurelessdust” component with the Si II emission from the central part of
the remnant (Rho et al. 2008). Since the dedicated calculationsof radiative transport at X-ray to optical wavelengths is beyond
the scope of this paper, we evaluate the contribution of theunshocked dust to the IR SED, assuming the same temperature
for all unshocked grains.
Figure 17 shows the contribution from unshocked newly
formed dust, together with the contribution of shock-heatedwarm dust at 330 yr (Figure 17(a)) and 340 yr (Figure 17(b))
for nH,1 = 120 cm−3 . The age of 340 yr is the expected ageof Cas A in the case where the forward shock has not been
decelerated (Thorstensen et al. 2001; Fesen et al. 2006a). As
can be seen from the figures, if the unshocked dust grains areheated up to a temperature around 40 K, their thermal emission
can significantly contribute to flux densities at λ  50 μm andcan successfully reproduce the observations of Cas A. Thus, theIR SED observed for Cas A can be naturally explained by theshocked warm component and unshocked cold component of
newly formed dust obtained by our calculations. We also notethat the calculated IR emission from shocked warm dust at t =340 yr slightly increases from that at t = 330 yr, giving a better
fit at λ  20 μm. This indicates that the IR flux from Cas A canchange during a short time interval of ∼10 yr.
Finally, the following should be pointed out here. We showthat the IR observations of Cas A are successfully reproduced
by 0.008 M shocked dust and 0.072 M unshocked dust,
considering the destruction and heating of newly formed dustin the SNR for nH,1 = 120 cm−3 . Although the derived dust
mass in Cas A SNR is superficially large enough to explaina vast amount of dust observed in the host galaxies of highredshift quasars at z > 5, these dust grains would be completely
destroyed in 2 × 104 yr and could not be supplied into the ISM,
as demonstrated in Section 3.2, if the CSM is more or lessspherical. We also should note that if the CSM is not spherical,
a portion of the dust grains in the unshocked ejecta could beejected into the ISM.
6. CONCLUSION
We investigate the formation of dust in the ejecta of ahydrogen-poor SN IIb, adopting the SN model with Ekin = 1051

372

NOZAWA ET AL.

erg, Meje = 2.94 M , and Menv = 0.08 M . Then we explore
the evolution of newly formed dust in the hot gas inside the
SNR by considering the two sets of density profile for the
spherical CSM. Based on the results of dust evolution in SNRs,
we also calculate the time evolution of thermal emission fromthe shocked dust within the SNR and compare the results withthe observations of Cas A. The results of our calculations are
summarized as follows.
1. In the unmixed ejecta of the SN IIb, various dust species
can condense depending on the elemental composition ineach layer at 300–700 days after the explosion. The total
mass of newly formed dust is as large as 0.167 M , andthe composition and mass of dust formed in the SN IIb
are similar to those in SNe II-P. However, the mass of thehydrogen envelope of the SN IIb is too small to significantly
decelerate the expansion of the He core. Thus, the gas
density in the He core is too low for large-sized grains to be
produced, and the resulting average radius of dust is smaller
than 0.01 μm. We propose that the size of dust formed in
SNe with low-mass envelopes such as SNe IIb as well as
the envelope-stripped SNe Ib/Ic is much smaller than thatformed in SNe II-P with massive hydrogen envelopes.
2. The evolution of dust within SNRs is strongly affected by
the mass of the outer envelope and the gas density in the
CSM. A less massive outer envelope and/or a denser CSM
lead to the earlier arrival of the reverse shock at the He core,and causes quicker and more efficient destruction of newly
formed dust in the denser hot gas. In the Type IIb SNR, asa result of the small size of dust and the early propagationof the reverse shock into the dust-forming region, all newly
formed dust grains are destroyed in the shocked gas without
being injected into the ISM for the ambient gas density ofnH > 0.1 cm−3 . If the CSM is more or less spherical, ourresults imply that low-mass envelope SNe do not play amajor role in the dust enrichment in the ISM.
3. The time evolution of IR SEDs by thermal emission fromshocked dust in SNRs well reflects the evolution of dust
through erosion by sputtering and stochastic heating. The
destruction and heating processes of dust in the hot gas
are heavily affected by the ambient gas density that affects
the passage of the reverse shock into the ejecta. Thus, thecomparison of theoretically modeled SEDs and observed
IR SEDs can be used to diagnose the size and mass of dustin SNRs and the density structure surrounding the SNe.
These in turn provide us with some hints on the formation
process of dust in the ejecta and the mass-loss activity ofthe progenitor stars during late evolution.
4. The IR SED observed for Cas A can be reasonably
reproduced by the shocked warm dust with Md = 0.008 M
and unshocked cold dust with Md = 0.072 M , both ofwhich were newly formed in the ejecta. The CSM density
required to reproduce the observed SED corresponds to thesteady stellar wind of a supergiant with a mass-loss rate of
8 × 10−5 M yr−1 . This mass-loss rate is consistent withthose estimated for the progenitors of SN 1993J and Cas A
within a factor of 2–4. It should be emphasized that these
conclusions are the natural outcomes derived by the selfconsistent treatments of formation, destruction, and heatingof dust given in this study.
The result of the dust formation calculation shows that the
total mass of dust formed in the ejecta is 0.167 M , which ismuch larger than the mass estimate of dust deduced from theVol. 713

observations of nearby dust-forming SNe. From the comparisonof calculated SEDs with the observed SED, we predict thatin Cas A SNR about half the newly formed dust grains havealready been swept up by the reverse shock and most of themhad been destroyed, while the other half of newly formed grains
have not yet been swept up by the reverse shock. The massof this unshocked dust (0.072 M ) is in good agreement withthe upper mass limit of cold dust (0.2 M ) in Cas A estimatedby Krause et al. (2004). On the other hand, our calculation
demonstrates that all dust grains formed in Cas A might becompletely destroyed later on and might not be injected into
the ISM, if the CSM was more or less spherical (see below).
Thus, the SN IIb that formed Cas A might not be representativeof SNe as major sources of interstellar dust, but Cas A could
remain as a unique and ideal object for investigating formationand evolution processes of dust in SNe.
We should bear in mind that all calculations here are performed for the spherically symmetric forward and reverse
shocks propagating into the homogeneous CSM and stratified
ejecta, respectively. In the binary scenario for SNe IIb (Nomoto
et al. 1995, 1996), the formation of aspherical CSM is predicted
to be as follows. The close binary consists of a massive SN IIb
progenitor and a small-mass companion star. In the common envelope phase, the companion star spirals into the envelope of the
SN IIb progenitor, which causes extensive mass loss from the
H-rich envelope of the progenitor in the direction of the equatorial plane. The resultant CSM might have a ring-like structure
as seen in SN 1987A, a torus, or a thick disk. In reality, theCSM around SN 1993J is considered to be more like a torus
shape (e.g., Fransson et al. 2005). Then since the ejecta of polar
direction cannot strongly interact with the CSM (e.g., Maeda
et al. 2002), the ejecta of SN 1993J can be composed of thereverse-shocked ejecta and the unshocked ejecta. Thus, if the
CSM is spherical, dust can be totally destroyed. If the CSM is
non-spherical like SN 1993J, unshocked dust can be partiallyejected.
In addition, IR and X-ray observations of Cas A have shownthat the ejecta of Cas A are very clumpy and asymmetric(Willingale et al. 2002; Ennis et al. 2006; Smith et al. 2009) with
the inverted compositions as represented by Fe-rich materials
overtaking the outer layer (e.g., Hughes et al. 2000). This
indicates that some dust species may encounter the reverse shockat different times and different gas densities than suggested inthis paper. Furthermore, if newly formed grains would residein dense clumps, it might be possible that a part of them
could survive the destruction and be injected into the ISM.
Although the mass of shocked and visible material is believed
to roughly account for all the mass ejected in the explosion, theIR spectral mapping observations of the entire region of Cas
A SNR suggest the presence of unshocked ejecta materials in
the central region of the remnant (Rho et al. 2008; Smith et al.
2009). However, it has been difficult to estimate how much dust
there is in the unshocked region from the observations covering
the wavelengths of λ  70 μm, as pointed out by Rho et al.
(2008). Since the mass of dust in Cas A is likely to be dominatedby the unshocked low-temperature dust, comprehensive far-IR
observations at λ  50 μm are necessary to reveal the mass ofdust formed in the Cas A SN.6 Unfortunately, Cas A suffers from6

After this paper was submitted, an article by Sibthorpe et al. (2009)
appeared on astro-ph reporting the presence of a cool emission component
peaked near the center of Cas A in the 90 μm image obtained by the AKARI.
They suggest that this emission comes from unshocked newly formed dust in
Cas A and estimate its mass to be 0.03–0.06 M .

No. 1, 2010

DUST FORMATION AND EVOLUTION IN SN IIb

contamination from interstellar dust in the foreground molecular
clouds, but the Herschel will be able to give more critical clues
on the mass of cold dust in Cas A.
The authors are grateful to the anonymous referee for criticalcomments that were useful for improving the manuscript.
T.N. and T.K. acknowledge Th. Henning and all members forthe kind hospitality during their stay at MPIA. This researchhas been supported in part by World Premier International
Research Center Initiative (WPI Initiative), MEXT, Japan,
and by the Grant-in-Aid for Scientific Research of the Japan
Society for the Promotion of Science (18104003, 19740094,
20340038, 20540226, 20540227, 20840007, 21840055) andMEXT (19047004, 20040004).
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