The Astrophysical Journal, 684:1343Y1350, 2008 September 10# 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A.

EARLY FORMATION OF DUST IN THE EJECTA OF TYPE Ib SN 2006jc
AND TEMPERATURE AND MASS OF THE DUST
Takaya Nozawa,1,2 Takashi Kozasa,1 Nozomu Tominaga,3, 4 Itsuki Sakon,4 Masaomi Tanaka,4 Tomoharu Suzuki,4Ken’ichi Nomoto,2, 4, 5 Keiichi Maeda,2, 6 Hideyuki Umeda,4 Marco Limongi,7, 8 and Takashi Onaka4
Received 2008 January 13; accepted 2008 May 8

ABSTRACTSN 2006jc is a peculiar supernova (SN ), in which the formation of dust has been confirmed at an early epoch of
50 days after the explosion. We investigate the possibility of such an early formation of dust grains in the expanding ejecta of SN 2006jc, applying the Type Ib SN model that is developed to reproduce the observed light curve. We
find that the rapid decrease of the gas temperature in SN 2006jc enables the condensation of C grains in the C-richlayer at 40Y60 days after the explosion, which is followed by the condensation of silicate and oxide grains until
200 days. The average radius of each grain species is confined to be less than 0.01 m due to the low gas density
at the condensation time. The calculated total dust mass reaches ’1.5 M , of which C dust shares 0.7 M . On theother hand, based on the calculated dust temperature, we show that the dust species and mass evaluated to reproduce
the spectral energy distribution observed by AKARI and MAGNUM at day 200 are different from those obtained by
the dust formation calculations; the dust species contributing to the observed flux are hot C and FeS grains with
masses of 5:6 ; 104 and 2:0 ; 103 M , respectively, although we cannot defy the presence of a large amount ofcold dust such as silicate and oxide grains up to 0.5 M . One of the physical processes responsible for the difference
between calculated and evaluated masses of C and FeS grains could be considered to be the destruction of small-sizedclusters by energetic photons and electrons prevailing within the ejecta at the earlier epoch.
Subject headinggs: dust, extinction — supernovae: general — supernovae: individual (SN 2006jc)

1. INTRODUCTION

the outcome of ongoing dust formation in the expanding ejectaof the SN.
Several pieces of evidence for dust formation in the SN ejecta
have been reported for Type II SNe (SNe II ): SN 1987A (Lucyet al. 1989; Whitelock et al. 1989; Meikle et al. 1993; Wooden
et al. 1993; Colgan et al. 1994), SN 1998S (Gerardy et al. 2000;
Pozzo et al. 2004), SN 1999em ( Elmhamdi et al. 2003), and SN
2003gd (Sugerman et al. 2006; Meikle et al. 2007). For theseSNe II except for SN 1998S, the onset of dust formation is estimated to be later than 400 days after explosion. The Type IIn
SN 1998S with the relatively low-mass hydrogen envelope (e.g.,
Liu et al. 2000; Fransson et al. 2005) exhibits signatures of dust
condensation at around 230 days (Gerardy et al. 2000). In addition, SN 1990I is the first SN Ib signifying the ongoing dust
formation, in which dust formation is observed at 230 days
( Elmhamdi et al. 2004). On the other hand, the signature of dust
formation in SN Ic has not been recorded so far. Although theoretical studies have shown the feasibility of dust formation in
SNe II (Kozasa et al. 1989, 1991; Todini & Ferrara 2001; Nozawa
et al. 2003), the possibility of dust formation in SNe Ib/c has neverbeen explored to date. Hence, how the formation process of dustin the ejecta depends on the type of SNe is an important subject
to be pursued.
Since the progenitor stars of SNe Ib/c have lost most of thehydrogen /helium envelopes before the explosion, their ejectedmasses are smaller, and the expansion velocities are significantly
higher than SNe II. This leads to a lower density of gas in the ejecta,
and the gas temperature drops down more quickly than those intypical SNe II. This allows us to expect earlier dust formation in
SNe Ib/c than SNe II. On the other hand, the lower gas density
may even result in unsuccessful dust formation. Furthermore,in the early epoch, energetic photons and electrons generated by
the Compton degradation of -rays from the decay of radioactive
elements such as 56 Ni and 56 Co prevail throughout the ejecta, andmay affect the formation process of dust grains. SN 2006jc is an

Supernova (SN) 2006jc is a peculiar Type Ib SN (SN Ib) inwhich the formation of dust has been observationally confirmed
at a very early time of 50 days after the peak brightness (Smithet al. 2008), which is more than a few hundred days earlier thanthose for the dust-forming SNe observed so far. Evidence fordust formation in SN 2006jc comes from an increase of the red
to near-infrared ( NIR) continuum ( Di Carlo et al. 2008) and thesimultaneous emergence of blueshifted narrow He i emission
lines (Smith et al. 2008). Smith et al. (2008) have proposed thatthe detected dust does not condense in the ejecta but forms in thedense postshock gas swept up by the forward and reverse shocks.
Although X-ray observations of Swift and Chandra ( Immler
et al. 2008) suggested the presence of a dense circumstellar (CS)shell ejected by the outburst similar to those seen in luminous
blue variables ( LBVs) 2 yr prior to the explosion ( Nakano et al.
2006; Pastorello et al. 2007), the postshock CS gas density estimated from the X-ray light curve ( Tominaga et al. 2008) is nothigh enough for dust grains to condense. Thus, it is reasonable toconsider that the appearance of dust toward SN 2006jc should be1
Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan; tnozawa@mail.sci.hokudai.ac.jp.
2 Institute for the Physics and Mathematics of the Universe, University ofTokyo, Kashiwa, Chiba 277-8568, Japan.
3
Optical and Infrared Astronomy Division, National Astronomical Observatory, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan.
4 Department of Astronomy, School of Science, University of Tokyo, Bunkyo-ku,
Tokyo 113-0033, Japan.
5 Research Center for the Early universe, School of Science, University ofTokyo, Bunkyo-ku, Tokyo 113-0033, Japan.
6 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Strasse 1, 85741
Garching, Germany.
7
Istituto Nazionale di Astrofisica-Osservatorio Astronomico di Roma, Via
Frascati 33, I-00040, Monteporzio Catone, Italy.
8
Center for Stellar and Planetary Astrophysics, School of Mathematical Sciences, P.O. Box 28M, Monash University, Victoria 3800, Australia.

1343

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NOZAWA ET AL.

ideal laboratory for examining the process of dust formation in
SNe Ib because a copious amount of observational data enable us
to compare with theoretical models. In this paper we investigate,
for the first time, the possibility of dust formation in the expanding ejecta of a SN Ib, based on the SN model that can well reproduce the light curve of SN 2006jc ( Tominaga et al. 2008).
The paper is organized as follows. In x 2 we summarize theobservational evidence for dust formation in SN 2006jc and its
interpretation, which are compared with the calculations of dust
formation in the later sections. In x 3 we investigate the dust formation in the ejecta and show that it is possible for dust grains tocondense in the ejecta of SN 2006jc at very early times of about
50 days after explosion. In x 4 we calculate the temperature ofpossible condensates obtained in x 3 and evaluate the amount of
dust grains contributing to the spectral energy distribution observedwith AKARI and MAGNUM at day 200. Formation processes ofdust grains in SN 2006jc are discussed in x 5, focusing on the interpretation of the difference between dust mass obtained by thedust formation calculation and that evaluated from the spectral
fitting. The summary is presented in x 6. In this paper we assume
that the explosion of SN 2006jc has occurred at 15 days before
its discovery.
2. OBSERVATIONS OF DUST FORMATIONIN SN 2006jc AND ITS INTERPRETATION
2.1. Evidence for Dust Formation
The first verification of the presence of dust in SN 2006jc
comes from the rebrightening at J, H, and K bands around day 50(Arkharov et al. 2006; Di Carlo et al. 2008). In addition, Di Carloet al. (2008) have noted a concomitant steep drop of the light
curve in the optical bands starting from 70 days, suggestive ofstrong extinction by the newly formed dust. It is also shownthat this rapid decline of the optical light curve continues up to120 days (Tominaga et al. 2008; G. C. Anupama et al. 2008, in
preparation; K. S. Kawabata et al. 2008, in preparation; Mattila
et al. 2008).
Definitive evidence for dust formation has been reported bySmith et al. (2008); the asymmetry of narrow He i emission lines
increased concurrently with an increase in the red-to-NIR continuum between 65 and 120 days. The increasing red /NIR continuum is interpreted as the thermal radiation from the newly formedcarbonaceous dust with a temperature of 1600 K, considering
its high temperature. At day 140, the excess of this continuum
disappeared, which indicates that the dust grains were completely
destroyed or the dust temperature became so low that its thermal
emission was shifted to longer wavelengths. The increasing asymmetry of narrow He i emission lines tracing the shocked CS gas
was caused by the dust obscuration of the redshifted side, whereas
broad emission lines tracing the SN ejecta such as Ca ii and O i
faded entirely. The blueshifts of He i emission lines persisted up
to day 180 ( Mattila et al. 2008), asserting that the newly formedcarbon grains were not destroyed but cooled down, which is supported by the NIR observations with AKARI (Sakon et al. 2007)
and MAGNUM (Minezaki et al. 2007) showing that the temperature of the carbon grains dropped down to 800 K at day 215.
The time evolution of the optical light curve and the He iemission-line profile during 50Y140 days strongly suggests theongoing formation of dust in SN 2006jc and reliably rules out as
origins of the red / NIR continuum the scenarios involving preexisting dust in the CS medium (CSM ), such as the IR light echo
(Smith et al. 2008; Mattila et al. 2008) and the heating of the CS
dust through the collision with the forward shock. However, assuggested by Sakon et al. (2007) and Mattila et al. (2008), theVol. 684

mid-IR spectrum observed at a later epoch (k200 days) can be attributed to the low-temperature CS dust, which is discussed in x 4.2.
2.2. The Site of Dust Formation
Smith et al. (2008) have supposed that dust grains are formedin the dense shell swept up by shocks but not in the freely expanding ejecta, based on (1) the geometrical considerations for
explaining the blueshifts of narrow He i lines and the overall fading of broad Ca ii and O i lines and (2) the time evolution of dust
temperature that remains nearly constant for about a month anddecreases after then; they considered that dust can continuously
form at a temperature of 1600 K in the rapidly cooling regions
behind the forward shock rather than the reverse shock, in thecourse of the passage of the forward shock through the dense CS
shell created by the LBV-like eruption 2 yr prior to the SN explosion. This scenario is supported by a flux ratio of He i k7065/
k5876 close to unity and the He ii k4686 emission feature that appeared during the putative time of dust formation. The detectionof these He lines is expected to indicate the presence of the postshock gas of 3 ; 1014 g cm3 that is comparable to the criticaldensity for carbon grain condensation (e.g., Clayton 1979), although Mattila et al. (2008) cannot find the sign of the He ii linein their spectrum during 88Y132 days.
Here we investigate whether dust formation in the postshockgas around SN 2006jc is possible or not, referring to the X-ray
observations and the hydrodynamical calculations for the ejectaCSM interaction. Observations with the Swift and Chandra satellites (Immler et al. 2008) have shown that the X-ray luminosity is in
the range of 1039 Y1040 ergs s1 from day 36 through day 180,witha gentle rise of the X-ray emission until 110 days. Immler et al.
(2008) have estimated the density of the postshock gas shell to be4 ; 1017 g cm3 , assuming that all of the measured X-rays atpeak are emitted from the dense shocked shell. However, the time
evolution of the X-ray luminosity indicates that the medium aroundSN 2006jc has a quite smooth density profile. Tominaga et al. (2008)
have performed the hydrodynamic calculations to reproduce the observed X-ray light curve and found that the density profile of the preshock CSM should be 0 ¼ 2:75 ; 1019 g cm3 for r < 2:2 ;1016 cm and  ¼ 0 (r/2:2 ; 1016 cm)6 g cm3 for r  2:2 ;1016 cm. Their result has shown that the gas density swept up by theforward and reverse shocks is P1017 g cm3 at 50 days (see Fig. 11
in Tominaga et al. 2008), which is too low for dust grains to nucleate.
Thus, on the basis of the hydrodynamical simulations, we conclude
that dust grains are not likely to be formed in the postshock CS gas.
On the other hand, it should be addressed that there are somestudies that advocate the formation of dust in the dense CS shell
produced by the LBV-like outburst before 2 yr ( Di Carlo et al.
2008; Mattila et al. 2008). Mattila et al. (2008) have shown thatthe observed X-ray luminosity is produced by the CS shell witha preshock density of (2:5Y4) ; 1015 g cm3 in aid of their calculations of shock evolution, and that the NIR light curve isreproduced by the IR light echo of the dust newly formed in thedense, cooling CS shell. However, the formation process of dust
heavily depends on the cooling history of the gas, and whether
dust formation can be realized in the rapidly cooling postshockgas should be fully explored in future work. In the following sections we pursue the possibility of dust formation in the expanding ejecta of SN 2006jc.
3. DUST FORMATION IN THE EJECTA OF SN 2006jc
3.1. Model of SN 2006jc and Calculation of Dust Formation
The time at which dust condenses in the SN ejecta and the size
and number density of the newly formed dust are sensitive to theNo. 2, 2008

DUST FORMATION IN THE EJECTA OF SN 2006jc

1345

Fig. 1.— Structures of (a) temperature and (b) density of the gas within the
He core of the SN 2006jc model (red lines) at day 50 (solid lines) and day 200(dashed lines) after the explosion. For comparison, also shown are those for the
SN II model (blue lines) with Mpr ¼ 25 M and E51 ¼ 1 ( Umeda & Nomoto
2002), which has a He core of 5.5 M comparable to that of SN 2006jc. The
mass coordinate is normalized by the mass of the He core.

time evolution of the gas temperature and density ( Kozasa et al.
1989; Todini & Ferrara 2001; Nozawa et al. 2003), given the elemental composition. In the calculation of dust formation, we apply the results of hydrodynamics and nucleosynthesis calculations
for the SN Ib model well reproducing the observed bolometriclight curve of SN 2006jc (Tominaga et al. 2008); the ejecta mass
is 4.9 M with the explosion energy of Eex /1051 ergs ¼ E51 ¼ 10
and the ejected 56 Ni mass of 0.22 M , where 56 Ni is uniformly
distributed in mass within the He core. The preexplosion mass ofthe progenitor is 6.9 M . The elemental composition in the ejecta
has an original onion-like composition, except for 56 Ni. The time
evolution of the gas temperature in the freely expanding ejecta
was calculated by solving the radiative transfer and the energy
equations, taking account of the energy deposition from 56 Ni
and 56Co.
Figure 1 shows the structures of the gas temperature (Fig. 1a)and density (Fig. 1b) within the He core of the SN 2006jc modelat 50 days (red solid lines) and 200 days (red dashed lines) after the explosion. Shown for comparison are those for the SN II
model with the progenitor mass Mpr ¼ 25 M and E51 ¼ 1 (bluesolid and dashed lines at 50 and 200 days, respectively; Umeda& Nomoto 2002), which has a He core of 5.5 M , comparable tothat of SN 2006jc. The gas temperature in SN 2006jc decreases
much earlier, and the density at a given time is more than 3 ordersof magnitude lower than that in the SN II. This is because theexpansion velocity in the He core of SN 2006jc is considerably
high, reflecting the absence of the hydrogen envelope and a 10 times
higher explosion energy than SNe II with E51 ¼ 1. The gas temperature in SN 2006jc drops down to 2000 K at 50 days and1000 K at 200 days. Thus, we can expect early formation ofdust grains between 50 and 200 days, since a typical dust condensation temperature ranges from 1000 to 2000 K.

Fig. 2.— (a) Condensation times and (b) average radii of dust grains formedin the ejecta of SN 2006jc as a function of mass coordinate.

The dust formation calculation is performed by applying a theoryof nonsteady state nucleation and grain growth described in
Nozawa et al. (2003). In the calculations, we assume the sticking
probability of s ¼ 1, and that the temperature of a small cluster
consisting of up to a few tens of atoms is the same as the gas
temperature.9
3.2. Results of Dust Formation Calculations
Figures 2a and 2b show the results of calculation. Figure 2a
indicates the condensation time of the newly formed dust, defined as the time when the nucleation rate reaches the maximum(see Nozawa et al. 2003). It can be seen that in the outermost
C-rich layer of the ejecta (see Fig. 8c in Tominaga et al. 2008),
C grains condense at very early times of 40Y60 days. This is dueto the rapid decrease of the gas temperature in the ejecta, as wellas the relatively high condensation temperature of C grains. It
should be emphasized that the condensation times of C grains
are in good agreement with the onset time of dust formation observed in SN 2006jc. Furthermore, the condensation of C grains
can explain both the blueshift of He i lines and the entire fading
9

There is a typographical error in eq. (3) for the nucleation rate in Nozawa
et al. (2003); replace c1j with c1j2 .

1346

NOZAWA ET AL.

of Ca ii and O i lines because the formation site is in the region
between the He-rich CSM and the O-rich layer in the ejecta, although they cannot absorb the zero-velocity component of narrow He i emission lines efficiently.
After C grains are formed, Al2O3, Mg2SiO4, MgSiO3, SiO2,
Fe3O4, MgO, and FeO grains form in the O-rich layer at 90Y150
days in this order, and FeS and Si grains condense in the Si-S-richlayer at 200 days. Since 56 Ni is uniformly mixed throughout
the ejecta, Fe3O4 and FeO grains are produced instead of Fe grains;
Fe grains are expected to form in the innermost Fe-Ni core unless56
Ni intrudes into the outer layers ( Nozawa et al. 2003). However, the mixing of elements is likely to be at the knotty level
rather than at the microscopic atomic level, as suggested by theobservations of the Cas A supernova remnant ( Douvion et al.
2001; Ennis et al. 2006; Rho et al. 2008). If 56 Ni is not mixed
at the atomic level, the formation of Fe grains is expected aswell. Nevertheless, Fe grains, which have a high-energy barrier
for nucleation and a resulting low condensation temperature(P800 K), cannot form in the ejecta considered here because
the gas density is too low at the time when the gas cools down to800 K (250 days). Also, Fe atoms originally existing in the
O-rich layer are not locked into grains significantly (condensation efficiency of P107 ) owing to their small abundances. Considering these uncertainties, we rule out Fe3O4 and FeO grains as
the newly formed dust species.
As is expected from the low gas density, as well as the rapid
cooling of gas in the ejecta, the average radius of each dust species given in Figure 2b is considerably small, being less than
0.01 m for all grain species. On the other hand, the condensation efficiency of dust is almost unity, and the amount of dust
formed is relatively large. The total mass of newly formed dust is
1.45 M , and the mass of C grains (0.7 M ) accounts for about ahalf of the total mass. The mass of each dust species M1; j obtained by the dust formation calculation is summarized in Table 1.
Other major grain species in mass are SiO2 (0.23 M ), Si (0.2 M ),and MgSiO3 (0.16 M ).
It should be noted here that the dust formation process as
demonstrated above is not influenced by the interaction between
the ejecta and the CSM. Our results show that dust grains cannot
condense in the region of 0.005 M from the outer edge of theejecta, where the gas density is too low. Although the ejecta-CSM
interaction causes the reverse shock penetrating into the ejecta, thehydrodynamic simulation shows that the reverse shock sweeps up
only 0.011 M of the outermost region in the ejecta by 50 daysand 0.053 M by 200 days (see Fig. 11 in Tominaga et al. 2008).
Thus, the reverse shock sweeps up 0.006 M from the outer edgeof the dust formation region at day 50, and 0.048 M at day 200.
The mass of C grains within the region swept up by 200 days is
only 1:3 ; 103 M, which is much smaller than 0.7 M at thetime of formation; thus, almost all of the C grains can form in
the freely expanding ejecta. Since the radii of C grains formedin the outermost region are smaller than 10 8 (see Fig. 2b), thetimescale of dust destruction by sputtering is estimated to be<6 hr ( Nozawa et al. 2006) in the shocked gas with density of1018 g cm3 (Tominaga et al. 2008). Hence, thermal emission
from shock-heated grains can be negligible.
4. EVALUATION OF DUST TEMPERATURE
AND MASS IN THE EJECTAThe NIR to mid-IR (MIR) observations with AKARI (Sakon
et al. 2007) and MAGNUM (Minezaki et al. 2007) have detected
thermal emission from dust in SN 2006jc at 200 days. Sakon
et al. (2007) have concluded that the obtained NIR spectrum
is fitted by amorphous carbon grains of 800 K with a mass ofVol. 684

TABLE 1Mass of Each Dust Species and References for Optical Constants

Dust Species
C...........................................
Al2O3 ....................................
MgSiO3 ................................
Mg2SiO4 ...............................
SiO2 ......................................
MgO .....................................
FeS .......................................
Si ..........................................
Total .................................

M1; j
(M )

M2; j
(M )

0.701
0.008
0.157
0.082
0.229
0.010
0.067
0.196
1.450

5:6 ; 10
0.008
0.157
0.082
0.229
0.0100.002...
0.489References
4

1
2
3
4
5
6
4
7

Notes.— The mass of grain species j obtained by the dust formation calculation is denoted by M1; j. The mass or upper mass limit of the dust necessary forreproducing the SED observed at 200 days is denoted by M2; j , where Si grainsare excluded because their condensation time could be much later than 200 days
(see text). References for the optical constants used in the calculation are shownin the last column. The optical constants of MgSiO3 at k  0:3 m are replacedby that of Mg2SiO4 (see Hirashita et al. 2008).
References.— (1) Edo 1983; (2) Toon et al. 1976; (3) Dorschner et al. 1995;(4) Semenov et al. 2003; (5) Philipp 1985; (6) Roessler & Huffman 1991;(7) Piller 1985.

6:9 ; 105 M , assuming optically thin thermal radiation. They
have also shown that the MIR excess emission over the amorphous carbon grains of 800 K can be explained either by silicate
and silica grains of 700Y800 K with 104 M or by amorphous
carbon grains of 320 K with 2:7 ; 103 M . In this section, referring to the grains species calculated in x 3 as possible condensates in the ejecta and deriving the dust temperature, we evaluate
the dust mass by reproducing the spectral energy distribution
observed at day 200 with AKARI and MAGNUM.
4.1. Temperature of Dust
The equilibrium temperature of dust in the ejecta is determinedby the balance between heating and cooling through radiation andcollision with gas. In order to calculate the heating due to theabsorption of ambient radiation, we evaluate the flux Fk (r; t) ata time t and a position r within the ejecta, assuming that the total
flux F(r; t) calculated by Tominaga et al. (2008) radiates as a
blackbody with temperature TBB (r; t).
Given the gas temperature Tgas (r; t) and number density ngas (r; t)
in the ejecta, the equilibrium temperature of dust Td (r; t) at agiven time and at a given position is determined by implicitly
solving the equationZ
F(r; t) 1 2
42
a Qk (a)Bk (TBB ) dk
4a B Td (r; t) hQk (a; Td )i ¼
4
B TBB
0
"





 #
kTgas 1=2
1
kTd 1=22
þ 4a ngas cv þ k Tgas
 Td
;
2
2mH
2mH
ð1Þ
where a is the radius of dust,  B is the Stefan-Boltzmann constant, hQk (a; T )i is the Planck-mean of absorption coefficient,
Bk (T ) is the Plank function, k is the Boltzmann constant, cv isthe heat capacity of a gas molecule (cv ¼ 3k /2 for a monatomic
molecule),  is the mean molecular weight, and mH is the atomic
mass unit. Here we consider that the gas colliding with dust iscompletely accommodated and is ejected from the surface withthe same temperature as the dust (see Landau & Pitaevski 1981).
In the calculations we assume TBB ¼ 5000 K throughout the ejecta,

No. 2, 2008

DUST FORMATION IN THE EJECTA OF SN 2006jc

Fig. 3.— Temperature of each dust species formed in the ejecta of SN 2006jc
at 200 days after the explosion. The dashed line depicts the temperature of
C grains at 60 days.

regardless of time, and a ¼ 0:01 m. Since in the ejecta considered here the total flux at day 200 is F  106 erg s1 cm2 almost
uniformly over the He core, the energy transfered through theradiative process is much larger than that by collision with gas,
and thus we can neglect the collisional heating and cooling. Notethat in this case the calculated dust temperature is independentof dust size because Qk (a)/a does not depend on the radius for
a P 0:05 m. The references for the optical constants of each
dust species used in the calculations are given in Table 1.
We also note that the effect of stochastic heating can be negligible as long as we assume a blackbody radiation with TBB 
5000 K under the given total flux. We have confirmed that for
C grains of 10 (20) 8, stochastic heating only makes the dust
temperature distribute symmetrically around the equilibrium temperature with the temperature width of 100 (30) K. Accordingly, the resulting emissivity of 10 8Ysized C grains does notchange significantly at wavelengths longer than 2 m, comparedwith that derived for equilibrium temperature; its difference is
10% at 2 m and less than 2.5% at 3 m. Therefore, stochastic
heating does not affect the results of the IR spectrum energy distribution calculated in x 4.2.
Figure 3 shows the temperatures of all dust species at 200 days(solid lines), along with the temperature of C grains at 60 days
(dashed lines).10 The temperature of the C grains is 1200Y1700 K
at 60 days and is higher for those formed in the inner region. Notethat this high temperature is in good agreement with the temperature of dust responsible for the red /NIR continuum appearing
in SN 2006jc two months after the explosion (Smith et al. 2008).
At 200 days, the C grains cool down to 500Y600 K, which is also
considered to correspond to the temperature of 800 K for amorphous carbon grains suggested by the observations with AKARI
and MAGNUM (Sakon et al. 2007), although the calculated temperature is relatively low. Thus, the calculated temperature of
C grains can reasonably explain the time evolution of the dust
temperature indicated by the observations toward SN 2006jc fromday 50 through day 200.
10Note that in the calculation we exclude Si grains; the temperature of Si
grains at the condensation time of 200 days is about 300 K higher than the gas
temperature. When we consider the non-LTE effect for dust formation, its condensation time is delayed to 240 days, as discussed in x 5.1, which is later than theobservation date of AKARI and MAGNUM.

1347

On the other hand, silicate grains have a temperature of only
100Y200 K at day 200, reflecting much lower absorption efficiency
at optical wavelengths than at IR wavelengths. This low temperature cannot explain the MIR excess emission over the amorphous
carbon grains with 800 K observed by AKARI (Sakon et al.
2007), and we can conclude that neither silicate nor silica grains
newly formed in the ejecta can be the carriers of the MIR excess
emission. In addition, our result shows that the temperature of
C grains spans the range from 500 to 600 K. Therefore, if the MIR
excess emission were attributed to the amorphous carbon grains
with 320 K, they might not be the grains formed in the ejecta but
could be the preexisting CS grains heated by the SN outburst, assuggested by Sakon et al. (2007).
In the calculations we assumed the ambient radiation field asa blackbody with TBB ¼ 5000 K. The calculated dust temperatures at day 200 is not sensitive to TBB as long as TBB is in
the range 5000Y6000 K; for TBB ¼ 6000 K, the temperature of
MgSiO3 and Mg2SiO4 grains increases by 50 K comparedwith that for TBB ¼ 5000 K, while the increase of temperature of
the other grains species is at most 30 K. Here, it should be kept inmind that, being different from normal SNe Ib, SN 2006jc shows
the strange optical spectrum in the early times until day 120, witha bright blue continuum whose origin is not clear ( Foley et al.
2007; Pastorello et al. 2007). This indicates that the spectrumof radiation at the early epoch within the ejecta of SN 2006jc is
not also expected to be approximated by a blackbody radiation.
Nevertheless, as shown above, we can reasonably explain the time
evolution of temperature of C grains indicated by the observations. Thus, we adopt the results for TBB ¼ 5000 in the following
discussions.
4.2. IR Spectral Energy Distribution and Dust Mass
In this subsection we calculate thermal emission from dust
grains based on the dust temperatures presented in Figure 3, andestimate the dust mass necessary for reproducing the spectralenergy distribution (SED) at day 200 observed with AKARI andMAGNUM.
Taking into account the self-absorption of dust, the observed
flux density Fkobs of thermal emission from dust grains formed in
the ejecta is evaluated by
1
Fkobs ¼
4D 2
Z RX
;
4r 2 md; j (r)k; j Bk ½Td (r) expf½ k (R)  k (r)g dr;
0

j

ð2Þ

where D ¼ 25:8 pc is the distance from observers (Pastorello
et al. 2007), R is the outermost radius of the dust-forming region
in the ejecta, md; j (r) is the mass of dust species j per volume at
the position r, and k; j ¼ 3Qk; j (a)/4aj is the mass absorption
coefficient, and the dust bulk density j is taken from Nozawa
et al. (2006). Note that k; j does not depend on the size as long as
a P 0:05 m. The optical depth k is given by
Z rX
md; j (r)k; j dr:
ð3Þk (r) ¼
0j

The magenta solid line in Figure 4 is the SED calculated byadopting the mass of each dust species M1; j given in x 3.2, andthe SED is dominated by thermal emission from C grains existing in the outermost ejecta as the result of the large optical depth
due to their large mass. It is clear that the derived IR spectrum

1348

NOZAWA ET AL.

Fig. 4.— SED by thermal radiation from the newly formed dust. The magenta
line is the spectrum obtained by adopting the mass of dust M1; j from the dust
formation calculation. The red line is the best-fitted spectrum obtained by taking
the dust masses and upper mass limits M2; j given as in Table 1, for which thecontribution from each dust species is depicted by the dashed lines. The cyan
symbols are for the photometric data at 200 days by AKARI (Sakon et al. 2007)
and MAGNUM ( Minezaki et al. 2007).

largely exceeds the observational data at k3 m and cannot reproduce the observed SED.
The NIR-to-MIR spectrum can be fitted using the derived
grain temperatures because dust temperature does not depend on
the mass of dust, as can be seen from equation (1), so the dust
mass can be used as a free parameter in order to reproduce the observations. We calculate thermal emission from dust grains bytaking the mass of each grain species at the position r as fj md; j (r)and fit the SED to the observational data, where the value of afree parameter fj (1) is assumed to be constant for a given dust
species. The best-fitted result is displayed by the red solid line in
Figure 4 and can well explain the observed NIR-to-MIR spectrum.
The contribution of each grain species is depicted by the dashedlines, for which we adopt the masses of C and FeS grains and theupper mass limits of the other dust species given as M2; j in Table 1.
Here the mass of C grains is 5:6 ; 104 M , reduced by a factorof 1250 in comparison with the mass obtained by the dust formation calculation. FeS grains can also contribute to the NIR spectrum because of its high temperature (900 K), and its mass is
reduced to 2 ; 103 M ( fj ¼ 0:03). On the other hand, silicatesand oxide grains do not contribute to the NIR spectrum because
their temperatures are too low (100Y200 K). Furthermore, thelarge optical depth of MgSiO3 and Mg2SiO4 at MIR wavelengths
prevents us from constraining the mass of these grain species.
Thus, we cannot defy the existence of a large amount of cold dust
reaching up to 0.5 M in the ejecta from the spectral fitting, andthe dust mass derived under the optically thin assumption should
be considered to be the lower limit (see also Meikle et al. 2007).
We also investigate the effect of the presence of amorphous
carbon grains in the CSM on the observed spectrum, which havebeen suggested to contribute to the MIR spectrum at k200 days
(Sakon et al. 2007; Mattila et al. 2008). In the calculations wetake the temperature of CS carbon grains to be 320 K (Sakon
et al. 2007). If their mass is smaller than 2:7 ; 104 M , the bestfitted spectrum in Figure 4 is not influenced by the preexisting
C grains. A further increase of CS dust mass can also reasonably
reproduce the observed IR spectrum as seen from Figure 5, where

Vol. 684

Fig. 5.— SED derived in the presence of CS carbon grains (thick red line),
where the mass of newly formed and preexisting C dust is 2:24 ; 104 M (black
dashed line) and 1:4 ; 103 M (black dotted line), respectively. The mass ofother newly formed dust is the same as that in Fig. 4. The cyan symbols show thephotometric data at 200 days by AKARI (Sakon et al. 2007) and MAGNUM( Minezaki et al. 2007).

the mass of newly formed and preexisting C dust is 2:24 ; 104
and 1:4 ; 103 M , respectively (the mass of other newly formed
dust is the same as that in Fig. 4). Therefore, the spectral fitting
can allow the presence of low-temperature C grains in the CSM.
The emission from CS grains can be the IR light echo but not
the thermal radiation from dust heated by the collision with theforward shock. This is readily demonstrated by considering theradius of dust cavity created by the evaporation of preexisting CS
grains due to strong radiation from a SN. Taking the evaporation
temperature of C grains to be 1800 K and using the SN peak luminosity of 10 42:7 ergs s1 with the blackbody temperature of6000 K (Tominaga et al. 2008), we estimate the radius of thedust cavity to be ’3 ; 1016 cm. Because the estimated radius of
the dust cavity is comparable with the radius of the forward shockat 200 days, the forward shock could not have swept a significant amount of CS dust. If we consider the radiation from theshock breakout as the heating source, which is expected to bebrighter and have a higher blackbody temperature, the dust cavity may be extended so far that any CS dust cannot be swept up
by the forward shock at 200 days. Note that in this spectral fitting, the mass of newly formed C grains depends on the temperature and mass of CS dust, and in the following discussion werefer to the mass of C grains derived by the spectral fitting without CS dust in Figure 4.
5. DISCUSSION
5.1. Mass of Dust Formed in the Ejecta
As shown in x 4.2, the mass of C grains (0.7 M ) obtained by
the dust formation calculation is 3 orders of magnitude larger
than that (5:6 ; 104 M ) estimated from the spectral fitting to theobservations. One of the reasons for this difference is considered
to be the clumpy structure in the ejecta. In order to evaluate thedust mass necessary for reproducing the observed spectrum of
SN 2003gd, Sugerman et al. (2006) performed the radiative transfer calculation taking account of the clumpy structure and foundan increase in the estimated mass of dust in the ejecta by about
1 order of magnitude, compared with the mass derived for theNo. 2, 2008

DUST FORMATION IN THE EJECTA OF SN 2006jc

uniform distribution of dust. Nevertheless, the consideration ofdust clumping does not seem to be sufficient to overcome the large
gap. Thus, the difference in dust mass should stem from theprocess of dust formation in the ejecta.
One of the processes influencing dust formation is the nonlocal thermal equilibrium (non-LTE) effect. As seen from Figures 1
and 3, the dust temperature is not the same as the gas temperature; at 200 days the temperature of C grains (500Y600 K) andsilicate and oxide grains (100Y200 K) is lower than the gas temperature with 700Y1000 K. In the ejecta with a strong radiation
field, the temperature of small clusters is expected to be higher
than the gas temperature depending on the optical property. In thiscase, the non-LTE effect retards or hinders the formation of dust
grains. Assuming that the optical properties of small carbon clusters are the same as those of small C grains, and applying a formula of nucleation rate taking into account the non-LTE effect by
Kozasa et al. (1996), we realized that the non-LTE effect does not
significantly affect the formation of C grains; the non-LTE effectonly retards the formation of C grains by less than 10 days anddoes not affect the mass of C grains because the temperature ofsmall carbon clusters is only 50 K higher than that of gas. Meanwhile, the non-LTE effect delays the formation of Si grains from200 to 240 days. This is the reason why we exclude Si grainsin reproducing the observed SED at day 200 in x 4.2.
Another process affecting the formation of dust in the ejecta is
the energy deposition on small-sized clusters through the latent
heat deposition at the condensation, as well as the collisions withhigh-energy photons and electrons. In the ejecta rich in condensible elements, the destruction of small-sized clusters by the deposition of latent heat could be significant unless the depositedenergy is released by collisional and /or radiative processes efficiently. Also, at an early epoch after the explosion, energetic
photons and electrons generated from the decays of radioactive
elements 56 Ni and 56Co prevail abundantly throughout the ejecta.
Since the nucleation rate is determined by the balance between thegrowth and destruction rate of small-sized clusters, the energy
deposition makes small-sized clusters unstable against the growth
and as a result reduces the nucleation rate.
Although the nucleation rate can be reduced by increasing thecritical cluster size, as demonstrated by Bianchi & Schneider(2007), there is no reason to cut the number of seed nuclei byincreasing the critical size arbitrarily, apart from the uncertainty
inherent in the standard nucleation theory arising from the evaluation of chemical potential of small-sized clusters. Thus, we examine the effect of energy deposition for dust formation at earlytimes observed in SN 2006jc by reducing the sticking probability
s for simplicity and comparing with the mass of dust evaluated in x 4.2. If we take s  3 ; 103 , we can obtain a mass of
C grains of 5 ; 104 M , while s is 0.3 to produce FeS grainsof 2 ; 103 M . In this case, the condensation times of C and
FeS grains is 40Y67 and 190Y200 days, respectively. While thedestruction rate of small-sized clusters depends on the properties of materials forming dust grains, the difference in the sticking probability may be caused by the collisions with energetic
photons and electrons, reflecting the difference in the condensation time of C and FeS grains; energetic photons and electrons
are more abundant at day 50 than at day 200. The details of thesemicroscopic processes are beyond the scope of this paper andwill be investigated in the future study on the dust formation inSNe.
5.2. Early Condensation of Dust in SNe Ib
In x 3.2 we show that the early formation of dust around50 days is possible in SN 2006jc, whose progenitor has lost most1349

of its He envelope ( Foley et al. 2007; Tominaga et al. 2008).
However, other dust-forming SNe Ib had not show such an early
formation of dust; SN 1990I displayed the diagnostics of dust
formation around 230 days ( Elmhamdi et al. 2004), although thecondensation time is relatively earlier than that of SNe II. The
peculiar Type Ib SN 2005bf shows a rapid decline of the light
curve from 50 days after the explosion, but does not exhibit NIR
brightening, in contrast to the case of SN 2006jc ( Tominaga et al.
2005). Maeda et al. (2007) have shown that the quickly faded
light curve of SN 2005bf can be explained by the newly born
magnetized neutron star at the center. On the other hand, they
have demonstrated that the blueshifted profiles of O i and Ca ii
observed at 270 days can be explained by the obscuration ofdust in the ejecta. If the blueshift of emission lines in SN 2005bf
is attributed to the newly formed dust grains, the time of dust
formation is considered to be later than 100 days and not to beso early as in SN 2006jc, although the epoch of dust formation in
SN 2005bf was not specified by the observations.
The results of calculations revealed that the early formationof dust in SN 2006jc can be realized by the rapid decline ofgas temperature, reflecting the large ratio of the explosion energy (E51 ¼ 10) to the ejected mass (Mej ¼ 4:9 M ); the ratio
E51 /(Mej /M ) ’ 2 is much greater than 0.125Y0.25 for SN 2005bf( Tominaga et al. 2005) and ’0.3 for SN 1990I (Elmhamdi et al.
2004). Unfortunately, no literature has reported the explosion energy of the Type IIn SN 1998S, which had a time of dust condensation of 230 days (Gerardy et al. 2000). Using the ejecta massestimated from the He core of 4Y6 M (Fassia et al. 2001; Pooley
et al. 2002) and hydrogen envelope of 0.1Y2 M (Fassia et al.
2000; Anupama et al. 2001) and taking E51 ¼ 1 as the typical
explosion energy, we can, however, deduce the ratio to be
E51 /(Mej /M ) ¼ 0:125Y0:25 for SN 1998S, which is similar
to or slightly less than those for SN 2005bf and SN 1990I. On
the other hand, the ratio for the dust-forming SNe II is of order
0.1:0.1Y0.2 for SN 1987A (Shigeyama et al. 1988; Woosley
1988), 0.05Y0.1 for SN 1999em ( Elmhamdi et al. 2003), and’0.12 for SN 2003gd ( Hendry et al. 2005). Dust formation has
not been yet observed on SNe Ic. However, the early dust formation in SNe Ic is also expected, because SNe Ic may well have
Mej similar to SNe Ib.
In conclusion, we can speculate that as the envelope of a star at
explosion is smaller and the explosion energy is higher, the condensation time of dust tends to be earlier. In order to prove thesehypothesises and to investigate the formation process of dust inSNe, we need further observational and theoretical studies on
dust formation in various types of SNe. In particular, the UV-toMIR observations at early times for SNe Ib/c are promising toclarify the formation process of dust because its condensation
time is much earlier than that for SNe II, as is shown above.
6. SUMMARY
We investigate the formation of dust grains in the ejecta of
SN 2006jc by applying the SN model that can nicely reproduce
its light curve. We find that the formation of dust in SN 2006jc
is possible at early times, thanks to the rapid decrease of the gas
temperature in the ejecta. The condensation of C grains is realized in the C-rich layer at very early times of 50 days after the
explosion. This is in good agreement with the time of the onsetof dust formation indicated by the observations. In addition to
C grains, the other grain species such as silicate and oxide grains
are formed until 200 days, with the average radii less than
0.01 m. We suppose that the formation of dust earlier thanSNe II is common to the hydrogen-deficient SNe and that SN
2006jc is its extreme case.

1350

NOZAWA ET AL.

Furthermore, we calculate the dust temperature by considering the radiation field in the ejecta at the early epoch as a blackbody with TBB ¼ 5000 K. C grains have a temperature of 1600 K
at 60 days and cool down to 600 K at 200 days. This temperatureof C grains can reasonably explain the time evolution of the dust
temperature suggested by the observations toward SN 2006jc
from day 50 through day 200. The temperatures of silicates andoxide grains are 100Y200 K at day 200 and are too low to contribute to the MIR spectrum observed with AKARI.
The comparison of the calculated SED with the observationsof AKARI and MAGNUM shows that dust grains contributing to
NIR/MIR flux are C and FeS grains whose masses are 5:6 ; 104
and 2 ; 103 M , respectively. The masses of hot C and FeS
grains obtained by the dust formation calculation are considerably larger than those estimated from the observations. Thisdifference in dust mass may be explained by the destruction ofsmall-sized clusters by the collisions with energetic photons
and electrons. On the other hand, we cannot constrain the mass of
low-temperature silicate and oxide grains in the ejecta from thespectral fitting. The spectrum fitting also shows that the observed

MIR spectrum can be attributed to preexisting CS carbon grains
with the mass up to 103 M . In order to reveal the process ofdust formation in the SN ejecta, it is essential to carry out UV-to-IR
observations of various types of SNe. In particular, SNe Ib/c are
the objects suitable for detecting signatures of dust formation by
the optical to NIR observations because the condensation time ofdust is much earlier than SNe II.
The authors are grateful to the anonymous referee for criticalcomments that were useful for improving the manuscript. The
authors thank H. Hirashita, T. T. Takeuchi, and A. K. Inoue for
their useful comments. This research has been supported inpart 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, 18540231, 19740094, 20340038, 20540226,
and 20540227) and MEXT (19047004 and 20040004). These
grants support T. N., T. K., N. T., M. T., T. S., K. N., K. M., H. U.,
and M. L.’s visit.

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