A

The Astrophysical Journal, 687:1208Y1219, 2008 November 10# 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A.

THE PECULIAR TYPE Ib SUPERNOVA 2006jc: A WCO WOLF-RAYET STAR EXPLOSION
N. Tominaga,1,2 M. Limongi,2,3,4 T. Suzuki,2 M. Tanaka,2 K. Nomoto,2,5 K. Maeda,5,6 A. Chieffi,7A. Tornambe,3 T. Minezaki,8 Y. Yoshii,8 I. Sakon,2 T. Wada,9 Y. Ohyama,9 T. Tanabé,9H. Kaneda,9 T. Onaka,2 T. Nozawa,10 T. Kozasa,10 K. S. Kawabata,11G. C. Anupama,12 D. K. Sahu,12 U. K. Gurugubelli,12T. P. Prabhu,12 and J. Deng13
Received 2007 December 4; accepted 2008 July 11

ABSTRACT
We present a theoretical model for Type Ib supernova (SN ) 2006jc. We calculate the evolution of the progenitor
star, hydrodynamics and nucleosynthesis of the SN explosion, and the SN bolometric light curve (LC). The synthetic
bolometric LC is compared with the observed bolometric LC constructed by integrating the UV, optical, near-infrared(NIR), and mid-infrared (MIR) fluxes. The progenitor is assumed to be as massive as 40 M on the zero-age main
sequence. The star undergoes extensive mass loss to reduce its mass down to as small as 6:9 M , thus becoming a
WCO Wolf-Rayet star. The WCO star model has a thick carbon-rich layer, in which amorphous carbon grains can beformed. This could explain the NIR brightening and the dust feature seen in the MIR spectrum. We suggest that theprogenitor of SN 2006jc is a WCO Wolf-Rayet star having undergone strong mass loss, and such massive stars areimportant sites of dust formation. We derive the parameters of the explosion model in order to reproduce thebolometric LC of SN 2006jc by the radioactive decays: the ejecta mass 4:9 M , hypernova-like explosion energy
1052 ergs, and ejected 56Ni mass 0:22 M . We also calculate the circumstellar interaction and find that a CSM with aflat density structure is required to reproduce the X-ray LC of SN 2006jc. This suggests a drastic change of the massloss rate and/or the wind velocity that is consistent with the past luminous blue variable ( LBV )Ylike event.
Subject headinggs: dust, extinction — infrared: ISM — nuclear reactions, nucleosynthesis, abundances —supernovae: general — supernovae: individual (SN 2006jc) — stars: Wolf-Rayet
Online material: color figures

14 and its duration was as short as 10 days. Since the event
was faint and short-lived, they speculated that the transient wasa luminous blue variable (LBV )Ylike event. The spatial coincidence between the LBV-like event and SN 2006jc was confirmed
by Pastorello et al. (2007). Because of such an intriguing association with the LBV-like event, many groups performed follow-up
observations of SN 2006jc in various wave bands: X-ray, ultraviolet (UV ), optical, infrared ( IR), and radio.
Spectroscopic observations showed many broad features andstrong narrow He i emission lines. According to the He detection,
SN 2006jc was classified as Type Ib (Crotts et al. 2006; Fesenet al. 2006; Benetti et al. 2006; Modjaz et al. 2006a, 2006b).
However, strange spectral features and their evolutions werereported. A bright blue continuum was prominent in the optical spectrum at early epochs ( Foley et al. 2007; Pastorello et al.
2007; Smith et al. 2008). Such a bright blue continuum had also
been observed in the Type II SN 1988Z (Turatto et al. 1993), but
the origin of this feature is still unclear. As the blue continuum
declined, the red wing brightened and the optical spectra showed
U-like shapes (Smith et al. 2008; K. S. Kawabata et al. 2008, in
preparation). This is a distinguishing feature of SN 2006jc incontrast to the spectra of usual SNe that have a peak in opticalbands.
Photometric observations in optical and IR bands were performed continuously. The optical light curve ( LC) showed a
rapid decline from 50 days after the discovery, as in the case of
SN 1999cq ( Matheson et al. 2000). At the same epoch, nearinfrared ( NIR) emissions brightened (Arkharov et al. 2006; Di
Carlo et al. 2007). The NIR brightness increased from 40 to70 days after the discovery and then declined ( Di Carlo et al.
2007). The epoch of the NIR brightening corresponds to that of

1. INTRODUCTION
On 2006 October 9, Nakano et al. (2006) reported K. Itagaki’s
discovery of a possible supernova (SN) in UGC 4904. Although
the SN was discovered after the peak, an upper limit of the R magnitude (MR > 12:2) was obtained at 20 days before the discovery (Pastorello et al. 2007). Interestingly, Nakano et al. (2006)
also reported that an optical transient had appeared in 2004 close
to the position of SN 2006jc. The transient was as faint as MR 
1
Optical and Infrared Astronomy Division, National Astronomical Observatory, 2-21-1 Osawa, Mitaka, Tokyo, Japan; nozomu.tominaga@nao.ac.jp.
2
Department of Astronomy, School of Science, University of Tokyo, 7-3-1
Hongo, Bunkyo-ku, Tokyo, Japan.
3
Istituto Nazionale di Astrofisica-Osservatorio Astronomico di Roma, Via
Frascati 33, I-00040, Monteporzio Catone, Italy.
4
Center for Stellar and Planetary Astrophysics, School of Mathematical
Sciences, P.O. Box, 28M, Monash University, Victoria 3800, Australia.
5Institute for the Physics and Mathematics of the Universe, University ofTokyo, 5-1-5 Kashiwa, Chiba, Japan.
6
Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Strasse 1, 85741
Garching, Germany.
7
Istituto Nazionale di Astrofisica-Istituto di Astrofisica Spaziale e Fisica
Cosmica, Via Fosso del Cavaliere 100, Roma, Italy.
8
Institute of Astronomy, School of Science, University of Tokyo, 2-21-1
Osawa, Mitaka, Tokyo, Japan.
9Institute of Space and Astronautical Science, Japan Aerospace Exploration
Agency, 3-1-1 Yoshinodai, Sagamihara, Kanagawa, Japan.
10
Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo, Japan.
11
Hiroshima Astrophysical Science Center, Hiroshima University, Hiroshima,
Japan.
12
Indian Institute of Astrophysics, Bangalore 560 034, India.
13
National Astronomical Observatories, Chinese Academy of Sciences, Beijing
100012, China.

1208

TYPE Ib SUPERNOVA 2006jc
the development of the red wing in the optical spectra (Smithet al. 2008).
The NIR brightening, as well as the fact that the redder sideof the He emission profile declined faster than the bluer side, hasbeen interpreted as an evidence of an ongoing dust formation(Smith et al. 2008). In addition, on 2007 April 29 (200 days
after the discovery), the AKARI satellite performed NIR and midinfrared (MIR) photometric and spectroscopic observations (Sakon
et al. 2007) and the MAGNUM telescope obtained the NIR photometries ( Minezaki et al. 2007). They report the formation of
amorphous carbon dust: another piece of evidences of the dust
formation.
X-ray and UVemissions have also been observed by the Swift
and Chandra satellites ( Brown et al. 2006; Immler et al. 2006,
2008; Holland et al. 2007). X-ray observations were performed atseven epochs and showed a brightening from 20 to 100 days
after the discovery (Brown et al. 2006; Immler et al. 2006, 2008).
The X-ray detection suggests an interaction between the SN ejecta
and the circumstellar matter (CSM ). On the contrary, the radio emission was not detected by the Very Large Array ( VLA;
Soderberg 2006).
We present a SN explosion model of a Wolf-Rayet star that
explains the bolometric and X-ray LCs. Hydrodynamics, nucleosynthesis, and LC synthesis calculations are performed assuming
the spherical symmetry. In this study, we assume the explosion
date of SN 2006jc to be 15 days before the discovery (t ¼ 0) andthe energy source of the light to be the 56NiY56Co decay.
The paper is organized as follows: in x 2 we describe how wederive the bolometric LC from observations in the various wave
bands; in x 3 we briefly discuss the presupernova evolutionary
properties of the progenitor star; in x 4 hydrodynamical andnucleosynthesis calculations are described; in x 5 LC synthesis
calculations are presented; in x 6 we calculate the X-ray emission
due to the ejecta-CSM interaction; in xx 7 and 8, conclusions anda discussion are presented.
2. PHOTOMETRIC OBSERVATIONSAND BOLOMETRIC LIGHT CURVEThe bolometric luminosities of SNe are usually estimated fromthe integration over the optical and NIR emission because theusual SNe radiate dominantly in the optical and NIR bands (e.g.,
Yoshii et al. 2003; T. Minezaki et al. 2008, in preparation). However, the spectra of SN 2006jc show the bright red and blue
wings (Smith et al. 2008; K. S. Kawabata et al. 2008, in preparation; Anupama et al. 2008), which implies that the emissions
in UV and IR bands contribute considerably to the bolometricluminosity.
We construct the bolometric luminosity with the integrationof the UV, optical, and IR photometries that are obtained with
the HCT (Anupama et al. 2008), AZT-24 (Arkharov et al.
2006; Di Carlo et al. 2007), MAGNUM ( Minezaki et al. 2007),and Subaru telescopes ( Kawabata et al. 2007; K. S. Kawabata
et al. 2008, in preparation) and the Swift ( Immler et al. 2008)
and AKARI satellites (Sakon et al. 2007). Since the UV fluxes areavailable only at t ¼ 17 days (Immler et al. 2008), the UV luminosity is estimated from the optical luminosity at the otherepoch. Available observations are shown in Figure 1. Details of
optical observations will be presented in forthcoming papers(e.g., Anupama et al. 2008; K. S. Kawabata et al. 2008, in
preparation). We adopt a distance of 25.8 Mpc, corresponding
to a distance modulus of 32.05 ( Pastorello et al. 2007) and areddening of E(B  V ) ¼ 0:05 (Schlegel et al. 1998; Pastorello
et al. 2007).

1209

Fig. 1.— Multicolor available observations of SN 2006jc. (a) X-ray and UV
luminosities obtained with the Swift and Chandra satellites (black: X-ray; red:
UVW2 band; green: UVM2 band; blue: UVW1 band; Immler et al. 2008). The
X-ray LC is shown in units of ergs s1 (right axis). (b) Optical luminosities
obtained with the HCT telescope ( filled circles; Anupama et al. 2008) and theSubaru telescope (open circles; Kawabata et al. 2007; K. S. Kawabata et al.
2008, in preparation). The upper limit is taken from Pastorello et al. (2007).
The colors represent the wavelengths (U band: red; B band: green; V band:
blue; R band: magenta; I band: cyan). (c) IR luminosities obtained with the
AZT-24 telescope ( filled circles; Arkharov et al. 2006; Di Carlo et al. 2007),the MAGNUM telescope (open circles; Minezaki et al. 2007), and the AKARI
satellite (squares; Sakon et al. 2007). The color of the circles represents the
wavelengths (J band: red; H band: green; and K band: blue). The contributions to
the IR luminosities from the hot dust ( filled square) and with the hot and warm
dust (open square) are shown in a unit of ergs s1 (right axis).

2.1. Optical Emission
The optical LCs were obtained with the HCT and Subaru
telescopes ( Kawabata et al. 2007; K. S. Kawabata et al. 2008, in
preparation; Anupama et al. 2008). We integrate the optical fluxes
with a cubic spline interpolation from 3 ; 1014 to 1 ; 1015 Hz.
The optical luminosities (Lopt ) are summarized in Table 1 andthe LC is shown in Figure 2. The optical LC declines monotonically after the discovery. The decline suddenly becomes
rapid at t > 70 days and the optical luminosity finally goes down
to Lopt  1039 ergs s1 at t  200 days.
The X-ray LC obtained with the Swift and Chandra satellites( Immler et al. 2008) shows that the X-ray luminosities, LX , aremuch fainter than the optical luminosities ( Brown et al. 2006;
Immler et al. 2006, 2008). Thus, the X-ray contribution to thebolometric luminosities is negligible. However, the UV luminosity,

1210

TOMINAGA ET AL.

Vol. 687

TABLE 1
Optical Luminosities

Date (JD 2,454,005)

Lopt(1040 ergs s1 )20............................................
21............................................
24............................................
27............................................
28............................................
33............................................
36............................................
38............................................
39............................................
40............................................
42............................................
44............................................
47............................................
49............................................
53............................................
58............................................
60............................................
62............................................
64............................................
65............................................
70............................................
77............................................
79............................................
81............................................
89............................................
92............................................
103..........................................
119..........................................
138..........................................
195..........................................

370
340
250
180
170
110
87
75
70
66
58
53
44
40
36
28
27
25
23
22
15
6.3
4.8
4.0
2.2
2.1
1.0
0.36
0.23
0.15

LUV , is comparable to the optical luminosity at t ¼ 17 days
(LUV  3 ; 1042 ergs s1 as estimated from the UVOT observations; Immler et al. 2008).14 The UV luminosity is 80% of
the optical luminosity, i.e., the total flux is 1.8 times brighter
than the optical flux ( Fig. 2). Since the UV flux declined as the
optical flux ( Holland et al. 2007), we assume that LUV  0:8Lopt
at every epoch. Although the blue wing declines with time and
LUV might be overestimated at t k 90 days (Smith et al. 2008),
the bolometric luminosity (Lbol ) should be reliable because the
IR contribution dominates in the bolometric luminosity at suchlate epochs (x 2.2).
2.2. Infrared Emission
The IR spectroscopy and photometries are obtained with the
AZT-24 and MAGNUM telescopes (NIR photometries; Arkharov
et al. 2006; Di Carlo et al. 2007; Minezaki et al. 2007) and the
AKARI satellite ( NIR spectroscopy and MIR photometries;
Sakon et al. 2007). As indicated by the red wing in the optical
spectra, the IR emission considerably contributes to the bolometric luminosity of SN 2006jc.
The MIR observation is available at t ¼ 215 days (Sakon
et al. 2007). The IR luminosity integrated over  < 3 ; 1014 Hz
is estimated from the NIR and MIR observations as LIR ( <3 ; 1014 Hz) ¼ 4:5 ; 1040 ergs s1 . Sakon et al. (2007) concluded that the IR emission is originated from amorphous carbon
grains with two temperatures of T ¼ 800 and 320 K. The large
14

The UV flux is estimated using the Swift UVOT calibration documents( http://swift.gsfc.nasa.gov/docs/swift /swiftsc.html).

Fig. 2.— Comparison of multicolor LCs of SN 2006jc. Lopt : green filled circles( Kawabata et al. 2007; K. S. Kawabata et al. 2008, in preparation; Anupama
et al. 2008); LUV þ Lopt : cyan filled circles ( Immler et al. 2008; Anupama et al.
2008); LIR;est ( < 3 ; 1014 Hz): red filled circles (Arkharov et al. 2006; Di Carloet al. 2007); Lopt þ LIR;est ( < 3 ; 1014 Hz): blue filled circles (Kawabata et al.
2007; K. S. Kawabata et al. 2008, in preparation; Anupama et al. 2008; Arkharov
et al. 2006; Di Carlo et al. 2007); LIR;hot ( < 3 ; 1014 Hz): magenta filled circle(Sakon et al. 2007); LIR ( < 3 ; 1014 Hz): magenta open circle (Sakon et al. 2007);and LX : black filled circles ( Immler et al. 2008).

difference between the two temperatures would imply that theorigin of the hot carbon dust with T ¼ 800 K is different fromthat of the warm carbon dust with T ¼ 320 K. The hot carbon
dust is suggested to be newly formed in the SN ejecta and heatedby the 56NiY56Co decay by a dust formation calculation ( Nozawa
et al. 2008). On the other hand, the origin of the emission fromthe warm carbon dust is suggested to be a SN light echo of theCSM carbon dust (Sakon et al. 2007; Mattila et al. 2008; see also
Nozawa et al. 2008). Therefore, we assume that the optical emission from SN 2006jc is absorbed and simultaneously reemitted
by the hot carbon dust and thus the luminosity emitted from the
hot carbon dust should be included in the bolometric luminosityof SN 2006jc. According to the estimated temperatures and massesof the hot and warm carbon grains (Sakon et al. 2007), the luminosities contributed by the hot and warm carbon grains are
LIR;hot ( < 3 ; 1014 Hz) ¼ 3:2 ; 1040 ergs s1 and LIR;warm ( <3 ; 1014 Hz) ¼ 1:1 ; 1040 ergs s1 , respectively.15
For the epochs when the IR photometries at  < 1:3 ; 1014 Hz
are unavailable, we estimate the contribution of the IR emission
by fitting the JHK-band photometries with amorphous carbon
emission.
From the Kirchhoff’s law, the thermal radiation from a spherical dust grain X with a uniform radius aX and temperature TX isgiven by 4aX2 B(; TX )QXabs (), where QXabs () is the absorption
efficiency of the grain. For the optically thin case, the observed
emission from dust grains X is written as
 2
aX
abs
;
ð1Þ
fX () ¼ NX B(; TX )QX ()R
15
The difference between LIR ( < 3 ; 1014 Hz) and LIR;hot ( < 3 ; 1014 Hz) þ
LIR;warm ( < 3 ; 1014 Hz) stems from the fact that the H-band luminosity isslightly brighter than the luminosity emitted from the hot carbon dust (Sakon
et al. 2007).

No. 2, 2008

TYPE Ib SUPERNOVA 2006jc

1211

TABLE 2
Parameters for Amorphous Carbon Fitting of the JHK-Band Photometries and the Estimated IR Luminosities

Date (JD 2,454,005)C (;10 )TC;hot( K)

49..................................................
57..................................................
67..................................................
70..................................................
72..................................................
77..................................................
79..................................................
127................................................
132................................................
154................................................
157................................................
159................................................
160................................................
167................................................
168................................................
169................................................
170................................................
171................................................
172................................................
192................................................
195................................................
197................................................
202................................................
215................................................

3.9
12
16
19
23
27
18
46
52
17
32
75
26
35
54
99
48
45
44
48
45
56
5.6
28

1580
1330
1340
1330
1300
1310
1400
1050
1010
1150
1010
900
1050
990
940
880
930
950
940
900
870
860
1190
870

34

where NX and R denote the total number of the dust particles andthe distance from the observer, respectively (Sakon et al. 2007).
In the followings, we convolve the -independent coefficients as
an emission coefficient C ¼ NX ð aX /RÞ2 . Applying the absorption efficiency for the amorphous carbon grain with aC ¼ 0:01 m,
we derive the temperature of the hot carbon dust, TC;hot , and C
to reproduce the JHK-band photometries.
To justify the above estimate, we compare the estimate withthe actual MIR observation at t ¼ 215 days (Sakon et al. 2007).
The fitting gives the temperature TC;hot ¼ 870 K and the emission coefficient C ¼ 2:8 ; 1035 for the HK-band photometries at
t ¼ 215 days. The luminosity integrated over  < 3 ; 1014 Hz is
LIR;est ( < 3 ; 1014 Hz) ¼ 2:7 ; 1040 ergs s1 . The temperatureand luminosity are roughly consistent with those of the hot carbon dust. The agreement indicates that the fitting gives a good
estimate of the IR emission due to the hot carbon dust. We notethat the estimate cannot account for the emission from the warm
carbon dust.
Table 2 summarizes the emission coefficient, temperature, estimated luminosity at  < 1:3 ; 1014 Hz, and luminosity emitted
below  ¼ 3 ; 1014 Hz. The dust temperature roughly declines
from TC;hot  1600 K at t ¼ 49 days to TC;hot  870 K at t ¼ 215
days. This is consistent with a picture that the hot carbon dust
was formed in the SN ejecta and cooled down gradually (Nozawa
et al. 2008). The IR LC is shown in Figure 2. The estimated luminosity at  < 1:3 ; 1014 Hz evolves as the JHK LCs, and thus the
IR LC brightens at t  50Y80 days and declines at t > 120 days.
Since there is no NIR data at t  80Y120 days, the bolometricLC cannot be estimated at this epoch. The bolometric luminosity
is derived from the summation of LUV ; Lopt , and LIR and summarized in Table 3, where LUV ¼ 0:8Lopt is applied.
3. THE PROGENITOR STARThe presupernova model has been extracted from a set of models already presented by Limongi & Chieffi (2006) and computed

LIR;est ( < 1:3 ; 1014 Hz)(1040 ergs s1 )LIR;est ( < 3 ; 1014 Hz)(1040 ergs s1 )

2.9
5.1
6.6
7.8
8.9
11
9.1
7.6
7.2
4.2
4.5
6.7
4.4
4.5
5.5
7.6
4.8
4.9
4.6
4.0
3.3
3.8
1.5
2.1

9.0
12
15
17
19
23
21
12
11
7.0
6.6
8.7
6.8
6.4
7.5
9.7
6.3
6.7
6.3
5.3
4.2
4.8
2.7
2.7

with the latest release of the stellar evolutionary code FRANEC(ver. 5.050218). Since all the features of this code have been already presented, we address here only the main points. The interaction between convection and local nuclear burning has beentaken into account by coupling together and solving simultaneously
the set of equations governing the chemical evolution due to the
nuclear reactions and those describing the convective mixing.
More specifically, the convective mixing has been treated bymeans of a diffusion equation where the diffusion coefficient iscomputed by the use of the mixing-length theory. The nuclear
network is the same as that adopted in Limongi & Chieffi (2003)
but the nuclear cross sections have been updated whenever possible (see Table 1 in Limongi & Chieffi 2006). A moderate amountof overshooting of 0.2 Hp has been included into the calculation
only on the top of the convective core during core H burning.
TABLE 3
Bolometric Luminosities

Date (JD 2,454,005)

Lbol(1040 ergs s1 )49..............................................................
51..............................................................
53..............................................................
58..............................................................
60..............................................................
62..............................................................
65..............................................................
66..............................................................
70..............................................................
77..............................................................
79..............................................................
119............................................................
138............................................................
195............................................................

81
81
75
64
61
59
55
54
45
33
29
14
10
4.7

1212

TOMINAGA ET AL.

Vol. 687

Fig. 3.— Abundance distributions of presupernova models with (a) Mms ¼ 25 M , (b) Mms ¼ 30 M , (c) Mms ¼ 40 M , and (d ) Mms ¼ 120 M . Note that the chemical composition of the outmost layer is C-rich in the WCO Wolf-Rayet stars (c, d ).

Mass loss has been taken into account following the prescriptions of Vink et al. (2000) for the blue supergiant phase (TeA >12;000 K ), de Jager et al. (1988) for the red supergiant phase(TeA < 12;000 K ), Nugis & Lamers (2000) for the WNL WolfRayet phase, and Langer (1989) during the WNE/ WCO WolfRayet phases. We adopt the following correspondence of themodels to the various WR phases according to the surface abundances, as suggested by Maeder & Meynet (2003): WNL [105 <X ( H )surf < 0:4], WNE [X ( H )surf < 105 and (C/ N )surf < 0:1],
WNC [0:1 < (C/ N )surf < 10], and WCO [(C/ N )surf > 10]. (Hereafter, C/N and C/O denote the number ratios.)
The X-ray emission, as well as the early bright blue continuum
and the narrow He i lines, clearly indicates an interaction between the SN ejecta and the CSM, i.e., the existence of a dense
CSM. Furthermore, the IR spectral energy distribution may be
explained by the formation of amorphous carbon grains in the
SN ejecta and the CSM (Sakon et al. 2007; see also Nozawa
et al. 2008). Since the C-rich environment (i.e., C/O > 1) isrequired to form carbon dust (e.g., Nozawa et al. 2003), the IR
observations suggest that the SN ejecta and CSM contain a
C-rich layer. This suggests that the progenitor star of SN 2006jc
is a WCO Wolf-Rayet star with a C-rich envelope and CSM( Fig. 3).

Inspection of all the presupernova models available in Limongi& Chieffi (2006) indicates that only massive models, i.e., Mms >40 M , fulfill the requirements from the IR observation and become WCO stars. Moreover, these are the only stars in which thechemical compositions of the mantle and CSM are dominatedmainly by C with a smaller amount of O ( Figs. 3c and 3d ).
In stars with initial masses smaller than Mms  35 M , themass of the He convective core increases or remains constantduring the core HeYburning phase. At core He exhaustion, a
sharp discontinuity of He abundance is produced at the outeredge of the CO core. Then, the CO core begins to contract toignite the next nuclear fuel while He burning shifts to a shell
inducing a formation of a convective zone. The He convective
shell forms beyond the He discontinuity at the outer edge of
the CO core. Hence, its chemical composition is dominated by
He [X ( He) > 0:9]. Because of the short lifetime of the advanced
burning stages, only a small amount of He is burned inside
the shell before the presupernova stage ( Figs. 3a and 3b). Sucha behavior is typical for stars in which the He core mass remains roughly constant during core He burning (e.g., Nomoto& Hashimoto 1988).
In stars with initial masses greater than Mms  35 M , on thecontrary, the mass loss is efficient enough (105 to 104 M yr1 )No. 2, 2008

TYPE Ib SUPERNOVA 2006jc

1213

TABLE 4
Basic Evolutionary Properties of the Progenitor Star
Key Quantities

Values

H BurningtH ( Myr)...................................................
MCC (M ).................................................
Mtot (M ) .................................................
tO ( Myr)...................................................
MHe (M ) .................................................

4.64
25.80
35.40
4.16
10.01

He BurningtHe ( Myr)..................................................
MHe;CC (M ).............................................
Mtot (M ) .................................................
Menv (M ) ................................................
X (12 C)cen ..................................................
tred ( Myr) .................................................
tWNL ( Myr), (X ( He)cen ) ...........................
tWNE ( Myr), (X ( He)cen ) ...........................
tWCO ( Myr), (X (He)cen )...........................

0.46
12.56
7.04
18.80
0.28
0.07
0.11, (0.77)
0.054, (0.44)
0.21, (0.31)

Advanced Burnings
t exp ( yr) ................................................
MHe (max) (M )........................................
MCO (max) (M ) .......................................
MFe;preSN (M )..........................................
MpreSN (M ) .............................................
RpreSN (cm) ...............................................
Mr (Heshell ) ( Int.YExt.) (M )....................
Mr (Cshell ) ( Int.YExt.) (M ) ......................
tWNL (tot) ( yr) ...........................................
tWNE (tot) ( yr) ...........................................
tWCO (tot) ( yr) ...........................................
tWR (tot) ( yr) .............................................

1.25(+4)
16.52
4.83
1.50
6.88
3.08(+10)
5.262Y6.648
2.736Y4.097
1.10(+5)5.43(+4)
2.21(+5)
3.86(+5)

to uncover the He core and they reduce progressively their mass
during the core HeYburning phase. The star enters the WNE WolfRayet stage and its subsequent evolution is governed by the actual
size of the He core. In particular, as the He core progressively
reduces due to the mass loss, the star tends to behave as an initially lower mass star, i.e., essentially reduces its central temperature. This induces the He convective core to shrink progressively
in mass as well, leaving a layer with a variable chemical composition that reflects the central abundances at various stages duringcore He burning. When the stellar mass is reduced below the maximum extension of the He convective core, the products of coreHe burning appear on the surface and the star becomes a WCO
Wolf-Rayet star. At core He exhaustion, He burning shifts to ashell inducing the formation of the convective shell. The convective shell forms in the region with variable chemical composition.
As a consequence, at variance with what happens in stars with
Mms P 35 M , in these stars, the chemical composition of the convective shell becomes a mixture of the central He-burning products.
Hence, it is mainly composed of C, O, and He (Figs. 3c and 3d).
Since all the models above 40 M have a similar presupernova structure, we selected a 40 M star as representative of atypical star becoming a WCO Wolf-Rayet star. The mass at thepresupernova stage (MpreSN ) is MpreSN ¼ 6:9 M because of thestrong mass loss. We underline that the Mms -MpreSN relation ishighly uncertain because it strongly depends on many details of
the stellar evolution (e.g., the mass loss, overshooting, rotation,and metallicity; see Langer 1989; Nugis & Lamers 2000; Meynet& Maeder 2003; Nomoto et al. 2006; Limongi & Chieffi 2006;

Fig. 4.— Presupernova evolutionary path of the progenitor star with Mms ¼
40 M in the Hertzsprung-Russell diagram. [See the electronic edition of the
Journal for a color version of this figure.]

Eldridge & Vink 2006). For this reason, for the purpose of this study,
we mainly focus on a WCO progenitor with MpreSN  6:9 M ,without giving much emphasis to Mms .
A detailed discussion of the presupernova evolution during
all the nuclear burning stages is beyond the purpose of this paper.
Hence, we report here in Table 4 some key properties during
the H, He, and advanced burning stages. In particular, for the
H-burning stage we report the following quantities: the H-burning
lifetime (tH ), the maximum extension of the convective core (MCC ),the total mass (Mtot ) at core H exhaustion, the time spent as an
O-type star (tO ), and the He core mass (MHe ) at H exhaustion.
Here we assume that the temperature of the O-type stars is
33;000 K < TeA < 50;000 K. For the He-burning phase wereport the following quantities: the He-burning lifetime (tHe ),the maximum size of the He convective core (MHe;CC ), Mtot atcore He exhaustion, the maximum depth of the convective envelope (Menv ), the central 12 C mass fraction at core He exhaustion [X (12 C)cen ], the time spent at the red side (log TeA < 3:8) of
the HR diagram (tred ), and the WNL, WNE, and WCO lifetimes(tWNL , tWNE , and tWCO , respectively)—in parenthesis we show
the central He mass fraction [X (He)cen ] when the star enters the
WNL, WNE, and WCO phases. For the advanced burning stage
we report the following key quantities: the time until the explosion (t exp ), the maximum size of the He core [MHe (max)],
the maximum size of the CO core [MCO (max)], the masses of
the iron core (MFe; preSN ) and the star (MpreSN ), the radius of thestar (RpreSN ) at the presupernova stage, the final extension inmass of the He convective shell [Mr (Heshell )] and of the convective C shell [Mr (Cshell )], and the total lifetimes during the
WNL [tWNL (tot)], WNE [tWNE (tot)], WCO [tWCO (tot)], and WR[tWR (tot), where tWR ¼ tWNL þ tWNE þ tWCO ] phases.
Figures 4 and 5 show the evolutionary path in the HR diagram
and the temperature and density profiles at the presupernova stage.
4. HYDRODYNAMICS AND NUCLEOSYNTHESISThe SN explosion and explosive nucleosynthesis are calculated for the progenitor star with MpreSN ¼ 6:9 M . We apply

1214

TOMINAGA ET AL.

Vol. 687

Fig. 5.— Temperature and density structures of the presupernova progenitor
star with Mms ¼ 40 M .

various explosion energies (E51 ¼ E/1051 ergs ¼ 1, 5, 10, and20) for the SN explosion calculations (e.g., Nomoto et al. 2006;
Tominaga et al. 2007b). The hydrodynamical calculation is performed by means of a spherical Lagrangian hydrodynamics codewith a piecewise parabolic method (PPM; Colella & Woodward1984) including nuclear energy production from the -network.
The equation of state takes account of the gas, radiation, e -eþpair (Sugimoto & Nomoto 1975), Coulomb interactions between
ions and electrons, and phase transition (Nomoto 1982; Nomoto& Hashimoto 1988). After the hydrodynamical calculations,
nucleosynthesis is calculated as a postprocessing with a reaction
network that includes 280 isotopes up to 79Br (see Table 1 in
Umeda & Nomoto 2005).
Since the explosion mechanism of a core-collapse SN for a
massive star with an iron core is still an unsolved problem (e.g.,
Janka et al. 2007), we initiate the SN explosion as a thermalbomb. Although there are various ways to simulate the explosion(e.g., a kinetic piston; Woosley & Weaver 1995), it is suggested
that the explosive nucleosynthesis does not depend sensitively
on the way the explosion energy is deposited (Aufderheide et al.
1991). We set an inner reflective boundary at Mr ¼ 1 M andr ¼ 1000 km within the iron core and elevate temperatures at
the inner boundary.
In the spherical symmetry case, for any given progenitor model,hydrodynamics and nucleosynthesis are determined by the explosion energy. During the SN explosion, a shock propagates
outward inducing local compression and heating, triggering explosive nucleosynthesis. Behind the shock front the matter isaccelerated and starts moving outward. However, if the progenitor has a deep gravitational potential and the explosion energy islow, the inner layers begin to fall back due to the gravitational
attraction. A more compact star and a lower explosion energy
lead to a larger amount of fallback. The fallback has a deep implication on the SN nucleosynthesis because it decreases thematter ejection, especially of the inner core (e.g., 56Ni).
Figure 6 shows density structures at 100 s after the explosions when homologously expanding structures are reached (v / r).
We find that the fallback takes place for the model with E51 ¼ 1
but not for the models with E51 ¼ 5, 10, and 20. Figure 7 shows acomparison between the escape velocity and the ejecta velocity
for the model with E51 ¼ 1 and demonstrates that the matter
below Mr ¼ Mfall ¼ 3:8 M will fall back. On the other hand, inthe models with E51 ¼ 5, 10, and 20, the matter above the innerboundary will be ejected.

Fig. 6.— Density structures at 100 s after the explosions for the models with
E51 ¼ 1 (solid line), E51 ¼ 5 (dashed line), E51 ¼ 10 (dash-dotted line), andE51 ¼ 20 (dotted line). [See the electronic edition of the Journal for a color
version of this figure.]

The abundance distributions after the explosions are shownin Figures 8aY8d. In every model, 58Ni is synthesized in the
innermost layer (Mr < MFe;preSN ¼ 1:5 M ) due to the low electron fraction. Thus, we can estimate the maximum amounts ofsynthesized 56Ni for given energies. The 56Ni-rich layer extending to Mr ¼ MFe [where X (56 Ni) ¼ X (28 Si)] and 28Si-rich layer
extending to Mr ¼ MSi [where X (28 Si) ¼ X (16 O)] expand farther
in the models with higher E because the temperature achieved ishigher in the outer layer for higher E. The MFe and MSi for eachmodel are summarized in Table 5.

Fig. 7.— Comparison between an escape velocity (dashed line) and an ejecta
velocity for the model with E51 ¼ 1 (solid line). [See the electronic edition of the
Journal for a color version of this figure.]

No. 2, 2008

TYPE Ib SUPERNOVA 2006jc

1215

Fig. 8.— Abundance distributions after the explosions of the progenitor star with Mms ¼ 40 M . The explosion energies are (a) E51 ¼ 1, (b) E51 ¼ 5, (c) E51 ¼ 10, and(d ) E51 ¼ 20.
56

Ni is synthesized at Mr < MSi . Since MSi < Mfall in themodel with E51 ¼ 1, the model is likely not to eject 56Ni. On theother hand, the models with E51 ¼ 5, 10, and 20 can eject allsynthesized 56Ni because the fallback does not occur. The total
amounts of synthesized 56Ni for the models with E51 ¼ 5, 10,
and 20 are summarized in Table 5.
5. LIGHT CURVEThe energy source of the LC of SN 2006jc is still under
debate. The possible sources include the 56NiY56Co decay likeType I SNe and the ejecta-CSM interaction like Type IIn SNe.
TABLE 5
Nucleosynthesis Properties of the Explosion Models
with MpreSN ¼ 6:9 M (Mms ¼ 40 M )Explosion Energy(1051 ergs)

MFe
(M )

MSi
(M )

M(56 Ni)
(M )

Mcut
(M )

1........................................
5........................................
10......................................
20......................................

1.8
2.1
2.3
2.5

2.1
2.5
2.7
3.0

...
0.5
0.6
0.7

...
1.8
2.0
2.3

However, both scenarios have the following problems. In thecase of the 56NiY56Co decay, the -ray photon and positron
emitted from the 56NiY56Co decay are absorbed by the SN ejecta
and the absorbed energy is thermalized. Thus, the spectra would
show a blackbody-like continuum as normal Type I SNe do.
However, the spectra of SN 2006jc do not resemble those of
normal Type I SNe but show a bright blue continuum in early
epochs (Foley et al. 2007; Smith et al. 2008). In the case of theejecta-CSM interaction, the kinetic energy is transformed to an
X-ray emission via bremsstrahlung radiation, and then converted
to UV, optical, and IR emissions. Thus, it is difficult to explainthat the X-ray luminosity is much fainter than the optical luminosity unless the optical depth for the X-ray emission is muchhigher than that for the optical emission. Another problem withthe ejecta-CSM interaction model is that the X-ray LC is notsynchronized with the bolometric LC. In addition, the LC powered by the ejecta-CSM interaction usually has a long-term plateau(e.g., SN 1997cy; Turatto et al. 2000). Thus, we assume that the
LC is powered by the 56NiY56Co decay.
5.1. Radioactive Decay Models
The bolometric LC of SN 2006jc is constructed from the UV,
optical, and IR observations as described in x 2. The estimated1216

TOMINAGA ET AL.

peak bolometric magnitude of SN 2006jc is M ¼ 18:4, being as bright as SN 2006aj (e.g., Pian et al. 2006). Thus, it isspeculated that the ejected amount of 56Ni [M(56 Ni)] is similar
to SN 2006aj, i.e., M (56 Ni)  0:2 M ( Mazzali et al. 2006,
2007; Maeda et al. 2007). According to x 4, the models with
E51 ¼ 5, 10, and 20 can eject a large enough amount of 56Ni,
while the 56Ni production of the model with E51 ¼ 1 is too
small.
The spherical explosion models with E51 ¼ 5, 10, and 20 yield
too much M(56 Ni) because of no fallback. However, no fallback
is a consequence of the assumption of the spherical symmetry.
The fallback takes place in an aspherical explosion even with ahigh explosion energy and thus the aspherical explosion may welldecrease M(56 Ni) and increase the central remnant mass Mrem
( Maeda & Nomoto 2003; Tominaga et al. 2007a; Tominaga2007). Therefore, assuming that aspherical fallback takes
place in the high-energy models with E51 ¼ 5, 10, and 20, we
estimate the amount of fallback to yield M (56 Ni)  0:2 M
and then the ejected masses for the models as Mej ¼ MpreSN Mrem . As a result, the sets of Mrem ; Mej , and E are derived tobe (Mrem /M ; Mej /M ; E51 ) ¼ (1:8; 5:1; 5), (2.0, 4.9, 10), and(2.3, 4.6, 20).
Applying the homologous density structures of the models( Fig. 6), we synthesize bolometric LCs for the models with
E51 ¼ 5, 10, and 20 using the LTE radiation hydrodynamics
code and the gray -ray transfer code ( Iwamoto et al. 2000). In
the radiative transfer calculation, the electron scattering is
calculated for the ionization states solved by the Saha equationand the Rosseland mean opacity is approximated with an empirical relation to the electron-scattering opacity ( Deng et al.
2005).
The peak width () of the SN LC depends on the ejected mass
Mej , explosion energy E, opacity , density structure, and 56Ni
distribution, as  / A1/2 Mej3/4 E 1/4 (Arnett 1982), where A represents the effects of the density structure and the 56Ni distribution. Here, we assume for sake of simplicity a uniform mixingof 56Ni in the SN ejecta. Also, the density structures after the SN
explosions with various E are analogous. Thus, the dependence
on A is negligible and we investigate the LC properties depending on ; Mej , and E. The synthetic LCs obtained for the models
with (Mej /M ; E51 ) ¼ (5:1; 5), (4.9, 10), and (4.6, 20) are shownin Figure 9. Figure 9 also shows the multicolor and bolometricLCs of SN 2006jc.
5.2. Comparison with Observations
The period of SN 2006jc is divided into four epochs depending on the available observations: (1) UV and optical photometries at t < 50 days; (2) optical and NIR photometries att  50Y80 days; (3) optical photometry at t  80Y120 days;and (4) optical, NIR, and MIR photometries and NIR spectroscopy at t > 120 days.
1. At t < 50 days, the IR contributions to the bolometricluminosity may well be small because the IR contribution
is only 10% at t  50 days. Thus, the peak bolometric luminosity derived from the UV and optical fluxes is reliable(x 2.1). If the bolometric LC peaked at the discovery, thepeak luminosity is reproduced by the 56NiY56Co decay ofM (56 Ni) ¼ 0:22 M . The rapid decline after the peak prefers such high-energy models as (Mej /M ; E51 ) ¼ (4:9; 10) and(4.6, 20).
2. At t  50Y80 days, the IR contribution to the bolometricluminosity increases from 10% at t ¼ 49 days to 70% at

Vol. 687

Fig. 9.— Comparison between the synthetic LCs for the models with E51 ¼ 5
and Mej ¼ 5:1 M ( green line), E51 ¼ 10 and Mej ¼ 4:9 M (blue line), andE51 ¼ 20 and Mej ¼ 4:6 M (red line) and the LCs of SN 2006jc. LUV þ Lopt :cyan filled circles ( Immler et al. 2008; Kawabata et al. 2007; K. S. Kawabata
et al. 2008, preparation; Anupama et al. 2008); LIR;est ( < 3 ; 1014 Hz): redfilled circles (Arkharov et al. 2006; Di Carlo et al. 2007); Lbol : blue filled circles( Immler et al. 2008; Kawabata et al. 2007; K. S. Kawabata et al. 2008, in
preparation; Anupama et al. 2008; Arkharov et al. 2006; Di Carlo et al. 2007);
LIR;hot ( < 3 ; 1014 Hz): magenta filled circle (Sakon et al. 2007); LIR ( < 3 ;1014 Hz): magenta open circle (Sakon et al. 2007). The luminosities denoted by
the circles without error bars have considerable contributions from the UV luminosity, estimated as LUV ¼ 0:8Lopt .

t ¼ 79 days. The contribution of LIR;est ( < 1:3 ; 1014 Hz) to
LIR;est ( < 3 ; 1014 Hz) changes from 30% at t ¼ 49 days to40% at t ¼ 79 days. At this epoch, the optical and IR emissions contribute to the bolometric luminosities. Combining the
IR brightening and the optical decline, the bolometric LC including LUV ( ¼ 0:8Lopt ) declines slowly. Such a slow decline
is consistent with the models of (Mej /M ; E51 ) ¼ (4:9; 10) and(4.6, 20).
3. At t  80Y120 days, NIR photometries are not available.
The decline of the optical luminosity at this epoch is more
rapid than at t < 80 days. Such a rapid decline of the optical
LC cannot be reproduced by the 56NiY56Co decay. However,the bolometric LC may well decline more slowly than the optical LC because the IR emission dominates in the bolometricluminosity.
4. At t > 120 days, NIR photometries are available continuously and optical photometries are available at t ¼ 120; 140;
and 195 days (K. S. Kawabata et al. 2008, in preparation). The
contribution of the optical emission to the bolometric luminosities is negligible (3% at t ¼ 120; 140; and 195 days). At thisepoch, the contribution of LIR;est ( < 1:3 ; 1014 Hz) to the totalluminosity increases from 60% at t ¼ 127 days to 80% at
t ¼ 215 days. The estimated IR luminosity is consistent with theluminosity emitted from the hot carbon dust at t ¼ 215 days
(x 2.2). Since the dust temperature decreases with time, the ratioof the MIR luminosities to the NIR luminosities becomes larger
with time. Therefore, the amorphous carbon emission model reasonably estimates the IR luminosity due to the hot carbon dust
at t P 215 days. The model with Mej ¼ 4:9 M ; E51 ¼ 10,
and M (56 Ni) ¼ 0:22 M reproduces well the LC decline at t >120 days and the IR luminosities due to the hot carbon dust at

No. 2, 2008

TYPE Ib SUPERNOVA 2006jc

1217

Fig. 10.— Comparison between the synthetic X-ray LCs contributed from thetotal emission (solid line), the SN ejecta (dashed line), and the CSM (dotted line)
and the X-ray LC of SN 2006jc (circles; Immler et al. 2008). [See the electronic
edition of the Journal for a color version of this figure.]t ¼ 215 days.16 Therefore, we conclude that the hypernovalike SN explosion model with Mej ¼ 4:9 M ; E51 ¼ 10, andM (56 Ni) ¼ 0:22 M is the most preferable model among the exploded models of a WCO Wolf-Rayet star with MpreSN ¼ 6:9 M .
6. INTERACTION WITH CIRCUMSTELLAR MATTER
X-rays from SN 2006jc were detected by the Swift andChandra satellites ( Immler et al. 2008). The X-ray detection
indicates that the expanding SN ejecta collides with the CSM.
We calculate X-ray emission from the ejecta-CSM interaction
for the SN model with (Mej /M ; E51 ) ¼ (4:9; 10), and estimate
the CSM density structure on the basis of a comparison with theobserved X-ray LC (e.g., Suzuki & Nomoto 1995). The observed
X-ray luminosities estimated with the distance of 24 Mpc in
Immler et al. (2008) are scaled using 25.8 Mpc.
We adopt a CSM density profile characterized by a power lawof ¼ 0 (r/r0 )n and assume that the interaction starts at a distance r ¼ 3 ; 1010 cm. The parameters 0 ; r0 , and n are determined so that the ejecta-CSM interaction reproduces the observed
X-ray LC.
The interaction generates reverse and forward shock waves
in the SN ejecta and CSM, respectively. Both regions are heatedby the shock waves and emit X-rays. In such a compact star,because the density in the shocked SN ejecta is higher than thatin the shocked CSM, the emitted X-rays from the shocked SN
ejecta are more luminous than those from the shocked CSM( Fig. 10).
16
After submission of this paper, the IR observation at t ¼ 425 days waspresented by Mattila et al. (2008) . They estimated the total luminosity and thedust temperature as L  1:2 ; 1040 ergs s1 and T ¼ 520 K, respectively. Ourmodel with Mej ¼ 4:9 M , E51 ¼ 10, and M (56 Ni) ¼ 0:22 M predicted a luminosity of Lbol  3 ; 1039 ergs s1 and a dust temperature of T  200 K( Nozawa et al. 2008) at t  430 days, which are lower than the observations.
This suggests that the observed IR emissions at t ¼ 425 days may originate not
only from the newly formed dust in the SN ejecta heated by the 56NiY56Co decay
but also from the light echo of the CSM dust.

Fig. 11.— (a) Density, (b) velocity, and (c) temperature structures of the SN
ejecta and the CSM at t ¼ 0 day (red), 10 days ( green), 20 days (blue), 50 days
(magenta), 100 days (cyan), and 200 days (black). The coordinate is the Lagrangianmass with the contact discontinuity between the ejecta (left) and the CSM(right).

Figure 10 shows the synthesized X-ray LC for 0 ¼ 2:75 ;1019 g cm3 and n ¼ 0 for r < 2:2 ; 1016 cm and n ¼ 6 forr > 2:2 ; 1016 cm; i.e., for a flat (inside) and steep (outside)
CSM density profile of ¼ 2:75 ; 1019 g cm3 for r < 2:2 ;1016 cm and 2:75 ; 1019 (r/2:2 ; 1016 cm)6 g cm3 for r >2:2 ; 1016 cm. The total mass of the CSM is 1:2 ; 102 M toreproduce the peak of the observed X-ray LC and the subsequentdecline.
The density, velocity, and temperature structures and theirevolutions are shown in Figure 11. The velocity of the reverse
shock is v  3:8 ; 104 km s1 . The reverse shock reaches 5:3 ;102 M from the outer edge of the SN ejecta at t ¼ 200 days
and heats up the swept-up SN ejecta. The temperature behind thereverse shock is higher than 108 K where dust cannot newly form
and the dust formed in the SN ejecta is destroyed (Nozawa et al.
2008). Our calculation does not show the formation of a coolingshell. This is because the CSM interaction is so weak as to emit
X-rays of 3 ; 1039 ergs s1 . If the bolometric luminosity is
powered by the CSM interaction, i.e., if the CSM interaction
emits as high luminosity as 8 ; 1042 ergs s1 , the cooling shellmight form and thus dust formation might be possible. Further
detailed studies, however, are required to confirm the dust formation behind the reverse shock.
Such a flat density profile of the inner CSM implies that thestellar wind was not steady because the steady wind should
form a CSM of / r2 . This circumstellar environment might
have been formed by a variable mass-loss rate Ṁ and /or a variable wind velocity v w. For example, assuming that the stellar
wind blew with a constant v w ¼ 3500 km s1 for 2 yr before
the explosion, the mass-loss rate must have changed from 1 ;102 to 2 ; 1014 M yr1 in 2 yr. Such a drastic change of the
mass-loss rate and /or the wind velocity is consistent with the1218

TOMINAGA ET AL.

fact that the progenitor of SN 2006jc was surrounded by thematter ejected by the LBV-like event 2 yr before the explosion.
7. CONCLUSIONSWe present a theoretical model for SN 2006jc whose properties are summarized as follows.
1. WCO progenitor and dust formation.—The progenitor is a
WCO Wolf-Rayet star whose total mass has been reduced fromMms ¼ 40 M to as small as MpreSN ¼ 6:9 M . The WCO starmodel has a thick C-rich envelope and CSM. This is consistent
with the formation of amorphous carbon grains in the SN ejecta
and the CSM suggested by AKARI observations (Sakon et al.
2007). Nozawa et al. (2008) have calculated dust formation in
the WCO star explosion model and shown that carbon dust isformed in the C-rich layer at t  50 days. This is much earlier
than the dust formation after t  1 yr in Type II SNe (SNe II ),because of the much smaller Mej in the WCO star than SNe II.
According to the models in Limongi & Chieffi (2006) the stars
with Mms > 40 M typically become WCO stars to form a thickC-rich layer and CSM. This limiting mass, however, is still uncertain and strongly depends on many details of the stellar evolution.
The early dust formation in the SN ejecta and the CSM suggeststhat the progenitor of SN 2006jc is a massive star becoming a
WCO Wolf-Rayet star.
2. Explosion and bolometric light curve.—The multicolor
LCs of SN 2006jc show peculiar evolutions, e.g., a rapid declineof the optical LC and brightening of the IR LC. These can be interpreted as an ongoing dust formation. Assuming the absorbed
optical light is reemitted in the IR band, the bolometric LC isconstructed as a summation of LUV (¼ 0:8Lopt ), Lopt , and LIR . By
calculating the hydrodynamics, nucleosynthesis, and the bolometric LC for the SN explosion with the various explosion energies, E51 ¼ 1, 5, 10, and 20, we find that the hypernova-like SN
explosion model with Mej ¼ 4:9 M ; E51 ¼ 10, and M (56 Ni) ¼
0:22 M best reproduces the bolometric LC of SN 2006jc withthe radioactive decays. Also, the temperature evolution of the
carbon dust heated by the 56NiY56Co decay reasonably well explains the IR observations for t  50Y220 days ( Nozawa et al.
2008).
3. CSM interaction and X-ray light curve.—Applying themodel with Mej ¼ 4:9 M and E51 ¼ 10, we calculate the ejectaCSM interaction and the resultant X-ray LC. We derive the CSM
density structure to reproduce the X-ray LC of SN 2006jc
as ¼ 2:75 ; 1019 g cm3 for r < 2:2 ; 1016 cm and 2:75 ;1019 (r/2:2 ; 1016 cm)6 g cm3 for r > 2:2 ; 1016 cm. The flat
density distribution in the inner CSM indicates a drastic changeof the mass-loss rate and/or the wind velocity that is consistent
with the LBV-like event 2 yr before the explosion.
8. DISCUSSIONLBV connection.—Our model does not take into account the
LBV-like event that occurred 2 yr before the explosion. The firstreason is that the mechanism of the outburst is still unclear. The
second reason is that, at least in the framework of the current
understanding of standard stellar evolution, the envelope of a
massive star practically freezes out after core He exhaustion(i.e., about 10,000 yr before the explosion) due to the more
rapid evolution of the core than the envelope. In addition, it isinteresting to note that, and this is a confirmation of the theoretical expectation, there is no observational evidence that any
Wolf-Rayet star has ever undergone such a luminous outburst

Vol. 687(Humphreys et al. 1999). Hence, there is no specific reason toassociate the occurrence of a LBV-like outburst to the presupernova evolution. Future studies on the mechanism of theoutburst are required to firmly conclude the origin of the LBVlike outburst. It would be possible that a possible binary companion star could undergo the LBV-like outburst.
Fallback.—According to our hydrodynamics and nucleosynthesis calculations, in the spherically symmetric models with
E51  5, the fallback does not take place and thus the amountof synthesized 56Ni is much larger than M (56 Ni) ¼ 0:22 M ,which is required to power the LC of SN 2006jc (x 5.1). In theaspherical explosions, however, the fallback takes place evenfor E51  5. In this paper we assume the fallback even for themodels with E51  5 and derive the amount of fallback to yield
the appropriate amount of 56Ni. To justify the above assumption, we calculate an aspherical explosion induced by a jet with
an opening angle of ¼ 45 and an energy deposition rate ofĖ ¼ 3 ; 1052 ergs s1 (Tominaga et al. 2007a; Tominaga 2007).
The jet-induced model realizes an explosion with Mej  4:9 M ,E51  10, and M (56 Ni)  0:22 M that is consistent with the
adopted model. We note that an aspherical radiative transfer
calculation is required to confirm that the jet-induced explosion
model can reproduce the LC of SN 2006jc.
Light-curve models.—The model with Mej ¼ 4:9 M ; E51 ¼
10, and M (56 Ni) ¼ 0:22 M is not a unique model to reproduce
the bolometric LC of SN 2006jc. In the case of usual SNe, thevelocities of the absorption lines can disentangle the degeneracyof Mej and E by means of the comparison with the photosphericvelocities (e.g., Tanaka et al. 2008). However, the spectra of
SN 2006jc are dominated by He emission lines and the nature isunclear. Thus, we cannot fully resolve the degeneracy. Since the
3/4
LC shape is proportional to M ej E 1/4 , the model with a larger
Mej requires a higher E. An explosion of the progenitor star witha larger MpreSN reproduces the LC of SN 2006jc with a higher E
and the X-ray LC with a lower CSM density. On the other hand,an explosion of the progenitor star with a smaller MpreSN reproduces the LC with a lower E, e.g., an explosion with Mej ¼
1:5 M and E51 ¼ 1 can explain the LC shape of SN 2006jc.
However, such low E explosions suppress explosive nucleosynthesis and enhance the fallback. As a result, the 56Ni production is reduced for a small MpreSN . If the LC of SN 2006jc
is powered by the 56NiY56Co decay, the bright peak indicatesa larger amount of 56Ni production (0.22 M) than a normal
SN [M (56 Ni)  0:07 M , e.g., SN 1987A; Blinnikov et al.
2000]. Therefore, SN 2006jc is likely a more energetic explosion than a normal SN with E51  1.
Dust formation.—We assume that the energy source of the
LC of SN 2006jc is the 56NiY56Co decay. This consistently explains the formation of carbon dust at the early epoch (t  50 days)
and the dust temperature at t  200 days (Nozawa et al. 2008).
In this scenario, however, the origin of the bright blue continuum
remains an unsolved problem (e.g., Pastorello et al. 2007; Smithet al. 2008; Immler et al. 2008). Such a spectrum might be explained by the ejecta-CSM interaction. In this scenario, however,the fine tunings are required to reproduce the bolometric LC;
most of the X-rays are absorbed and converted to the opticalluminosity, which only a small fraction of the X-rays are emitted
with, changing the fraction from 103 at t  30 days to 0.1 att  180 days. Moreover, the formation of carbon dust with twotemperatures would not be explained. Since both scenarios areinconclusive so far, further investigations may give important
implications on the emission mechanism of SN 2006jc.

No. 2, 2008

TYPE Ib SUPERNOVA 2006jc

We would like to thank A. Arkharov, N. Efimova, A. Di Paola,
C. Corsi, E. Di Carlo, and M. Dolci for providing us the dataof the JHK-band photometries. We also would like to thankS. Immler for the preprint on the Swift observations. M. L. thanks
the support from the 21st Century COE Program (QUEST)
of JSPS (Japan Society for the Promotion of Science) for
his stay in the University of Tokyo and the hospitality of the
Department of Astronomy. G. C. A., D. K. S., and T. P. P. aresupported by the JSPS-INSA ( Indian National Science Acad-

1219

emy) exchange programme. N. T. and M. T. are supported
through the JSPS Research Fellowship for Young Scientists.
This work has been supported in part by World Premier International Research Center Initiative ( WPI Initiative), MEXT,
Japan, and by the Grants-in-Aid for Scientific Research of the
JSPS (10041110, 10304014, 11740120, 12640233, 14047206,
14253001, 14540223, 16740106, 18104003, 18540231, and20540226) and MEXT (19047004, 20040004, 20041005, and
07CE2002).

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