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C+O star models for SNe Ic

C+O star models for SNe Ic

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SKe 1998bw and 1997ef,respectively. The former is the explosion of a C+O

ergs, while the

star of MC+O 13.8 Ma (MmS 40 Ma) with 5 x

latter is that of a C+O star of MC+O 10 MQ (Mms 35 M a ) with

1.8 x






........... ....








9 -










-13 -14

















Figure 1 . Density profiles of models COMDH (solid line; for SN 2003dh, [20]),

C0138ES0 (dashed line; for SN 19!38bw, [21]), and C0100E18 (dottedline; for SN 1997ef,





C0100E18 [18]


C0138ES0 [21]






COMDH [20]







a Values required to reproduce the peak brightness of SN 2003dh

Model COMDH was constructed for SK 2003dh. We note that in early

phases the spectra of SK 2003dh are similar to those of SK 1998bw, while

in late phases they are similar to those of SK 1997ef. Therefore, we used

C0100E18/2 for o < 15000 km s-', C0138E50 for o > 25000 km s - l ,

and merged the two models linearly in between [20]. Kote C0100E18/2


is a model where the density of COlOOEl8 is reduced by a factor of two


In the following sections, we will show that the model COMDH can well

reproduce both the spectra of SIX 2003dh and its LC.

3. Spectrum Synthesis

We have compared the synthetic spectra of model COMDH with observations a t three epochs [20].

The first spectrum was obtained a t the M M T on 2003 April 10 [17]. This

12 days after the GRB, i.e.

10 rest-frame days into the life of the


SIX, assuming that the SIX and the GRB coincided in time. The spectrum

is characterized by very broad absorption lines, and it is similar to those

of SIX 1998bw a t a comparable epoch. A good match can be obtained for

logL[erg] = 42.83 and v(ph) = 28000 km s-' (Figure 2). A t this epoch,

the photosphere is located far outside, and this SK 1998bw-likespectrum

is formed in the C0138E50-like part of COMDH.



Figure 2. T h e observed 2003 April 10

spectrum (top, black line), subtracted afterglow spectrum (observed on 2003 April

1, middle, thin gray line), 'net' SN spectrum (bottom, thick gray line), and our

synthetic spectrum (bottom, black line).

Figure 3. T h e observed 2003 April 24

spectrum (top, black line), subtracted afterglow spectrum (observed on 2003 April

1, bottom, thin gray line), 'net' SN spectrum (middle, thickgray line), and our synthetic spectrum (middle, black line).

The next spectrum was obtained a t the M M T on 2003 April 24 [l'i].

Its rest-frame epoch is 23 days. At this epoch, the photosphere falls in the

joining region. So this spectrum is a good test for the merged model. We


obtained a good match with logL[erg] = 42.79 and v(ph) = 18000 km s-'

(Figure 3).

Figure 4. The observed 2003 May 10 spectrum (black line), spectrum of SN 1997ef

obtained on 1998 January 1 (thin gray line), and our synthetic spectrum (thick gray


Our third spectrum was obtained with Subaru on 2003 May 10 1121,

a rest-frame epoch

36 days, and it resembles that of SK 1997ef a t a

comparable epoch. At this epoch, model COMDH gives a good fit using

logL[erg] = 42.43 and v(ph) = 7500 km s-' (Figure 4). It means that

the photosphere has receded deep inside, and that this SN 1997bw-like

spectrum is determined by the COlOOE18-like part of COMDH.


4. Light Curve Construction

We extracted the SIX component from the observed spectra of [l'i],[la],

[13]. The spectrum taken on April 4 was adopted as the fiducial nonSIX afterglow (AG) spectrum (following Matheson17 et al. 2003), scaled in

flux, and then subtracted from the observations together with a host galaxy

component [12]. We adjusted the scaling factor to make the flux between

3200 A and 3600 A in the rest frame roughly disappear from the results.

This is justified by the fact that! type Ib/c SNe, like SNe Ia, always show

flux deficiency to the blue of

3600 8, due to line-blanketing (e.g. [MI).

The AG flux deduced this way can be fitted using a power-law function of

0.08. The extrapolated AG flux was

time, f M t P a ,where a = -2.18

subtracted from the spectrum taken on May 10, which does not cover the

wavelength range mentioned above.




We derived the absolute V-band LC of SK 2003dh from the decomposed

spectra. We then transformed it to the bolometric LC by using the bolonoting their spectral similarity. The

metric corrections of SK 1998bw

bolometric light curves are ploted in the rest frame in Figure 5. Ref. 13

have estimated the SP; photometry on .June 22 from a spectrum taken with

the Subaru telescope. They assumed a negligible AG contribution, while

our fitting AG evolution predicts about 27% the total flux at that epoch.

Our LC differs from those reported by refs. 8 and 17, which are also

different from one another. It roughly follows that of SK 1998bw before

the peak, while it is fainter than SK 1998bw by about 0.6 mag after the

peak. Though the likely time of peak is not covered, it is possibly 2 - 5

days earlier than SK 1998bw and the peak brightness may be a bit fainter.

The light curve in [8], however, rises much more rapidly, reaches a brighter

peak, and then drops much faster, while the one in [l7] appears to resemble

that of SK 1998bw. It is likely we subtracted more A C flux than ref. 17 did

because we intended to avoid the un-physical ”blue excess” in the decomposed spectra. Refs. 8 and 17 used a ?I-square fitting method t o decompose

the spectra. We tried that, method, only t o get a LC similar to the one

reported here.

We also constructed another bol LC using BVRI photometry 1141. The

LC from the spectra is similar to that from the photometry (figure 5).


5 . Light Curve Fitting

Synthetic bolonietric LCs were computed using an LTE radiation t,ransfer

code and a gray 7-ray transfer code [lo]. Generally speaking, y-rays created

in radioactive decays of 561’;i and %o can be either absorhed by SK ejecta

or escape, as determined by transfer calculations. The heated ejecta material then emits optical photons, which escape from optically thin regions.

A constant line opacity of 0.03 om3 g-’ was assumed in our computation.

The whole optical opacity was found t o be dominated by electron scattering. The balance between photoionizations and recombinations has been

taken into account.

First, we discuss the general dependance of the synthetic light curve on

various model parameters. The width of the LC peak, n c , can be roughly

i4 x I E , ~ ~ ~ / ~ A ~ [1],

~ , where

~ / ~ IEE K

, ~ is

-~ ~optical

/ ~

expressed as mc

opacity and A is a function of the density structure and 56Ki distribution.

The rising time of the LC is strongly affected by the 56Ki distribution. If

56Ki is absent from the outer region, -/-rays and optical photons are long


trapped in optically thick regions and hence the LC rises slow-ly. After the

peak and in later phases, the whole ejecta becomes transparent to optical

photons. So the decline rate of the LC is mainly determined by the optical

R M2EK-’t-2,

depth of the ejecta to y-rays, which roughly scales as K , ~ cc

where K? is y-ray opacity.



Lipkin el al. 2004




-1 9







Figure 5. The observed bolonietric LC of SN 2003dh (filled suqares; this paper), synthetic LC of the merged model COMDH (solid line), and that of model C0138E50

(dashed line).

We tested two models to fit the LC of SIX 2003dh, C0138E50 and

COMDH. 56Ki distribution and the total 561Xi mass were treated as free

parameters. As shown in Figure 5, both niodels can reproduce the observed LC peak. This is consistent with the above parameter analysis. The

best-fit 56Ki mass for each model is listed in Table 1. The synthetic LC

of C0138E50, however, declines faster than observations in later phases.

Model COMDH, on the other hand, has a denser core compared with

C0138E50 (see Figure 1). The denser core increases the efficiency of yray trappings and results in a LC being brighter and slower in later phases

than that of C0138E50.

6. Discussion

We have studied the properties of SK 2003dh and constructed model

COMDH for it. We summarize in Figure 6 the model parameters of core-


collapse SSe and hypernovae for comparison [25]. It shows that normal

core-collapse SKe occur for stars having main-sequence mass less than 20

M,, which probably explode with the canonical kinetic energy of 1x 1051

ergs and eject 0.1 M, 56Ki [22], [Z]


. originated from more massive

stars can be divided into two branches. One is the hypernova branch, which

features high kinetic energy and large ejected 56Ki mass [32]. The other

is the faint SK branch, showing low kinetic energy and small ejected 56Si

mass. It is clear that S S 2003dh belongs to the hypernova branch.

Our spectra and LC fitting require a dense core for SK 2003dh. Such

a dense core is unlikely the outcome of any realistic 1-D hydrodynamical calculations. Actually, all spherically symmetric explosion models, e.g.

C0100E18 and C0138E50 in Figure 1, are very flat inside, and they all

have an inner mass-cut defining a ‘hole’ in the density profile. In 2-D jetinduced explosions, however, a dense core can be formed through accretion

along the equatorial direction and the LC declines slowly according to the

2-D hydrodynamical and light curve calculations [16].


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E c








Main Sequence Mass, (Mo)

Figure 6. Top panel: main-sequence m a s of the progeniton for core-collapse

SNe/hypernovae V . S . kinetic energies. Bottorn panel: main-sequence m a 5 V.S. total 56 Ni

mass. The parametersof these SNe were estirnatedby previous papers (SN I1 1987A, [29];

SN IIb 19935, [3O]; SN Ic 19941, [9]; SN I1 1997D, [32]; SN I1 1999br, [35]; SN Ic 1997ef,

[18]; SN Ic 1998bw, [21]; SN Ic 1999as, [7]; SN Ic 2002ap, [19]; SN Ic 2003dk1,[ZO]).





Mas-Planck-Institut b r Astrophysik, Garchi.q, Germany

E-mail: inouemu@MPA-Garctiii,ig.MPG.DE


Dept. of Astronomy, University of Tokyo, Tokyo, Japan

E-mail: wiwamoto@astron.s.u-tolCiyo.ac.jp


Research Lab. for Nuclear Reacto,rs, Tokyo finst. of Tech., Toleyo, Japan

E-mail: orito@nr.titech.ac.jp


Center for Nuclear Study, Uwiversity of Tokyo, Wako, Saitama, Japan

E-mail: mari.ik‘o~acris.s.u-tokrJo.ac.jp

Recent observational and theoretical advances in studies of gamma-ray bursts

(GRBs) indicate t h a t there can be a significant “dark side” to the GRB energy budget: besides the ultrarelativistic jet giving rise t o the bright gamma-ray emission,

there can be an even greater amount of “dark” energy contained in an accompanying, mildly relativistic outflow. T h e occurrence of such outflows are strongly

supported in theoretical models, particularly for collapsar-type GRB progenitors,

and also has been directly confirmed in observations of GRB030329/SN2003dh.

This outflow component, which should be more baryon-rich than the G R B jet,

can have interesting implications for nucleosynthesis. Inside the outflow, light elements may be produced through reactions similar t o big bang nucleosynthesis.

Heavy element synthesis by neutron capture can also take place, sometimes by a

moderately rapid “n-process” rather than an r-process. The resulting nucleosynthetic products may be observationally relevant for the most metal-poor stars, as

well as the companion stars of black hole binary systems.



1. Introduction

Successful generation of GRBs requires the formation of a narrowlycollimated, ultrarelativistic outflow with bulk Lorentz factor r 2 100, implying very low baryon-loading (e.g.[14]). Since the temperature at the

base of the outflow should be of order MeV and the baryons are likely to

contain a high fraction of neutron^,^^^^ some production of nuclei starting

from free protons and neutrons is expected to occur in the expanding flow.

However, as shown in several recent papers,1r10i18in the very high entropy

and extremely rapid expansion characteristic of GR.B jets, nucleosynthesis

is limited to only small production of D and 4He, which are difficult to


Nevertheless, most GRB progenitors should also give rise to associated outflows with higher baryon-loads and lower velocities (baryon-rich

outflows, or BROs), as discussed in the next section. The lower entropy,

slower expansion and higher ejecta mass of BROs compared to GRB jets

make them much more interesting from a nucleosynthesis viewpoint. As

a first study of nucleosynthesis in BROs associated with GRBs, we have

investigated this problem utilizing the simple dynamical framework of the

basic fireball model, but incorporating detailed iiuclear reaction networks

including both light and heavy elements. More details can be found in [6].

2. Evidence for BROs: the “Dark Side” of GRBs

Besides the ultrarelativistic jet giving rise to the conspicuous GRB emission, there is growing evidence, both theoretical and observational, for the

existence of different types of BROs which constitute a “dark” component

to the GRB energy budget. Theoretically, it is highly probable that different types of “circum-jet winds” of baryon-loaded material surround and

coexist with the narrowly collimated GR.Bjet. In general, the GRB jet production mechanism is likely to act not only on the baryon-poor zones near

the jet axis, but also on the more baryon-contaminated, peripheral regions,

leading to BROs as a natural byproduct. Models involving core collapse

and jet penetration in massive stars”,27 have recently gained strong support through observations of SN2003dh associated with GRB030329.5i13 In

such models, BROs should be induced through entrainment and mixing

with the stellar material. High-resolution numerical simulations of jet-star

~ ~ demonstrate the inevitable generation of

interaction in c ~ l l a p s a r sindeed

a peripheral, low r outflow containing a significant fraction of the total

energy. In generic black hole accretion disk models, baryon-rich winds

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