Mon. Not. R. Astron. Soc. 384, 1725–1732 (2008)

doi:10.1111/j.1365-2966.2007.12834.x

Extinction curves flattened by reverse shocks in supernovae
Hiroyuki Hirashita,1 Takaya Nozawa,2 Tsutomu T. Takeuchi3 and Takashi Kozasa2
1 Centre for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Japan
2 Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan
3 Institute for Advanced Research, Nagoya University, Nagoya 464-8601, Japan

Accepted 2007 December 7. Received 2007 December 6; in original form 2007 October 30

ABSTRACT

We investigate the extinction curves of young galaxies in which dust is supplied from Type IIsupernovae (SNe II) and/or pair instability supernovae (PISNe). Since at high redshift (z >5), low-mass stars cannot be dominant sources for dust grains, SNe II and PISNe, whose
progenitors are massive stars with short lifetimes, should govern the dust production. Here, wetheoretically investigate the extinction curves of dust produced by SNe II and PISNe, taking
into account reverse shock destruction induced by collision with ambient interstellar medium.
We find that the extinction curve is sensitive to the ambient gas density around a SN, since theefficiency of reverse shock destruction strongly depends on it. The destruction is particularly
efficient for small-sized grains, leading to a flat extinction curve in the optical and ultraviolet
wavelengths. Such a large ambient density as nH  1 cm−3 produces too flat an extinction
curve to be consistent with the observed extinction curve for SDSS J1048+4637 at z = 6.2.
Although the extinction curve is highly sensitive to the ambient density, the hypothesis thatthe dust is predominantly formed by SNe at z ∼ 6 is still allowed by the current observational
constraints. For further quantification, the ambient density should be obtained by some othermethods. Finally, we also discuss the importance of our results for observations of high-z
galaxies, stressing a possibility of flat extinction curves.
Key words: supernovae: general – dust, extinction – galaxies: evolution – galaxies: highredshift – galaxies: ISM – quasars: individual: SDSS J104845.05+463718.3.

1 INTRODUCTION
Dust grains play an important role in the formation and evolutionof galaxies. Dust grains control the energy balance in the interstellar medium (ISM) by absorbing stellar light and reemitting it in
far-infrared (FIR). Also, the surface of dust grains is a site for an
efficient formation of H2 molecules (e.g. Cazaux & Tielens 2004),
which act as an effective coolant in metal-poor ISM. Those effectsof dust turn on even at ∼1 per cent of the solar metallicity according
to the calculation by Hirashita & Ferrara (2002), who argue that thestar formation rate is enhanced because of the first dust enrichment
in the history of galaxy evolution. The first sources of dust in the
Universe are Type II (core-collapse) supernovae (SNe II) or pairinstability supernovae (PISNe), since the lifetimes of their progenitors are short (∼106 yr). In the local Universe, dust grains are also
produced by evolved low-mass stars (Gehrz 1989), but this production mechanism requires much longer (1 Gyr) time-scales. The
first dust supplied by SNe II or PISNe may trigger the formation

 E-mail: hirasita@ccs.tsukuba.ac.jp
C 2008 The Authors. Journal compilation 
C 2008 RAS

of low-mass stars via dust cooling (Schneider et al. 2003; Omukai
et al. 2005).
To quantify the above effects of dust in the early stages of galaxy
evolution, it is crucial to know how much dust and what species ofgrains form in supernovae (SNe). It has been suggested by someobservations of nearby SNe that dust is indeed produced in SNe,although the quantity of formed dust is still debated (e.g. Moseley
et al. 1989; Dunne et al. 2003; Morgan et al. 2003; Hines et al.
2004; Sugerman et al. 2006; Meikle et al. 2007; Rho et al. 2008). By
treating the nucleation and accretion in SNe, the dust compositionand size distribution are theoretically calculated (Kozasa, Hasegawa& Nomoto 1989, 1991). Recently, in order to examine the effectsof dust in Population III (Pop III) objects, the formation of dust in
SNe II and PISNe is extensively examined (Todini & Ferrara 2001;
Nozawa et al. 2003, hereafter N03; Schneider, Ferrara & Salvaterra
2004). The motivation for considering PISNe comes from someevidence indicating that the stars formed from metal-free gas, Pop III
stars, are very massive with a characteristic mass of a few hundred
solar masses (e.g. Nakamura & Umemura 2001; Bromm & Larson
2004). Such massive stars are considered to begin pair creation ofelectron and positron after the helium burning phase, and finally an
explosive nuclear reaction disrupts the whole stars (Fryer, Woosley

1726

H. Hirashita et al.

& Heger 2001; Heger & Woosley 2002). This explosion is called
PISN.
Recently, the hypothesis that the dust formation is dominated by
SNe II and/or PISNe at high redshift (z) is observationally examined
for some objects. We expect that at z > 5, when the cosmic age isless than 1 Gyr, the main sources of dust grains are SNe II and PISNe(e.g. Dwek, Galliano & Jones 2007). Extinction curves can be used
to investigate the dust properties (e.g. Mathis 1990). By using a sample of broad absorption line (BAL) quasars, Maiolino et al. (2004a)show that the extinction properties of the low-z (z < 4) sample aredifferent from those of the high-z (z > 4.9) sample. This result issuggestive of a change in the dust production mechanism in thecourse of galaxy evolution. The highest z BAL quasar in their sample, SDSS J104845.05+463718.3 (hereafter SDSS J1048+4637) atz = 6.2 shows an extinction curve flat at wavelength λ  1700 Å
and rising at λ  1700 Å. Maiolino et al. (2004b) show that the extinction curve of SDSS J1048+4637 is in excellent agreement with
the Type II SN dust models by Todini & Ferrara (2001). Bianchi &Schneider (2007) consider dust destruction by reverse shock in SNe,suggesting that 2–20 per cent of the initial dust mass survives, andthat the extinction curve after the destruction is still consistent withthat of SDSS J1048+4637. More recently, Stratta et al. (2007) showthat the dust extinction in the host galaxy of GRB 050904 at z =6.3 can be explained by the extinction curve of SDSS J1048+4637,
further supporting that the SNe II are the main sources of dust atz > 6. Also, Willott et al. (2007) find a similar extinction property
for CFHQS J1509−1749 (z = 6.12) to that of SDSS J1048+4637.
There are other series of theoretical papers on the extinction
curves of high-z objects. Hirashita et al. (2005, hereafter H05) calculate the extinction curve based on the dust production calculation by N03. They also reproduce the extinction curve of SDSS
J1048+4637 by using the dust production in SNe II, although thedust composition and size distribution are different from those of
Todini & Ferrara (2001). Recently, Nozawa et al. (2007, hereafterN07) have treated the dust destruction by the reverse shock as done
by Bianchi & Schneider (2007), but considering the motion of dust
relative to gas caused by the drag force and the destruction of dust in
the radiative phase as well as in the non-radiative phase of supernova
remnants. Then, they show that the size distribution of grains supplied in the ISM is strongly modified by the reverse shock. Grains
smaller than ∼0.02 μm are efficiently destroyed if the ambient hydrogen number density is larger than 0.1 cm−3 . Thus, it is importantto re-examine the consistency between the observed extinction curve
and the reverse shock destruction.
In this paper, we calculate the extinction curves based on the
dust properties calculated by N07, who have focused on the effectof reverse shock destruction in SNe. Then, we compare the resultswith observed extinction curves at high z. This paper is organized asfollows. First, we describe our theoretical treatment to calculate theextinction curves of SN II and PISN dust in Section 2. We show andexamine our results in Section 3. We discuss our results from theobservational viewpoint in Section 4, and finally give the conclusionof this paper in Section 5.

struction by N07. By using the results of N07, the extinction curves
are calculated by the same method as in H05. The outline of ourcalculation is reviewed as follows.
2.1 Dust production and destruction in SNe II and PISNe
N03 calculate the dust composition and size distribution in the ejecta
of Pop III SNe II and PISNe based on the supernova model of Umeda& Nomoto (2002), carefully treating the radial density profile andthe temperature evolution. As mentioned in H05, the resulting graincomposition and size distribution are not sensitive to the metallicity of progenitor (N03). Thus, the assumption of zero-metallicity
is not essential in this paper, and our results can be applicable tometal-enriched systems. Since it is still uncertain how efficiently
the mixing of atoms within SNe occurs, N03 treat two extreme
cases for the mixing of elements: one is the unmixed case in which
the original onion-like structure of elements is preserved, and theother is the mixed case in which the elements are uniformly mixed
within the helium core. They show that the formed dust species depend largely on the mixing of seed elements within SNe, because
the dominant reactions change depending on the ratio of available
elements. The formed grain species in the calculation of N03 arelisted in Table 1.
In the unmixed ejecta, a variety of grain species (Si, Fe, Mg2 SiO4 ,MgSiO3 , MgO, Al2 O3 , SiO2 , FeS and C) condense, while in themixed ejecta, only oxide grains (SiO2 , MgSiO3 , Mg2 SiO4 , Al2 O3
and Fe3 O4 ) form. The species are summarized in Table 1. Based on
the results in N03, N07 treat the dust destruction by the reverse shockin the supernova remnant. They find that small-sized grains suffer
dust destruction by the reverse shock and that the final grain-size
distribution is biased to larger grains than the original distribution
calculated by N03. We adopt their results as the properties of grains
supplied to the interstellar space. Following H05, we adopt the representative progenitor mass of SNe II as 20 M and that of PISNe as
170 M . We also investigate the mixed and unmixed cases. Therefore, we treat four cases:(i) mixed SNe II;(ii) unmixed SNe II;(iii) mixed PISNe andTable 1. Summary of grain species.
Species

Conditiona

Referencesb

Density (δ j )(g cm−3 )

C
Si
SiO2
Fe
FeS
Fe3 O4
Al2 O3MgO
MgSiO3Mg2 SiO4

u
u
m/u
u
u
m
m/u
u
m/u
m/u

1
2
3
4
4
5
6
7
8
4

2.28
2.34
2.66
7.95
4.87
5.25
4.01
3.59
3.20
3.23

2 MODELa The classifications ‘m’, ‘u’ and ‘m/u’ mean that the species is formed in

We derive the theoretical extinction curves of dust grains producedin SNe II and PISNe, and subsequently destroyed by the reverse
shock. Those grains are considered to be supplied in the interstellar
spaces. The grain composition and size distribution in SNe before
the destruction are calculated by N03, whose results are adopted
as the initial conditions for the calculations of reverse shock de-mixed, unmixed and both SNe, respectively.
b References for optical constants: (1) Edo (1983); (2) Piller (1985);(3) Philipp (1985); (4) Semenov et al. (2003); (5) A. Triaud andH. Mutschke (private communication, and see http://www.astro.unijena.de/Laboratory/OCDB/soxsul.html); (6) Toon, Pollack & Khare (1976);(7) Roessler & Huffman (1991); (8) Semenov et al. (2003) (The opticalconstants of Mg2 SiO4 are used for λ  0.3 μm).

C 2008 The Authors. Journal compilation 
C 2008 RAS, MNRAS 384, 1725–1732

Flattened extinction curves

1727

All the formulation and the results can be seen in N03 and N07. The
grains are assumed to be homogeneous and spherical.

at wavelength λ, and λ0 is a reference wavelength). The extinction in units of magnitude is proportional to the optical depth as
Aλ,j = 1.086τ λ,j , where Aλ,j is the extinction of species j in units ofmagnitude as a function of λ. The total extinction Aλ is calculated
by summing Aλ,j for all the concerning species:

2.2 Optical constants and extinction curves

Aλ =(iv) unmixed PISNe.

In order to calculate extinction curves, the optical constants of grains
are necessary. We adopt the references listed in Table 1 for the
optical constants. Here, we only explain the difference from H05.
The optical constants are updated for Fe3 O4 . For MgSiO3 , we adopt
the optical constants of Mg2 SiO4 at λ  0.3 μm, where the currently
available experimental data are relatively poor (Dorschner et al.
1995). For Si and SiO2 , we adopt the optical constants for amorphous
instead of crystal since the grains rapidly grow in SNe. Subsequent
sputtering due to the reverse shock may also tend to destroy crystal
structures and to form more complicated amorphous solids. The
infrared broad feature at λ  21 μm is also better explained byamorphous SiO2 than by crystal SiO2 (Rho et al. 2007). We discuss
the uncertainty in the assumed optical constants in Appendix A.
By using those optical constants, we calculate the absorption andscattering cross-sections of homogeneous spherical grains with various sizes based on the Mie theory (Bohren & Huffman 1983). Then,the opacity of grain j (j denotes a grain species) as a function of
wavelength, τ λ, j , is calculated by weighting the cross-sections according to the size distribution. The extinction curve is presented
in the form of Aλ /Aλ0 (Aλ is the extinction in units of magnitudeAλ, j .

(1)j

For more details, see H05. Since we normalize the extinction at a
certain wavelength λ0 , only relative values of τ λ,j are important.
3 R E S U LT S
3.1 Extinction curves after the reverse shock destruction
As shown in N07, the final size distribution of grains after the reverse
shock destruction is sensitive to the density of the ambient ISM.
Here, we start from the results for nH = 1 cm−3 , where nH is thehydrogen number density in the ambient medium, to examine theeffect of grain destruction on the extinction curve. In Fig. 1, weshow the resulting extinction curves of the four cases in Section 2.1.
The contribution of each species is also shown. We normalize theextinction to AV (i.e. λ0 = 0.55 μm).
The extinction curves of dust produced by the mixed SNe II andPISNe are dominated by SiO2 (Figs 1a and c; in the PISN case, only
the contribution from SiO2 appears, and the total extinction curveis identical to the extinction curve of SiO2 ). The extinction curve

Figure 1. Extinction curves of grains produced in (a) the mixed ejecta with the progenitor of 20 M , (b) the unmixed ejecta with the progenitor of 20 M , (c)the mixed ejecta with the progenitor of 170 M and (d) the unmixed ejecta with the progenitor of 170 M . The ambient hydrogen number density is assumed
to be nH = 1 cm−3 . The extinction is normalized to the value at λ = 0.55 μm. The correspondence between the species and the lines is shown in each panel.
Note that some of the species are almost completely destroyed and do not appear on the figures and that in Panel (c), only SiO2 contributes to the total extinction
curve.
C 2008 The Authors. Journal compilation 
C 2008 RAS, MNRAS 384, 1725–1732

1728

H. Hirashita et al.

is flatter than that without destruction because the reverse shock
efficiently destroys small grains and the mean grain size becomeslarger.
The extinction curve for the unmixed SNe II (Fig. 1b) is dominated by Si and C. However, as shown in H05, the extinction curve
without reverse shock destruction is dominated by Mg2 SiO4 and
FeS for λ  0.5 μm and by Si for λ  0.5 μm. Since Si and C grains
are larger than the other species, they survive the reverse shock morethan the others. For the same reason, the extinction curve of unmixed
PISNe is dominated by Si. Also for the unmixed SNe II and PISNe,
the extinction curves of grains after the reverse shock destruction
are flatter, since small-sized grains are selectively destroyed and themean size of the grains becomes large.

Section 4, our results are compared with high-z data of extinction
curve.
Bianchi & Schneider (2007) also state that the extinction curve
becomes flatter, although they start from a different dust formation
model based on Todini & Ferrara (2001). The differences between
Bianchi & Schneider (2007) and the present work are partly due tothe differences in optical constants: amorphous carbon is responsible for most of the extinction in their work. Furthermore, theirresults show more survival of small grains than those of N07. As
mentioned in N07, the difference comes from the treatment of grain
motion: in N07, the trap of grains in a hot and dense zone between
forward and reverse shocks is properly treated, and this effect enhances the destruction of small-sized grains. Thus, our results show
flatter extinction curves than those of Bianchi & Schneider (2007)
especially when the ambient gas density is large.

3.2 Dependence on the ambient medium density
As shown by N07, the efficiency of the reverse shock destruction issensitive to the density of the ambient medium. Here, we investigate
the variation of the extinction curve for various ambient densities.
N07 have examined three cases for the ambient hydrogen number
density: nH = 0.1, 1 and 10 cm−3 . N07 show that the grains arealmost completely destroyed for nH = 10 cm−3 . Thus, we calculate
the cases for nH = 0.1 and 1 cm−3 . For comparison, we also show
the results without the reverse shock destruction (this case is called
non-destruction case). For the details of the non-destruction case,see N03 and H05. The results are shown in Fig. 2. As expected,
the extinction curve becomes flatter for a larger ambient density
because the destruction efficiency of small-sized grains is larger. In

4 O B S E RVAT I O N A L D I S C U S S I O N
4.1 Comparison with high-z data
H05 show that the dust production model of the unmixed SNe II in
N03 is consistent with the extinction curve of SDSS J1048+4637.
However, it is crucial to compare our new results including thereverse shock destruction with SDSS J1048+4637. In particular,
we may obtain constraints on the ambient gas density as well as theprogenitors. We compare our results with the restframe ultraviolet(UV) extinction curve of SDSS J1048+4637. The plausible range

Figure 2. Extinction curves of grains for various ambient hydrogen number densities (nH = 1 and 0.1 cm−3 for the solid and dashed lines, respectively). The
case without the reverse shock destruction (non-destruction case) is also shown in each panel (the dashed line). The progenitor model in each panel is the sameas that in Fig. 1.
C 2008 The Authors. Journal compilation 
C 2008 RAS, MNRAS 384, 1725–1732

Flattened extinction curves

1729

Figure 3. Extinction curves normalized at λ = 0.3 μm. The same theoretical curves as those in Fig. 2 are plotted. The shaded area in each panel shows therange observationally derived by Maiolino et al. (2004b) for SDSS J1048+4637 at z = 6.2.

derived by Maiolino et al. (2004b) is shown by the shaded areas inFig. 3.
In each panel of Fig. 3, we show the theoretical extinction curves
calculated for various ambient hydrogen number densities (sameas Fig. 2 but normalized to the extinction at λ = 0.3 μm, i.e.
λ0 = 0.3 μm). We also show the results of the non-destruction case.
Because of the variation caused by the destruction, various typesof progenitors may be allowed. For example, the mixed SNe II are
consistent with the observed extinction curve if nH ∼ 1 cm−3 . In allcases, the ambient number density nH  1 cm−3 produces too flat
extinction curves to be consistent with the data.

4.2 Ambient density around SNe
In the previous section, we have shown that the extinction curves
are sensitive to the ambient density of SNe. Thus, it is important toconstrain the density first. Unfortunately, there is no direct observational constraint on the gas density in SDSS J1048+4637.
It is rather interesting to point out that the extinction curves fornH  0.1 cm−3 of the unmixed SNe II are quite consistent with theextinction curves of SDSS J1048+4637. The mixed SNe II also
reproduce the observational extinction curve quite well if the ambient hydrogen number density is ∼1 cm−3 . The extinction curves of
PISNe are too flat for nH  1 cm−3 . Considering the uncertainty inthe observational data, however, the extinction curves of PISNe are
not rejected for nH ∼ 0.1–1 cm−3 .

Theoretically, it is possible to examine the density evolution
around the progenitors of SNe. Kitayama et al. (2004) show thatin small objects whose typical halo mass is ∼106 M , the entire
gas cloud is completely swept by the ionization front, and the dynamical expansion of the ionized region reduces the ambient density
down to nH  1 cm−3 . On the contrary, in more massive objects, theevacuation of the gas around a massive star does not efficiently occur
and the final gas density is much higher. However, if we consider
three-dimensional complex structure of ISM, the density around a
massive star is hard to predict theoretically. Thus, at this moment,a direct constraint on the gas density in SDSS J1048+4637 by using, for example, excitation states of molecular or atomic lines isdesired.
In summary, the current observational extinction curve at z ∼ 6 canbe explained by the hypothesis that dust is produced by SNe II and/or
PISNe, and destroyed subsequently by reverse shocks. In addition,
the results in this paper newly propose that the ambient density
should be less than ∼1 cm−3 , since the reverse shock destruction
flattens the extinction curve too much if nH  1 cm−3 .

4.3 Flat extinction curves at high z?
As shown in Section 3, a flat extinction curve is naturally produced
by reverse shock destruction in SNe. At z > 5, where it is probablethat SNe II or PISNe predominantly supply dust grains, it is worth
investigating possibility that extinction curves are flat.


C 2008 The Authors. Journal compilation 
C 2008 RAS, MNRAS 384, 1725–1732

1730

H. Hirashita et al.

Indeed, there are some pieces of supporting evidence for flat
extinction curves at z > 5. Among the sample in Maiolino et al.
(2004a), two BAL quasars, SDSS J1044−0125 at z = 5.8 andSDSS J0756+4104 at z = 5.1, show no reddening but are detected
at submm (Priddey et al. 2003). The submm observations yield dust
masses in the range 108 –109 M for those two quasars. The absenceof reddening and the presence of submm emission (dust emission)
may be contradictory, but they are consistent if we assume a flat
extinction curve. An extremely small reddening of a BAL quasar
SDSS 1605−0112 at z = 4.9 (Maiolino et al. 2004a) may also be
attributed to a flat extinction curve. In the future, extinction curvesof high-z submm samples (Bertoldi et al. 2003; Priddey et al. 2003;
Robson et al. 2004; Beelen et al. 2006) in comparison with theoretical modelling of submm emission (e.g. Takeuchi et al. 2003, 2005)
enable us to further investigate the properties and origins of dust
grains in the early Universe.
Also at lower z (5), it may be worth to consider possibilityof flat extinction curves. Direct indications of dust at z  5 come,for example, from the reddening of background quasars (Fall, Pei& McMahon 1989; Zuo et al. 1997). The depletion of heavy elements in quasar absorption line systems, especially damped Lyα
clouds (DLAs), also supports the presence of dust in distant systems (e.g. Pettini et al. 1994; Vladilo 2002; Ledoux, Petitjean &Srianand 2003). However, there are some observational results thatshow no significant reddening of DLAs (Murphy & Liske 2004;
Ellison, Hall & Lira 2005). The flat extinction curve proposed above
has importance that the lack of reddening does not necessarily mean
the absence of dust. Other than DLAs, some objects whose extinction curves are derived by γ -ray bursts (Chen, Li & Wei 2006) orby gravitational lensing (e.g. Falco et al. 1999; Muñoz et al. 2004)
seem to have a flat extinction curve in UV.

4.4 Possibility of subsequent steepening
Dust grains supplied into interstellar spaces suffer various processes
that modify their size distribution. One of such processes is the destruction by forward shocks of supernova remnants. The dust destruction by forward shocks has already been examined by Nozawa,
Kozasa & Habe (2006). Here, we have examined the effect of forward shock destruction and have confirmed that one passage of asupernova forward shock has negligible influence on the extinction curve. This is because after an efficient sputtering in supernova
remnants, the opacity is already dominated by large grains which
are hard to destroy. However, shattering may increase the numberof small-sized grains (Borkowski & Dwek 1995; Jones, Tielens &Hollenbach 1996), steepening the extinction curve. Quantitative
study of the effect of shattering on the extinction curve is left for
future work.

5 CONCLUSION
We have theoretically investigated the extinction curves of grains
produced in SNe II and PISNe. Since at high z(>5), low-mass stars
cannot be dominant sources for dust grains, SNe II and PISNe,
whose progenitors are massive stars with short lifetimes, can govern
the dust production. While our previous works (N03 and H05) did
not consider the reverse shock destruction induced by a collision
with ambient ISM, we adopt the composition and size distribution ofgrains of N07, who take into account the reverse shock destruction.
We have found that the extinction curve is sensitive to the ambient gas density around SNe, since the efficiency of reverse shock

destruction is largely dependent on it. The destruction is significant
for small-sized grains, leading to a flat extinction curve in the opticaland UV. Such a large ambient density as nH  1 cm−3 produces tooflat an extinction curve to be consistent with the observed extinction
curve for SDSS J1048+4637 at z = 6.2. Although the extinction
curve is highly sensitive to the ambient density, the hypothesis thatthe dust is predominantly formed by SNe at z ∼ 6 is still allowed
if nH is smaller than 1 cm−3 . For further quantification, the ambientdensity should be constrained by some other methods.
It is worth noting that a flat extinction curve produced by effective
reverse shock destruction may explain the absence of reddeningof systems in which dust is known to be present by FIR/submm
emission or by depletion of heavy elements.

AC K N OW L E D G M E N T S
We thank R. Maiolino and his collaborators for kindly providing uswith their data on the extinction curve of SDSS J1048+4637. We
are also grateful to S. Bianchi for helpful comments that improved
this paper very much. HH has been supported by Grants-in-Aid for
Scientific Research of the Ministry of Education, Culture, Sports,
Science and Technology (MEXT) of Japan (Nos. 18026002 and
18740097). TN also has been supported by the same grants (Nos.
18104003 and 19740094). TTT has been supported by the Special
Coordination Funds for Promotion Science and Technology (SCF)
commissioned by the MEXT (MEXT) of Japan. We fully utilized
the NASA’s Astrophysics Data System Abstract Service (ADS).

REFERENCES
Beelen A., Cox P., Benford D. J., Dowell C. D., Kovács A., Bertoldi F.,
Omont A., Carilli C. L., 2006, ApJ, 642, 694
Bertoldi F., Carilli C. L., Cox P., Fan X., Strauss M. A., Beelen A., Omont
A., Zylka R., 2003, A&A, 406, L55
Bianchi S., Schneider R., 2007, MNRAS, 378, 973
Bohren C. F., Huffman D. R., 1983, Absorption and Scattering of Light by
Small Particles. Wiley, New York
Borkowski K. J., Dwek E., 1995, ApJ, 454, 254
Bromm V., Larson R. B., 2004, ARA&A, 42, 79
Cazaux S., Tielens A. G. G. M., 2004, ApJ, 604, 222
Chen S. L., Li A., Wei D. M., 2006, ApJ, 647, L13
Dorschner J., Begemann B., Henning Th., Jaeger C., Mutschke H., 1995,
A&A, 300, 503
Dunne L., Eales S., Ivison R., Morgan H., Edmunds M., 2003, Nat, 424, 285
Dwek E., Galliano F., Jones A. P., 2007, ApJ, 662, 927
Edo O., 1983, PhD Dissertation, Univ. Arizona
Edward D. F., 1985, in Palik E. D., ed., Handbook of Optical Constants ofSolids. Academic Press, San Diego, USA, p. 547
Ellison S. L., Hall P. B., Lira P., 2005, AJ, 130, 1345
Falco E. E. et al., 1999, ApJ, 523, 617
Fall S. M., Pei Y. C., McMahon R. G., 1989, ApJ, 341, L5
Fryer C. K., Woosley S. E., Heger A., 2001, ApJ, 550, 372
Gehrz R. D., 1989, in Allamandola L. J., Tielens A. G. G. M., eds, Proc.
IAU Symp. 135, Interstellar Dust. Kluwer, Dordrecht, p. 445
Heger A., Woosley S. E., 2002, ApJ, 567, 532
Hines D. C. et al., 2004, ApJS, 154, 290
Hirashita H., Ferrara A., 2002, MNRAS, 337, 921
Hirashita H., Nozawa T., Kozasa T., Ishii T. T., Takeuchi T. T., 2005,
MNRAS, 357, 1077 (H05)
Jones A. P., Tielens A. G. G. M., Hollenbach D. J., 1996, ApJ, 469, 740
Kitayama T., Yoshida N., Susa H., Umemura M., 2004, ApJ, 613, 631
Kozasa T., Hasegawa H., Nomoto K., 1989, ApJ, 344, 325
Kozasa T., Hasegawa H., Nomoto K., 1991, A&A, 249, 474
Ledoux C., Petitjean P., Srianand R., 2003, MNRAS, 346, 209

C 2008 The Authors. Journal compilation 
C 2008 RAS, MNRAS 384, 1725–1732

Flattened extinction curves
Maiolino R., Oliva E., Ghinassi F., Pedani M., Mannucci F., Mujica R.,
Juarez Y., 2004a, A&A, 420, 889
Maiolino R., Schneider R., Oliva E., Bianchi S., Ferrara A., Mannucci F.,
Pedani M., Roca Sogorb M., 2004b, Nat, 431, 533
Mathis J. S., 1990, ARA&A, 28, 37
Meikle W. P. S. et al., 2007, ApJ, 665, 608
Morgan H. L., Dunne L., Eales S. A., Ivison R. J., Edmunds M. G., 2003,
ApJ, 597, L33
Moseley S. H., Dwek E., Glaccum W., Graham J. R., Loewenstein R. F.,
1989, Nat, 340, 697
Muñoz J. A., Falco E. E., Kochanek C. S., McLeod B. A., Mediavilla E.,
2004, ApJ, 605, 614
Murphy M. T., Liske J., 2004, MNRAS, 354, L31
Nakamura F., Umemura M., 2001, ApJ, 548, 19
Nozawa T., Kozasa T., Umeda H., Maeda K., Nomoto K., 2003, ApJ, 598,
785 (N03)
Nozawa T., Kozasa T., Habe A., 2006, ApJ, 648, 435
Nozawa T., Kozasa T., Habe A., Dwek E., Umeda H., Tominaga N., Maeda
K., Nomoto K., 2007, ApJ, 666, 955 (N07)
Omukai K., Tsuribe T., Schneider R., Ferrara A., 2005, ApJ, 626, 627
Pettini M. H., Smith L. J., Hunstead R. W., King D. L., 1994, ApJ, 426, 79
Philipp H. R., 1985, in Palik E. D., ed., Handbook of Optical Constants ofSolids. Academic Press, San Diego, p. 719
Piller H., 1985, in Palik E. D., ed., Handbook of Optical Constants of Solids.
Academic Press, San Diego, p. 571
Priddey R. S., Isaak K. G., McMahon R. G., Robson E. I., Pearson C. P.,
2003, MNRAS, 344, L74
Rho J. et al., 2008, ApJ, 673, 271
Robson I., Priddey R. S., Isaak K. G., McMahon R. G., 2004, MNRAS, 351,
L29
Roessler D. M., Huffman D. R., 1991, in Palik E. D., ed., Handbook of
Optical Constants of Solids II. Academic Press, San Diego, p. 919
Schneider R., Ferrara A., Salvaterra R., Omukai K., Bromm V., 2003, Nat,422, 869
Schneider R., Ferrara A., Salvaterra R., 2004, MNRAS, 351, 1379
Semenov D., Henning Th., Helling C., Ilgner M., Sedlmayr E., 2003, A&A,
410, 611
Stratta G., Maiolino R., Fiore F., D’Elia V., 2007, ApJ, 661, L9
Sugerman B. E. K. et al., 2006, Sci, 313, 196

1731

Takeuchi T. T., Hirashita H., Ishii T. T., Hunt L. K., Ferrara A., 2003,
MNRAS, 43, 839
Takeuchi T. T., Ishii T. T., Nozawa T., Kozasa T., Hirashita H., 2005,
MNRAS, 362, 592
Todini P., Ferrara A., 2001, MNRAS, 325, 726
Toon O. B., Pollack J. B., Khare B. N., 1976, J. Geophys. Res., 81, 5733
Umeda H., Nomoto K., 2002, ApJ, 565, 385
Vladilo G., 2002, A&A, 391, 407
Willott C. J. et al., 2007, AJ, 134, 2435
Zuo L., Beaver E. A., Burbidge E. M., Cohen R. D., Junkkarinen V. T., Lyons
R. W., 1997, ApJ, 477, 568

A P P E N D I X A : C O M PA R I S O N B E T W E E N
C RY S TA L A N D A M O R P H O U S G R A I N S
As mentioned in Section 2.2, the optical constants of crystal Si
and SiO2 are available, while we have used those of amorphous Si
and SiO2 . Since those species dominate the extinction curves, it isimportant to examine the uncertainty caused by assumed material
states. The optical constants of crystal Si and SiO2 are taken from
Edward (1985) and Philipp (1985), respectively. As a representative,
we examine the case of nH = 1 cm−3 . In the mixed and unmixed
cases, the difference between crystal and amorphous is examined
for the dominant species, SiO2 and Si, respectively.
In Figs A1(a) and (b), we show the extinction curves withthe progenitor masses of 20 and 170 M , respectively, for themixed SNe. From those figures, we observe that the overall trend
is similar between the two species of SiO2 . Thus, we conclude
that the two species of SiO2 are indistinguishable in the extinction curve within the uncertainty in the current observational
data.
In Fig. A2, we make the same kind of comparison for unmixed
SNe, but the difference between crystal and amorphous species is
examined for Si. As can be seen from the figure, the difference issmaller than the uncertainty in the observational data.

Figure A1. The same as Fig. 3 for the mixed SN II and PISN for nH = 1 cm−3 (solid lines in panels a and b, respectively). For SiO2 , we adopt the opticalconstants of amorphous and crystal solids for the solid and dotted lines. For other species, the same optical constants as those in Fig. 3 are applied.


C 2008 The Authors. Journal compilation 
C 2008 RAS, MNRAS 384, 1725–1732

1732

H. Hirashita et al.

Figure A2. The same as Fig. 3 for the unmixed SN II and PISN for nH = 1 cm−3 (solid lines in panels a and b, respectively). For Si, we adopt the opticalconstants of amorphous and crystal solids for the solid and dotted lines. For other species, the same optical constants as those in Fig. 3 are applied.

This paper has been typeset from a TEX/LATEX file prepared by the author.

C 2008 The Authors. Journal compilation 
C 2008 RAS, MNRAS 384, 1725–1732