Mon. Not. R. Astron. Soc. 418, 625–637 (2011)

doi:10.1111/j.1365-2966.2011.19512.x

Extinction law in ultraluminous infrared galaxies at z ∼ 1
T. Shimizu,1 K. Kawara,1 H. Sameshima,1 N. Ienaka,1 T. Nozawa2 and T. Kozasa3
1 Institute of Astronomy, The University of Tokyo, Osawa 2-21-1, Mitaka, Tokyo 181-0015, Japan
2 Institute for the Physics and Mathematics of the Universe, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8568, Japan
3 Department of Cosmosciences, Hokkaido University, Sapporo 060-0810, Japan

Accepted 2011 July 26. Received 2011 July 26; in original form 2011 May 5

ABSTRACTWe analyse the multiwavelength photometric and spectroscopic data of 12 ultraluminous
infrared galaxies (ULIRGs) at z ∼ 1 and compare them with models of stars and dust inorder to study the extinction law and star formation in young infrared (IR) galaxies. Fiveextinction curves, namely the Milky Way (MW), the pseudo-MW which is MW-like without
the 2175 Å feature, the Calzetti and two supernova (SN) dust curves are applied to the databy combining with various dust distributions, namely the uniform dust screen, the clumpy
dust screen, the internal dust geometry, and the composite geometry with a combination ofdust screen and internal dust. Employing a minimum χ 2 method, we find that the foregrounddust screen geometry, especially combined with the 8–40 M SN extinction curve, provides
a good approximation to the real dust geometry, whereas internal dust is only significant in
two galaxies. The SN extinction curves, which are flatter than the others, reproduce the dataof eight (67 per cent) galaxies better. Dust masses are estimated to be in excess of ∼108 M .
The inferred ages of the galaxies are small, eight of which range from 10 to 650 Myr. The
SN-origin dust is the most plausible to account for the vast amount of dust masses and theflat slope of the observed extinction law. The inferred dust mass per SN ranges from 0.01 to
0.4 M per SN.
Key words: supernovae: general – dust, extinction – galaxies: evolution – galaxies: ISM –galaxies: starburst – infrared: galaxies.

1 I N T RO D U C T I O N
Recent developments in far-infrared (FIR) and submillimetre astronomy have revealed new populations of galaxies associated withthermal dust emission, such as dusty quasars and infrared galaxies. Thermal dust emission detected in quasars and galaxies at highredshifts exhibits inferred dust mass in excess of ∼108 M . Such avast amount of dust observed at z  6 (Bertoldi et al. 2003; Robson
et al. 2004; Beelen et al. 2006) strongly suggests that the dust has
been condensed in the ejecta of core-collapsed supernovae (SNe II)promptly after the onset of the initial star formation. Asymptotic
giant branch (AGB) stars are known to be the major source of dust in
the present-day Universe. However, the importance of AGB stars at
high redshifts is in controversy, because they inject dust grains into
the interstellar medium (ISM) only after their progenitor stars have
evolved off the main sequence. While a delay time of 500 Myr
since their formation has been suggested (e.g. Dwek 1998), Valiante
et al. (2009) proposed that AGB stars can dominate dust production in a delay time of 150 Myr if the starburst is instantaneous.
 E-mail: tshimizu@ioa.s.u-tokyo.ac.jp (TS); kkawara@ioa.s.u-tokyo.ac.jp(KK)C 2011 The Authors
C 2011 RASMonthly Notices of the Royal Astronomical Society Michałowski et al. (2010) pointed out that AGB stars are not efficient enough to form dust in dusty quasars at z > 5, whereas SNe II
may be able to account for the dust, and underlined the importanceof dust grain growth in the ISM.
Quasars have been frequently used to study the extinction law
at high redshifts. This is because of their simple dust geometry, inwhich the central point-like emitting source is surrounded by dust
grains which are physically separated from the source itself. This isanalogous to the classical configuration assumed when dereddening
single stars. There is a line of evidence that active galactic nuclei(AGNs) have extinction curves that differ from those observed in the
Milky Way (MW) and Large and Small Magellanic Clouds (LMCand SMC). Gaskell et al. (2004) analysed a large sample of AGNs
and found indications of a very flat extinction curve in ultraviolet(UV). On the other hand, exploring large samples of quasars fromthe Sloan Digital Sky Survey (SDSS), Richards et al. (2003) andHopkins et al. (2004) found that the extinction law in quasars at
z < 2.2 is described by SMC reddening but neither by LMC and
SMC reddening nor by that found in the Gaskell et al. (2004) sample.
Recently, Gallerani et al. (2010) proposed that quasars at z = 3.9–6.4
have reddening that deviates from that of the SMC with a tendency
to flatten at λ  2000 Å. Maiolino et al. (2004) found that SDSS
J1048+4647, a broad absorption line quasar (BALQSO) at z = 6.2,

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requires a flat extinction curve which is quite different from thoseobserved in the MW, LMC and SMC, but in excellent agreementwith SN extinction curves by Todini & Ferrara (2001).
Although it is reasonable to expect that the extinction law inyoung galaxies would be dominated by SN-condensed dust, thecomplications introduced by dust geometries have hampered thisline of studies; the attenuation of extended starlight by dust depends not only on the optical properties of dust but also on the
distribution geometry of the dust. Calzetti (2001) derived the empirical extinction law in local starbursts and blue compact galaxies,
assuming that the dust geometry is described in a foreground screen,i.e. an apparent attenuation of starlight to be e−τν . If a dust geometry in their galaxies is indeed a foreground screen, the slope (i.e.
wavelength dependence) of the extinction curve (i.e. the opticaldepth τ ν ) is significantly flatter than those observed in the MW,
LMC and SMC. The spectral energy distribution (SED) and spectroscopic data of a young, ultraluminous infrared galaxy (ULIRG)1
at z ∼ 1 were analysed by Kawara et al. (2011), who found thatthe data require a flat extinction curve and the dust geometry of aforeground dust screen, which would result in a better agreementwith the extinction curve synthesized from SN-condensed dust byHirashita et al. (2005) than those observed in local starbursts, MW,
LMC and SMC.
The slope of the extinction curve is expected to reflect the sites ofdust formation and the subsequent processing in the ISM. The extinction curves can be ordered as the SMC, LMC, MW and Calzetti
curves from the steepest to the flattest. The synthetic extinction
curves of newly condensed dust grains in SN ejecta before the ISM
reprocessing (hereafter called original SN extinction curves) areflatter than the Calzetti curve (Todini & Ferrara 2001; Nozawa et al.
2003; Maiolino et al. 2004; Hirashita et al. 2005; see also fig. 3
in Kawara et al. 2011). Then, the bulk of dust grains condensed
in the ejecta is destroyed through the passage of the reverse shock(Bianchi & Schneider 2007; Nozawa et al. 2007; Hirashita et al.
2008). Finally, grains that survive the reverses shock are shatteredin the warm ionized ISM (Hirashita et al. 2010). None the less,the final SN extinction curves, after taking into account the reverse
shock and shattering, are expected to have a slope as flat as thoseof the original extinction curves. The shattering may also be important in old galaxies such as MW, LMC and SMC, where AGB
stars are dominant sources of dust production, because some observations (Groenewegen 1997; Gauger et al. 1999) suggest AGB
stars form large grains. Dust grain growth in the ISM would be
efficient in infrared galaxies where there must be many molecular
clouds near SN remnants, and it is suggested that the dust mass inthe high-redshift quasars is dominated by grain growth in the ISM(Dwek 1998; Draine 2009; Michałowski et al. 2010; Valiante et al.
2011). It seems that this process results in flat extinction curves inthe sense that the larger grains show the flatter extinction curve.
However, the extinction laws found in the high-redshift quasars andlocal starbursts are flatter than those found in the MW for which
Draine (2009) attributes the bulk of the dust mass to the growth ofgrains in the ISM.
As discussed so far, z < 2.2 quasars show a striking contrast in theslopes of the extinction curves against the z ∼ 1 ULIRG and higher

1 Infrared galaxies are classified according to bolometric infrared luminosity

LIR (8–1000 µm); LIR > 1011 L as luminous infrared galaxies (LIRGs),
LIR > 1012 L as ultraluminous infrared galaxies (ULIRGs), and LIR >1013 L as hyperluminous infrared galaxies (HyLIRGs) (Sanders & Mirabel1996).

redshift quasars. In this paper, we explore this issue by expanding
our previous work on a single young ULIRG (Kawara et al. 2011)
to 12 young ULIRGs at z ∼ 1.
2 DATAThe sample consists of 12 infrared galaxies at z = 0.85–1.44. The
redshifts and data sources of our 12 galaxies are shown in Table 1.
They are SST J1604+4304, HR10 (ERO J164502+4626.4), and 10
galaxies found in the Cosmological Evolution Survey (COSMOS)
field. We have searched archives and the literature for those galaxies
which meet the following criteria: (1) the FIR emission is detected;(2) the optical spectrum indicates a redshift of ∼1, and gaseousemission lines such as [O II]λ3727 and/or stellar absorption lines
such as Ca H/K and H I absorption lines were detected; (3) broadband photometry has been done from the UV to mid-infrared; (4)there is no contamination from foreground galaxies; (5) the bolometric luminosity is dominated by the undergoing star formation
with the criterion of fν (8 μm)/fν (4.5 μm) < 1.9 (Pope et al. 2008)
and no obvious evidence of emission caused by an AGN such as
X-ray emission. As a result, we have found these 12 galaxies all ofwhich are classified as starburst-dominated ULIRGs.
The data for SST J1604+4304 were taken from Kawara
et al. (2010) where the multiwavelength data covering the X-ray,
UV/optical, infrared and radio and the optical spectrum are given.
For HR10, Stern et al. (2006) compiled the multiwavelength datafrom the UV/optical to radio, and the optical spectrum (strictly
speaking, from 2750 to 3850 Å) is given in Dey et al. (1999).
The photometric and spectroscopic data for the 10 COSMOS
galaxies are available in the COSMOS archive at http://irsa.
ipac.caltech.edu/data/COSMOS/. Fig. 1 illustrates postage stamp
images of the COSMOS galaxies from u∗ to 70 μm. For full detailsof the observations of the COSMOS galaxies, we refer the reader toCapak et al. (2007) for optical to near-infrared imaging performedon the Hubble Space Telescope and ground-based telescopes including the Subaru 8.3-m telescope, the Kitt Peak National Observatory(KPNO) 4-m telescope, the Cerro Tololo Inter-American Observatory (CTIO) 4-m telescope, and the Canada–France–Hawaii (CFH)
3.6-m telescope; to Sanders et al. (2007) for the COSMOS Spitzer
Table 1. Sample galaxies at z ∼ 1.
No.

Name

Redshift

Reference

1
2
3
4
5
6
7
8
9
10
11
12

COSMOS J100121.29+023535.8
COSMOS J100125.12+024506.5
COSMOS J100158.31+023505.2
COSMOS J100143.83+015325.0
COSMOS J100021.79+014916.1
COSMOS J100030.12+020513.3
COSMOS J100123.22+021013.3
COSMOS J100100.22+021503.6
COSMOS J100008.36+022244.6
COSMOS J095910.21+022523.3
SST J1604+4304
HR10 (ERO J164502+4626.4)

0.850
0.980
1.021
1.066
0.995
0.894
0.850
0.893
1.093
1.026
1.135
1.44

1
1
1
1
1
1
1
1
1
1
2
3, 4

References: 1, Cosmos archive at http://irsa.ipac.caltech.edu:
2, Kawara et al. (2010); 3, Stern et al. (2006); 4, Dey et al. (1999).
COSMOS Photometry Catalog 2006 January:
S-COSMOS IRAC four-channel Photometry Catalog 2007 June;
S-COSMOS MIPS 24 µm Photometry Catalog 2008 October;
S-COSMOS MIPS 70 µm Photometry Catalog v3 2009 January;
COSMOS MAGELLAN Data Version 3.1 (spectroscopy);zCOSMOS data released in 2008 October (spectroscopy).
C 2011 The Authors, MNRAS 418, 625–637
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627

Figure 1. Postage stamp images of the 10 COSMOS galaxies. The size of each image is 4 × 4 arcsec2 for F814W to Ks, 10 × 10 arcsec2 for 3.6–8.0 µm,
20 × 20 arcsec2 for 24 µm, and 50 × 50 arcsec2 for 70 µm. North is up and east is to the left. Refer to Kawara et al. (2010) and Stern et al. (2006) for theimages of No. 11 (SST J1604+4304) and No. 12 (HR10), respectively.

survey (S-COSMOS); to Le Floc’h et al. (2009) for the 24-μm
observations; to Frayer et al. (2009) for the 70- and 160-μm observations; to Trump et al. (2009) for 5600–9200 Å spectroscopy on
the Magellan 6.5-m telescope; and to Lilly et al. (2007) for 5500–
9700 Å spectroscopy on the European Southern Observatory (ESO)
8-m Very Large Telescope (VLT).
For the COSMOS galaxies, the optical counterparts of FIR
sources were selected as follows. We first selected objects at z =0.8–1.21 in the spectroscopy catalogues and searched for the counterparts in the optical imaging data catalogues. If there is a single
object in the optical imaging data within an error circle radius of
0.2 arcsec from the spectroscopic position, we identified the spectroscopic object with the object in the optical imaging catalogues. We
then searched for the mid-infrared counterpart in the IRAC (3.6, 4.5,
5.6, 8.0 μm) catalogue. Again, if there is one IRAC object within
an error circle radius of 0.5 arcsec from the position of the optical,
spectroscopic object, we regard the IRAC object as optically identified. This process was repeated for the 24-μm counterpart withinC 2011 The Authors, MNRAS 418, 625–637
C 2011 RASMonthly Notices of the Royal Astronomical Society an error radius of 1.0 arcsec, and for the 70-μm counterpart within
4.0 arcsec. We found no 160-μm counterparts within 8.0 arcsec. As
a result, we found 10 starburst-dominated ULIRGs at z = 0.8–1.2.
Kartaltepe et al. (2010), applying more relaxed criteria than ours,
found 50 70-μm sources having spectroscopic data in the same field
and the same redshift range. Assuming that 70-μm sources with
>10 mJy are ULIRGs at z > 0.8, 25 of the 50 sources are ULIRGs
with spectroscopic data. They suggest that an AGN fraction is about
50 per cent, thus starburst-dominated ULIRGs are about 12, fairly
consistent with the number of ULIRGs in our sample.
Optical data were taken in many photometric bands for COSMOS galaxies. If we use all these data in the following analysis, theweight of the SED in the optical will overwhelm the other data. We
thus use u∗ taken on the CFH telescope; g+ , r+ , i+ , z+ on the Subaru
telescope; and Ks on the CTIO 4-m telescope. Aperture photometry
with a 3-arcsec diameter is given in the catalogue. We applied thecorrection to the total magnitude as described by Capak et al. (2007).
The aperture photometry with a 2.9-arcsec diameter given in the628

T. Shimizu et al.
Table 2. Optical and 2-µm photometry of the 10 COSMOS galaxies.
No.

u∗

g+

r+

i+

z+

Ks

1
2
3
4
5
6
7
8
9
10

0.530 ± 0.033
0.888 ± 0.048
0.096 ± 0.022
0.892 ± 0.052
2.20 ± 0.06
0.225 ± 0.023
2.07 ± 0.06
1.23 ± 0.05
1.10 ± 0.04
1.13 ± 0.04

0.924 ± 0.041
1.27 ± 0.05
0.164 ± 0.024
1.50 ± 0.07
2.51 ± 0.06
0.403 ± 0.003
3.22 ± 0.07
1.97 ± 0.06
1.26 ± 0.04
1.83 ± 0.05

3.04 ± 0.07
3.05 ± 0.07
0.656 ± 0.034
3.97 ± 0.09
5.10 ± 0.08
1.38 ± 0.05
6.50 ± 0.09
4.60 ± 0.09
2.13 ± 0.06
3.68 ± 0.07

8.43 ± 0.10
7.76 ± 0.11
1.95 ± 0.06
9.52 ± 0.14
9.46 ± 0.11
4.43 ± 0.08
12.6 ± 0.1
11.1 ± 0.1
4.03 ± 0.07
7.73 ± 0.10

14.2 ± 0.2
13.5 ± 0.2
3.78 ± 0.11
19.2 ± 0.2
13.8 ± 0.2
7.91 ± 0.13
18.4 ± 0.2
18.1 ± 0.2
6.98 ± 0.12
13.8 ± 0.2

62.6 ± 3.0
63.8 ± 2.9
38.0 ± 3.0
97.8 ± 4.6
44.0 ± 3.4
47.6 ± 2.9
49.3 ± 3.1
75.7 ± 3.5
30.8 ± 3.1
50.6 ± 3.0

Note. Total fluxes are given in the unit of µJy.
Table 3. Spitzer photometry of the 10 COSMOS galaxies.
No.

3.6 µm

4.5 µm

5.8 µm

8.0 µm

24 µm

70 µm

1
2
3
4
5
6
7
8
9
10

106 ± 0.2
89.6 ± 0.2
81.7 ± 0.2
128 ± 0.7
68.4 ± 0.2
79.0 ± 0.2
67.2 ± 0.2
93.0 ± 0.2
57.2 ± 0.5
91.2 ± 0.2

81.6 ± 0.3
73.1 ± 0.3
66.5 ± 0.3
111 ± 0.7
54.5 ± 0.3
62.1 ± 0.3
50.1 ± 0.3
69.8 ± 0.3
51.6 ± 0.5
71.3 ± 0.3

74.7 ± 1.1
66.0 ± 1.2
72.9 ± 1.2
78.6 ± 1.3
49.1 ± 1.2
50.7 ± 1.2
62.5 ± 1.1
68.9 ± 1.1
35.1 ± 1.2
46.5 ± 1.1

76.5 ± 2.8
58.9 ± 2.9
82.1 ± 3.0
87.9 ± 2.9
60.7 ± 2.8
62.6 ± 2.7
81.4 ± 2.8
56.4 ± 2.5
53.3 ± 2.7
53.4 ± 2.9

940 ± 252
797 ± 19635 ± 20780 ± 221000 ± 92
553 ± 161190 ± 256
849 ± 165
573 ± 179
590 ± 199

20900 ± 3300
11700 ± 2600
11100 ± 2600
11600 ± 2700
14200 ± 2800
14900 ± 2700
20800 ± 3100
9900 ± 2500
16100 ± 2300
7300 ± 1800

Note. Total fluxes are given in the unit of µJy.

S-COSMOS IRAC four-channel catalogue was converted to the total fluxes by applying correction factors of 0.90, 0.90, 0.84 and 0.73
for 3.6, 4.5, 5.8 and 8.0 μm, respectively (see README attachedto this catalogue). The total fluxes of the COSMOS galaxies are
summarized in Tables 2 and 3 in the units of μJy. The SEDs of
the 12 galaxies are plotted as a function of the rest wavelength in
Fig. 2.
The optical spectra of our 12 galaxies are illustrated in Fig. 3 alongwith the vertical lines showing the positions of the [O II]λ3727 emission line from H II regions and the stellar absorption lines, namely,
Mg II λ2798, Ca II H and K, Hζ and H. [O II]λ3727 indicates thepresence of OB stars, while the absorption lines are useful to measure the age of the relatively old stellar populations (Kawara et al.
2011). The equivalent widths of the lines are given in Table 4along with the D(Ca II) index. This index is defined as D(Ca II) =2 × EW(Ca II K)/[EW(Hζ )+EW(Ca II H + H)] (Kawara et al.
2010), where EW(Ca II K), EW(Hζ ) and EW(Ca II H + H) are theequivalent widths of Ca II K, Hζ and the blend of Ca II H and H,respectively.
Table 5 gives the 8–1000 μm luminosity LIR and the mass ofdust M d of the 12 sample galaxies. We obtained LIR by fitting theDale & Helou (2002) ULIRG template to the 70-μm data except
for SST J1604+4304 for which the 70- and 160-μm data were used
for fitting. Deriving FIR colours fν (160 μm)/fν (70 μm) of 70-μm
sources that are not detected at 160 μm from the stacking of the
160-μm data points, Kartaltepe et al. (2010) found that those notdetected at 160 μm have hotter FIR colours than those detected at
160 μm, and that the FIR colours of 70-μm sources not detected
at 160 μm scatter around the Dale & Helou (2002) ULIRG templateat z ∼ 1. It is thus appropriate to utilize this template to derive LIR
for those not detected at 160 μm. The typical uncertainty for LIR

using the 70 μm data is estimated to be ∼0.2 dex (Kartaltepe et al.
2010). SST J1604+4304 was re-analysed in the same way as theother galaxies. While the Arp 220 template was used to estimate
LIR and the dust temperature in our previous analysis (Kawara et al.
2011), we apply the Dale & Helou (2002) ULIRG template in thepresent analysis. In addition, we include a new term of the dust massin the minimum χ 2 method. The new results are quite consistent
with our previous results.
The dust mass was estimated using the formula of Md /fν =DL2 /[(1 = z)κνe Bνe (Td )], where f ν is the observed flux density at
frequency ν, νe = (1 + z)ν, DL is the luminosity distance to theemitter, Bνe (Td ) is the Planck function for T d the temperature ofdust at νe , and κνe is the absorption cross-section per unit dust massat νe . As can be seen in this formula, M d depends on the productκ ν Bν (T d ) ∝ ν β Bν (T d ) if κ ν ∝ ν β .
It is known that there is an anticorrelation between β and Td(Blain, Barnard & Chapman 2003; Bracco et al. 2011). This degeneracy may be due to the intrinsic properties of dust grains orapplication of a single-temperature model to the SEDs which average various temperatures along the line of sight (Bracco et al.
2011). Thus, when fitting a single-temperature model to the SED,
the resultant Td depends on β or the properties of the dust extinction
curves; the extinction curves we study here are the MW, pseudoMW, Calzetti, SN curves, as fully described in Section 3.1.2.
The dust temperatures cannot be directly derived from our data,
because of the lack of data longward of 160 μm. We thus estimatedT d by fitting to the Dale & Helou (2002) ULIRG template, resulting
in T d = 40.5 ± 9.3 for the SN dust with β  1.6 and T d = 37.0 ±8.9 for the MW dust with β  2; T d derived with the SN dust is
10 per cent higher than that with the MW dust. This temperature
difference is expected to result from the degeneracy between β and
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629

Figure 2. 0.1–100 µm SEDs of the 12 galaxies, illustrating νf ν (erg cm−2 s−1 ) as a function of rest wavelength (µm).

T d . Table 5 gives M d for the 8-40 M SN dust. M d in Table 5 should
be multiplied by 0.81 for the 8–30 M SN dust and 0.78 for the
MW dust. It is noted that M d is derived by using κνe at 80 μm which
is 44 cm2 g−1 for MW dust, 24 cm2 g−1 for 8–30 M SN dust, and20 cm2 g−1 for 8–40 M SN dust (see fig. 7 in Kawara et al. 2011).
3 A N A LY S I S
We take a similar approach as performed in our previous study.
Synthetic spectra of stellar populations reddened by various dust
models are applied to reproduce the data of the 12 sample galaxies.
For full details of this approach, we refer the reader to Kawara et al.
(2011) and references therein.
3.1 Dust
Our dust models are a combination of an optical properties of dust
and a geometry of the dust distribution.

3.1.1 Geometries of dust distribution
The attenuation produced by dust in front of an extended source
depends not only on the optical properties of dust grains, but also
on the geometry of spatial distribution of dust, especially whenstarlight is attenuated by a thick, clumpy dust layer or dust is internal
to the extended source. Analytic solutions to determine the dust
parameters for various geometries are extensively studied by NattaC 2011 The Authors, MNRAS 418, 625–637
C 2011 RASMonthly Notices of the Royal Astronomical Society & Panagia (1984) and Code (1973). Code (1973) applied the twostream approximation to the radiative transfer for a circumstellar
dust shell and this approximation was developed for a dust slab
containing emitters and absorbers in the appendix by Kawara et al.
(2011). It is noted that the slab approach is a good approximation to aspherical geometry. The reader may also refer to an excellent review
and discussion in Calzetti, Kinney & Storchi-Bergmann (1994).
We consider the following geometries of dust distribution: (1)Internal dust geometry – absorbers(dust grains) and emitters(stars)
are uniformly mixed and distributed; (2) Foreground dust screen
geometry – absorbers are physically separated from and located ina screen in front of emitters, where we assume that there are N
clumps on average along the line of sight, thus the dust distribution
is clumpy (small N) or uniform (very large N); (3) Composite
geometry – dust grains distribute both within the system of stars asinternal dust and in the screen in front of the system.
The effects of dust also depend on the physical distance between
the dust and the stars (Calzetti et al. 1994). If the dust is locatedphysically distant from the stars, the effect of dust is to remove
photons from the line of sight through absorption and scattering.
Hereafter, we call this distant configuration no scattering. On theother hand, if the dust is located close to the stars, the effect is not
only to remove photons from the line of sight but also to convey
photons back into the line of sight by scattering. We examine thisclose configuration in two extreme cases, namely, forward-only
scattering and isotropic scattering. In the internal dust geometry
where the dust is located close to the stars, we account for theeffect of the scattering through the relations τeff = (1 − γ )τext

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T. Shimizu et al.

Figure 3. Optical spectra of the 12 galaxies. The relative flux densities (per Å) are plotted as a function of rest-frame wavelength (Å). The vertical lines markthe positions of Mg II at 2798 Å; [O II] at 3727 Å; Ca II H and K at 3968 and 3934 Å, respectively; Hζ at 3889 Å; and H at 3970 Å.

Table 4. Spectroscopic properties of the 12 galaxies.
(1)
No.

(2)
EW([O II])(Å)(3)
D(Ca II)

1
2
3
4
5
6
7
8
9
10
11a
12b

45.6 ± 2.4
27.3 ± 2.7
10.1 ± 3.5
31.4 ± 3.3
65.3 ± 1.8
9.8 ± 1.8
35.0 ± 0.6
23.4 ± 1.3
63.2 ± 6.0
9.1 ± 2.1
31.1 ± 4.3
47 ± 50.28 ± 0.13
0.11 ± 0.13
0.27 ± 0.36
0.15 ± 0.05
0.18 ± 0.22
0.51 ± 0.26
0.13 ± 0.26
0.18 ± 0.41
0.02 ± 0.14
0.37 ± 0.26
0.03 ± 0.11

(4)
EW(Hζ )(Å)

(5)
EW(Ca K)(Å)

10.6 ± 1.6
3.5 ± 1.5
4.3 ± 1.9
1.0 ± 1.1
12.6 ± 5.2
2.6 ± 3.4
6.5 ± 1.4
1.6 ± 0.6
6.4 ± 2.6
1.0 ± 1.2
8.4 ± 3.7
4.9 ± 2.2
1.8 ± 0.6
0.3 ± 0.6
3.6 ± 1.0
0.6 ± 1.2
6.1 ± 1.9
0.1 ± 1.0
5.8 ± 2.0
2.6 ± 1.8
7.6 ± 2.1
0.4 ± 1.4
EW(Mg II) = 7.6 ± 3.1(6)
EW(Ca H + H)(Å)
14.2 ± 2.2
12.8 ± 1.5
6.8 ± 3.8
15.4 ± 1.2
4.7 ± 1.9
10.8 ± 2.6
2.9 ± 0.7
2.6 ± 2.3
9.0 ± 1.9
8.4 ± 2.4
16.7 ± 2.2

Note. Column 2 for the equivalent width of the [O II] line at 3727 Å. Column 3 for
the Ca II index defined as D(Ca II) = 2 × EW(Ca II K)/[EW(Hζ )+EW(Ca II H +H)] (Kawara et al. 2010). Columns 4–5 for the equivalent width for the Hζ line at
3889 Å and the Ca II K line at 3934 Å, respectively. Column 6 for the equivalent
width of the blends of the Ca II H and H lines at 3968 and 3970 Å, respectively.
a The equivalent widths were taken from Kawara et al. (2010).
b EW([O II]) was taken from Dey et al. (1999), and EW(Mg II λ2798) was measured
using the spectrum given by Dey et al. (1999).
C 2011 The Authors, MNRAS 418, 625–637
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Table 5. Infrared luminosity, dust mass and dust shellradius of the 12 galaxies.
No.

LaIR (1012 L )M bd (108 M )rc (arcsec)

1
2
3
4
5
6
7
8
9
10
11
12

2.60 ± 1.14
2.87 ± 1.25
2.66 ± 1.18
2.65 ± 1.20
3.73 ± 1.63
1.63 ± 0.74
2.78 ± 1.21
1.82 ± 0.81
2.93 ± 1.39
2.12 ± 0.95
1.04 ± 0.50
7.05 ± 3.25

1.66 ± 1.06
1.55 ± 1.02
1.73 ± 1.15
2.15 ± 1.43
2.00 ± 1.30
1.42 ± 0.91
1.65 ± 1.05
0.94 ± 0.63
3.30 ± 2.11
1.16 ± 0.78
1.94 ± 0.91
3.72 ± 2.69

0.63
0.74
0.47
0.52
0.80
0.61
0.85
0.61
0.62
0.60
0.48
0.47

IR is the 8–1000 µm bolometric infrared luminosity.
b The 8–40 M SN dust is assumed. For the MW dust,aLa factor of 0.78 should be multiplied.
c r is the radius of dust shell. It can be approximated√as r ∼ rx ry which were obtained from HST I 814
images.

for forward-only scattering and τeff = (1 − γ )0.75 τext for isotropic
scattering (Kawara et al. 2011), where γ is albedo, τeff is the effective
absorption optical depth, and τext is the sum of the optical depth ofabsorption and scattering. In the foreground screen geometry, if thedust screen is physically distant from the stars, no scattering applies.
On the other hand, if the dust screen is physically close to the stars,
the scattering can put photons into the line of sight. We thus consider
three cases for the foreground geometry: τeff = τext for no scattering,τeff = (1−γ )τext for forward-only scattering, and τeff = (1−γ )0.5 τext
for isotropic scattering. The relation between the observed flux f νand the unobscured flux f 0ν is fν /fν0 = (1−e−τeff )/τeff for an internal
dust geometry and fν /fν0 = e−τap with τap = N (1 − e−τeff /N ) for adust screen geometry with the number of N clumps along the lineof sight (Natta & Panagia 1984). It is noted that there is a definite
difference between attenuation and extinction curves; we regard
attenuation curves as f ν /f 0ν and extinction curves as τext .
3.1.2 Extinction curves
We examine two extinction curves synthesized in the ejecta of
SNe II, the empirical extinction curve derived by Calzetti (2001), theMW extinction curve given by Draine (2003), and the pseudo-MW
extinction curve.
The MW extinction curve exhibits a pronounced feature at
2175 Å. This feature is known to be absent in the typical extinction curves of the SMC and some galaxies. To check the effectof the feature on the extinction law in our galaxies, we create thepseudo-MW extinction curve which is made by removing the 2175
Å feature, namely the extinction bump and albedo dip, from the
MW extinction curve.
The Calzetti extinction curve is based on the attenuation law
that was derived in a range from 0.12 to 2.2 μm by analysing
local starbursts and blue compact dwarf galaxies (Calzetti et al.
1994). Calzetti (2001) expresses this law in a functional form combined with a geometry of a uniform dust screen with no scattering(i.e. fν = e−τν fν0 ). This cannot be used for longer wavelengths,
because the extinction curve (τ ν ) sharply drops beyond 2.2 μm.
The Calzetti extinction curve is almost identical to the MW curvefrom 0.6 to 1.6 μm. We thus extend the Calzetti curve to longerC 2011 The Authors, MNRAS 418, 625–637
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631

wavelengths by adopting the MW extinction curve for wavelengths≥1.6 μm. Because the Calzetti curve has already been processedby the foreground screen, we consider this geometry only for theCalzetti curve.
Combining the optical constants in the literature with the grain
species and size distribution of SN-condensed dust derived by
Nozawa et al. (2003), and using the Mie theory, Hirashita et al.
(2005) calculated absorption and scattering cross-sections of homogeneous spherical grains with various sizes condensed in mixed
and unmixed ejecta. Comparing their models to the extinction curveof SDSS J1048+637 (a BALQSO at z ∼ 6.2), Hirashita et al. (2005)
suggest the mass range of SN progenitors to be 30 M , whereas
the upper mass of SN progenitors is usually assumed to be 40 M .
We thus adopt the two extinction curves of SNe II for the Salpeter(1955) initial mass function (IMF); one has a mass range of progenitors from 8 to 30 M , and the other from 8 to 40 M . These wereobtained by interpolating or extrapolating the extinction curves that
Hirashita et al. (2005) calculated for unmixed SNe II with progenitor masses of 13, 20, 25 and 30 M . We adopt these in the present
study and call the original SN extinction curves in a sense that thesubsequent processing of dust destruction is not considered. Recent studies indicate that the original SN extinction curves become
flatter through the reverse shock destruction (Bianchi & Schneider
2007; Hirashita et al. 2008), while Hirashita et al. (2010) show theimportance of the shattering in a warm ionized medium (WIM) in
starburst environments and this effect makes the extinction curves
steeper. They suggest that the final extinction curves, after the reverse shock destruction and the shattering, have a slope similar tothat of the original curve. The degree of the reverse shock destruction and shattering critically depends on the assumed parameters,
especially gas density of the ISM. Considering these uncertainties
and the similarity between the original and final extinction curves,
we decided to adopt the original SN extinction curves in the present
study.
3.2 Star formation history
The evolutionary synthesis codes given by Bruzual & Charlot (2003)
are used to generate synthetic spectra of evolutionary stellar population models. We adopt the Salpeter (1955) IMF with the masscutoffs of 0.1–100 M . The star formation histories are exponentially declining models with the star formation rate (SFR) ∝t−1
SFR exp(−t/tSFR ), where tSFR is the e-folding time-scale and t is theage. The synthetic spectra are generated in the parameter range asshown in Table 6.
The equivalent widths of [O II]λ3727 and Mg IIλ2798, andD(Ca II) were calculated from the synthetic spectra. [O II] is a nebular line and unpredictable directly from the synthetic spectra. We
first obtain the Hα luminosity by counting ionizing photons in the
Table 6. Parameters of synthetic template spectra.
Parameter

Range

Z
t

0.005–2.5 Z at 0.005, 0.02, 0.2, 0.4, 1.0, 2.5 Z
1–6300 Myr in a step of 0.2 dex
10–10 000 Myr in a step of 0.3 dex
0–15 mag in a step 0.1 mag
15–100 mag in a step of 1 mag

tSFR
A0.3 µm

Note. Z, t, tSFR and A0.3 µm are the metallicity, age after the
onset of the star formation in Myr, e-folding time-scale of thestar formation in Myr, and extinction at 0.3 µm in magnitude,
respectively.

632

T. Shimizu et al.

synthetic spectra. The metallicity scaling of [O II]/Hα for the ionized parameter q = 3 × 107 cm s−1 was given by Kewley, Geller& Jansen (2004). We thus adopt their theoretical curves with anadditional condition, which is applied to avoid a negative or unrealistic value, of [O II]/Hα > 0.1. Kewley et al. (2004) estimated theuncertainty in the [O II] intensity to be ∼30 per cent.

related to r and δr as τin = ρin κext r and τsc = ρsc κext δr, where ρinand ρsc are the mass density of the internal and screen dust, respectively. The dust mass is derived directly from τin , τsc and r with no√need to assume δr, ρin and ρsc . r can be approximated as r ∼ rx ry
which were obtained from HST I 814 images, where rx and ry are
the semimajor and the semiminor axes, respectively. r is given in
Table 5.

3.3 Minimum χ 2 method
We search for the best set of parameters by using a minimum χ 2
method as defined below:

 2
2
2
2
2
(1)
+ W χ[Oχ 2 = χSED
II] + χEW(abs) + χLIR + χMd .
The weighting factor W is introduced to balance the weight between the SED data.2
Each term is defined as
Nfilters
2
=
χSED



2
,
(Fobs − bFtemp )2 /σSED

(2)

2
2
2
χ[O
II] = (EW([O II])obs − EW([O II])temp ) /σ[O II] ,

(3)

2
2
= (EW(abs)obs − EW(abs)temp )2 /σEW(abs),
χEW(abs)(4)

χL2IR = (LIR − LIR temp )2 /σL2IR ,(5)

2= (Md − Md temp )2 /σM2 d .
χM
d

(6)

Equation (2) is related to photometric data of the continuum fromstellar atmosphere. b is a normalization constant between the template flux density Ftemp and the observed Fobs , and the number ofphotometric filters Nfilters from UV to 5.8 μm. 8.0-μm data are excluded from the SED data, because dust emission may be significant
in the 8.0-μm band. In order to avoid too small and non-realistica photometric error, 5 per cent of the flux is added in the quadratic2= σph + (0.05Fobs )2 .
form to the photometric error σph , i.e. σSED
Equation (3) is related to the [O II] line from H II regions ionized by young OB stars. EW([O II]) predicted using the Kewley
et al. (2004) theoretical curve contains ∼30 per cent uncertainty,
2222thus σ[OII] = σEW([O II])obs + (0.3EW([O II])temp ) , where σEW([O II])obs
is the observed error. Equation (4) measures the absorption lines instellar atmosphere. EW(abs) is EW(Mg II) for HR10 and D(Ca II)2
is the observed error.
for the others and σEW(abs)
Equation (5) compares LIR given in Table 5 with the prediction
from the model, i.e. LIR temp ∝ (fν0 −fν )dν, where f 0ν and f ν are intrinsic and reddended synthetic spectra. Equation (6) compares Md
derived from FIR data with Md temp the dust mass estimated from thedust extinction (i.e. optical depth) and the assumed dust geometry.
Md temp was derived as follows. We first assume a composite geometry consisting of screen dust and internal dust. Suppose a sphericalshell with a radius of r and a thickness of δr, where the internal andscreen dust fills inside and in the shell, respectively. Then, assuming
δr/r
1, the mass of the internal dust is Min = 4π(τin /κext )r 2 /3,
while that of the screen dust is Msc = 4π(τsc /κext )r 2 . τin and τsc
are τext for internal dust and screen dust, respectively, and they are

4 R E S U LT S
The results of the minimum χ 2 analysis are illustrated in Fig. 4. The
left-hand panels of the first three rows plot χ 2ν (=χ 2 /ν, where ν isdegree of freedom)3 as a function of τin /(τin + τsc ) for a composite geometry consisting of uniform screen dust and internal
dust; τin /(τin + τsc ) = 0 for the foreground screen geometry, whileτin /(τin + τsc ) = 1 for the internal dust geometry. The scattering
properties are assumed to be no scattering, isotropic scattering (g =0), or forward-only scattering (g = 1). In case of no scattering, thescattering properties are no scattering for screen dust and forward
scattering for internal dust because no scattering cannot be assumed
for internal dust. The middle and right-hand panels of the first threerows show χ 2ν as a function of N, the number of clumps, along theline of sight in the foreground screen geometry and the composite
geometry with τ in /(τ in + τ sc ) = 0.4. Several linestyles are used to
specify the extinction curve: solid lines to the 8–30 M SN curve,
dash to the 8–40 M SN, dot to the Calzetti, dash–dotted to theMW, and dash–triple dot to the pseudo-MW.
The four panels in the fourth row plot A0.3 µm the extinction (τ in +
τ sc ) in magnitude at 0.3 μm, t the age (i.e. the time after the onsetof the star formation) in Myr, Z the metallicity in solar units, andtSFR the e-folding time-scale of star formation in Myr as a functionof τ in /(τ in + τ sc ). The left-hand panel in the bottom row plots thebest-fitting SED along with the unreddened SED and the righthand panel the contour map of χν2 − χν2 (min) where χν2 (min) is thesmallest χ 2ν among all the models.
The trends of the results are as follows.
(1) The SN dust curves generally have reducing χ 2ν as τin /(τin +τsc ) is approaching zero (more dominated by screen dust) and N
approaching ∞ (more uniform screen).
(2) Some galaxies have a small χ 2ν in a clumpy foreground screen
geometry, especially galaxies numbers 5 and 12 have the minimum
χ 2ν at N of 10 and 3, respectively.
(3) The MW and pseudo-MW curves sometimes have reducing
χ 2ν as a geometry gets more dominated by internal dust at τin /(τin +τsc ) = 0.8–0.9.
The data point around rest 4 μm in the SED plots is the IRAC
8.0 μm data, and shows an excess from the model for most of thegalaxies. As discussed in Section 3.3, the data of this band were
not used in the analysis, because dust emission may be significant
in this band. The SED plots in Fig. 4 indeed suggest dust emission
around 4 μm.
Table 7 compares the smallest χ 2ν of the respective extinction
curves along with the dust geometry, the scattering property, andthe total extinction including internal and screen dust. There are
two obvious features: (1) the optical depth (A0.3 µm ) in the geometry

2 The number of photometric data points was chosen so that the SED fitting

did not outweigh the other data. However, we found at a later stage of theanalysis that the weight of the SED still overwhelmed the other data formany galaxies. W was thus introduced to ensure that the χ 2 of the SED
has the similar magnitude as that of the other data. As a result, we obtained
W = 1 for galaxies 2, 4, 6, 12, and W = 3 for the others.

3 Degree of freedom is defined as ν = N
filter + 4W − 5, where Nfilter is the2number of photometric data used for χSED
and W the weighting factor. The
number of fitted parameters is 5 (i.e. b, t, tSFR , A0.5 µm , Z); Nfilter = 9 for

the COSMOS galaxies, 13 for SST J1604, and 10 for HR 10.

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633

Figure 4. Results of the minimum χ 2 analysis. The source number and the scattering property are indicated in each panel. The left-hand panels in the first
three rows show χ 2ν for a uniform screen as a function of τ in /(τ in + τ sc ). The middle and right-hand panels in the first three rows represent a screen of N
clumps for τ in /(τ in + τ sc ) = 0 and τ in /(τ in + τ sc ) = 0.4, respectively. In case of no scattering, the scattering properties are no scattering for screen dust andforward scattering for internal dust. Solid lines represent 8–30 M SN dust, dashed 8–40 M SN dust, dash–dot MW dust, and dash–triple dot pseudo-MW
dust, dotted the Calzetti dust. The fourth row panels show τ in + τ sc at 0.3 µm in magnitude A0.3 µm , the metallicity Z, the age t(yr), and the time-scale tSFR asa function of τ in /(τ in + τ sc ). The bottom-row panels show the best-fitting SED along with the unreddended SED and the contour map of χ 2ν − χ ν 2 (min). The
full version of this figure is available with the online version of the paper – see Supporting Information.

C 2011 The Authors, MNRAS 418, 625–637
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634

T. Shimizu et al.
Table 7. Comparison of dust models.
Reduced χ 2 (χ 2ν a )τin /τin+sc (N b )No.

Scattering property
A0.3 µm

MW

pMW

Cal

SN30

SN40

MW

pMW

Cal

SN30

SN40

1

2.18
0.9 (–)

2.72
0.0 (∞)

2.18
–

5.27
0.0 (∞)

0.79*
0.0 (∞)

Isotrop17.5

Isotrop
7.1

–
4.3

No
2.4

No
4.3

2

3.35
0.9 (–)

2.87
0.6 (–)

2.04
–

3.65
0.0 (∞)

1.61*
0.0 (∞)

Isotrop
14.4

No
7.3

–
3.9

Isotrop
4.1

No
3.4

3

2.09
0.8 (–)

1.98
0.0 (∞)

2.42
–

2.51
0.9 (–)

1.62*
0.0 (∞)

Isotrop23.8

Isotrop
8.8

–
5.9

No
18.8

No
6.0

4

3.93
0.9 (–)

0.86*
0.0 (∞)

3.02
–

8.72
0.0 (∞)

2.33
0.0 (∞)

Forward25.0

Isotrop
5.9

–
2.8

No
2.5

No
3.5

5

1.52
0.9 (–)

2.19
0.7 (–)

2.07
–

2.45
0.0 (∞)

0.80*
0.0 (10)

No
13.1

No
7.5

–
3.3

No
2.9

No
4.8

6

1.88
0.8 (–)

1.72
0.0 (∞)

1.61
–

1.51
0.0 (∞)

1.37*
0.0 (∞)

No
11.9

Isotrop
6.8

–
4.3

No
2.8

No
4.9

7

4.30
0.0 (10)4.59
0.0 (∞)

5.00
–

5.61
0.0 (∞)

2.35*
0.0 (∞)

No
3.3

Isotrop
4.4

–
3.0

No
2.6

No
3.6

8

1.35
0.0 (10)1.99
0.0 (∞)

1.51
–

3.00
0.0 (∞)

0.98*
0.0 (∞)

No
4.0

Isotrop
5.4–
3.6

Isotrop
2.9

No
3.6

9

2.15
1.0 (–)

1.02*
0.9 (–)

1.51
–

2.10
0.0 (∞)

1.88
0.0 (10)No
32.5

Isotrop
21.3

–
3.5

No
3.6

No
4.9

10

2.88
0.8 (–)

1.23
0.0 (∞)

0.75*
–

2.37
0.0 (∞)

2.08
0.0 (∞)

Isotrop9.4

Isotrop
4.5–
3.6

Foward
4.0

No
3.6

11

5.09
0.0 (10)5.55
0.9 (–)

5.05
–

3.56*
0.0 (∞)

3.75
0.0 (∞)

No
8.8

Isotrop
42.5

–
5.8

No
5.4

Foward
17.5

12

0.84*
0.4 (3)0.84*
0.4 (3)

1.36
–

1.71
0.0 (∞)

1.41
0.0 (∞)

Isotrop20.0

Isotrop
20.0

–
5.0

No
4.0

No
4.4

Note. The smallest χ 2ν is given per galaxy per dust model. ‘*’ marks χ 2ν of the best-fitting model for each galaxy. ‘MW’,‘pMW’, ‘Cal’, ‘SN30’ and ‘SN40’ denote a dust model of the MW, pseudo-MW, Calzetti, 8–30 M SN and 8–40 M
SN, respectively. ‘Isotrop’, ‘Forward’ and ‘No’ denote isotropic, forward, and no scattering, respectively.
a χ 2 = χ 2 /ν, where ν is the degree of freedom.
ννb The number of clumps N is given in parentheses for a geometry dominated by foreground screen dust.

dominated by internal dust is several times greater than that in theforeground screen geometry; (2) the MW curve generally has thesmallest χ 2ν in the composite geometry dominated by internal dust,
whereas the SN curves do so in the foreground screen geometry, andthe pseudo-MW dust model is in midway. Finding a higher opticaldepth for the internal absorption is an expected and obvious result,because the screen geometry always maximizes the extinction.
The contour plots in Fig. 4 appear to show the age(t)/extinction(A0.3 µm ) degeneracy, suggesting that t and tSFR given in Table 7
are not very accurate. The uncertainties in the age determination
were propagated to the uncertainty to determine the stellar mass ofgalaxies, because the luminosity-to-mass ratio strongly depends on
the age of stellar populations. This degeneracy can be resolved byadding data from 100 μm to the submillimetre, greatly reducing thepresent uncertainty in LIR .
Table 8 summarizes the best-fitting models. Out of our 12galaxies, 10 (83 per cent) have a pure foreground dust screen, andnine of the 10 galaxies have a uniform foreground screen. Eight(67 per cent) of the 12 galaxies have the best-fitting model with oneof the SN dust curves, all of which are associated with a pure foreground dust screen. Internal dust is only significant in two galaxies,
both of which have the best-fitting models with the MW or pseudo-

MW extinction curve. Because the extinction curves analysed here
can be ordered from the steepest to the flattest as the MW, pseudoMW, Calzetti, 3–40 M SN and 3–30 M SN, the MW andpseudo-MW curves are too steep to agree with a pure foregroundscreen, and need to be associated with a geometry dominated byinternal dust or a clumpy foreground screen to make the attenuation
curve flat or grey. This requires a few times more dust mass thanthat in a pure, uniform foreground screen. Our results indicate thatthe 8–40 M SN curve with a uniform foreground screen is thebest dust model to account for z ∼ 1 ULIRGs.
5 DISCUSSION
Gordon, Calzetti & Witt (1997) applied models of stars and dust
to the SEDs of 30 local starburst galaxies using the MW and SMC
extinction curves, and found that the dust has an extinction curvelacking a 2175 Å feature with a slope intermediate between the MW
and SMC curves. The dust geometry has a pure foreground screenwith clumps. Gaskell et al. (2004) found indications of a very flat
extinction curve in the ultraviolet (UV) from an analysis of 1090
AGNs. Large samples of SDSS quasars indicate that the extinction
law in quasars at z < 2.2 is described by SMC reddening but not byC 2011 The Authors, MNRAS 418, 625–637
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635

Table 8. Properties of the best-fitting models.
No.
(1)

τin /τin+sc (N )
(2)

1
2
3
4
5
6
7
8
9
10
11
12

0.0 (∞)
0.0 (∞)
0.0 (∞)
0.0 (∞)
0.0 (10)0.0 (∞)
0.0 (∞)
0.0 (∞)
0.9 (–)
0.0 (∞)
0.0 (∞)
0.4 (3)0.4 (3)

Dust model(3)

Scattering
(4)

χ 2ν
(5)

Z
(6)

t
(7)

tSFR
(8)

A0.3 µm
(9)

Min
(10)

Msc
(11)

M∗
(12)

Md /SN
(13)

SN40
SN40
SN40
pMW
SN40
SN40
SN40
SN40
pMW
Calzetti
SN30
MW
pMW

No
No
No
IsotropNo
Isotrop
No
No
Isotrop
No
No
Isotrop
Isotrop

0.79
1.61
1.62
0.86
0.80
1.37
2.35
0.98
1.02
0.75
3.56
0.84
0.84

0.2
1.0
1.0
1.0
0.4
1.0
0.4
1.0
1.0
0.4
1.0
0.4
0.4

1500
800
60
100
60
1500
40
150
150
60
630
2000
2000

10000
630
10
40
20
320
10
40
160
10
160
630
630

4.3
3.4
6.0
5.9
4.8
4.9
3.6
3.6
21.3
3.6
5.4
20.0
20.0

–
–
–
–
–
–
–
–
2.4
–
–
0.7
0.7

1.6
1.9
1.0
1.3
2.8
1.7
2.5
1.2
0.8
1.0
0.9
2.2
2.2

27.5
6.5
1.4
1.2
1.9
11.3
0.6
1.5
1.5
1.0
3.6
42.0
42.0

0.0079
0.031
0.16
0.19
0.25
0.017
0.38
0.085
0.23
0.12
0.058
0.00980.0098Note. Columns 1–5 are defined in Table 7.
Columns 6–9: Metallicity (Z) in solar, age (t) in Myr, e-folding time-scale (tSFR ) in Myr, and extinction at 0.3 µm (A0.3 µm ) in magnitude,
respectively.
Columns 10–11: Mass of internal dust (Min ) and screen dust (Msc ), respectively, in the unit 108 solar mass.
Column 12: Stellar mass (M ∗ ) in the unit 1011 M that is estimated as LIR /(L/M∗ ), where L/M ∗ is the luminosity-to-mass ratio for thestellar population models.
Column 13: Dust mass (Md ) per SN where (Md ) is in solar units. The number of SNs per galaxy is derived from the IMF of the modelof star formation history and integration of all stars with 8 M .

reddening in the LMC and MW (Richards et al. 2003; Hopkins et al.
2004). Gallerani et al. (2010) proposed that reddening of quasars
at z = 3.9–6.4 has a tendency to be flat at λ  2000 Å. Maiolino
et al. (2004) found that the BALQSO at z = 6.2 requires a flat
extinction curve which is quite different from those observed in
the MW, LMC and SMC, but in an excellent agreement with thesynthetic SN curves (Todini & Ferrara 2001). The flat extinction
law that we found in z ∼ 1 ULIRGs are probably incompatible
with the steep SMC-like extinction law reported for z < 2.2 AGNs,
and in agreement with the flat extinction law found in high-redshiftquasars.
It needs to be reiterated that the SN-dust models generally predict flat extinction curves but there are intrinsic differences among
the models. Maiolino et al. (2004) adopted the SN-dust model by
Todini & Ferrara (2001) to derive the extinction curves expected
in high-z quasars. The calculated curves show a flat feature at UV
wavelengths as a result of the main contribution of amorphous
carbon grains with radii around 300 Å, added by the minor contributions of small silicate and Fe3 O4 grains with radii around 20 Å.
Bianchi & Schneider (2007) revisited the dust formation model by
Todini & Ferrara (2001) and also followed the evolution of thedust grains from the time of formation to their survival through thepassage of the reverse shock. They showed that the reverse shock
predominantly destroys small silicate and Fe3 O4 grains, and theresultant extinction curves become flatter, being dominated by carbon grains whose extinction coefficients are relatively insensitive towavelengths. On the other hand, Hirashita et al. (2005) calculated
the extinction curves using the SN II-dust model by Nozawa et al.
(2003). The derived extinction properties more or less depend on
the SN progenitor mass, but are quite flat as a result of the dominant
contribution of large (0.1 μm) amorphous carbon or Si grains.
As discussed in Section 3.1.2, the reverse shock efficiently destroys
small grains (Nozawa et al. 2007), making the extinction curves
much flatter than the original curves (see Hirashita et al. 2008).
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C 2011 RASMonthly Notices of the Royal Astronomical Society 

Then large grains that survive the destruction through the reverse
shock are shattered in the WIM, producing a large number of small
grains. This finally leads to the extinction curves similar to the original SN extinction curves (Hirashita et al. 2010). The growth of
dust grains through accretion in the ISM would also be efficientin infrared galaxies (Dwek 1998; Draine 2009; Michałowski et al.
2010), and also cause flat extinction curves.
As shown in Table 8, our z ∼ 1 ULIRGs have an age of mostly t ≤650 Myr with four exceptions (i.e. t = 800, 1500, 1500, 2000 Myr),a stellar metallicity of z = 0.2–1.0 solar, and a dust mass of Md ∼108 M . Michałowski et al. (2010) suggested that AGB stars are
not sufficient to form dust at such an early epoch of galaxy evolution
history, whereas SN-condensed dust followed by grain growth in
the ISM is important to account for the inferred dust mass. It is notedthat our analysis cannot rule out a possible contribution from AGB
stars, because some observations (Groenewegen 1997; Gauger et al.
1999) suggest that large-sized dust grains are formed in AGB stars
and that larger grains have flat extinction curves. The dust mass
per SN in our z ∼ 1 ULIRGs mostly ranges from 0.01 to 0.3 M .
This should be compared with the theoretical prediction of the dust
yield per SN, which is 0.01–0.1 M with dust destruction and
0.1–1 M per SN without dust destruction. If the ISM processof dust growth is important, the expected yield will be more thanthese. However, there would be a possible bias effect on the dust
mass per SN inferred from the observations, because a significant
correlation between the age t and Md /SN can be seen in Table 8.
This correlation seems spurious and simply reflects the uncertainty
of determining t caused by the t and A0.3 µm degeneracy, because
the mass-to-luminosity ratio strongly depends on t.
Our results indicate that the dust geometry of a pure foregrounddust screen generally explains the data of the z ∼ 1 ULIRGs better
than that dominated by internal dust. Colour–colour plots of opticaland UV data of local starbursts were compared with various dust
distribution models by Gordon et al. (1997), and they found that the636

T. Shimizu et al.

observed spread cannot be explained by the internal dust geometry,
but the foreground screen geometry can explain it. Calzetti et al.
(1994) also showed that the failure of the internal dust geometry
explains the spread of data of local starbursts, suggesting a foreground screen geometry with a flat extinction curve (i.e. Calzetti
curve). Meurer et al. (1995) showed that a strong correlation between the FIR excess and the UV spectral slope for local starbursts
can be explained by dust in a foreground dust screen geometry
with the Calzetti curve, but not by an internal dust geometry. They
attributed the dust in a foreground screen to the Galactic winds frequently observed in starbursts that will sweep out any diffuse ISM
from the starburst sites on a time-scale of a few Myr (Heckman,
Armus & Miley 1990). The foreground dust screen geometry weare looking at in z ∼ 1 ULIRGs may also result from the dust thatwas swept by the Galactic winds.
6 CONCLUSIONSIn order to study the extinction law in galaxies (ULIRGs) at z ∼ 1, we
have analysed the multiwavelength photometric and spectroscopic
data of 12 ULIRGs which are archived or published in the literature;
10 galaxies come from the COSMOS survey catalogues, and theothers are SST J1604+4304 and HR10.
The data are compared with models of stars and dust. We applied
five extinction curves, namely the MW, the pseudo-MW which is
MW-like without the 2175 Å feature, the Calzetti, and two SN dust
curves, by combining with various dust distributions, namely theforeground screen geometry, the internal dust geometry, and thecomposite geometry with a combination of dust screen and internal
dust. Several scattering properties are used: no scattering, isotropic
scattering and forward scattering. In case of no scattering, the effectof dust to convey photons into the line of sight is ignored, while thiseffect is included in isotropic scattering and forward scattering.
The two SN extinction curves that we applied here were calculated by Hirashita et al. (2005) based on the grain properties of
SN-condensed dust derived by Nozawa et al. (2003). These SN
extinction curves were calculated assuming the unmixed ejecta of
SNe II for the Salpeter IMF in a progenitor mass range of 8–30 or
8–40 M and do not include the effects of the reverse shock in theejecta and interaction between SN dust grains and the ambient ISM.
Employing a minimum χ 2 method, we find that the foregrounddust screen geometry, especially combined with the 8–40 Mcurve, provides a good approximation to the real dust geometry,
whereas internal dust is significant only for two galaxies. The SN
extinction curves, which are flatter than the other extinction curves,
reproduce the data of eight (67 per cent) galaxies better than theother curves do. Our z ∼ 1 ULIRGs require an age of mostly t ≤650 Myr, a stellar metallicity of z = 0.2–1.0 solar, and a dust mass of
Md ∼ 108 M . Considering these physical features, we conclude
that SN-origin dust is the most plausible to account for the vast
amount of dust masses and the flat slope of the observed extinction
law. The inferred dust mass per SN ranges from 0.01 to 0.4 M .
AC K N OW L E D G M E N T S
We thank H. Hirashita for helpful comments and suggestions andBrice Ménard for his critical reading of the final draft. Simon
Bianchi provided us with extremely constructive comments and criticism which improved this work very much. This work has been supported in part by Grants-in-Aid for Scientific research (20340038,
22111503) and Specially Promoted Research (20001003) fromJPSP.

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S U P P O RT I N G I N F O R M AT I O N
Additional Supporting Information may be found in the online version of this article:
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Figure 4. Results of the minimum χ 2 analysis.
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