Mon. Not. R. Astron. Soc. 362, 592–608 (2005)
doi:10.1111/j.1365-2966.2005.09337.x
A model for the infrared dust emission from forming galaxies
Tsutomu T. Takeuchi,1⋆ † Takako T. Ishii,2 ‡ Takaya Nozawa,3 Takashi Kozasa3
and Hiroyuki Hirashita4,5,6 ‡
1 Laboratoire
d’Astrophysique de Marseille, Traverse du Siphon BP8, 13376 Marseille Cedex 12, France
Observatory, Kyoto University, Yamashina-ku, Kyoto 607–8471, Japan
3 Division of Earth and Planetary Sciences, Hokkaido University, Sapporo 060–0810, Japan
4 Division of Particle and Astrophysical Sciences, Nagoya University, Nagoya 464–8602, Japan
5 SISSA-ISAS, International School for Advanced Studies, Via Beirut 4, 34014 Trieste, Italy
6 Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305–8577, Japan
2 Kwasan
ABSTRACT
Dust plays various important roles in galaxy formation and evolution. In the early epoch of
galaxy evolution, dust is only supplied by supernovae (SNe). With the aid of a new physical
model of dust production by SNe developed by Nozawa et al. (N03), we constructed a model
of dust emission from forming galaxies on the basis of the theoretical framework of Takeuchi
et al. (T03). N03 showed that the produced dust species depends strongly on the mixing within
SNe. We treated both unmixed and mixed cases and calculated the infrared (IR) spectral energy
distribution (SED) of forming galaxies for both cases. Our model SED is less luminous than
the SED of T03 model by a factor of 2–3. The difference is due to our improved treatment
of the ultraviolet (UV) photon absorption cross-section, as well as the different grain size
and species newly adopted in this work. The SED for the unmixed case is found to have an
enhanced near to mid-IR (N–MIR) continuum radiation in its early phase of the evolution
(age 107.25 yr) compared with that for the mixed case. The strong N–MIR continuum is
due to the emission from silicon grains, which only exist in the species of the unmixed dust
production. We also calculated the IR extinction curves for forming galaxies. N03 dust was
found to yield a smaller extinction than that of T03 model. For the unmixed case, near-IR
(NIR) extinction is dominated by large grains of silicon and amorphous carbon, and silicate
features are less prominent compared to the curve given by T03. To the contrary, the extinction
curve of the mixed case has a similar shape to that of T03. Then we calculated the SED of a
local starbursting dwarf galaxy SBS 0335−052. Our present model SED naturally reproduced
the strong N–MIR continuum and the lack of cold far-IR emission of SBS 0335−052. We
found that only the SED of unmixed case can reproduce the NIR continuum of this galaxy. We
then made a prediction for the SED of another typical star-forming dwarf, I Zw 18. The MIR
continuum of I Zw 18 is expected to be much weaker than that of T03 SED. We also presented
the evolution of the SED of Lyman-break galaxies. Finally, we discussed the possibility of
observing forming galaxies at z 5.
Key words: dust, extinction – Galaxy: formation – galaxies: dwarf – galaxies: ISM – infrared:
galaxies.
1 I N T RO D U C T I O N
In spite of the recent vast progress in both observational and theoretical studies, our understanding of the physics of galaxy formation
and evolution is still far from sufficient.
⋆ E-mail: tsutomu.takeuchi@oamp.fr
†Postdoctoral Fellow of the Japan Society for the Promotion of Science for
research abroad.
‡Postdoctoral Fellow of the Japan Society for the Promotion of Science.
The cosmic star formation (SF) history, introduced by Tinsley
& Danly (1980) and developed by subsequent studies (e.g. Lilly
et al. 1996; Madau et al. 1996), has always drawn much attention.
Now the observations reach up to ∼6–8 (e.g. Stanway, Bunker &
McMahon 2003; Bouwens et al. 2004a,b). In such studies, the role
of dust has been increasingly recognized when we try to understand
the evolution of galaxies in the context of cosmic SF history, because
dust grains absorb stellar light and re-emit it in the far-infrared (FIR).
Even a small amount of dust can lead to a significant underestimation
of the SF rate (SFR) (Steidel et al. 1999; Adelberger & Steidel 2000).
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Accepted 2005 June 20. Received 2005 June 17; in original form 2005 February 14
Dust emission from forming galaxies
1
More specifically, core-collapse SNe.
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2005 RAS, MNRAS 362, 592–608
mixed case, because the carbon and oxygen are mixed and combined
to form CO molecules. To the contrary, it forms in unmixed SN, as
there is a carbon-rich region at a certain location in the ejecta of
SNe. In addition, N03 predicts a dust mass larger than that of TF01
for SNe II.
The amount of dust produced in SNe is thus still a matter of debate.
Morgan & Edmunds (2003) adopted a dust production smaller than
those of TF01 or N03 in their theoretical calculation, in line with IR
observations at the time. On the other hand, various observational
efforts have been devoted to constrain the dust production efficiency
of SNe (e.g. Arendt, Dwek & Moseley 1999; Dunne et al. 2003;
Morgan et al. 2003; Green, Tuffs & Popescu 2004; Hines et al.
2004; Krause et al. 2004; Wilson & Batrla 2005). These results range
from 0.003 M⊙ to 1.0 M⊙ per SN, and N03 dust production seems
consistent with the upper range of these observational constraints.
However, in these observational evaluations, a large uncertainty still
remains due to the uncertainties in the estimation of dust mass in
Cas A caused by the foreground contamination (Krause et al. 2004),
although the evidence for dust in some SN remnants (SN1987A
and Kepler) is still pointing towards SN origin. Thus, further close
interaction between theoretical and observational works is required
to overcome the uncertainties and obtain a reasonable picture of dust
production in SNe.
In order to examine the dust properties of such high-z galaxies, the most direct observable is their spectral energy distribution
(SED), especially at the FIR wavelengths. Hirashita, Hunt & Ferrara
(2002) modelled the evolution of FIR luminosity and dust temperature in a young starburst on the basis of SNe II grain formation
model of TF01. Takeuchi et al. (2003a) (T03) subsequently constructed a model of infrared (IR) SED of galaxies starting from
the model of Hirashita et al. (2002). T03, for the first time, properly consider the dust size distribution peculiar to the very early
stage of galaxy evolution in the model of the IR SED of very
young galaxies, and successfully reproduced the peculiar MIR SED
of SBS 0335−052 (though their result seems to have overestimated the FIR continuum). Takeuchi & Ishii (2004) (T04) applied
the T03 model to the Lyman-break galaxies (LBGs). They found
that the suggested hot dust in the LBGs (e.g. Ouchi et al. 1999;
Chapman et al. 2000; Sawicki 2001) can be naturally explained by
the T03 model.
As these works are based on TF01 conjecture, the dust formation
model used is based on the classical nucleation theory (Feder et al.
1966). Recently, however, the importance of non-equilibrium (nonsteady state) effects on the dust grain formation has been recognized
in various astrophysical contexts (e.g. Gail, Keller & Sedlmayr 1984;
Tanaka, Tanaka & Nakazawa 2002, N03). In addition, N03 found
that the radial density profile of the SN progenitor and the temperature evolution of the ejecta also affect the dust grain formation.
Hence, now is the time to take into account these concepts to further
investigate the dust emission from young galaxies. In this work, we
construct a new model of IR SED of extremely young galaxies based
on N03 SN dust formation model. Starting from the size distribution and the amount of dust predicted by N03, we calculate the dust
emission model by extending the T03 model to treat multiple dust
species.
The paper is organized as follows. In Section 2 we explain the
framework of our SED model. We present the basic result, the
evolution of the SED of extremely young galaxies, in Section 3.
Related discussions on local star-forming dwarf galaxies and high-z
galaxies will be in Section 4. Section 5 is devoted to our conclusions. Throughout this paper, we use a cosmological parameter set of
(h, 0 , λ 0 ) = (0.7, 0.3, 0.7), where h ≡ H 0 /100 [km s−1 Mpc−1 ].
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Indeed, there is another extreme category of high-z galaxies which
have large amount of dust and are extremely luminous in the FIR
and submillimetre (submm) wavelengths (e.g. Hughes et al. 1998;
Eales et al. 2003). Heavily hidden SF is suggested in these galaxies
(e.g. Takeuchi et al. 2001a,b; Totani & Takeuchi 2002).
Furthermore, from a physical point of view, dust grains are one of
the fundamental ingredients in the activity of galaxies. As they are
formed in a variety of environments ranging from explosive ejecta
of novae and supernovae (SNe) to the outflowing gas of evolved
low-mass stars, the dust formation is closely related to the SF activity (Dwek 1998). Moreover, the existence of dust is crucial in
the physical process of galaxy formation and evolution through the
formation of molecular hydrogen (e.g. Hirashita & Ferrara 2002).
The dust itself plays a leading part in the physics of SF activity in
galaxies in the whole period of the cosmic history.
Then, how about very young galaxies in the early Universe at
z 5? It is often assumed, without deliberation, that the effect of dust
is negligible for such young galaxies, because of their low metallicities. There is, however, a good counter-intuitive example in the local
Universe: a local dwarf star-forming galaxy SBS 0335−052 has a
very young stellar age (107 yr) and low metallicity (1/41 Z⊙ ),
but has a heavily embedded active SF and strong continuum radiation in the near to mid-infrared (N–MIR) wavelength regime (Dale
et al. 2001; Hunt, Vanzi & Thuan 2001). In addition, there are increasing number of observations suggesting the existence of dust in
high-z systems such as Lyman α systems (e.g. Ledoux, Bergeron &
Petitjean 2002; Ledoux, Petitjean & Srianand 2003) or quasi-stellar
objects (e.g. Bertoldi et al. 2003).
To produce dust effectively in such a young system, the dust
enrichment should have occurred primarily in the ejecta of SNe,
especially Type II SN (SN II) explosions,1 because the lifetime
of the progenitor is short enough (∼106 yr) (e.g. Dwek & Scalo
1980; Kozasa, Hasegawa & Nomoto 1989). Recent theoretical studies claim the possibility of very massive stars for the first generation
stars, which end their lives as pair-instability SNe (PISNe) (Heger &
Woosley 2002; Umeda & Nomoto 2002). We should also take
into account for the PISNe to study the very early evolution of
dust. Recently, the dust formation in SNe ejecta has been observationally supported (e.g. Douvion et al. 2001; Morgan et al. 2003;
Dunne et al. 2003).
For investigating the properties of dust in details, theoretical predictions for the amount and composition of dust are required. So
far, some theoretical models of dust production by SNe have been
developed. Todini & Ferrara (2001, hereafter TF01) showed that the
dust mass produced by a SN II is 0.1–0.4 M⊙ applying the theory
of nucleation and grain growth by Kozasa & Hasegawa (1987). In
the calculations, they assumed an adiabatic cooling in the ejecta
with uniform gas density as well as elemental composition within
the He core. They also found that SNe form amorphous carbon with
size around 300 Å and silicate grains around 10–20 Å. Schneider,
Ferrara & Salvaterra (2004) extended the progenitor mass range to
the regime of PISNe (140–260 M⊙ ) and found that 10–60 M⊙ of
dust forms per PISN. The grain radius depends on the species and
is distributed from 0.001 to 0.3 µm.
Recently, (Nozawa et al. 2003) (hereafter N03) carefully took into
account the radial density profile and the temperature evolution in
the calculation of the dust mass in the ejecta of SNe II and PISNe.
N03 showed that the produced dust species depends strongly on the
mixing within SNe. In particular, carbon dust is not produced in the
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T. T. Takeuchi et al.
2 SED MODEL FOR FORMING GALAXIES
Table 1. Dust grain species.
2.1 Species and size distribution of dust grains produced
by SNe II
Species
2.1.1 Dust production model of Nozawa et al. (2003) (N03)
2.1.2 Dust grain species produced by the N03 model
In the unmixed ejecta, a variety of grain species (Si, Fe, Mg 2 SiO 4 ,
MgSiO 3 , MgO, Al 2 O 3 , SiO 2 , FeS and C) condense, and in the mixed
ejecta, in contrast, only oxide grains (SiO 2 , MgSiO 3 , Mg 2 SiO 4 ,
Al 2 O 3 and Fe 3 O 4 ) form. This is because carbon atoms are consumed
to form CO molecules. We summarize the species formed in SNe
in Table 1, where the species marked with a circle are relevant for
unmixed and mixed SNe. The size of the grains spans a range of
three orders of magnitude, depending on the grain species. The size
spectrum summed up over all the grain species has a very broad
distribution, and very roughly speaking, it might be approximated
by a power law. This size distribution is different from that of the
SN II calculation of TF01, which has typical sizes of 300 Å for
amorphous carbon and 10–20 Å for oxide grains.
In this work, we adopt the representative progenitor mass of SNe
II as 20 M⊙ . N03 have shown that the size distribution of each
grain species is almost independent of the progenitor mass, if the
◦
◦
◦
◦
◦
◦
◦
◦
◦
Mixed
◦
◦
◦
◦
◦
Density (ρ i )
(g cm−3 )
Ref.a
2.28
2.34
2.66
7.95
4.87
5.25
4.01
3.59
3.20
3.23
1
2
3
4
5
6
7
8
9
5
a References
for optical constants: (1) Edo (1985), (2) Edward (1985), (3)
Philipp (1985), (4) Lynch & Hunter (1991), (5) Semenov et al. (2003), (6)
Mukai (1989), (7) Toon, Pollack & Khare (1976), (8) Roessler & Huffman
(1991), and (9) Dorschner et al. (1995).
SN type is fixed (i.e. SN II or PISN). We examine the unmixed
and mixed cases. The size distributions of dust grains in the mixed
and unmixed cases calculated by N03 are shown in Fig. 1. We used
these size distributions after binning with a bin width of 0.2 dex for
our calculations. Throughout this work, we assume a uniform and
spherical grain. It should be mentioned that a different shape of dust
grains in SN is suggested (e.g. Dwek 2004).
2.2 SF, chemical evolution and dust production
For constructing the chemical evolution model of a young galaxy,
we adopt the following assumptions.
(i) We use a closed-box model, i.e. we neglect an infall and outflow of gas in the scale of a star-forming region.
(ii) For the initial mass function (IMF), we adopt the Salpeter
IMF (Salpeter 1955)
φ(m) ∝ m −2.35
(1)
with mass range of (m l , m u ) = (0.1 M⊙ , 100 M⊙ ).
(iii) We neglect the contribution of SNe Ia and winds from lowmass evolved stars to the formation of dust, because we consider
the time-scale younger than 109 yr.
(iv) The interstellar medium is treated as one zone, and the growth
of dust grains by accretion is neglected. Within the short time-scale
considered here, it can be assumed safely (see, e.g. Whittet 1992,
pp. 223–224).
(v) We also neglect the destruction of dust grains within the young
age considered (see e.g. Jones, Tielens & Hollenbach 1996).
(vi) We assumed a constant SFR for simplicity.
using these assumptions, we calculate the chemical evolution. Details of the formulation are presented in Appendix A.
The evolution of the total dust amount for SFR = 1 M⊙ yr−1
is shown in Fig. 2. The dust mass fraction for unmixed and mixed
cases are summarized in Tables 2 and 3, respectively. Comparing the
evolution of dust mass given by T03, dust mass starts to accumulate
later than the case of T03, and gradually approaches the T03 result
towards the age of about 108 Gyr. This difference is caused by the
different formulae we adopted in the calculations of stellar lifetime:
the formula of Schaerer (2002) gives a longer lifetime for the same
stellar mass than that of Inoue, Hirashita & Kamaya (2000) which
is used in T03. At 108 Gyr, T03 and present work yield the same
dust mass.
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N03 investigated the formation of dust grains in the ejecta of Population III SNe (SNe II and PISNe, whose progenitors are initially
metal free). As we mentioned already, they treat some aspects which
TF01 have not taken into account: (i) the time evolution of gas temperature is calculated by solving the radiative transfer equation including the energy deposition of radioactive elements; (ii) the radial
density profile of various metals is properly considered; and (iii)
unmixed and uniformly mixed cases in the He core are considered.
In the unmixed case, the original onion-like structure of elements
is preserved, and in the mixed case, all the elements are uniformly
mixed in the helium core.
It should be mentioned here again that TF01 assumed an adiabatic
cooling in the ejecta and adjusted the adiabatic index γ to 1.25,
referring to the formation episode of dust grains observed in SN
1987A. As pointed out by Kozasa et al. (1989), the condensation
time as well as the resulting average size of dust grains strongly
depend on the value of γ . SN 1987A is somehow a peculiar SN
in the sense that the progenitor is not a red supergiant but blue
supergiant: see Arnett et al. (1989) for details. Using SN 1987A as a
template may not be appropriate in comparisons to SNe as a whole.
Therefore in this paper, we use the result of N03 as a standard model.
We should note that N03 also assume the complete formation
of CO and SiO molecules, neglecting the destruction of those
molecules, i.e. no carbon-bearing grain condenses in the region of
C/O < 1 and no Si-bearing grain, except for oxide grains, condenses in the region of Si/O < 1. The formation of CO and SiO
may be incomplete because of the destruction by energetic electron
impact within SNe. TF01 treat both formation and destruction of
CO and SiO, finding that both are mostly destroyed. The decrease
of CO leads to the formation of carbon grains, which could finally
be oxidized with available oxygen. The destruction of SiO could
decrease the formation of grains composed of SiO 2 , MgSiO 3 and
Mg 2 SiO 4 , and increase other oxidized grains and silicon grains.
Observationally, it is still a matter of debate if CO and SiO are efficiently destroyed or not. For the detailed discussions on this issue,
see Appendix B of N03.
C
Si
SiO 2
Fe
FeS
Fe 3 O 4
Al 2 O 3
MgO
MgSiO 3
Mg 2 SiO 4
Unmixed
Dust emission from forming galaxies
595
Figure 2. Evolution of the mass for each grain species. The thick lines indicate the total amount of dust mass. We assumed the closed-box model and a constant
SFR. The mass fraction of each grain species is constant in time and is given by the size distribution function (Fig. 1).
Table 2. Mass fraction of dust species (unmixed).
Table 3.
(mixed).
Species
Species
C
Si
Fe
FeS
Al 2 O 3
MgSiO 3
Mg 2 SiO 4
SiO 2
MgO
Mass fraction
0.102
0.303
0.050
0.156
0.002
0.010
0.222
0.099
0.056
2.3 SED construction
In this subsection, we present the construction of the SED from dust.
As most of the formulations are in parallel to those in T03 and T04,
here we list the essence of our calculation.
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Al 2 O 3
MgSiO 3
Mg 2 SiO 4
SiO 2
Fe 3 O 4
Mass fraction of dust species
Mass fraction
0.001
0.105
0.202
0.583
0.108
(i) Stochastic heating of very small grains
Very small grains cannot establish thermal equilibrium with the
ambient radiation field, which is called stochastic heating (e.g.
Krügel 2003). To treat this effect, we applied the Debye model
to the specific heat of the grain species as discussed in T03 and
T04. We adopt a multidimensional Debye model (e.g. Draine
& Li 2001) (DL01) for carbon (C) and silicate (SiO 2 , MgSiO 3
and Mg 2 SiO 4 ) grains. For other species, we adopt the classical
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Figure 1. Dust size distributions of the SN II model with the progenitor mass of 20 M⊙ by Nozawa et al. (2003). The thick lines are the total dust size
distribution function. The labels ‘unmixed’ and ‘mixed’ indicate the adopted assumption of the mixing of elements in the ejecta. We assumed 20 M⊙ as a
representative for the SN progenitor mass in this work.
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Table 4. The specific heat of each species.
Species
Debye temperature
(K)
Refa
863
616
—
500
384
511
1030
762
—
—
1
2
1
3
4
5
6
7
1
1
C
Si
SiO 2
Fe
FeS
Fe 3 O 4
Al 2 O 3
MgO
MgSiO 3
Mg 2 SiO 4
N atom
(1022 cm−3 )
11.4
5.00
7.96
8.50
6.62
28.4
23.5
10.7
9.57
9.63
C(T) modelb
Multi-Debye
Debye
Multi-Debye
Debye
Debye
Debye
Debye
Debye
Multi-Debye
Multi-Debye
for Debye temperatures: (1) Draine & Li (2001), (2) Oganov,
Brodhold & Price (2000), (3) Siethoff & Ahlborn (1996), (4) Grønvold
et al. (1991), (5) Shepherd et al. (1991), (6) Mezzasalma (2000), (7) Hama
& Suito (1999).
b ‘Debye’ means that the specific heat C(T) is modelled by the classical
Debye model, while ‘Multi-Debye’ means that the multidimensional Debye
model proposed by Draine & Li (2001) is adopted. For the species to which
we adopt the multidimensional Debye model, we do not give the classical
Debye temperature.
three-dimensional Debye model with a single Debye temperature.
The specific heat model is summarized in Table 4.
(ii) Emission
The emission from dust is calculated in the same way as T03/T04,
basically according to Draine & Anderson (1985). Total dust emission is obtained as a superposition of the emission from each grain
species. The total mass of each grain component is given by N03.
With this value and material density of each species (Table 1), we
can determine the normalization of the dust size distribution (see
Appendix B).
We constructed Q(a, λ) of each grain species from available experimental data via Mie theory (e.g. Krügel 2003, Chapter 2). The
extinction efficiencies are presented in Fig. 3. T03 adopted Draine
& Lee (1984) for the optical properties of these species, being different from the present work. In contrast, we treat detailed species
in the present work. Hence, the mass fraction distributed to carbon
and silicate are significantly reduced comparing to the case of T03.
In the IR, Q(a, λ) of these grains is much larger than other grains
at the whole range of grain size. As a result, the sum of the contributions of all grains are less than that of the case where only two
species are considered as T03.
(iii) Extinction
Self-absorption in the MIR for a very optically thick case is treated
by a thin shell approximation, in the same manner as T04.
3 R E S U LT S
3.1 Evolution of IR SED
We first show the evolution of the IR SED of forming galaxies
based on our baseline model. For these calculation we adopted
SFR = 1 M⊙ yr−1 . We adopt rSF = 30 and 100 pc, the same as those
used in T03. These values are relevant when describing ‘dwarf-like’
young galaxies. The former successfully reproduce various properties of active star-forming dwarf galaxies like SBS 0335−052,
whereas the latter is representative of the size of quiescent dwarf
galaxies like I Zw 18 (Hirashita & Hunt 2004). We will revisit these
representative dwarf starburst galaxies in Section 4.
3.2 Contribution of each species to the SED
The dust species treated here are much more detailed than those of
T03. In order to see the detailed contributors to the total SEDs, we
show the individual SED of each species in Fig. 6. We show the SED
with the age of burst 106.75 yr, where the effect of self-absorption is
negligible.
In both the unmixed and the mixed cases, the smallest dust grain
species is Al 2 O 3 (Fig. 1). However, because of its small fraction
in mass (Fig. 2), Al 2 O 3 contributes to the total SED very little.
The main contributor to the (unextinguished) N–MIR continuum
is silicon for unmixed case and Fe 3 O 4 in mixed case, respectively.
These species are the second smallest grains. For the unmixed case,
as the emissivity of silicon grains with the size of ∼10−7 cm is
much smaller than that of Fe 3 O 4 at λ 1 µm, the grain temperature
becomes much higher than that of Fe 3 O 4 , which makes the very
strong N–MIR continuum emission. In contrast, as Q(a, λ) of Fe 3 O 4
is large, the resultant SED for the mixed case does not have a strong
N–MIR continuum.
At λ = 10–20 µm, several species contribute equally to the
SED in unmixed case, while SiO 2 play a dominant role for mixed
case. At longer wavelengths, the main contributors to the SED
are Mg 2 SiO 4 and amorphous carbon for the unmixed case, and
MgSiO 3 and Mg 2 SiO 4 in the mixed case. In addition, especially at
λ 200 µm, FeS (unmixed) and Fe 3 O 4 (mixed) are also important
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a References
The results are presented in Figs 4 and 5. Fig. 4 is the SED of a
galaxy with rSF = 30 pc, while Fig. 5 is the one for rSF = 100 pc. We
calculated the evolution of the SED in the age range of 106.5 –108 yr.
In a very young phase (age = 106.75 –107.25 yr), unmixed-case SED
has an enhanced N–MIR continuum. After 107.25 yr, the N–MIR
continuum is extinguished by self-absorption in the case of rSF = 30
pc. In contrast, self-absorption is not significant for rSF = 100 pc.
In both cases, the SEDs have their peaks at a wavelength λ ≃ 20–
30 µm, which is much shorter than those of dusty giant galaxies at
z = 1–3 detected by Submillimetre Common User Bolometer Array
(SCUBA). At submm wavelengths, the shape of the continuum is
very similar to each other for mixed and unmixed cases, though
the unmixed case predicts stronger fluxes by a factor of 2. This is
explained by the grain size distributions of the unmixed and mixed
cases: carefully examining Fig. 1, we see that the largest-size dust
grains are more abundant for the unmixed-case size distribution. It
means that larger grains contribute more significantly than smaller
ones. As larger grains radiate their energy at longer wavelengths,
the total SED has a stronger FIR-submm continuum.
As a whole, our model SEDs are less luminous than those of T03
by a factor of 2–3. This is due to the difference in considered grain
species, and more importantly, also due to the improvement of the
treatment of Q(a, λ) at the ultraviolet (UV); Q(a, λ) was approximated to be unity in T03. Also T03 treated the size dependence of
Q(a, λ) by a simple scaling law, which was not very accurate. As
seen in Fig. 3, the size dependence of Q(a, λ) cannot be described by
a simple scaling law, especially at the MIR (see, e.g. Si, Fe and FeS).
We, in this work, used the exact value of Q(a, λ) in all the wavelengths. As some elements have a very small value for Q(a, λ) at the
UV regime, the total absorption probability of UV photons is smaller than that of T03. A strong N–MIR continuum at a very young
phase and the dependence on rSF are qualitatively consistent with the
previous result of T03. However, the dust grains expected from the
N03 model predict a peak of the SED at shorter wavelengths than
those of T03. In addition, a relatively small amount of small dust
grains also makes the N–MIR SED weaker than the T03 one.
Dust emission from forming galaxies
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Figure 3. Extinction efficiency Q(a, λ) for the grain species produced by the SN model of Nozawa et al. (2003). We show Q(a, λ) for the radius a = 10−7 ,
10−6 , 10−5 and 10−4 cm by the curves from bottom to top in each panel.
because of their shallow slope of the extinction efficiency at the
longer wavelength regime. Note that, for the mixed case, Fe 3 O 4
contribute to both NIR and FIR.
In this work we concentrate on the extinction curve in the IR. Detailed discussions of the extinction curves in the optical wavelength
regime are given in Hirashita et al. (2005).2
3.3 Opacity and its evolution
The extinction curve A λ is obtained as
Aλ = 1.086τdust (λ).
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(2)
2 As we assume a very simple geometry, the extinction curve is directly
related to the ‘attenuation curve’, in which the geometrical effect is also
included (for a thorough discussion on this subject, see, e.g. Inoue 2005).
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Figure 5. Same as Fig. 4, but the size of the star-forming region, r SF , is 100 pc.
Fig. 7 presents the evolution of the IR opacity for a young galaxy
with the age of 106.75 –108 yr (from the bottom to the top). In the
case of rSF = 30 pc, the extinction becomes almost unity at 10 µm
when the age is 107.25 yr. Hence, after this age, the N–MIR regime
of the SED becomes optically thick, and this makes the continuum
extinguished in Fig. 4. On the other hand, for rSF = 100 pc, it remains
optically thin even at the age of 108 yr at 10 µm.
In Fig. 7, we find an interesting difference between the extinction
curves of the unmixed and mixed cases. Though their behaviour is
similar to each other at wavelengths λ 10 µm, there is no dip at
λ 10 µm in the curve of the unmixed case. This makes the extinction stronger for the unmixed-case galaxies at N–MIR. In addition,
the MIR bumps at 10 and 20 µm are less prominent for the unmixed
case.
Comparing these IR extinction curves with the T03 model, we
find that the amount of the extinction is smaller than that of T03 by
a factor of 2–10, depending on the wavelength and unmixed/mixed
production. This is explained by the discussion presented in
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Figure 4. The evolution of the IR SED of a very young galaxy. The size of the star-forming region, rSF , is 30 pc. Solid and dotted lines represent the SEDs
based on the unmixed and mixed model of dust production (Nozawa et al. 2003), respectively. For Figs 4 and 5, a constant SFR of SFR = 1 M⊙ yr−1 is adopted.
Dust emission from forming galaxies
599
Figure 7. The evolution of the opacity of a very young galaxy at IR wavelengths. The left panel shows the IR extinction curves calculated with the star-forming
region size r SF = 30 pc, and the right panel shows the curves with r SF = 100 pc. From the bottom to the top, the ages of galaxies are 106.75 , 107.0 , 107.25 , 107.5 ,
107.75 and 108.0 yr, respectively. The solid and dashed curves represent the IR extinction curves based on the unmixed and mixed model, respectively.
Section 2.3: T03 supposed silicates and carbon grains as the constituents of dust grains from SNe. As their Q(a, λ) is larger than the
other species predicted by N03, the total extinction becomes smaller
in this work.
As for the shape of the curve, the extinction curve for the mixed
model resembles that of T03 extinction curves, while the curve for
the unmixed model is qualitatively different at MIR, because of the
weak MIR bump features and the lack of the MIR dip mentioned
above.
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Fig. 8 demonstrates the contribution of each dust grain species
to the total IR extinction curves. The adopted age is 107 yr as a
representative, but the contribution is constant with time.
For the extinction curve of the unmixed case, bump features at
MIR are relatively weak (Fig. 7). Similar to those of the Galactic
IR extinction curve, they are due to silicate grains. In the unmixedmodel extinction, the bumps are dominated by Mg 2 SiO 4 , and the
contribution from MgSiO 3 is not important. We also find a strong
contribution from amorphous carbon grains which have very smooth
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Figure 6. The contribution of each dust species to the total SED of a young galaxy. In this figure we set the galaxy burst age to be t = 106.75 yr and the radius
of the star-forming region to be r SF = 30 pc. The left panel is the SED calculated from the unmixed dust production, and the right panel is obtained from the
mixed dust production.
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dependence of Q(a, λ) on wavelength. They makes the silicate features rather weak, because of their comparable contribution with
Mg 2 SiO 4 . We note that the amorphous carbon does not have any dip
at λ ≃ 5–10 µm. Further, large grains of silicon have a large Q(a, λ)
at these wavelength regime. We find that both the amorphous carbon and the silicon grains equally contribute to the total extinction
at N–MIR, and these species plug up the MIR dip of Mg 2 SiO 4 . At
NIR wavelengths close to 1 µm, FeS also contributes to the total
extinction.
We next see the mixed case. In this case, MgSiO 3 and Mg 2 SiO 4
equally contribute to the total extinction around the MIR bumps. In
contrast to the unmixed case, there is no species which fill up the
dip of silicates, hence we see clear silicate bump features and dips
in the IR extinction curve. In the N–MIR, the main contributors to
the opacity are Fe 3 O 4 and SiO 2 . The contribution from Al 2 O 3 is not
important at any wavelength.
4 DISCUSSION
4.1 Nearby forming dwarf galaxies
It is still a difficult task to observe galaxies in the very first phase
of the SF, especially to detect their dust emission directly. Along
the line of studies made by Hirashita et al. (2002), T03 considered
two local star-forming dwarf galaxies, SBS 0335−052 and I Zw 18,
for investigating the dust emission from very young small galaxies.
Here we revisit these representative star-forming dwarfs with our
framework. As a recent observation of SBS 0335−052 by Spitzer
has been reported (Houck et al. 2004), it is timely to reconsider these
‘textbook objects’ with the new data. In addition, understanding the
SEDs of these objects will shed light to the physics of interstellar
matter and radiation of high-z galaxies also via empirical studies
(e.g. Takeuchi, Yoshikawa & Ishii 2003b; Takeuchi et al. 2005).3
3
We should keep in mind that the following discussion is limited to a particular class of dwarf galaxies dominated by newly formed stars. For the
4.1.1 SBS 0335−052
SBS 0335−052 is a local galaxy (∼54 Mpc) with SFR =
1.7 M⊙ yr−1 (Hunt et al. 2001) and extremely low metallicity
Z = 1/41 Z⊙ . This galaxy is known to have an unusual IR SED
and strong flux at N–MIR. It has a very young starburst (age
5 Myr) without a significant underlying old stellar population (Vanzi
et al. 2000). T03 have modelled the SED of SBS 0335−052 and
reported good agreement with the available observations at that
time.
However, Houck et al. (2004) presented new data of the MIR
SED by Spitzer, and reported a deviation of the model by a factor
of 2 or 3. Their observation indicated that SBS 0335−052 has even
more FIR-deficient SED than ever thought. Hence, it is interesting to
examine whether our present model can reproduce the extreme SED
of this galaxy. We are also interested in the possibility to determine
which of the two pictures, unmixed or mixed, is plausible, by a direct
measurement of the SED.
We show the model SEDs for SBS 0335−052 in Fig. 9. We have
calculated the SED for r SF = 10, 20 and 30 pc for both unmixed
and mixed cases. The SFR is fixed to be 1.7 M⊙ yr−1 , and the age is
106.5 yr. The solid squares are the observed data from the Infrared
Space Observatory ISO, while open squares represent the upper limits obtained from IRAS and ISO observations. The open triangles are
the expected contribution of dust emission calculated by the recipe
of Joy & Lester (1988). The filled triangles depict the measured SED
of SBS 0335−052 by Spitzer IRS taken from Houck et al. (2004)
in the MIR. The filled triangle at FIR is the estimate from the radio
observation of Hunt et al. (2004), which is used by Houck et al.
(2004). Details of the other observational data are found in Section
4 of T03.
In the FIR regime, our model SEDs are consistent with the strong
constraint given by Houck et al. (2004), both for the unmixed and
mixed cases. This is because our present model predicts a peak of
modelling of the SED of normal star-forming dwarfs, see, e.g. Galliano
et al. (2003, 2005).
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Figure 8. The contribution of each dust species to the total IR extinction curve of a young galaxy. In this figure we set the galaxy burst age of t = 107 yr. The
left panel is the extinction curve calculated from the unmixed dust production, and the right panel is obtained from the mixed dust production.
Dust emission from forming galaxies
601
the SED at shorter wavelengths than that of T03. At MIR, though
we cannot give an excellent fit to the observed data, the model SEDs
roughly agree with them, and the unmixed-case SEDs with r SF =
10–20 pc give a better fit. The very strong N–MIR continuum of
SBS 0335−052 is well reproduced by the SED of the unmixed dust
production picture. In contrast, the SEDs of the mixed case seriously
underpredicts the observationally suggested N–MIR continuum. As
we can also calculate the extinction value A λ , we can distinguish
between a mixed-case SED and heavily extinguished unmixed SED
without ambiguity.
In summary, the SED for the unmixed dust production with r SF =
10–20 pc yields a reasonable fit to the latest observations by Spitzer.
This result suggests that we may determine the dust production
(unmixed or mixed) of SNe through the observation of the N–MIR
SEDs of forming galaxies. As for SBS 0335−052, the unmixed dust
production is suggested to take place. In a previous work, we have
modelled a high-z (z = 6.2) extinction curve (Maiolino et al. 2004)
and found that it is well represented by dust produced in unmixed
SNe (Hirashita et al. 2005). This conclusion is strengthened by our
earlier result.
The dust mass calculated by our model at this age of SBS
0335−052 is 1–2 × 103 M⊙ , consistent with the observationally
estimated value by Dale et al. (2001). We note that the mass estimation is strongly dependent on the assumed dust species and
their emissivities, and grain size distribution. As we discussed in
Section 3, the continuum radiation in the N–MIR is dominated by
stochastically heated dust emission, which is completely different
from a modified blackbody. Therefore, when we try to estimate the
dust mass, we must take care to determine the corresponding grain
properties, i.e. radiative processes and grain which are related to the
observed SED of galaxies.
4.1.2 I Zw 18
I Zw 18 is the most metal-deficient star-forming galaxy in the local
Universe (Z = 1/50 Z⊙ ). We adopt its distance of 12.6 Mpc (Östlin
2000), and the SFR of 0.04 M⊙ yr−1 . The existence of the under
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lying old stellar population is suggested for this galaxy, but their
contribution is not dominant (Hunt, Thuan & Izotov 2003). Thus,
it is not unreasonable to adopt our present model to predict the IR
SED of I Zw 18.
Cannon et al. (2002) estimated the total dust mass Mdust = 2–3 ×
103 M⊙ from Hubble Space Telescope (HST) Wide-Field Planetary
Camera 2 (WFPC2) narrow-band imaging. In our model, the dust
mass reaches this value at a burst age of 107.25 –107.5 yr. This age
is consistent with the observationally suggested age of its major SF
(e.g. Hunt et al. 2003). Cannon et al. (2002) obtained the extinction
of AV = 0.5 mag for some patches in this galaxy, which is reproduced
by our model with the above age.
We show our model prediction for the SED of I Zw 18 in Fig. 10.
We present the SED for the age 107.25 yr and 107.5 yr. The NIR flux
measurements are taken from Hunt et al. (2003). I Zw 18 is not
detected at all the four IRAS bands, hence we calculated the upper
limits in the M–FIR from the sensitivity limits of IRAS observation.
At 850 µm, the upper limit is converted from the data reported by
Hunt, Bianchi & Maiolino (2005).
The IR luminosity is slightly smaller than the previous prediction
of T03. We also find that the FIR peak wavelength is located at
λ ∼ 60 µm, shorter than that of the T03 model SED. In addition,
the peak intensity is larger for the mixed model, as the mixed model
produces about 30 per cent more dust than the unmixed model does
(see Fig. 2). As the system still remains optically thin at this age
because of the large r SF value, this difference is directly reflected to
the difference of the peak intensity.
The low opacity of I Zw 18 also leads to a low flux at N–MIR
in the model SED in Fig. 10 both for unmixed and mixed cases
compared with the T03 model SED. As mentioned by T03, the NIR
continuum of I Zw 18 is expected to be dominated by stellar and
nebular continuum radiation, and the contribution of dust may be
negligible.
We expect that these features will be found commonly in young
galaxies if they are optically thin in the IR. Hence, it may be
useful to obtain some suggestions for the observational strategy of young galaxies at high z. We will discuss a well-known
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Figure 9. The model for the SED of a nearby star-forming dwarf galaxy SBS 0335−052. We adopt the SFR SFR = 1.7 M⊙ yr−1 (Hunt et al. 2001). The
galaxy burst age is found to be t = 106.5 yr and the radius of the star-forming region is set at r SF = 10, 20 and 30 pc. Solid squares are the observed data from
ISO, while open squares represent the upper limits obtained from IRAS and ISO observations. Open triangles are the expected contribution of dust emission
calculated by the recipe of Joy & Lester (1988). Solid triangles are taken from recent observation of SBS 0335−052 by Spitzer (Houck et al. 2004). The
left panel is the SED calculated from the unmixed dust production, and the right panel is obtained from the mixed dust production. Clearly, the mixed dust
production poorly reproduces the observed SED of SBS 0335−052.
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real sample of such population of galaxies, LBGs, in the next
subsection.
4.2 LBGs
LBGs are one of the most well-studied categories of high-z starforming galaxies (e.g. Steidel et al. 1999, 2003). Even in LBGs,
there is clear evidence that they contain a non-negligible amount of
dust (e.g. Adelberger & Steidel 2000; Calzetti 2001). A high dust
temperature (70 K) is suggested by subsequent studies (Ouchi et al.
1999; Chapman et al. 2000; Calzetti 2001; Sawicki 2001).
In order to make a consistent picture of the dust emission from
LBGs, T04 applied the T03 model and made various predictions for
these galaxies. They also considered a power-law dust size distribution to examine its effect on the resulting SEDs. The T04 model
reproduced the known observational properties of the dust emission
from LBGs.
In this paper, we investigate the expected appearance of the LBGs
with the improved dust grain formation of N03.
4.2.1 Evolution of the SED of LBGs
We set the input parameters of the SED model for LBGs as follows.
The SFR of LBGs spreads over the range of SFR ≃ 1–300 M⊙ yr−1
with a median of SFR ≃ 20 M⊙ yr−1 (e.g. Erb et al. 2003). A constant SFR up to the age of 109 yr is suggested to be a good approximation (e.g. Baker et al. 2004). Thus, the basic framework of the
T03 model is also valid for LBGs. In this work, we consider the
moderate case of SFR = 30 M⊙ yr−1 over the age of 106.5 –108 yr.
The most important information to calculate the IR SED is the
effective size of the star-forming region, but it is the most uncertain
quantity (see discussion of T04). As the mean half-light radius of
LBGs is estimated to be ∼1.6 kpc from HST observations (Erb et al.
2003), we use the galaxy radius as the radius of a star-forming region,
and set r SF = 2 kpc according to T04.
The SED evolution of LBGs is shown in Fig. 11. Note that the
scale in the ordinate of Fig. 11 is different from those in Figs 4
and 5. Apart from luminosity, the behaviour of the SED evolution
of LBG is qualitatively very similar to that of a dwarf-like forming
galaxy with r SF = 100 pc (i.e. a weak NIR continuum and a strong
M–FIR emission is commonly seen in both). This is because both
the UV photon number density and dust number density are in the
same order for an LBG and dwarf galaxy (r SF = 100 pc). As the IR
luminosity depends on the dust column density, the total luminosity
is different, but the shape of the SED is determined by the balance
between the densities of UV photons and dust grains, they are similar
with each other as for the shape.
The difference between the SEDs of the unmixed and mixed cases
is small, and they give almost the same result especially in the
M–FIR. This is explained as follows: the most prominent difference
between the two is the N–MIR continuum, which is produced mainly
by stochastic heating of grains. If the UV photon density is low,
they are almost always in the lowest temperature state because the
incidence of a UV photon is less frequent. In this case the N–MIR
continuum from stochastically heated dust does not contribute to the
continuum significantly, and the global SED shape is determined by
larger grains in the equilibrium with the ambient UV radiation field.
Under such a condition, they are similar in shape to each other. Thus,
we see that it will be difficult to determine which scenario of dust
production is correct from the observation of LBGs.
4.2.2 Observability of the dust emission from LBG
The flux density of a source at the observed frequency, ν obs is
obtained by
Sνobs =
(1 + z)L νem
(1 + z)L (1+z)νobs
=
4πdL (z)2
4πdL (z)2
(3)
where d L (z) is the luminosity distance corresponding to a redshift z, and ν obs and ν em are the observed and emitted frequency,
respectively.
We show the observed IR/submm SEDs of LBGs at z = 2, 3
and 4 in Fig. 12. For simplicity we only show the SED with the
age of 108 yr. The thick black short horizontal lines indicate the
3σ detection limits for an 8-h observation by ALMA (Atacama
Large Millimeter Array).4 Here we assumed 64 antennas and three
wavelength bands, 450, 850 and 1080 µm. We also show the 3σ
source confusion limit of Herschel5 at 75-, 160-, 250- and 350-µm
4
5
URL: http://www.alma.info/
URL: http://www.rssd.esa.int/herschel/
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Figure 10. A prediction for the SED of a nearby ‘quiescent’ star-forming dwarf galaxy I Zw 18. We adopt SFR = 0.04 M⊙ yr−1 and r SF = 100 pc. The age
of the SF is set to be 107.25 yr (dashed lines) and 107.5 yr (solid lines). As the NIR continuum of I Zw 18 is expected to be dominated by stellar and nebular
continuum radiation, the contribution of dust may be negligible, and it is not necessary to reproduce these NIR observed fluxes by the present model.
Dust emission from forming galaxies
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Figure 12. The expected flux densities of an LBG. In this figure we set the galaxy burst age of t = 108 yr. Confusion limits of Herschel and detection limits
of ALMA 8-h survey are also shown by grey and black thick horizontal lines, respectively.
bands by thick grey horizontal lines. These limits are based on ‘the
photometric criterion’ of (Lagache, Dole & Puget 2003). See also
Ishii, Takeuchi & Sohn (2002) and Takeuchi & Ishii (2004a).
As discussed in T04, the detectability of LBGs is not strongly dependent on their redshifts. The predicted IR luminosity is factor of
2 smaller than that of T04, hence it is more difficult to detect LBGs
than the discussion in T04: we need roughly four times longer an
integration time than that derived from T04, if we fix all the other
conditions. Detection at 350 µm seems impossible for moderateSFR LBGs. However, at longer wavelengths, for ages 108 yr and
SFR 30 M⊙ yr−1 , LBGs can be detected at a wide range of redshifts in the submm by the ALMA deep survey. In the FIR, Herschel
will detect the dust emission from LBGs at z ≃ 2, but it is difficult
at higher z values. As the SED does not differ for the unmixed or
mixed dust formation, our evaluation of the observability of LBGs
holds both for the mixed and unmixed dust formation.
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4.3 Toward higher redshifts
Based on the previous discussions, we give a brief consideration
on the observation of very high-z galaxies (z 5) here. Direct
observation of such galaxies are of vital importance to explore the
physics of galaxy formation.
First, assume a LBG at these redshifts. Fig. 13 shows such a
situation. We assumed the same physical parameters for LBGs. From
Fig. 13, we find that LBG-like objects can be detectable even at z ≃
10 if SFR 30 M⊙ yr−1 . At z ≃ 20, it may be more difficult, but
might be possible to detect LBGs with very high SFR, by an ALMA
ultra-deep survey with a much longer integration time than 8 h.
However, it may not be reasonable to assume galaxy-like LBGs
at z ≃ 10 because they are rather massive system in general (M star ≃
1010 M⊙ ), and, from a modern cosmological viewpoint, such a massive system is very rare with such a high-z, young universe.
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Figure 11. The evolution of the SED of a typical LBG. The SFR is set to be SFR = 30 M⊙ yr−1 , and the size of the star-forming region r SF = 2 kpc.
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Figure 14. The expected flux densities of a dwarf star-forming galaxy located at z = 5, 10 and 20. The solid lines represent the SEDs for the unmixed case
of dust production, and the dotted lines for the mixed case. We assumed SFR = 10 M⊙ yr−1 and r SF = 30 pc. The thick lines are the expected SEDs for an
unlensed galaxy, while the thin lines are the ones for a gravitationally lensed galaxy by a magnification factor of 40. Again the detection limits are the same as
those of Fig. 12.
Here we discuss an object less massive than LBGs. In modern
hierarchical structure formation scenarios, it would be more reasonable to assume a small, subgalactic clump as a first forming
galaxy. Consider a dark halo of mass ∼109 M⊙ , it is then expected
to contain a gas with mass ≃108 M⊙ . For this purpose, we calculate
the SEDs for a dwarf star-forming galaxy. If gas collapses on the
free-fall time-scale with an efficiency of ǫ SF (we assume ǫ SF = 0.1),
we obtain the following evaluation of the SFR Hirashita & Hunt
(2004):
ǫSF
SFR ≃ 0.1
0.1
Mgas
107 M⊙
nH
100 cm−3
1/2
[M⊙ yr−1 ] (4)
and
n H ≃ 100
rSF
100 pc
−3
Mgas
107 M⊙
[cm−3 ],
(5)
where n H is the hydrogen number density. Then we have
ǫSF
SFR ≃ 0.1
0.1
Mgas
107 M⊙
3/2
rSF
100 pc
−3/2
[M⊙ yr−1 ] . (6)
If we consider Mgas ≃ 108 M⊙ , we have SFR ≃
3(r SF /100 pc)−3/2 M⊙ yr−1 . In addition, as we see below, an
extremely high-z galaxy observed by HST has a very compact
morphology (Kneib et al. 2004). We also mention that, from a
theoretical side, high-z galaxies are suggested to be dense and
compact compared to nearby galaxies (Norman & Spaans 1997;
Hirashita & Ferrara 2002). Hence, it may be reasonable to assume
a same type of galaxy as local dwarfs discussed in Section 4.2.1.
Thus, we consider a dwarf galaxy with SFR = 10 M⊙ yr−1 as an
example, and we adopt r SF = 30 and 100 pc. The age is set to be
107 yr. If the age is older, they will become easier to detect if a
constant SFR takes place. We show the expected SEDs for such
galaxies at z = 5, 10 and 20 in Figs 14 and 15. As expected, it
seems almost impossible to detect such objects by Herschel or
ALMA.
There is, however, the possibility of observing such a small forming galactic clump directly: gravitational lensing works very well as
a natural huge telescope. For example, MS 1512−cB58 is an ideal
case of a lensed LBG (Nakanishi et al. 1997; Baker et al. 2004),
and more recently, a small star-forming galaxy has been detected
by HST and Spitzer observations (Kneib et al. 2004; Egami et al.
2005). Hence, we can expect a forming galaxy which is intrinsically small and faint but magnified by a gravitational potential of a
cluster of galaxies. If we assume a lens magnification factor of 40,
such a small galaxy becomes detectable. This is depicted by the thin
lines in Figs 14 and 15. As the expected SED of such a compact
dwarf galaxy has a strong MIR continuum at their rest frame, it
can be feasible to detect at the FIR in the observed frame. Indeed,
at z = 5 they appear above the confusion limits of Herschel. As
the confusion limit of Herschel may be, in fact, very difficult to
reach in actual observations, a cooled FIR space telescope is more
suitable for such observation, and this will be a strong scientific
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Figure 13. The expected flux densities of an LBGs hypothetically located at z = 5, 10 and 20. The assumed parameters are the same as those for Fig. 12. The
solid lines represent the SEDs for the unmixed case of dust production, and dotted lines for the mixed case. We put the same observational detection limits as
in Fig. 12 for Herschel and ALMA.
Dust emission from forming galaxies
605
motivation for a future project like SPICA.6 In the FIR wavelength
regime (50–200 µm), the SEDs of unmixed and mixed cases might
be distinguishable. If FIR spectroscopy is performed, the picture of
dust production is plausible might be examined. At higher z values,
they can be detected by the ALMA survey. Even at z ≃ 20, they
can be detected by a standard 8-h survey of ALMA, if lensing takes
place. It is interesting to note that, at z ≃ 10, the peak of their SED
happens at the wavelength range where the detection limits of both
Herschel and ALMA are not very good. A new effective (probably
space) facility should be developed to overcome this observational
difficulty.
With this line of study, we must estimate how frequently such
lensing events occur for high-z objects. Suppose a cluster of galaxies at z l ≃ 0.1–0.2 whose dynamical mass M dyn is 5 × 1014 M⊙
and whose mass distribution obeys the singular isothermal sphere.
We denote the strong lensing cross section, i.e. the area of the region in the source plane for which the resulting magnification by a
cluster is larger than µ, as σ (>µ). Perrotta et al. (2002) presented
σ (>µ) as a function of M dyn for z lens = 1.0. As σ (>µ) ∝ D ls 2 [D ls
is the angular-diameter distance between the lens and the source
(e.g. Asada 1998)] (Covone, Sereno & de Ritis 2005), we can convert their result to our condition and obtain σ (>10) ≃ 30 arcsec2 on
the source plane.7 This result is almost independent of the source
redshifts. Setting the limiting flux density S ν = 1 µJy and using the
number counts of Hirashita & Ferrara (2002) for galaxies at z > 5,
we have an expected number of galaxies suffering a strong lensing
of ≃1–3. Thus, we expect at least a few strongly lensed IR galaxies
to this survey depth.
To have a concrete idea for the observational strategy, we must
consider an important aspect of the lensing. It is known that the
gravitational lensing affects the galaxy number counts in two opposite directions: (i) it magnifies the flux density of galaxies; and (ii)
it stretches the sky area and decreases their number density on the
sky. This is called the ‘magnification bias’ (Fort, Mellier & DantelFort 1997; Bézecourt, Pelló & Soucail 1998). The unlensed number
count N 0 (>S ν ) is generally approximated by a power law
N0 (>Sν ) ∝ Sν β .
(7)
Then, by denoting the magnification factor as µ, we obtain the lensed
number counts N lens (>S ν ) as
Nlens (>Sν ) = N0 (>Sν )µ−(β+1)
6
7
URL: http://www.ir.isas.jaxa.jp/SPICA/index.html
On the image plane, the area corresponds to ≃µσ (>µ).
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(8)
(e.g. Fort, Mellier & Dantel-Fort 1997; Takeuchi, Yoshikawa &
Yonehara 2000). Equation (8) shows that whether the number counts
increases or decreases depends on the slope of the counts, β: if
β < −1 lensing works as an enhancement of the counts. As the
slope of the number counts of such galaxies is expected to be steeper
than −1 (e.g. Hirashita & Ferrara 2002), the source density on the
image plane will increase (see also Perrotta et al. 2002). Thus, we
are confident that the lensing will work as a really useful tool to
detect small galaxies forming via dust emission.
5 CONCLUSION
Dust plays various important roles even in the very early phase of
galaxy evolution (e.g. Hirashita & Ferrara 2002). In such a young
phase with a typical age less than 109 yr, dust is predominantly
supplied by SNe. With the aid of a new physical model of dust
production by SNe developed by N03, we constructed a model of
dust emission from very young galaxies according to T03.
N03 carefully took into account the radial density profile and the
temperature evolution in the calculation of the dust formation in the
ejecta of SNe II and PISNe. They also showed that the produced
dust species depends strongly on the mixing within SNe. We treated
both unmixed and mixed cases and calculated the IR SED of young
galaxies for both cases.
The SEDs constructed from N03 dust production are less luminous than those by T03 model by a factor of 2–3. This difference is
due to the improvement in the treatment of Q(a, λ) at UV and the
considered grain species. The SED for the unmixed case is found to
have a strong N–MIR continuum radiation in its early phase of the
evolution (age 107.25 yr) compared with that for the mixed case.
The N–MIR continuum is due to the emission from silicon grains,
which only exist in the species of the unmixed dust production.
We also calculated the IR extinction curves for young galaxies. N03 dust gives a weaker extinction than that of T03 model
because of the small relative number of very small dust grains.
This is also the cause of the smaller IR luminosity of the present
model. For the unmixed case, NIR extinction is dominated by large
grains of silicon and amorphous carbon, and silicate features are
less prominent compared to the curve given by T03. In contrast, the
extinction curve of the mixed case has a similar shape to that of
T03.
The SED of a local starbursting dwarf galaxy, SBS 0335−052,
was calculated. Recent Spitzer observations (Houck et al. 2004) have
implied a hotter dust than previously thought. Our present model
SED naturally reproduces the strong N–MIR continuum and the lack
of cold FIR emission of SBS 0335−052. We found that only the SED
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Figure 15. The same as Fig. 14, except that r SF = 100 pc.
606
T. T. Takeuchi et al.
AC K N OW L E D G M E N T S
First we are grateful to the anonymous referee for many insightful
comments which have improved the clarity of this paper so much.
We deeply thank Akio K. Inoue, Jean-Paul Kneib and Giovanni
Covone for illuminating discussions. We made extensive use of the
NASA Astrophysics Data System. TTT, TTI and HH have been
supported by the Japan Society of the Promotion of Science. TK
is supported by a Grant-in-Aid for Scientific Research from JSPS
(16340051).
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Dust emission from forming galaxies
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2005 RAS, MNRAS 362, 592–608
A P P E N D I X A : D E TA I L S O F T H E C H E M I C A L
E VO L U T I O N
Here we present a detailed description of the chemical evolution
used in this work. Full treatment of the present chemical evolution
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the framework of the closed-box model, the total baryonic mass of
a galaxy, M T , is conserved as
MT = Mgas (0) = Mgas (t) + Mdust (t) + Mstar (t) + Mrem (t),
(A1)
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given by
dMISM
= −ψ(t) +
dt t
mu
ml
[m − m rem (m)] ψ(t − τm )φ(m)dm,
(A2)
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by Umeda & Nomoto (2002)
m rem (m) = 0.06m + 0.93(8 < m < 40 M⊙ ).
(A3)
For other progenitor mass ranges, we set mrem (m) = 0 at m < 8 M⊙
(no remnants), and mrem (m) = m at 40 M⊙ < m < 100 M⊙ (all the
mass is swallowed by a black hole). In this work, we do not treat
PISNe in the calculation. By equation (A3), the time evolution of
Mrem (t) is expressed by
dMrem
=
dt t
mu
m rem (m)ψ(t − τm )φ(m)dm.
(A4)
ml
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Mdust (t)
dMdust
=−
ψ(t) +
dt t
MISM (t)
mu
ml
m dust (m)ψ(t − τm )φ(m)dm
(A5)
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20 M⊙ for the fraction and the size distribution of dust grain species,
hence the mass fraction and size distribution are constant in time
along with the evolution.
A P P E N D I X B : N O R M A L I Z AT I O N O F T H E
NUMBER DENSITY OF GRAIN SPECIES
In this Appendix, we show how to obtain the normalization of the
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dNi
da ≡ A f i (a) da
da
(B1)
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607
608
T. T. Takeuchi et al.
where subscript i denotes the species of dust, and f i is the mass
fraction of dust of species i, given by N03, and A is the normalization
constant. We denote the material density of i-species dust by ρ i , and
the SF region radius as r SF 0. The total mass of dust species i, Mi , is
then written as
Mi = ρi
3
4πa dNi
da = ρi
3 da
4πA
ρi
=
3
3
4πa
A f i (a) da
3
a 3 f i (a) da.
(B2)
Hence
A=
4π
3M
.
ρ
f i (a)a 3 da
i i
(B4)
Thus we can determine A from the available data. Note that only M
depends on time t, hence the time dependence of A is given only
through M. The total number of grains, Ni , is expressed as
Ni =
dNi
dai .
dai
(B5)
The total dust mass of all the species, M, is
M=
i
3
ρi
4πA
f i (a)a da =
ρi f i (a)a 3 da . (B3)
3
3
This paper has been typeset from a TEX/LATEX file prepared by the author.
i
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4πA
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2005 RAS, MNRAS 362, 592–608