MNRAS 447, L16–L20 (2015)

doi:10.1093/mnrasl/slu175

Evolution of grain size distribution in high-redshift dusty quasars:
integrating large amounts of dust and unusual extinction curves
Takaya Nozawa,1‹ Ryosuke S. Asano,2 Hiroyuki Hirashita3 and Tsutomu T. Takeuchi2
1 National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan
2 Department of Particle and Astrophysical Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
3 Institute of Astronomy and Astrophysics, Academia Sinica, PO Box 23-141, Taipei 10617, Taiwan

ABSTRACTThe discoveries of huge amounts of dust and unusual extinction curves in high-redshift quasars(z  4) cast challenging issues on the origin and properties of dust in the early Universe. In thisLetter, we investigate the evolutions of dust content and extinction curve in a high-z quasar,based on the dust evolution model taking account of grain size distribution. First, we showthat the Milky Way extinction curve is reproduced by introducing a moderate fraction (0.2)
of dense molecular-cloud phases in the interstellar medium for a graphite–silicate dust model.
Then we show that the peculiar extinction curves in high-z quasars can be explained by taking
a much higher molecular-cloud fraction (0.5), which leads to more efficient grain growth andcoagulation, and by assuming amorphous carbon instead of graphite. The large dust content
in high-z quasar hosts is also found to be a natural consequence of the enhanced dust growth.
These results indicate that grain growth and coagulation in molecular clouds are key processes
that can increase the dust mass and change the size distribution of dust in galaxies, and that,along with a different dust composition, can contribute to shape the extinction curve.
Key words: stars: formation – ISM: clouds – dust, extinction – galaxies: evolution – galaxies:
general – galaxies: ISM.

1 I N T RO D U C T I O NThere are some pieces of evidence that the extinction curves observed for high-redshift (z  4) quasars are different from those forthe lower redshift counterparts. Maiolino et al. (2004) found that thequasar SDSS J1048+4637 (hereafter J1048+4637) at z = 6.2 exhibits an unusual UV extinction curve, being flat at wavelengths
λ  1700 Å and rising at λ  1700 Å. Gallerani et al. (2010)
showed that the UV extinction curves in seven reddened quasars
at z = 3.9–6.4 have no 2175 Å bump and are flatter than those inquasars at z  2 which are described by the extinction curve in the
Small Magellanic Cloud (SMC; Richards et al. 2003; Hopkins et al.
2004). It has also been suggested that the extinction laws in thequasars CFHQS J1509−1749 at z = 6.12 (Willott et al. 2007) andSDSS J1044−0125 at z = 5.8 (Maiolino et al. 2004) are similar tothat in the quasar J1048+4637 (but see Hjorth et al. 2013). The UV
extinction curve in J1048+4637 is successfully reproduced by themodels of dust produced by Type II supernovae (SNe II; Maiolino
et al. 2004; Hirashita et al. 2005, 2008; Bianchi & Schneider 2007),
which seems to support the idea that the interstellar dust in such

 E-mail: takaya.nozawa@nao.ac.jp

early epochs was predominantly supplied by SNe II generating frommassive stars with short lifetimes.
On the other hand, a significant fraction of high-z quasars, including J1048+4637, manifest the presence of dust mass in excess
of 108 M in their host galaxies (e.g. Calura et al. 2014). Suchhuge amounts of dust grains can be explained by dust production in
SNe II if one SN ejects more than 1 M of dust (Dwek, Galliano &Jones 2007; Dwek & Cherchneff 2011) and/or if the stellar initial
mass function (IMF) is biased to a much higher mass than the local
one (Valiante et al. 2009; Gall, Andersen & Hjorth 2011a,b). However, many studies have argued that, in addition to the contributions
from SNe II and asymptotic giant branch (AGB) stars, grain growth
via accretion of gaseous metals in the interstellar medium (ISM) is
required to account for the observed dust mass (Michalowski et al.
2010; Mattsson 2011; Pipino et al. 2011; Valiante et al. 2011; Kuo& Hirashita 2012). Thus, if grain growth is the dominant process forincreasing the dust mass, as is considered in the Milky Way (MW;
Dwek & Scalo 1980; Zhukovska, Gail & Trieloff 2008; Inoue 2011;
Hirashita & Kuo 2011; Asano et al. 2013a), then the observed unusual extinction curves may not necessarily reflect the SN origin of
dust in high-z quasars.
Most of the dust evolution models focused only on reproducing
the observed dust mass by estimating the contributions of dust formation and destruction to the total dust budget in galaxies. TheseC 2014 The Authors
Published by Oxford University Press on behalf of the Royal Astronomical Society

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Accepted 2014 October 24. Received 2014 October 23; in original form 2014 August 22

Dust evolution in high-z quasars

2 D U S T E VO L U T I O N M O D E L A N D
R E P RO D U C T I O N O F E X T I N C T I O N C U RV E I N
THE MW
2.1 Review of the adopted model
In this study, we adopt the evolution model of dust in galaxies constructed by Asano et al. (2013b). This model self-consistently treats
the time variation of size distribution of interstellar dust caused by
the following dust processes: dust formation by SNe II and AGB
stars, grain growth due to the accretion of gaseous metals, dust destruction by interstellar shocks, shattering and coagulation due tograin–grain collisions in the ISM.
In the model, the composition, size distribution and mass of dust
ejected by SNe II are taken from the calculations of dust formationin the ejecta and dust destruction in the reverse shocks by Nozawa
et al. (2003, 2007). The masses of various grain species produced
by AGB stars are taken from Zhukovska et al. (2008), assuming thatthe size distributions of those grains are lognormal with a peak at a
grain radius a = 0.1 µm. The initial stellar mass ranges of SNe II and
AGB stars are set to be 8–40 M and 1–7 M , respectively, under
the Salpeter IMF in the stellar mass range of 0.1–100 M . The starformation rate at a time t is calculated as SFR(t) = MISM (t)/τ SF ,where MISM (t) is the total mass of gas and dust in the ISM, and τ SF
is the time-scale of star formation.
In this dust evolution model, the size distributions of grain species
except for carbonaceous grains are summed up so that they are integrated as silicate grains. This corresponds to the fact that two
dust species, carbonaceous (graphite) and silicate grains, are taken

1 As in the previous studies, we here assume that the extinction curvesof high-z quasars are shaped by the interstellar dust in the host galaxies.
However, it may be possible that they reflect the properties of dust in thelocal environments such as the nuclear tori (e.g. Gaskwell et al. 2004).

as major components of interstellar dust, to simplify the calculations of grain growth, shattering and coagulation, as well as thecalculations of extinction curves. For the growth process of grains,
the accretion of refractory elements on to pre-existing grains is
calculated with the sticking probability of unity, by following theprescription in Hirashita & Kuo (2011). As for the destruction ofinterstellar dust in high-velocity shocks driven by SNe, the modification of grain size distribution by sputtering is computed on thebasis of the formulae in Yamasawa et al. (2011).
The model also takes into account the processing of dust throughshattering and coagulation in the interstellar turbulence (Hirashita& Yan 2009). It is assumed that shattering occurs if the relative
velocity of grains is higher than 1.2 and 2.7 km s−1 for carbonaceous and silicate grains, respectively (Jones, Tielens & Hollenbach 1996). Coagulation occurs for the relative velocities lower
than 10−3 –10−1 km s−1 , depending on the composition and radiusof grains (Chokshi, Tielens & Hollenbach 1993). Grain velocities
in turbulence are taken from the results of magnetohydrodynamic
calculations by Yan, Lazarian & Draine (2004).
In order to follow the contributions of shattering and coagulationin different phases of the ISM, multiple phases are considered withina framework of the one-zone closed model; the contributions of dust
processes in each phase are weighted by a mass fraction of each
ISM phase ηi , where i denotes the phase of the ISM. Asano et al.
(2013b) considered a two-phase model of the ISM: warm neutral
medium (WNM, with gas temperature Tgas = 6000 K, and hydrogen
number density nH = 0.3 cm−3 ) and cold neutral medium (CNM,
Tgas = 100 K, nH = 30 cm−3 ) with ηWNM = ηCNM = 0.5. In thistwo-phase model, grain growth, whose rate is proportional to thegas density, occurs only in the CNM. Shattering due to collisions
between grains occurs in the WNM, whereas coagulation due tocollisions between grains occurs predominantly in the CNM.
We also calculate the extinction curves following Asano et al.
(2014), who used the optical constants of graphite and silicate takenfrom Draine & Lee (1984). In this Letter, we also adopt the opticalconstants of amorphous carbon (see Section 3).

2.2 New features in this work
Asano et al. (2014) found that the extinction curve derived from thedust evolution model by Asano et al. (2013b) shows too steep a UV
slope and too large a 2175 Å bump to be consistent with that in the
MW (see fig. 6 in Asano et al. 2014). This indicates that the grain
size distribution predicted by this model is largely overabundant insmall grains, compared with the interstellar dust models deduced
from the fitting to the average MW extinction curve (Mathis, Rumpl& Nordsieck 1977; Weingartner & Draine 2001; Zubko, Dwek &Arendt 2004). The classical interstellar dust model by Mathis et al.
(1977) has a power-law size distribution in the range of a = 0.005–
0.25 µm, while the grain size distribution by Asano et al. (2013b)
has a bump at a = 0.01–0.03 µm.
Asano et al. (2014) argued that one of the reasons for thisoverabundance of small grains (underabundance of large grains)might be inefficient coagulation resulting from the unreasonably low
threshold velocities of coagulation. Thus, they also examined a casewhere the threshold velocity of coagulation is removed, keeping theother parameters unchanged (τ SF = 5 Gyr and ηWNM = ηCNM = 0.5).
However, as shown in Fig. 1, the resulting extinction curve at
t = 10 Gyr is still too steep with too strong a UV bump, although
it is nearer to the observed MW extinction curve than the originalmodel with the coagulation threshold. The absence of coagulation
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models assumed a representative grain size or a specific grain size
distribution throughout the galaxy evolution, and thus cannot makeany prediction on extinction curves. In addition, the efficiencies ofdust destruction and grain growth, as well as the efficiency of extinction by dust, heavily depend on the size distribution of the dust
grains. In particular, the efficiency of grain growth is higher for asmaller surface-to-volume ratio of the grains, and the efficient production of small grains through shattering by grain–grain collisions
is found to be necessary for boosting the mass of dust via grain
growth (Hirashita & Kuo 2011; Kuo & Hirashita 2012; Asano et al.
2013b). Hence, to model properly the evolution of dust mass and to
predict the extinction curves, it is essential to clarify how the size
distribution of grains changes in the course of galaxy evolution.
Recently, Asano et al. (2013b) constructed an evolution model ofgrain size distribution taking into account the fundamental physicalprocesses of formation and destruction of dust. This model enables
us to predict the extinction curves in galaxies as a function of time
(Asano et al. 2014). In this Letter, we apply their dust evolution
model to investigate the evolution of grain size distribution andthe expected extinction curves in high-z quasars.1 In Section 2, we
briefly describe our dust evolution model, and illustrate how theMW extinction curve is reproduced by our model. In Section 3, we
present the results for the evolution of dust and extinction curves
in high-z dusty quasars. In Section 4, we provide the conclusions.
Throughout this Letter, we assume dust grains to be spherical.

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our dust evolution model can reproduce the MW extinction curvewith a reasonable choice of ηi if the coagulation threshold velocity
is excluded. In what follows, we assume no threshold velocity forthe calculation of coagulation.

3 D U S T E VO L U T I O N I N H I G H - R E D S H I F T
Q UA S A R S

threshold is supported by the studies of the variation of extinction
curves in the MW (Hirashita & Voshchinnikov 2014).
To overcome this defect, in the present calculations, we include
the third phase of the ISM, molecular clouds (MCs, Tgas = 25 K,
nH = 300 cm−3 ), where the gas density is high enough to increase
the efficiency of coagulation. In fact, a three-phase ISM model issuggested, for which the MC phase has a similar mass fraction
to the CNM (e.g. Whittet 2003). The solid line in Fig. 1 showsthe extinction curve for the three-phase ISM with ηWNM = 0.5,
ηCNM = 0.3 and ηMC = 0.2. The extinction curve becomes flatter
thanks to the enhanced production of large grains by coagulation(and grain growth) in MCs, and much better agrees with the MW
extinction curve, although the agreement is not perfect. Nevertheless, given the variety of extinction curves along the lines of sight(Fitzpatrick & Massa 2007; Nozawa & Fukugita 2013), we regard
that the agreement is satisfactory. This allows us to conclude that

Figure 2. Left: time evolutions of dust-to-gas mass ratios with grain growth (thick solid) and without grain growth (thin solid) calculated with τ SF = 0.5 Gyr,ηWNM = 0.3 and ηMC = 0.7. The dashed line draws the time evolution of metallicity (MZ /MISM ), where MZ is the total mass of metals in a galaxy. Right: grain
size distributions for the dust evolution with grain growth given by the thick solid line in the left-hand panel. The dot–dashed, dotted, dashed and solid lines
show the grain size distributions at t = 0.1, 0.3, 0.5 and 1 Gyr, respectively. The thin dot–dashed line indicates the MRN size distribution.

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Figure 1. Extinction curves at a galactic age of t = 10 Gyr obtained from thecalculations of the dust evolution with no threshold velocity of coagulation
for the star formation time-scale of τ SF = 5 Gyr. The dotted line is the resultfor ηWNM = ηCNM = 0.5, which was discussed in Asano et al. (2014). The
solid line shows the extinction curve for ηWNM = 0.5, ηCNM = 0.3 andηMC = 0.2, which is examined in this study. The filled diamonds denote theaverage extinction curve in the MW (Whittet 2003).

In the last section, we demonstrated that the evolution model ofgrain size distribution reasonably reproduces the MW extinction
curve. Thus, it is a powerful tool with which we can discuss thedifference in the extinction curve, according to the properties andages of galaxies. In this section, we apply this model to high-z dusty
quasars to investigate the evolution of dust grains and extinction
curves in such young systems. It should also be emphasized that amass fraction of each ISM phase is important in regulating the size
distribution of interstellar dust grains, as shown in Section 2.2.
For high-z dusty quasars, it is deduced from their extremely highfar-infrared luminosities that intense starbursts are ongoing with thestar formation rates of 103 M yr−1 (e.g. Bertoldi et al. 2003).
This implies that a huge amount of dense MCs, in which stars
are born, are present in their host galaxies. In fact, according to
the compilation of high-z quasars in Calura et al. (2014), a massfraction of H2 molecules to the total hydrogen (H + H2 ) is in therange of 70–97 per cent, suggesting that a mass fraction of the MCphase is significantly high in these quasar hosts. Therefore, in thecalculations of dust evolution in high-z quasars, we adopt a twophase model of WNM and MC with ηWNM = 0.3 and ηMC = 0.7.
Fig. 2 (left-hand panel) shows the evolutions of dust-to-gas mass
ratios (Md /MISM ) and metallicity (MZ /MISM ) calculated by our dust
evolution model. Since the star formation rates are found to be very
high for high-z dusty quasars, we here adopt τ SF = 0.5 Gyr, which
is 10 times shorter than in the case of the MW. At the initial phasesof the galaxy evolution (t  0.2 Gyr), stellar ejecta enrich the ISM
with dust grains of a = 0.1–1 µm (see the right-hand panel of Fig. 2).
Then, shattering becomes effective at t  0.2 Gyr, producing a large
number of small grains. Since the ISM is considerably enrichedwith metals (MZ /MISM  0.005  0.3 Z ) by this epoch, thesesmall grains efficiently grow through the accretion of gaseous metals in MCs, enhancing the dust-to-gas mass ratio quickly. AroundDust evolution in high-z quasars

t = 1 Gyr, the dust mass produced by grain growth accounts formore than 80 per cent of the total dust mass, and the dust-to-gas
mass ratio increases up to 0.01. Given that these high-z quasars
have the ISM mass well above MISM = 1010 M (Calura et al.
2014), this result can fully explain the observed masses of dust inexcess of 108 M .
Fig. 2 also presents the evolution of dust-to-gas mass ratio without grain growth (thin solid line). If grain growth does not work,
the dust-to-gas mass ratio reaches only  1.5 × 10−3 at t = 1–
2 Gyr. This value exceeds a lower limit of dust-to-gas mass ratios(8 × 10−4 ), derived by taking the dynamical mass as the total massof the ISM (Kuo & Hirashita 2012). However, the dynamical mass
includes all components (gas, stars and dark matter), so this lower
limit is likely to underestimate largely the dust-to-gas mass ratio
for most of the high-z quasars. Although we could not completely
reject the model without grain growth, the model with grain growthmore robustly explains the large dust-to-gas ratio in high-z quasars(see also Valiante et al. 2011).
Fig. 3 shows the time evolution of the UV extinction curve (normalized to the extinction at λ = 0.3 µm) corresponding to the dust
evolution with grain growth given in Fig. 2. At t = 0.1 Gyr, when
SNe II predominantly inject large grains into the ISM, the extinction
curve is flat. From t  0.2 Gyr, at which small grains are produced
due to shattering, the extinction curve becomes steep and its shapeis regulated by the dust processes in the ISM (shattering and grain
growth) not by the properties of dust supplied by stellar sources.
After that, the UV extinction curve becomes flatter again due tothe increase in large grains by efficient coagulation in MCs. At
t = 1 Gyr, the extinction curve has the prominent 2175 Å bump,
but its overall slope is much flatter than the SMC extinction curve,
which is considered to be valid for low-z quasars.
We note that, if SNe II are only the sources of interstellar dust
(i.e. without grain growth) throughout the galaxy evolution, the resulting extinction curves remain too flat, like the one at t = 0.1 Gyr(dot–dashed line) in Fig. 3. Such flat extinction curves would be inconsistent with the z = 6.2 extinction curve (see also Hirashita et al.
2008). Furthermore, it is hard to explain the observed dust content
only by dust production in SNe II. Thus, the above results indicate

Figure 4. UV extinction curves (AV /A0.3 µm ) at t = 1 Gyr derived with theoptical constants of amorphous carbon for carbonaceous grains. The dotted,
thick solid and dashed lines show the cases with (ηWNM , ηMC ) = (0.5,0.5), (0.3, 0.7), (0.1, 0.9), respectively. The hatched region is the rangeof the extinction curve including the uncertainty derived for the quasar
J1048+4637 at z = 6.2 (Maiolino et al. 2004). The SMC extinction curveis drawn by the thin solid line.

that the high dust-to-gas mass ratio and the tendency that extinction
curves are moderately flat in high-z quasars can be simultaneously
explained only by introducing a large MC fraction which leads tohigh rates of grain growth and coagulation.
It should be noticed here that the calculated extinction curves
show the prominent 2175-Å bump, which disagrees with the extinction curves observed for high-z quasars. This might be a discrepancy
arising from the grain material rather than from the grain size distribution. We used graphite to fit the 2175-Å bump, but it has beensuggested that the carrier of this UV bump is polycyclic aromatichydrocarbons (PAHs; Joblin, Leger & Martin 1992; Weingartner &Draine 2001). PAHs are likely to form through photofragmentationof small amorphous hydrocarbon (Jones 2009) and/or shattering oflarge carbonaceous grains (Seok, Hirashita & Asano 2014), while
PAHs are efficiently destroyed by SN shocks and/or UV radiationfrom massive stars, which is not included in our model. The observations of some carbonaceous features including mid-infrared PAH
emissions in high-z galaxies may give us a clue to the properties ofcarbonaceous dust in the early Universe (e.g. Riechers et al. 2014).
Because of poor knowledge on the properties of carbonaceous
materials in high-z galaxies, we also calculate the extinction curves
by adopting the optical constants of amorphous carbon by Zubko
et al. (1996), instead of graphite. The results are shown in Fig. 4,
where the extinction curves at t = 1 Gyr are plotted for the cases of(ηWNM , ηMC ) = (0.5, 0.5), (0.3, 0.7) and (0.1, 0.9). For a higher ηMC ,the extinction curve is flatter because more efficient coagulation isrealized. As is evident from Fig. 4, changing the properties of carbonaceous materials with a large ηMC ( 0.5) leads to a successful
fit to the high-z quasar extinction curve represented by the one in
J1048+4637.
The above results imply that the primary form of carbonaceous
grains in high-z dusty quasars is amorphous carbon, and that thefraction of MCs is higher than 0.5 in the host galaxies. Although
the origin of the different composition of carbonaceous materials
in high-z galaxies from those in the local galaxies cannot be resolved by our dust evolution model, the absence of the 2175-Å
bump in high-z extinction curves may suggest inefficient formation
and/or efficient destruction of small size of graphite and PAHs. Furthermore, a high fraction of MCs is the key in explaining a high
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Figure 3. Time evolution of the UV extinction curve (AV /A0.3 µm ) for thedust evolution with grain growth given in Fig. 2. Here, the optical constantsof graphite are used for carbonaceous grains. The dot–dashed, dotted, dashedand thick solid lines show the extinction curves at t = 0.1, 0.3, 0.5 and 1 Gyr,respectively. For reference, the SMC extinction curve is depicted by the thinsolid line, and the range of the extinction curve including the uncertainty
derived for the quasar J1048+4637 at z = 6.2 (Maiolino et al. 2004) are
drawn as the thin hatched region.

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dust-to-gas mass ratio in high-z quasars, since MCs are unique sites
in which dust mass growth by accretion, as well as dust size growthby coagulation, occurs efficiently.
4 CONCLUSION

AC K N OW L E D G E M E N T S
We are grateful to the anonymous referee for critical comments.
We are also grateful to Y. Matsuoka and T. Minezaki for usefulcomments. We thank R. Maiolino for kindly providing us withthe data on the extinction curve of J1048+4637. TN and TTT aresupported by JSPS KAKENHI (22684004, 23224004, 23340046,
26400223). HH thanks the support from the Ministry of Scienceand Technology (MoST) grant 102-2119-M-001-006-MY3.
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We investigated how the massive amounts of dust and the extinction
curves in high-z dusty quasars can be reproduced in a self-consistentmanner, and discussed the difference in the ISM condition between
the MW and the high-z quasars. First, we found that the MW extinction curve is successfully reproduced by our dust evolution modelwith a three-phase ISM including the phase of MCs. We also showedthat our model can simultaneously account for the large amount of
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