The Astrophysical Journal Letters, 787:L17 (5pp), 2014 June 1

doi:10.1088/2041-8205/787/2/L17

C 2014. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

DUST PRODUCTION FACTORIES IN THE EARLY UNIVERSE: FORMATION OF CARBON
GRAINS IN RED-SUPERGIANT WINDS OF VERY MASSIVE POPULATION III STARS
Takaya Nozawa1,2 , Sung-Chul Yoon3 , Keiichi Maeda4,2 , Takashi Kozasa5 , Ken’ichi Nomoto2,7 , and Norbert Langer6
1 National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan; takaya.nozawa@nao.ac.jp

2 Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
3 Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea
4 Department of Astronomy, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
5 Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan
6 Argelander-Institut für Astronomie der Universität Bonn, Aufdem Hügel, D-53121 Bonn, Germany

Received 2013 October 11; accepted 2014 April 19; published 2014 May 9

ABSTRACT
We investigate the formation of dust in a stellar wind during the red-supergiant (RSG) phase of a very massive
Population III star with a zero-age main sequence mass of 500 M . We show that, in a carbon-rich wind with aconstant velocity, carbon grains can form with a lognormal-like size distribution, and that all of the carbon available
for dust formation finally condenses into dust for wide ranges of the mass-loss rate ((0.1–3) ×10−3 M yr−1 )and wind velocity (1–100 km s−1 ). We also find that the acceleration of the wind, driven by newly formed dust,
suppresses the grain growth but still allows more than half of the gas-phase carbon to finally be locked up in dust
grains. These results indicate that, at most, 1.7 M of carbon grains can form during the RSG phase of 500 M
Population III stars. Such a high dust yield could place very massive primordial stars as important sources of dust at
the very early epoch of the universe if the initial mass function of Population III stars was top-heavy. We also briefly
discuss a new formation scenario of carbon-rich ultra-metal-poor stars, considering feedback from very massive
Population III stars.
Key words: dust, extinction – galaxies: high-redshift – stars: massive – stars: Population III – stars: winds, outflows
Online-only material: color figures

play an important role in the chemical enrichment of the early
universe. Yoon et al. (2012) found that non-rotating models
with MZAMS > 250 M undergo convective dredge-up of large
amounts of carbon and oxygen from the helium-burning coreto the hydrogen-rich envelope during the red-supergiant (RSG)
phase. This may lead to enrichment of the surrounding medium
with CNO elements via RSG winds. More importantly, such
CNO-enriched RSG winds can serve as dust formation sites
in the early universe. In this Letter, we elaborate on this new
scenario of dust formation by Pop III stars, using an exemplarymodel with MZAMS = 500 M . We show that C grains canform efficiently in the stellar wind with a constant velocity for areasonable range of mass-loss rates and wind velocities. We also
discuss the effect of the wind acceleration on dust formation.

1. INTRODUCTION
Discoveries of huge amounts of dust grains in high-redshiftquasars (Bertoldi et al. 2003; Priddey et al. 2003) have posed
fundamental problems in regards to the origin of dust in theearly universe. At such an early epoch, core-collapse supernovae(CCSNe) arising from massive stars are considered to be themost promising sources of dust (e.g., Dwek et al. 2007). On
the other hand, the contribution from asymptotic giant branchstars evolving from intermediate-mass (MZAMS  3–8 M ) stars
has also been invoked to explain the large content of dust in
high-redshift objects (Valiante et al. 2009; Dwek & Cherchneff2011). What stellar mass range can mainly contribute to thedust budget in the early universe strongly depends on the initial
mass function (IMF) of the stars (Valiante et al. 2011; Gall et al.
2011a, 2011b).
Numerical simulations of the formation of metal-free stars
have shown that the IMF of the first generation of stars, so-called
Population III (Pop III) stars, would be weighted toward muchhigher mass than those in the present universe (Bromm & Larson
2004; Hirano et al. 2014). However, the characteristic mass of
Pop III stars remains to be clarified, spanning from ∼40 M
(Hosokawa et al. 2011; Susa 2013) up to more than 300 M
(Omukai & Palla 2003; Ohkubo et al. 2009). In particular,
Pop III stars with masses exceeding ∼250 M emit numerous
ionizing photons and finally collapse into black holes (BHs),
serving as seeds of supermassive BHs. Thus, such very massive
Pop III stars would have crucial impacts on the reionization of
the universe and dynamical evolution of galaxies.
Even though most of the very massive Pop III stars are notsupposed to explode as supernovae (SNe), they are likely to
7

2. THE MODEL
For the properties of a 500 M RSG, we refer to the model
sequence, m500vk00, without rotation in Yoon et al. (2012); theaverage luminosity and effective temperature of this RSG are
L∗ = 107.2 L and T∗ = 4440 K, respectively, with a stellar
radius of R∗ = 6750 R . This very massive RSG undergoes
convective dredge-up during helium-core burning, enriching thehydrogen envelope with a large amount of carbon and oxygen;the average number fractions of the major elements in theenvelope are AH = 0.701, AHe = 0.294, AC = 3.11 × 10−3 ,and AO = 1.75 × 10−3 , leading to a high C/O ratio (C/O =1.78).
2.1. Hydrodynamic Model of the Outflowing Gas
As the first step to assess the possibility of dust formation
in a Pop III RSG wind, we consider a spherically symmetricHamamatsu Professor.

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Nozawa et al.

Table 1
Chemical Reactions for the Formation of C Clusters Considered in This Letter(1) Model A(2) Model B

Key Molecule

Chemical Reaction

A/104 K

B

a0
(Å)

σ
(erg cm−2 )C
C2 H

Cn−1 + C  Cn (n  2)
2(C2 H + H)  C2n + 2H2 (n = 2)
C2(n−1) + C2 H + H  C2n + H2 (n  3)

8.37158.642522.150918.9884

1.281
1.614

1400
1400

Notes. The key molecule is defined as the gas species whose collisional frequency is the lowest among the reactants. The Gibbs freeenergy Δg̊ for the formation of the condensate from reactants per key molecule is approximated by Δg̊/kT = −A/T + B with thenumerical values A and B derived by least-squares fittings of the thermodynamic data (Chase et al. 1985). The radius of the condensate
per key molecule and the surface tension of bulk grains are a0 and σ , respectively.

gas flow with a constant wind velocity. In this case, the density
profile of the gas flow is given by
 −2
r
Ṁ
= ρ∗
,
(1)
ρ(r) =
4π r 2 vw
R∗

conditions given above, the major carbon-bearing gas species,
other than CO, is atomic carbon at T  1750 K and C2 H at T 
1400–1700 K. Thus, the formation of C clusters is expected toproceed at high temperatures through the successive attachmentof carbon atoms as given in reaction (1) of Table 1, which wecall Model A. Independently of this, we consider another dust
formation path involving C2 H, for which the possible chemical
reactions are given under reaction (2) of Table 1, hereafterreferred to as Model B. In the calculations, we assume that afraction, fC , of the carbon that is not locked up in CO molecules
exists as carbon atoms in Model A and as C2 H moleculesin Model B. Since fC linearly changes the number density ofcarbon available for dust formation, decreasing fC is identicalwith reducing the mass-loss rate or the C/O ratio in the envelopeby the same factor. The time evolutions of the gas density andtemperature are calculated by substituting r = R∗ + vw t into
Equations (1) and (2). The sticking probability of gas species isassumed to be unity and C clusters that contain more carbon
atoms than n∗ = 100 are treated as bulk grains. We referreaders to Nozawa & Kozasa (2013) for the formulation of
the dust formation process and a detailed prescription of thecalculations.

where Ṁ is the mass-loss rate, vw is the wind velocity, and r is
the distance from the center of the star. The radial profile of thegas temperature is assumed to beT (r) = T∗

r
R∗

− 12
,

(2)

following the previous studies on dust formation in stellar winds(e.g., Gail et al. 1984).
Mass loss from an RSG was not considered in Yoon et al.
(2012), and both the mass-loss rate and the wind velocity are
hardly known for Pop III RSGs. Given that the underlying
physics of mass-loss mechanisms is not well understood, elaborately modeling the mass-loss history is beyond the scope of
this Letter. Instead, to cover various physical conditions of the
mass-loss winds, we treat Ṁ and vw as free parameters and examine how these quantities affect the formation process of dust.
In what follows, we take as fiducial values vw = 20 km s−1 andṀ = 3 × 10−3 M yr−1 ; the latter corresponds to the constantmass-loss rate with which the 500 M star loses 90% (208 M )of the envelope during the last 7 × 104 yr of the RSG phase.8

3. RESULTS OF DUST FORMATION CALCULATIONS
Figure 1 shows the results of the calculations for the fiducial
case with fC Ṁ = 3 × 10−3 M yr−1 and vw = 20 km s−1 ;Figure 1(a) plots the formation rate of seed clusters withn∗ = 100 divided by the concentration of key species without
depletion due to cluster/grain formation (I∗ ), condensation
efficiency (fcon ), and average grain radius (aave ) as a functionof distance from the center of the star (r/R∗ ). Here, thecondensation efficiency, fcon (t), is defined as the fraction offree carbon atoms that are locked up in grains. In Model A(thick lines) and Model B (thin lines), dust grains start to form
at 7.2 R∗ and 10.8 R∗ , respectively, with I∗ being peaked around
7.5 R∗ and 12.3 R∗ . In both of the models, the final condensation
efficiency fcon,∞ = fcon (t → ∞) is unity.
The final average grain radius is only a little higher for
Model A (aave,∞ = 0.025 μm) than for Model B (aave,∞ =0.021 μm); for Model B, the concentration of key molecules at
the time of dust formation is lower than for Model A by a factorof 5, but the resulting decrease in the formation rate of seedclusters is compensated with the decrease in the growth rate.
As a result, the final average radius is similar in both Model A
and Model B, though lower rates (longer timescales) of bothprocesses for Model B lead to a broader lognormal-like size
distribution of grains, as seen from Figure 1(b). These results
demonstrate that the final condensation efficiency and averagegrain radius are almost independent of the chemical reactions
for the formation of C clusters in the context of this study.

2.2. Model of Dust Formation
The calculations of dust formation are performed by applying
the formulation of non-steady-state dust formation in Nozawa& Kozasa (2013). The formulae self-consistently follow theformation of small clusters and the growth of grains, consideringthat the collisions of key molecules, defined as the gas species
with the least collisional frequency among the reactants, control
the kinetics of the dust formation process. The formulae enable
us to evaluate the size distribution and condensation efficiencyof newly formed grains for given temporal evolutions of gas
temperature and density, chemical composition of the gas, andchemical reactions for the formation of clusters.
In a carbon-rich cool gas, all oxygen atoms are boundto carbon atoms to form CO molecules, and carbon atoms
and/or carbon-bearing molecules left after the CO formation
can participate in the formation of C clusters and grains. The
chemical equilibrium calculations along the gas flow (e.g.,
Kozasa et al. 1996) show that, for the physical and chemical
8

We note that, even if there were no wind, the floating-off of the looselybound RSG envelope, as a result of the core’s collapse into a BH at the end ofits life, may also lead to mass ejection of CNO elements into the interstellar
medium and production of dust grains (Zhang et al. 2008; Kochanek 2014).

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Nozawa et al.

Figure 1. (a) Formation rate of seed clusters with n∗ = 100, divided by thenominal concentration of the key molecules (I∗ , solid), condensation efficiency(fcon , dotted), and average grain radius (aave , dashed) as a function of distancefrom the center of the star (r/R∗ ) and (b) final size distribution spectrum by massa 4 f (a) of newly formed C grains for a mass-loss rate Ṁ = 3 × 10−3 M yr−1 ,a wind velocity vw = 20 km s−1 , and fC = 1. The thick lines represent theresults for Model A where the chemical reaction (1) in Table 1 is considered forthe formation of clusters, while the thin lines represent those for Model B withthe chemical reactions (2).
(A color version of this figure is available in the online journal.)

Figure 2. Final average radius aave,∞ and final condensation efficiency fcon,∞of C grains formed in the outflowing gas; (a) as a function of product fC Ṁ forvw = 20 km s−1 , and (b) as a function of vw for fC Ṁ = 3 × 10−3 M yr−1 .
The thick solid lines represent the results for Model A, while the thin dashedlines represent those for Model B.
(A color version of this figure is available in the online journal.)

could not be destroyed by the blast wave resulting from an SN
explosion because such a very massive Pop III star would finallycollapse into a BH (Heger & Woosley 2002; Yoon et al. 2012,
but see also Ohkubo et al. 2006). The ratio of dust mass tothe initial stellar mass (XVMS = Mdust /MZAMS  3.4 × 10−3 )and the dust-to-metal ratio (Mdust /Mmetal  0.24) are in theranges of those supplied by Pop III CCSNe, for which XCCSN =(0.1–30)×10−3 and Mdust /Mmetal = 0.01–0.25, depending on
the destruction efficiency of newly formed dust by the reverse
shocks (Bianchi & Schneider 2007; Nozawa et al. 2007). Thisimplies that, if very massive Pop III stars had really formed,
they could have been rapid and efficient sources of C grains in
the early universe.

Figure 2(a) indicates the final condensation efficiency andfinal average radius of newly formed C grains as a functionof the product fC Ṁ for vw = 20 km s−1 . For both Model A
and Model B, fcon,∞ = 1 at fC Ṁ  10−4 M yr−1 , where
the average grain radius scales as aave,∞ ∝ (fC Ṁ)0.88 . On theother hand, aave,∞ is more sensitive to the wind velocity, as seenin Figure 2(b); aave,∞ is smaller for a higher vw and scales asaave,∞ ∝ vw−1.75 for vw = 1–100 km s−1 . The increase in vw
leads to a lower gas density for a fixed Ṁ and causes more rapid
cooling of the gas, both of which favor producing a number ofsmaller grains.
The results of the calculations show that the final condensation efficiency of C grains is unity if the following condition is
met:


−2
fC Ṁ
vw
 0.04.
(3)
3 × 10−3 M yr−1
20 km s−1

4. EFFECTS OF WIND ACCELERATIONON DUST FORMATIONIn the previous section, we considered the formation of dust
in stellar winds with constant velocities. However, the radiationpressure acting on newly formed grains will drive the wind tohigher outflow velocities, which may suppress the growth ofthe dust grains. Here, according to Ferrarotti & Gail (2006), we
examine the effect of wind acceleration on dust formation bysolving the following simplified momentum equation:Thus, as an example, for vw = 20 km s−1 and fC = 1, the total
mass of C grains produced over the lifetime of the RSG withMZAMS = 500 M is estimated as Mdust /M = 1.7 (Ṁ/3 ×
10−3 M yr−1 ) for 1×10−4 M yr−1  Ṁ  3×10−3 M yr−1 .
It should be emphasized here that these newly formed grains
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Nozawa et al.

Figure 4. Solid lines show the dependence of aave,∞ and fcon,∞ on vw,0 in thecase with wind acceleration for Model A with fC Ṁ = 3 × 10−3 M yr−1 . The
dashed lines show the average radius aave,1 and condensation efficiency fcon,1
just before the grain growth is depressed by wind acceleration.
(A color version of this figure is available in the online journal.)
Figure 3. Wind velocity vw (upper panel), formation rate of seed clustersI∗ , condensation efficiency fcon , and average grain radius aave (lower panel)
as a function of r/R∗ for Model A with the wind acceleration. The initialwind velocity and mass-loss rate are set to be vw,0 = 30 km s−1 andṀ = 3 × 10−3 M yr−1 , respectively. The dashed lines in the lower panel
are the results without wind acceleration.
(A color version of this figure is available in the online journal.)vwL∗ κext (T )
GM∗
dvw
1−
=− 2
D ,
dr
r
4π cGM∗

Note that, in these calculations, we consider the accelerationof the winds by assuming the position coupling between the
dust and the gas. In reality, dust grains pushed by the radiationpressure move outward relative to the gas, then the drag force
between them drives the acceleration of the outflowing gas.
Thus, the wind acceleration must be less efficient than that inthis study. On the other hand, the high-velocity motion of dust
relative to the gas can cause the erosion of dust by sputtering(Tielens et al. 1994; Nozawa et al. 2006). In particular, dust
grains are accelerated above 100 km s−1 in the present case,so the processing of dust by sputtering is expected to haveconsiderable impacts on the final condensation efficiency. These
processes will be explored in future work.

(4)

where G is the gravitational constant, c is the light speed,
D is the dust-to-gas mass ratio, and κext (T ) is the
Planck-averaged mass extinction coefficient of C grains. We
take κext = 2.1 × 104 cm2 g−1 (for T = 4440 K; Zubko et al.
1996) and M∗ = 400 M as a representative value.
Figure 3 shows the acceleration of the wind and the formation
process of dust for the initial outflow velocity of vw,0 =30 km s−1 and the mass-loss rate of Ṁ = 3 × 10−3 M yr −1
in Model A. Because of the high stellar luminosity, the wind is
rapidly accelerated to 100 km s−1 once fcon is above 2×10−3 .
The resulting rapid dilution of the gas largely decreases both thegrowth rate of grains and the formation rate of seed clusters
but still allows the dust grains to grow slowly. Furthermore, theexpansion of the gas reduces the gas temperature, so very small
grains continue condensing from carbon atoms that were notlocked up in dust grains, as seen from the later increase in I∗ .
As a consequence, aave,∞ becomes very small as a whole, andfcon,∞ increases to 0.45.
The dashed lines in Figure 4 plot the average radius (aave,1 )and condensation efficiency (fcon,1 ) at the time (t = t1 ) justbefore the grain growth is suppressed by the wind acceleration,
as a function of vw,0 for Model A with fC Ṁ = 3×10−3 M yr−1 .
For a lower vw,0 with which dust grains form in the region closer
to the star, the gas outflow is more efficiently accelerated andthe condensation efficiency of (large) grains, formed before thewind acceleration, is smaller. Nevertheless, the formation ofsmall grains at later phases, as well as the gradual growth oflarge grains, enhances fcon,∞ up to the range of 0.45–0.95 withvery small aave,∞ (see the solid lines in Figure 4). Thus, thewind acceleration influences the size distribution of dust but is
not likely to significantly affect the final condensation efficiency.

5. CONCLUSION AND DISCUSSION
We have investigated the formation of C grains in a mass-loss
wind of a Pop III RSG with MZAMS = 500 M . We find that, in astellar wind with a constant velocity, the condensation efficiency
of C grains is unity under the condition in Equation (3), and that,at most, 1.7 M of C grains can be produced during the lifetimesof Pop III RSGs. We also find that the wind acceleration causedby newly formed dust can change the final size distribution of
the dust, but still leads to the high final condensation efficiency(fcon,∞  0.5). Such dust masses would be high enough to havean impact on the dust enrichment history in the early universe
if the IMF of Pop III stars was top-heavy.
Recent sophisticated simulations of the first star formation(Hirano et al. 2014) have suggested that the number of very massive stars (VMSs) with MZAMS  250 M (NVMS ) is likely to be
as large as that of massive stars exploding as CCSNe (NCCSN ).
If this is true and if all of the VMSs lead to XVMS = 3.4 × 10−3 ,then the contribution of the interstellar dust from VMSs is comparable to, or even higher (NVMS XVMS /NCCSN XCCSN  1) thanthat from CCSNe in the case that the destruction of dust by thereverse shock is efficient (XCCSN  1.0 × 10−3 ).9 Thus, very
For pair-instability SNe occurring from stars with MZAMS  130–250 M ,XPISN  0.05 and Mdust /Mmetal  0.15, depending on the destruction
efficiency of dust by the reverse shocks (Nozawa et al. 2007). We also note thatpair-instability SNe might be inefficient sources of C grains (Nozawa et al.
2003).
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Nozawa et al.

massive Pop III stars could be potentially dominant sources ofdust grains at very early times of the universe.
Our results also have important indications on the formation
scenario of carbon-rich ultra-metal-poor (UMP) stars with
[Fe/H] < −4, which would record the chemical imprints of
Pop III stars (Beers & Christlieb 2005). The formation of suchlow-mass metal-poor stars is considered to be triggered throughthe cooling of gas by dust ejected from Pop III SNe (Schneider
et al. 2012a, 2012b; Chiaki et al. 2013). Ji et al. (2014) suggested
that the formation of carbon-rich UMP stars relies on the coolingby fine structure lines of C and O atoms, assuming that the first
SNe produced no C grains.
Here, we propose another possible channel for the formationof carbon-rich UMP stars. As shown in this study, very massive
Pop III RSGs are efficient sources of C grains as well as
CNO elements. Thus, in the gas clouds enriched by these
Pop III RSGs, C grains enable the formation of low-mass stars
whose chemical compositions are highly enhanced in carbon
and oxygen. As the investigated 500 M model undergoes mild
hot bottom burning, some nitrogen is also produced, giving rise
to [N/C] = −4.2 to −1.3 depending on the assumed mass-loss
history, where observations of carbon-rich UMP stars indicate[N/C]  −1.7 (Christlieb et al. 2002; Norris et al. 2007; Frebel
et al. 2008). From our zero-metallicity model, we do not predictthe presence of any heavier metals. Further observations andmore quantitative theoretical studies are needed to show whether
any UMP stars have formed through our scenario.

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We are grateful to the anonymous referees for criticalcomments. This research has been supported by the World
Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, and by the Grant-in-Aid for JSPS Scientific Research (22684004, 23224004, 23540262, 26400222,
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