The Astrophysical Journal, 794:100 (12pp), 2014 October 20

doi:10.1088/0004-637X/794/2/100

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

THE ORIGIN OF THE MOST IRON-POOR STAR
S. Marassi1 , G. Chiaki2 , R. Schneider1 , M. Limongi1,3 , K. Omukai4 , T. Nozawa5 , A. Chieffi6 , and N. Yoshida2,7
1 INAF/Osservatorio Astronomico di Roma, Via di Frascati 33, I-00040 Monteporzio, Italy; stefania.marassi@oa-roma.inaf.it
2 Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan

3 Kavli Institute for the Physics and Mathematics of the Universe, Todai Institutes for Advanced Study, The University of Tokyo, Kashiwa 277-8583, Japan
4 Astronomical Institute, Tohoku University, Sendai 980-8578, Japan
5 National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan
6 INAF/IASF, Via Fosso del Cavaliere 100, I-00133 Roma, Italy
7 National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan

Received 2014 May 7; accepted 2014 August 8; published 2014 September 26

ABSTRACT
We investigate the origin of carbon-enhanced metal-poor (CEMP) stars starting from the recently discovered[Fe/H] < −7.1 star SMSS J031300. We show that the elemental abundances observed on the surface of SMSS
J031300 can be well fit by the yields of faint, metal-free, supernovae (SNe). Using properly calibrated faint SN
explosion models, we study, for the first time, the formation of dust grains in such carbon-rich, iron-poor SN
ejecta. Calculations are performed assuming both unmixed and uniformly mixed ejecta and taking into account thepartial destruction by the SN reverse shock. We find that, due to the paucity of refractory elements beside carbon,
amorphous carbon is the only grain species to form, with carbon condensation efficiencies that range between (0.15
and 0.84), resulting in dust yields in the range (0.025–2.25) M . We follow the collapse and fragmentation of astar-forming cloud enriched by the products of these faint SN explosions and we explore the role played by finestructure line cooling and dust cooling. We show that even if grain growth during the collapse has a minor effectof the dust-to-gas ratio, due to C depletion into CO molecules at an early stage of the collapse, the formation of
CEMP low-mass stars, such as SMSS J031300, could be triggered by dust cooling and fragmentation. A comparison
between model predictions and observations of a sample of C-normal and C-rich metal-poor stars supports the ideathat a single common pathway may be responsible for the formation of the first low-mass stars.
Key words: dust, extinction – ISM: general – ISM: supernova remnants – supernovae: general
Online-only material: color figures2010, Hirschi 2007), or in the ejecta of Population III SNe
in which mixing was minimal and fallback was large. In
the latter model, the small iron abundance thus reflects thefact that in these so-called “faint” SNe iron was made, butfailed to be mixed sufficiently far out to be ejected (Umeda& Nomoto 2003). Alternatively, the large C/Fe could result
from multiple generations of SNe, where the ejecta of a“normal” SN is combined with that from a low-energy SN in
which only the outer layers are ejected (Limongi & Chieffi
2003), or from a jet-induced SN explosion (Tominaga et al.
2007).
Understanding the origin of CEMP stars is complicated by
the fact that these do not form a homogeneous group and show
various heavy-element abundance patterns: depending on thelevel of enrichment of neutron capture elements formed by the“s” or “r” processes, these fall in different sub-classes (CEMPno, CEMP-rs, CEMP-s; Beers & Christlieb 2005). Generally,
CEMP-s and CEMP-rs stars have abundance patterns thatsuggest mass transfer from companion AGB stars (Masseron
et al. 2010); indeed, most of the stars falling in these subclasses are members of binary systems (Lucatello et al. 2005).
However, at [Fe/H] < −3, 90% of CEMPs are CEMP-no stars,
which do not show large enhancements of heavy neutron capture
elements (Aoki et al. 2010). Using a homogeneous chemical
analysis of 190 metal-poor stars (Yong et al. 2013a). Norris
et al. (2013) have recently investigated a sample of CEMPno stars with [Fe/H] < −3. They conclude that the observed
chemical abundances are best explained by models that invoke
the nucleosynthesis of Population III SNe with mixing andfallback, of rotating massive and intermediate mass stars andof SNe with relativistic jets.

1. INTRODUCTION
Stellar archaeology of the most metal-poor stars observed in
the halo of our Galaxy provides valuable insights on the starformation and chemical enrichment histories at high redshifts.
The observed surface elemental abundances and the metallicity
distribution function of Galactic halo stars shed light on thenature and properties of the first supernovae (SNe; Population
III SNe) that pollute the interstellar medium (ISM) with the firstmetals and dust grains.
Galactic halo metal-poor stars have a well-defined abundance
pattern at [Fe/H] < −2.5 (Cayrel et al. 2004) that can bereasonably well reproduced by theoretical yields of Population III core-collapse SNe with progenitor masses in the range
10–100 M (Heger & Woosley 2010, Limongi & Chieffi 2012).
An exception are the so-called carbon-enhanced extremely
metal-poor stars (CEMP, defined as those with [C/Fe] > +1
(Beers & Christlieb 2005), which comprise a fraction of∼10%–20% of metal-poor stars at [Fe/H] < −2; Yong et al.
2013b). Interestingly, the observed fraction of C-rich metalpoor stars increases with decreasing iron abundance and, at[Fe/H] < −4.5, four out of the five stars currently known are
CEMP, including the recently discovered SMSS J031300.36670839.3 (hereafter SMSS J031300) with [Fe/H] < −7.1
(Keller et al. 2014).
A number of theoretical scenarios have been proposed to
explain the origin of CEMP stars, invoking mass transfer inPopulation III binary systems (Suda et al. 2004, Masseron
et al. 2010, Campbell et al. 2010), formation from material
enriched in stellar winds of rotating massive and intermediate
mass Population III stars (Meynet et al. 2006, Meynet et al.
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The Astrophysical Journal, 794:100 (12pp), 2014 October 20

Marassi et al.

Similar conclusions have been drawn by Keller et al. (2014) intheir discovery paper of SMSS J031300, a Galactic halo star with
only an upper limit on the iron abundance of [Fe/H] < −7.1.
The observed abundance pattern of this extremely iron-deficientstar is optimally matched by the nucleosynthetic yields of a
60 M Population III SN with a small amount of ejecta mixing
due to Rayleigh-Taylor instabilities, followed by extensive
fallback of material onto the black hole remnant (Joggerst et al.
2009, Heger & Woosley 2010). They argue against a jet-like
explosion as this would lower the [Mg/Fe] below that observed;
in addition, rapidly rotating star models are also disfavored by
the low upper limit on N compared to C (Keller et al. 2014).
A general conclusion of the above analyses is that below[Fe/H] ∼ −3 there appear to be two populations of stars,
carbon-normal and carbon-rich, whose observed elemental
abundances reflect the nucleosynthetic products of “normal”
and “faint” Population III SNe, respectively. The different composition in the material out of which these low-mass stars form
have stimulated the hypothesis that their formation relies on two
different cooling channels (Norris et al. 2013): fine-structureline cooling and dust cooling. In particular, C-rich stars form
from C-enriched material where gas cooling and fragmentation
is dominated by C ii (and eventually O i) fine structure lines(Bromm & Loeb 2003).
Frebel et al. (2007) have introduced the so-called transition
discriminant Dtrans = log(10[C/H] + 0.9 × 10[O/H] ) and predictedthat metal-poor stars forming through this mechanism must have
Dtrans > −3.5 ± 0.2 (Frebel & Norris 2013). They predict thatmetal-poor stars forming through this mechanism must have
Dtrans > −3.5 ± 0.2. Nearly all stars satisfy this criterion withthe exception of SDSS J1029151+1729 (Caffau et al. 2011).
This is a carbon-normal star with [Fe/H] = −4.99 and a solarlike chemical abundance pattern, leading to a total metallicity
of Z = 4.5 × 10−5 Z and representing the most chemicallypristine object currently known. The origin of the star has been
investigated by Schneider et al. (2012b), who suggest that theobserved abundance pattern of SDSS J1029151 can be wellmatched by yields of “normal” Population III SNe with 20 and
35 M ; the mass of dust formed in these SN ejecta is enough tosatisfy the minimal conditions to activate dust-induced fragmentation, which require the gas to be pre-enriched above a criticaldust-to-gas mass ratio Dcr = [2.6–6.3] × 10−9 , with the spreadreflecting the dependence on the grain properties (Schneider
et al. 2003, 2010, 2012a). Note that even if dust formation in
the first SNe is less efficient or if strong dust destruction by the
SN reverse shock occurs, grain growth during the collapse of
the parent gas cloud is sufficiently rapid to activate dust coolingand fragmentation (Nozawa et al. 2012; Chiaki et al. 2013).
In principle, the values Dcr = [2.6–6.3] × 10−9 and Dtrans >−3.5 ± 0.2 could provide a way to test dust cooling and on finestructure-line cooling against the observations. This has been
recently explored by Ji et al. (2014), who, however, make the apriori assumption that dust is made by silicates. In this way they
estimate the critical silicate abundance, which corresponds to
Dcr , and compare these values to chemical abundances of metalpoor stars, with [Fe/H] < −4. They find that the stars exhibit
either high carbon with low silicon abundances or the reverse. A
silicate dust scenario would thus support the hypothesis that theearliest low-mass star formation in the most metal-poor regime
may have proceeded by means of two distinct cooling pathways:
fine-structure line cooling and dust cooling.
Here we intend to investigate the origin of CEMP-no stars,
and in particular of the recently discovered most iron-deficient

member of this class, SMSS J031300 (Keller et al. 2014). For the
first time, we consider the formation of dust in faint Population
III SN ejecta. Our aim is to verify if dust can form in these C-rich,iron-poor ejecta, and what is the relative role of fine-structureline cooling and dust cooling in the collapse of material enrichedby these explosions.
Having this goal in mind, we first compare the observed
abundances of SMSS J031300 with the nucleosynthetic yields ofmodel Population III SNe that range in progenitor mass, internal
mixing, and explosion energy (extent of fallback; Section 2).
We perform dust calculation in the ejecta of the selected SN
models with a revised version of the Bianchi & Schneider(2007) model, which includes an improved, non-steady-state,molecular network, updated radiative association reactions for
CO, SiO, C2 , and O2 molecules, and formation/destruction
processes between molecules (Marassi et al. 2014; S. Marassi
et al. 2014, in preparation; Section 3). We follow the collapse ofa gas cloud assuming that the newly formed dust and the metals
present in the ejecta are uniformly mixed into the collapsing
cloud with the same total metallicity that is observed on thesurface of SMSS J031300 and verify under which conditions
the formation of low-mass star is enabled (Section 4). Finally,
we discuss the implications of our results for the origin of thefirst low-mass stars in the universe (Section 5).
2. FAINT SUPERNOVA PROGENITORS
Our aim here is to identify a set of plausible Population III SN
models that may have polluted the birth cloud of SMSS J031300.
The procedure that we follow is to minimize the scatter withthe observed abundance pattern, adopting the chemical yields
produced by a set of Population III core-collapse SN models
with mixing and fallback.
We refer the interested reader to Limongi & Chieffi (2012)
for a thorough presentation of the models. Similarly to what
has been done in Schneider et al. (2012b), we consider a setof models that extends in mass between 13 and 80 M , whichappear to be consistent with the mass range found by the mostrecent simulations of first star formation (Hirano et al. 2014).
These models have been followed from the pre-main-sequencephase up to the onset of the iron core collapse by means of the
FRANEC stellar evolutionary code. The initial composition is
set to the pristine Big Bang nucleosynthesis (Y = 0.23) and massloss is switched off during all the evolutionary stages.
The explosive nucleosynthesis has been computed in theframework of the induced explosion (Limongi & Chieffi 2006)
approximation. For each progenitor model, we identify a combination of mixing and fallback that provides the best-fit tothe observed elemental abundance ratios (or upper limits) on
the surface of SMSS J031300. The observational data points
are shown in Figure 1: black points with arrows show the inferred one-dimensional/three-dimensional (1D/3D) model atmosphere upper limits and the filled black dots with error bars
are the 1D/3D model atmosphere detections (see Keller et al.
2014 for a description of the model atmosphere used for theabundance analysis). Among the three elements that have been
detected—C, Mg, and Ca—we show the elemental abundances
relative to Ca.
The low upper limit on [N/Ca] disfavors SN progenitors withinitial masses in the range [20–35] M . In fact, their evolution
leads to comparable C and N abundances in the ejecta (seeFigure 7 and the discussion in Limongi & Chieffi 2012), in
contrast to the observed pattern in SMSS J031300. Hence, we
include in the analysis SN progenitors with initial masses equal
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Marassi et al.

Figure 1. Comparison between the observed element abundance ratios of the star SMSS J031300 and the chemical yields of a Population III faint SN with progenitor
masses of 13, 15, 50, and 80 M . Mixing and fallback are chosen so as to minimize the scatter with the observations using a 1D (left panel) or 3D (right panel) model
atmosphere (black points). Dots with arrows show upper limits and filled points with errorbars indicate the detections, where an error of 0.1 (0.2) has been associatedto the observed Ca and Mg (C) abundances.
(A color version of this figure is available in the online journal.)that are more sensitive to the mixing and fallback prescription
adopted. As a result, in Table 1 we show the ejecta composition
for both sets of observed abundances and refer to the models as
80 M -1D or 80 M -3D.

to 13, 15, 50, and 80 M . For each of these models, we haveapplied the optimal combination of mixing (set by minimum
and maximum mass coordinates within which the mass of eachelement is uniformly mixed in the ejecta) and fallback (setby the mass-cut) that minimizes the scatter with the observed
abundance pattern. Since the elemental abundances inferredfrom the analysis using 1D or 3D model atmospheres lead tosensible differences in the observed abundances (or upper limits)of elements that are critical for the resulting dust mass, such as
C, O, and Mg, for each progenitor mass we have independently
inferred best-fit models using 1D and 3D observed elemental
abundances. The resulting models are shown by the starred
points joined with dotted lines in Figure 1. It is clear fromthe figure that while all the models show an overall agreementwith the observed abundance pattern, it is hard to simultaneously
accommodate the upper limit on [O/Ca] and the detected [Mg/Ca]; this is particularly true for low-mass progenitors, whose
evolution leads to a lower [Mg/O] in the ejecta. The best-fit
model appears to be the most massive progenitor with 80 M :adopting the abundance pattern inferred from 1D atmospheremodels, the predicted ejecta composition is compatible withall the data points. This is not true, however, when the 3D data
points are considered (see the right panel in Figure 1) as the more
stringent upper limit on [O/Ca] and the larger [Mg/Ca] cannot
be reproduced. Note that in Keller et al. (2014) the model thatprovides the optimal match to the observed abundance pattern
is a 1.8 × 1051 erg explosion of a 60 M star of primordial
composition with a small amount of ejecta mixing and a strong
fallback. These properties closely resemble our best-fit modeland indeed the predicted [Mg/H] falls below the observational
data point (see Figure 3 in Keller et al. 2014).
Table 1 summarizes the main properties of the SN progenitors. For all models, we choose the interval of mixing andmass-cut to reproduce the observed [C/Ca] and maximize the[Mg/Ca], getting as close as possible to the observed value
without exceeding the [O/Ca] and [Fe/Ca] upper limits. We
find that for all but the most massive model, the ejecta composition is insensitive to the reference set of observed abundances,whether derived with 1D or 3D model atmosphere (the values
quoted in the table refer to the 3D set). Conversely, the chemical
structure of the 80 M progenitor, characterized by a more extended Mg shell, leads to [O/Ca] and [C/Ca] abundance ratios

3. DUST FORMATION IN FAINT SN
The formation of dust in SN ejecta has been modeled
following either classical nucleation theory (CNT; Todini &Ferrara 2001; Nozawa & Kozasa 2003; Nozawa et al. 2010;
Bianchi & Schneider 2007, and references therein) or a chemical
kinetic approach (Cherchneff & Dwek 2009, 2010; Sarangi &Cherchneff 2013). As recently pointed out in Cherchneff &Dwek (2009, 2010) and Sarangi & Cherchneff (2013), thesemethods lead to different estimates of the mass and compositionof newly formed dust due to the questionable applicability ofthe standard CNT in SN ejecta (Donn & Nuth 1985) and to
non-equilibrium chemical processes related to the formation/
destruction of molecules (Cherchneff & Dwek 2009). Recently,
Paquette & Nuth (2011) have shown that the assumption ofchemical equilibrium at nucleation, adopted within CNT, hasonly a minor effect on the grain mass and size distribution.
In addition, Nozawa & Kozasa (2013) have demonstrated
that a steady-state nucleation rate is a good approximation in
SN ejecta, at least until the collisional timescales of the key
molecule is much smaller than the timescale with which thesupersaturation ratio increases.
Here we follow CNT to compute the nucleation and accretionof dust species using a previously developed code that has been
applied to core-collapse (Todini & Ferrara 2001; Bianchi &Schneider 2007) and pair-instability SNe (Schneider et al. 2004)
and that can successfully reproduce observational data of SNeand young SN remnants (Schneider et al. 2014; Valiante &Schneider 2014).
For the present study, the code has been improved allowing
to solve the non-steady-state formation of important molecularspecies, such as CO, O2 , C2 , and SiO. A full description of the
upgraded molecular network with the reactions rates will begiven in Marassi et al. (2014). Here we restrict the discussion to
those aspects that are relevant for carbon dust formation in faintSN ejecta. It is important to stress that the upgraded molecular
network has been tested against the results obtained by chemical
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Marassi et al.

Table 1
Properties of Faint SN Progenitors, Including the Explosion Energy [1051 erg], the Ejecta Velocity (km s−1 ), the Gas Number Density (cm−3 ), and the Radius of He
Core, R0 (cm) at t = t0 (s) when Adiabatic Expansion Starts (see Text); in Addition, we also Show the Helium Core Mass, the Mass of the Ejecta, and the Initial
Masses of the Elemental Yields that are Observed on the Surface of SMSS J031300, C, N, O, Na, Mg, Al, Si, Ca, and Fe (M )
13 M

15 M

50 M

80 M

80 M

80 M

80 M

3D

3D

3D

3D

1D

1D-A

1D-B

0.5
2.81
1.7
2722
11.3

0.7
3.40
2.1
3011
12.9

2.6
18.11
11
3344
39

5.2
31.94
22.5
3891
57.5

5.2
31.94
24
3943
56

5.2
31.94
24
3943
56

5.2
31.94
24
3943
56

R0
t0
n0

2.65 × 1014
2.11 × 106
1.14 × 1011

2.44 × 1014
1.78 × 106
2.73 × 1011

2.51 × 1014
3.12 × 106
4.37 × 1012

4.78 × 1014
4.14 × 106
7.64 × 1011

4.78 × 1014
4.14 × 106
5.17 × 1011

2.29 × 1014
2.24 × 106
2.33 × 1013

4.57 × 1014
4.14 × 106
3.31 × 1011

MC
MN
MO
MNa
MMg
MAl
MSi
MCa
MFe

0.065
2.72 × 10−8
0.032
1.29 × 10−8
1.81 × 10−5
1.91 × 10−8
1.26 × 10−6
7.03 × 10−8
8.62 × 10−7

0.118
3.71 × 10−8
0.065
1.74 × 10−8
2.36 × 10−5
4.06 × 10−8
2.41 × 10−6
1.28 × 10−7
1.76 × 10−6

0.989
4.45 × 10−6
2.551
7.79 × 10−8
8.84 × 10−4
5.89 × 10−8
1.42 × 10−5
1.07 × 10−6
1.47 × 10−5

1.089
3.93 × 10−7
3.213
3.70 × 10−8
5.90 × 10−3
6.70 × 10−8
1.57 × 10−5
1.18 × 10−6
1.05 × 10−5

0.887
3.93 × 10−7
1.973
1.31 × 10−8
3.26 × 10−3
2.17 × 10−8
5.19 × 10−6
3.82 × 10−7
4.7 × 10−6

0.547
...
1.948
1.31 × 10−8
3.26 × 10−3
2.17 × 10−8
5.19 × 10−6
3.82 × 10−7
4.7 × 10−6

0.339
...
0.024
...
...
...
...
...
...

Eexp
MHecore
Mcut
v eje
Meje

Notes. Each model name identifies the progenitor mass; the additional labels—where present—1D or 3D specify the set of observed abundances used in model
calibration (with default values being 3D, see text). The last two columns identify the two layers (A and B) of the unmixed ejecta of the 80 M -1D model.
Table 2Masses of CO, SiO, O2 , C2 Molecules in Faint SN Progenitor Ejecta and Masses of AC Grains (M )
13 M

15 M

50 M

80 M

80 M

80 M

80 M

3D

3D

3D

3D

1D

1D-A

1D-B

MCO
M2
MC2
MSiO

0.0246
2.91 × 10−8–8.60 × 10−8

0.074
5.77 × 10−8–
2.73 × 10−7

2.29
6.21 × 10−5–
2.02 × 10−5

2.15
6.29 × 10−5–
1.49 × 10−5

1.44
2.42 × 10−5–
3.48 × 10−6

1.276
0.513
...
8.11 × 10−6

0.043
...
0.21
...

MAC

0.05440.08620.00557

0.165

0.269

—

0.112

Notes. Each model name identifies the progenitor mass; the additional labels—where present—1D or 3D specify the set of observed abundances used in model
calibration (with default values being 3D, see text). The last two columns refer to the two layers (A and B) of the unmixed ejecta of the 80 M -1D model.

kinetic approach: in S. Marassi et al. (2014, in preparation) wehave applied the model to a 15 M Type IIP SN with solar
metallicity and a stratified ejecta, and we find that the mass of
CO at the onset of dust nucleation is in excellent agreement withresults obtained by Sarangi & Cherchneff (2013) for the same
SN progenitor.
We construct the ejecta models using as initial conditions
the thermo-dynamical properties obtained by the SN explosion
simulations (Limongi & Chieffi 2012). The ejecta follow anadiabatic expansion and the temperature evolution is given by
veje 3(1−γ )T = T0 1 +t,R0outputs. The initial time t0 is chosen to correspond to the time
when the radius of the He core, RHecore , reaches a temperature of
T0 = 104 K. All these quantities and the initial gas number
density n0 (t = t0 ) are shown in Table 1 for different SNprogenitor models.
It is well known that the formation of CO molecules subtracts
C-atoms, limiting the formation of carbon grains. In the C-richand Fe-poor ejecta of faint SNe, the main molecular destruction
process, collisions with energetic electrons produced by theradioactive decay of 56 Co, is strongly inhibited.
For all the faint SN models we have explored, the formationof CO is dominated by radiative association reaction (Dalgarno
et al. 1990),
C + O → CO + hν
(3)

(1)

where γ = 1.41 is the adiabatic index, v eje is the ejecta
expansion velocity,
10 Ekinveje =,(2)
3 Mejeand by bimolecular, neutral-neutral reactions (UMIST database
2012)
C + O2 → CO + O

O + C2 → CO + C(4)that involve O2 , C2 molecules, and C, O atoms. As a result,the mass of CO that is formed ranges between 0.0544 M and
0.269 M (see Table 2). The formation of SiO in faint SN ejecta
is strongly suppressed with respect to ordinary core-collapse

and T0 and R0 are the temperature and radius of the He coreat the initial time t = t0 and are extracted from the simulation
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Marassi et al.

SNe, as a consequence of the very small initial abundance of Si(see Tables 1 and 2). Additional molecular species, such as O2
and C2 , form through radiative association reactions (Andreazza& Singh 1997, Babb & Dalgarno 1995),
C + C → C2 + hν

O + O → O2 + hν

the temperature has dropped below the AC grain condensation
temperature, ∼1940 K, roughly 60 days after the explosion,
when the number density is n0 = 2.58×1010 cm−3 . Conversely,in the 80 M SN model, the gas temperature drops to ∼2000 K
only 86 days after the explosion, when the number density is
n0 = 7.15 × 109 cm−3 . Comparing the chemical reaction rates
to the expansion rate, kdyn , defined as(5)and through the inverse bimolecular process showed in
Equation (4) in a non-negligible amount only if the ejecta is
stratified (see Table 2).
Following Bianchi & Schneider (2007), our dust calculation
is based on CNT. When a gas becomes supersaturated, particles(monomers) aggregate in a seed cluster that subsequently growsby the accretion of other monomers. The accretion process isregulated by the collision rate of the key species and depends
on the sticking coefficient, defined as the probability that an
atom colliding with a grain will stick to it. We show theresults obtained assuming that the seed clusters are formed bya minimum of two monomers and that the sticking coefficientis equal to 1 for all grain species. The chemical compositionand size at condensation and the basic data necessary for thedust formation calculations are shown in Table 2 of Nozawa& Kozasa (2003). The thermal and optical properties of theresulting dust materials can be found in Table A1 of Bianchi &Schneider (2007), to which we refer the interested reader. The
nucleation process, together with accretion, results in typical
log-normal grain size distributions (Todini & Ferrara 2001;
Nozawa & Kozasa 2003).
If faint SN are believed to be powered by a sphericallike explosion, mixing occurs by means of Rayleigh–Taylor
instabilities only in the innermost shells (Joggerst et al. 2009),
up to a mass-coordinate that is very close to the mass-cut(Mcut ). Hence the material beyond the mass cut is likely to be
stratified and dust nucleation in unmixed ejecta provides a more
realistic estimates of the total mass of dust produced. To enable
a more direct comparison with previous results (Schneider et al.
2012b), where dust formation in uniformly mixed, Population
III ordinary core-collapse SNe has been considered, we firstpresent the results adopting uniformly mixed ejecta and thenextend the calculation to stratified ejecta.

kdyn = 1/t =

veje
,
R(t)

(6)

where v eje is the ejecta velocity and R(t) is the ejecta position
at a given time t after explosion, we can determine t = tfo ,the time at which each reaction rate becomes longer than the
expansion rate, leading to a “freeze-out” of the corresponding
chemical species (Cherchneff & Dwek 2009). The mass of CO
molecules at tfo and at the onset of dust nucleation (tnucl ) largely
determines the resulting dust mass. For the 50 M model, we
find that MCO (tfo ) = 2.21 M and, at this stage, the carbon
mass locked in CO molecules is 0.945 M . When nucleation
starts, MCO (tnucl ) = 2.29 M and 0.982 M mass of carbon islocked in CO molecules. Hence, out of the 0.988 M of C atoms
initially present in the ejecta (see Table 1), only ∼6 × 10−3 M
are available to form C-grains. If we do the same calculation
for the 80 M -3D model, we find MCO (tfo ) = 1.258 M ,MCO (tnucl ) = 1.438 M , and the mass of carbon atoms locked
in CO at nucleation is 0.616 M , so that there are still 0.27 M
of carbon free to form C-grains. Hence, the reason why the
50 M model forms the least amount of dust is the higher
efficiency of CO formation, which leads to a carbon depletionin CO molecules of 95% at freeze-out. Note that in less massive
progenitor models, the ejecta composition is characterized byan initial mass of C greater than the O mass (see Table 1);
this contributes to decreased C depletion in CO molecules,
increasing the resulting mass of AC grains.
3.2. Dust Formation in Unmixed Ejecta
Recently, Joggerst et al. (2009) have pointed out that zerometallicity SN progenitors experience more fallback and asmaller degree of mixing, induced by Rayleigh–Taylor instabilities, than their solar metallicity counterparts. As a result, we
expect that the ejecta of faint SNe are likely to be unmixed.
Hence, it is important to explore how the mass of dust estimatedabove depends on the adopted mixing efficiency. We consider a
80 M -1D SN progenitor model. The stratified ejecta consistsof two layers, which differ mainly for the different abundanceof carbon and oxygen: the inner one (layer A) is characterized
C/O < 1 whereas in the outer one (layer B) C/O > 1 (seeTable 1). In Figure 3, we show the time evolution of the temperature, density, AC, and molecular masses formed in the twolayers A and B. In the inner layer A, all the carbon is rapidly
locked in CO molecules and consequently C-grains do not form.
The oxygen is first depleted in CO molecules and then in O2
molecules. Conversely, in the outer layer B, only ∼5% of carbon is locked in CO, ∼26% of carbon is locked in C2 , and theremaining C atoms are free to form 0.112 M of AC grains asshown in the right bottom panel in Figure 3. O2 and C2 form
mainly due to radiative association processes. Note that in thepresent formalism, there is no connection between the formation of C2 and the formation of carbon dust; however, if all theC2 were to transform into carbon dust, the final AC mass would
amount to ∼0.2 M . In the stratified ejecta, due to the different
temperature evolution of the two layers, CO molecules start to3.1. Dust Formation in Uniformly Mixed Ejecta
Contrary to ordinary core collapse SNe (Schneider et al.
2012b), the only grain species that form in non-negligible
amounts in faint SNe is amorphous carbon (AC). This is dueto the peculiar metal composition of faint SN ejecta, that are
dominated by C-atoms and where the abundances of Mg, Si,
Al, and Fe are too small to enable the formation of silicates,
magnetite, or alumina grains. In Table 2 we show the resulting
masses of molecules and of AC grains for all the explored faintSN models. We show that the mass of dust increases with themass of the SN progenitor, ranging from Mdust = 5.4×10−2 M
for the 13 M model to Mdust = 0.269 (0.165) M for the
80 M -1D (3D) model, consistent with the larger metal mass
initially present in the ejecta. The only exception is represented
by the 50 M model, which produces the smallest mass ofdust, Mdust = 5.6 × 10−3 M . The reason for this behavior
resides in the larger mean ejecta density of the 50 M model,
which increases the rates of the major processes leading to theformation of CO molecules. This can be understood by looking
at Figure 2 where we show the time evolution of temperature,density, CO, and AC masses for the 50 M , and the 80 M
models. In the 50 M SN model, dust nucleation starts when
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Figure 2. Upper panels: temperature and density evolution for 50 M and 80 M 3D mixed models. Bottom panels: time evolution of CO molecule and dust for
50 M and 80 M 3D mixed models.
(A color version of this figure is available in the online journal.)

form at an earlier time than in the corresponding mixed model,
and the resulting dust mass is ∼40% smaller.

We assume that dust grains are distributed uniformly within
the ejecta, and that the size distribution is the same everywhere.
In Figure 4 we show the grain size distribution that results fromgrain condensation and accretion in the (fully mixed) ejectaof the 50 M and 80 M SN models. Initially, the grain sizes
follow a log-normal distribution in the range (10−2 –0.5) μm.
However, in the shells that have been visited by the reverse
shock, dust grains are bathed in a gas heated to high temperature(of the order of 107 –108 K). In addition, the gas is slowed down,
decoupled from the grains and transfer thermal and kinetic
energy to the grains by means of collisions. Following Bianchi& Schneider (2007), we consider both thermal and non-thermal
sputtering. Note that since the reverse shock velocity, which isof the order of 103 km s−1 , is larger when the SN explodes ina denser circumstellar medium (Truelove & McKee 1999), thereverse shock travels faster inside the ejecta and encounters a
gas at higher density. This increases the effect of sputtering.
The effects of the reverse shock on the grain size distributionfunction is also shown in Figure 4: the larger grains are eroded
and this produces a shift of the distribution to lower grain
sizes, with a tail extending to a few Å. Note that when thenumber of monomers in each grain becomes less than 2, thegrain is evaporated, returning the metals into the gas phase (seeEquation (2) in Bianchi & Schneider 2007).

3.3. Dust Destruction by the Reverse ShockAs the ejecta expand, a forward shock is driven into the ISM,
which compresses and heats the ambient gas. The shocked
ambient gas drives a reverse shock in the ejecta, which in∼103 years has swept over a considerable fraction of its volume.
The passage of the reverse shock can be particularly destructive
for the small dust grains, due to the transfer of thermal andkinetic energy during impact with gas particles (sputtering). We
estimate the mass of newly formed dust that is able to survive
the passage of the reverse shock and enrich the ISM following
the same model developed by Bianchi & Schneider (2007).
The dynamics of the reverse shock is described using theanalytical approximations of Truelove & McKee (1999) for a
uniform density distribution inside the ejecta, which allow us
to compute the velocity of the shock as a function of the SN
explosion energy, Ekin , the mass of the ejecta, Meje , and thedensity of the ISM, ρISM . For each SN model, we compute thedynamics of the reverse shock using the same values for Ekin andMeje that have been used in the dust formation calculations (seeTable 1). In addition, we study the effect of three different ISM
environments, with ρISM = 10−25 , 10−24 and 10−23 g cm−3 .
6The Astrophysical Journal, 794:100 (12pp), 2014 October 20

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Figure 3. Upper panels: temperature and density evolution for the stratified 80 M -1D (left panels, layer A; right panels, layer B). Bottom panels: time evolution of
the mass in dominant molecular species, and carbon and oxygen in layer A (left panel) and in layer B (right panel).
(A color version of this figure is available in the online journal.)of the mass of AC grains relative to the initial mass of C atoms
present in faint SN ejecta are shown in Table 3. These, together
with the gas-phase abundances of the other elements present
in the ejecta represent the initial conditions for the collapse
calculations described in the next section.

The destructive efficiency of the reverse shock is shown in
Figure 5, where we plot the mass of dust that survives forincreasing shock strengths. Depending on the progenitor model,
the fraction of newly formed dust that is able to survive ranges
between 80% to a few percent. These numbers are in agreementwith what has been found by other studies using hydrodynamical
simulations (Nozawa et al. 2007; Silvia et al. 2010, 2012). In
particular, by post-processing an idealized numerical simulationof a planar shock wave impacting a dense, spherical clump,
Silvia et al. (2010, 2012) have calculated grain sputtering for avariety of species and size distributions. By altering the clump
overdensity and the shock velocity, they find that grains withradii smaller than 0.1 μm are sputtered to much smaller radiiand often completely destroyed, and that the percentage of dust
mass that survives critically depends on the initial grain size
distribution and on the velocity of the reverse shock, ranging
between complete destruction to ∼44% survival for the largest
and most robust grains.
Given that the dust produced in faint SN ejecta is composed
only by AC grains, the fraction of mass that gets destroyed isreturned into the gas phase under the form of C atoms. The
resulting carbon condensation efficiencies, defined as the ratio

4. THE STAR FORMING ENVIRONMENTOF SMSS J031300
In this section, we test the hypothesis that SMSS J031300
has formed out of the collapse and fragmentation of a gas
cloud that has been pre-enriched by the ejecta of one of the
Population III faint SNe studied in the previous section. We first
discuss the expansion of the ejecta into the surrounding ISM
and then the subsequent recollapse of the star forming cloud, toassess the relative role of fine-structure line and dust cooling forthe formation of SMSS J031300.
4.1. Ejecta Expansion and Mixing with the ISM
The mixing and fallback model—as first introduced by
Umeda & Nomoto (2002)—naturally predicts a stratified ejecta:
the inner material is assumed to be mixed by the growth of7

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Table 3
Properties of Models that we Investigate with the Critical Abundances of Carbon, [C/H]cr , for Low-mass Star Formation
SN Progenitor

Model

ini
fC,cond

Dini

Dtrans,ini

rCcool(μm)∗
fC,cond(C/H)cr

13 M

norev
rev1
rev2
rev3
norev
rev1
rev2
rev3
norev
rev1
rev2
rev3
norev
rev1
rev2
rev3

0.84
0.53
0.26
0.10
0.73
0.53
0.29
0.12
0.00560.00130.00040.0001
0.15
0.08
0.03
0.01

9.10 × 10−6
5.77 × 10−6
2.83 × 10−6
1.05 × 10−6
7.90 × 10−6
5.78 × 10−6
3.16 × 10−6
1.32 × 10−6
6.10 × 10−8
1.38 × 10−8
4.26 × 10−91.30 × 10−91.64 × 10−6
8.07 × 10−7
3.69 × 10−7
1.17 × 10−7

−4.07
−3.07
−2.82
−2.71
−4.23
−3.26
−2.94
−2.80
−3.41
−3.40
−3.40
−3.39
−3.25
−3.12
−3.07
−3.04

0.108
0.104
0.119
0.148
0.177
0.170
0.191
0.228
0.014
0.012
0.012
0.012
0.073
0.067
0.064
0.061

0.84
0.63
0.63
0.63
0.73
0.59
0.59
0.59
0.00590.00130.00040.0001
0.15
0.08
0.03
0.01

−4.65
−4.54
−4.48
−4.39
−4.37
−4.30
−4.25
−4.17
−3.38
−2.79
−2.30
−1.77
−4.07
−3.80
−3.49
−3.01

15 M

50 M

80 M -3D

Notes. We here show our models with metal abundances fitted for 3D stellar atmospheric models by Keller et al. (2014).
∗
rCcool and fC,cond
are, respectively, the characteristic radii of carbon grains (see text) and the carbon condensation
efficiency at density nH = 1012 cm−3 , resulting from our collapse calculations with the effects of grain growth.
Carbon abundance is set to the observed value, [C/H] = −2.60. The values in bold face are below the corresponding
critical limits, Dtrans > −3.5 ± 0.2 and Dcr = [2.6–6.3] × 10−9 .

Figure 5. Histograms showing the mass of dust at the end of nucleation,
and after the passage of a reverse shock of increasing intensity for all thefaint SN progenitors considered in the present study. From top to bottom: noreverse shock models (norev), models with a circumstellar medium density ofρISM = 10−25 (rev1), 10−24 (rev2), and 10−23 g cm−3 (rev3). For the 50 M
model the rev2 and rev3 cases are out of scale.
(A color version of this figure is available in the online journal.)

Figure 4. Size distribution for grains formed in the ejecta of 80 M -3D and
50 M -3D models, for no reverse shock model (norev) and for models witha circumstellar medium density of ρISM = 10−25 (rev1), 10−24 ( rev 2) and
10−23 g cm−3 ( rev 3), from top to bottom. For the 50 M model, the rev2 andrev3 cases are out of scale.
(A color version of this figure is available in the online journal.)ejecta material has uniformly enriched the parent star-forming
cloud. Hence, whatever the degree of mixing at nucleation,
45–80 days after the explosion, or after the passage of the reverse
shock, (2.6–3.4)×103 years later, the ejecta material needs to be
perfectly mixed into the star forming cloud before its subsequentcollapse.
An estimate of the maximum timescale available to fully mix
the enriched material can be obtained by computing the total
mass and radius of the cloud, Mcloud , in which the ejecta needs
to be diluted in order to match the observed metallicity on thesurface of SMSS J031300, Zobs ∼ 2.67 × 10−3 Z (Keller et al.
2014),

Rayleigh–Taylor instabilities during shock propagation, while
the ejecta is dominated by the external material plus a small
fraction of the mixed gas near the mass-cut. The mixing
efficiency is still a matter of debate due to the complexity ofthe mixing/fallback scenario, which depends on the explosion
energy, the gravitational potential, and the asphericity during
the collapse. This is the reason why we have studied dust
formation in both perfectly mixed and stratified ejecta. Yet,when we compare the observed surface elemental abundance ofa stellar fossil, such as SMSS J031300, with the yields of a single
Population III SN, we make the implicit assumption that theMcloud =8Mmet,ejecta,
Zobs XH(7)

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Figure 6. Temperature evolution as a function of the central density of clouds pre-enriched by Population III faint SN explosions of 15 M (left), 50 M (middle), and80 M -3D (right) stars. Solid curves represent models with no reverse shock, dotted-, dashed- and dot-dashed curves represent models with a circumstellar medium
density of ρISM = 10−25 , 10−24 and 10−23 g cm−3 , hence an increasing reverse shock destructive efficiency. Red triangles mark the states where gas fragmentation
conditions are met.
(A color version of this figure is available in the online journal.)

where XH = 0.75 and we have assumed an ISM with primordial
composition. We find that Mcloud is an increasing function of theprogenitor mass, since more massive progenitors have larger
metal yields, and ranges between 104 and 2 × 105 M . Thisgas mass is roughly consistent with the baryonic content of a∼106 M mini-halo. The radius of the cloud depends on thedensity of the ISM (ρISM ): to be consistent with the reverse
shock models described in the previous section, we assume
values in the range [10−26 –10−23 ] g cm−3 , where the lower limit
approximately corresponds to the critical density at z = 10. The
corresponding cloud radius is
Rcloud =3Mcloud4πρISM

H3 O+ , O+2 , O2 , Si, SiO, and SiO2 ) with a chemical networkof 55 reactions. Radiative cooling owing to atoms/ions (C i,
C ii, and O i) and molecules (H2 , HD, CO, OH, and H2 O), andthe heating/cooling by H2 formation/destruction are computed
self-consistently at each time. Gas cooling by heat transfer between gas and dust is calculated as the sum over all dust species
and size bins. In addition to the dust mass that is present in thegas cloud at the onset of collapse, we also treat accretion of gasphase metal species onto dust grains during the collapse (grain
growth, Nozawa et al. 2012; Chiaki et al. 2014). For the purposeof the present analysis, we set the cosmic microwave background (CMB) temperature at TCMB = 27.3 K, correspondingto (1 + z) = 10 (see Schneider & Omukai 2010 for the effects of
the CMB temperature floor on the collapse of clouds at different
metallicities).
Figure 6 shows the cloud evolution in the temperature–density
plane. Each panel represents the results assuming that thecloud has been pre-enriched by the explosion of an individual
Population III faint SN model. We have selected the results ofthree different progenitor masses (the 13 and 15 M models leadto very similar results) adopting dust yields formed in uniformly
mixed ejecta (3D models, although the results are not affectedby the set of reference abundances adopted in the explosion
calibration). For each of these, we consider the decreasing dustto-metal ratios that emerge from the passage of the reverse shockof increasing intensity. The initial dust-to-gas mass ratio at theonset of collapse, Dini and initial transition discriminant Dtrans,ini
are shown in Table 3, where we have written in bold only thevalues that are below the corresponding critical limits. Hence,
we would expect metal-line cooling to be effective for all but
models 13 and 15 M in the no reverse shock case, and dust
cooling to be effective for all but models 50 M in the twostronger reverse shock cases (rev2 and rev3).
We can compare these simple expectations with full collapse
calculations. The circles and triangles in the figure mark thestates where fragmentation conditions are met (Schneider et al.
2010). At densities nH ∼ 105 cm−3 , fragmentation is due to linecooling. In the 13 and 15 M models, the dominant coolants are
HD and C i. For models with moderate reverse shock destructionini(norev, rev1), fC,cond> 0.5 and—as a result—H2 formation
on grain surface is very efficient, enabling the formation

1/3
(8)

and varies in the range 20 pc  Rcloud  100 pc, whichis reached by the SN shock in its Sedov–Taylor phase on a
5/2
timescale texp = Rcloud (ρISM /Eexp )1/2 ∼ 0.2–10 Myr.
Following Madau et al. (2001), we can estimate the growthtimescale of Rayleigh–Taylor instabilities as tRT ≈ (ls /2πg)1/2 ,where g is the gravitational acceleration and ls is the spatial
scale to be mixed. Using the values computed above for the
cloud mass and radius, we find tRT = 0.4–3 Myr, depending on
the ISM density. Hence, in less than a few megayears after the
explosion of a faint Population III SN, the ejecta material may
have already mixed and enriched the gas out of which second
generation stars form. The resulting stellar mass depends onthe cooling and fragmentation properties of the collapsing gas,
which we investigate in the following section.
4.2. Cooling and Fragmentation of the Collapsing Cloud

We perform a one-zone semi-analytic collapse calculation tofollow the temperature evolution of the cloud (Omukai 2000,
Omukai et al. 2005), setting the abundances of heavy elements
and dust species as inferred from the SN dust models describedin the previous section. We refer the interested reader to Chiaki
et al. (2014) for a detailed description of the model.
In this collapse calculation, we solve non-equilibrium chemistry of 27 gas-phase species (H+ , e− , H, H− , H2 , D+ , D, HD,
C+ , C, CH, CH2 , CO+ , CO, CO2 , O+ , O, OH+ , OH, H2 O+ , H2 O,
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of HD molecules. On the other hand, C i cooling efficiency
is comparable to (3D cases) or exceeds (1D cases, where[C/H] is larger than 3D) HD cooling for rev2 and rev3 models.8
For the larger progenitor mass models (50 and 80 M ), thedominant coolant at intermediate densities is C i as a result of
the lower initial condensation efficiencies. Yet, as shown by the
diagonal lines in the three panels, the characteristic masses ofthe fragments formed in this early stage of collapse (the Jeansmass at the density where instability occurs) are estimated to be∼100 M .
It is important to note that although sputtering of AC grains
releases C atoms in the gas phase that may be potentiallyaccreted onto the surviving grains at a later stage of thecollapse, grain growth has a non-negligible impact on the results
only if C/O > 1 at the onset of collapse. In fact, AC grain
growth is prevented by efficient formation of CO molecules
at nH ∼ 104 cm−3 (Chiaki et al. 2014). This is confirmed bycomparing the carbon condensation efficiencies at the onset ofini∗
collapse, fC,cond, and a later stage of the collapse, fC,cond, whenthe density is large enough for grain growth to occur efficiently(nH = 1012 cm−3 , see below). The values predicted by eachmodel are shown in Table 3; as expected, grain growth has a
non-negligible effect only for the 13 and 15 M models withreverse shock. Hence, for all but the smallest progenitor massmodels, the conditions for dust cooling and fragmentation arelargely determined by the dust-to-gas ratio initially present in
the cloud as a result of the SN explosion and the associatedreverse shock.
Figure 6 shows that dust cooling is efficient at high densities
nH = 1010 –1014 cm−3 triggering fragmentation and potentiallyleading to the formation of a low-mass star such as SMSS
J031300. The only two unsuccessful cases are associated withthe 50 M faint SN explosion with the stronger reverse shockmodels. Not surprisingly, in these two models the amount of
dust that survives the passage of the reverse shock is not enoughto keep the initial dust-to-gas mass ratio above the critical one,
Dcr = [2.6–6.3] × 10−9 (see Table 3).
Finally, it can be shown that the full collapse calculations
confirm that even in unmixed models, which are characterized
by smaller dust yields, dust-driven fragmentation conditions aremet for all reverse shock cases considered, consistent with thefact that the initial dust-gas ratios are super-critical, varying in
the range D = 7.94 × 10−8 –1.11 × 10−6 .
Following Chiaki et al. (2014), we can estimate the criticalelemental abundances that enable dust-induced fragmentation.
For CEMP stars enriched by faint Population III SN explosions,carbon grains are the dominant species in the parent cloud;therefore, the critical dust-to-gas ratio can be easily associatedwith a critical carbon abundance,
AC,cr = 1.4 × 10−3

×

T
103 K

4 sC rCcool
3XfC,cond (t) μC
−1/2 n
H

1012 cm−3

−1/2

cooling radii and the critical carbon abundances normalized tothe solar value (AC, = 2.69×10−4 taken from the photosphericvalue in Asplund et al. 2009). Since the observed carbon
abundance of SMSS J031300 is [C/H] = −2.60 (Keller et al.
2014). the critical conditions are satisfied by all the models
but the 50 M rev2 and rev3. This is consistent with the fullcollapse calculations. Hence we conclude that the formationof the CEMP star SMSS J031300, even with the lowest ironcontent currently observed, may have been triggered by dust
cooling and fragmentation.
5. DISCUSSION AND CONCLUSIONS
The results presented in the previous section have beenobtained using the dust and metal yields predicted for faintPopulation III SN explosions tailored to reproduce the observed
elemental abundances of SMSS J031300. For the first time,
we have studied the process of dust formation in carbon-rich,iron-poor ejecta that characterize these explosions. We findthat carbon can be significantly depleted onto AC grains, withcondensation efficiencies that can be as large as 75%. Dueto the small abundance of other refractory elements in theejecta, silicates, alumina, or magnetite grains do not form in
the ejecta of faint Population III SNe. For most of the models
we have explored, when normalized to the observed [C/H] thatcharacterizes CEMP stars, the predicted dust-to-gas ratios in
the parent star-forming cloud are large enough to trigger dust
cooling and fragmentation, even without the contribution ofgrain growth.
If these results can be considered as representative for thegeneral class of CEMP-no stars, which represent 90% of CEMPs
with [Fe/H] < −3, then our study suggests that dust coolingand fragmentation may have been responsible for the formationof these low-mass stars.
In a recent work, Ji et al. (2014) have suggested that the early
formation of low-mass stars may follow two potential pathways:
in the dynamic pathway, many sub-clumps are formed throughfine-structure line cooling. Dynamical interactions can lead tothe ejection of a protostar from the parent cloud, so that a lowmass star can form even in the absence of dust cooling. In thethermal pathway, fragmentation due to fine-structure coolingis inhibited by the small abundance of gas-phase elements,
and the entire cloud collapses. A high-density protostellar disk
is formed at the center of the cloud, which then fragments
and forms low-mass stars due to dust-cooling. Observational
evidence for these two alternative pathways comes from the
distribution of a sample of metal-poor halo stars and dwarf
galaxy stars with [Fe/H] < −3.5 in a plane where the transition
discriminant for line-cooling, Dtrans , is on the y -axis and the[Si/H] (see their Figure 6) is on the x -axis; the latter quantity
is used as an indication of the dust-to-gas ratio in the parent
cloud, assuming that the dust is mostly made of silicates. When
compared with the critical values for fine-structure-line anddust cooling, they find that stars that have an [Si/H] too low
to form through silicon-based dust cooling are characterized
by a large transition discriminant, and satisfy the criterion forfine-structure-line cooling and vice versa.
Our study questions this interpretation as it shows that CEMP
stars form in C-rich gas, where silicates do not form and carbon
dust is the dominant dust species. Hence, for CEMP stars,[C/H] is a better proxy for dust cooling than [Si/H]. In addition,
we also show that fine-structure-line and dust cooling are notmutually exclusive: the collapsing gas cloud undergoes two
distinct phases of fragmentation, one driven by line cooling,where sC is the material density of carbon grains (sC =2.28 g cm−3 ) and rCcool = r 3 C /r 2 C is the characteristic grainradius for gas cooling (Chiaki et al. 2014). Table 3 shows the8

In our calculations, gas cooling is dominated by C i because we areneglecting the presence of a far-UV (FUV) radiation field. If some FUV ispresent, C i is photo-ionized and—as a result—C ii dominates cooling.
However, this does not affect our conclusions as the two cooling rates are
similar.

10

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Figure 7. Conditions for the formation of low-mass C-normal (left panel) and C-rich stars (right panel). Observations are taken from [Fe/H] < −3 sample of Norris
et al. (2013). Points with triangles indicate the sub-sample of the five ultra-iron poor stars, with [Fe/H] < −4 currently known. The horizontal lines indicate thecritical transition discriminant Dtrans,cr = −3.5 ± 0.2 for fine-structure-line cooling (Frebel & Norris 2013). The vertical shaded regions indicate the range of critical
Si (left panel) and C (right panel) abundances that would enable Si-dominated dust and C-dominated dust to activate dust cooling (see text). The arrows indicate stars
where either the C or the O abundances was not measured and only an upper limit was available.
(A color version of this figure is available in the online journal.)(either by metal lines, such as C i, C ii or by molecular transitionsof H2 and HD) at nH ∼ 104 cm−3 , which leads to the formationof ∼100 M sub-clumps; and the other, driven by dust coolingat nH = 1010 –1014 cm−3 , which triggers the formation of
low-mass stars (see also Tanaka & Omukai 2014). Thus, thethermal pathway may be responsible for the formation ofboth C-rich and C-normal stars, even at the lowest [Fe/H]
currently observed, although the dynamic pathway may operate
as well.
Unfortunately, it is not straightforward to estimate the dustto-gas ratio of the parent gas cloud from the observed elemental
abundances, similar to what is done for the transition discriminant. In fact, the dust properties (its composition and size distribution) depend on the nature of the SN explosions that havedominated the early enrichment and on the level of destruction
suffered by the newly formed dust by the passage of the reverse
shock, although the latter process may be mitigated by grain
growth during the collapse. Using the results that we have obtained in the present study as a proxy for the general class of Crich metal-poor stars and the results obtained by Schneider et al.
(2012b) and Chiaki et al. (2014) for the star SDSS J1029151
as a proxy for the general class of C-normal metal-poor stars,
we can draw the following guidelines: for C-rich stars, carbon condensation efficiencies into dust of 0.01–0.84 translate
into critical carbon abundances of −4.65 < [C/H]cr < −3.01;
for C-normal stars, the dominant dust compounds are forsterite(Mg2 SiO4 ) and enstatite (MgSiO3 ), with Mg and Si condensation efficiencies which range between 0.2 and 0.6 and associated critical abundances of −5.02 < [Mg/H]cr < −4.73 and−5.24 < [Si/H]cr < −4.73 (see Table 1 in Chiaki et al. 2014).
In Figures 6 and 7, we compare these predictions withobservational data taken from the sample of C-normal and Crich stars with [Fe/H] < −3 investigated by Norris et al. (2013).
As shown in Caffau et al. (2011), SDSS J1029151 is the only
star, discovered until now, that falls in the forbidden zone forfine-structure line cooling (indicated by the triangle below Dcr inFigures 7 and 8) and no stars appear to fall in the forbidden zone
for dust cooling, although there are two C-rich stars, HE0557-

Figure 8. Same as in Figure 6 but the data are not plotted as a function of
the estimated dust-to-gas mass ratio; for each star we show two values of thedust-to-gas mass ratio, obtained using the maximum (filled data points) andminimum (empty data points) condensation efficiencies for C (C-rich) and Si(C-normal) stars (see text). The vertical shaded region represent the criticaldust-to-gas ratio of Dcr = [2.6–6.3] × 10−9 for dust-cooling (Schneider et al.
2012a).
(A color version of this figure is available in the online journal.)

4840 (Norris et al. 2007) and HE0057-5959 (Yong et al. 2013b),
which appear to be close to the critical range.
If we represent the critical conditions in terms of the dustto-gas ratio, as in Figure 8, we see that C-normal and C-richstars do not appear to follow different distributions on the plane,
although—as expected—the C-normal stars have systematicallylower Dtrans and lower dust-to-gas-ratios, D.
11

The Astrophysical Journal, 794:100 (12pp), 2014 October 20

Marassi et al.

More importantly, the two criteria for low-mass star formation
do not appear to be mutually exclusive, but rather point to asingle pathway for the formation of the first low-mass stars in
the universe.

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We thank Simone Bianchi for his kind collaboration. The
research leading to these results has received funding fromthe European Research Council under the European Unions
Seventh Framework Programme (FP/2007-2013)/ERC Grant
Agreement No. 306476. G.C. is supported by Research Fellowships of the Japan Society for the Promotion of Science (JSPS)
for Young Scientists. N.Y. is grateful for financial support by
the Grants-in-Aid by the Ministry of Education, Science, andCulture of Japan (25287050). We acknowledge financial support from the PRIN MIUR 2010–2011, project “The Chemicaland dynamical Evolution of the Milky Way and Local Group
Galaxies,” prot. 2010LY5N2T.
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