MNRAS 472, L115–L119 (2018)

doi:10.1093/mnrasl/slx163

Advance Access publication 2017 October 5Classification of extremely metal-poor stars: absent region in
A(C)–[Fe/H] plane and the role of dust cooling
Gen Chiaki,1‹ Nozomu Tominaga1 and Takaya Nozawa2
1 Department of Physics, Konan University, 8-9-1 Okamoto, Kobe 658-0072, Japan
2 Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan

Accepted 2017 October 2. Received 2017 September 8; in original form 2017 September 8

ABSTRACT

Extremely metal-poor (EMP) stars are the living fossils with records of chemical enrichment history at the early epoch of galaxy formation. By the recent large observation campaigns, statistical samples of EMP stars have been obtained. This motivates us to reconsider
their classification and formation conditions. From the observed lower limits of carbon andiron abundances of Acr (C) ∼ 6 and [Fe/H]cr ∼ −5 for C-enhanced EMP (CE-EMP) andC-normal EMP (CN-EMP) stars, we confirm that gas cooling by dust thermal emission is indispensable for the fragmentation of their parent clouds to form such low mass, i.e. long-lived
stars, and that the dominant grain species are carbon and silicate, respectively. We constrain
the grain radius ricool of a species i and condensation efficiency fij of a key element j as
cool
/fSil,Mg = 0.1 µm to reproduce Acr (C) and [Fe/H]cr , which giverCcool /fC,C = 10 µm and rSil
[C/H] − 2.30
+ 10[Fe/H] > 10−5.07 for the formation of every EMP star.
a universal condition 10
Instead of the conventional boundary [C/Fe] = 0.7 between CE-EMP and CN-EMP stars, thiscondition suggests a physically meaningful boundary [C/Fe]b = 2.30 above and below whichcarbon and silicate grains are dominant coolants, respectively.
Key words: stars: formation – stars: low-mass – stars: Population II – ISM: abundances – dust,
extinction – galaxies: evolution.

1 I N T RO D U C T I O NLong-lived stars with metallicities lower than our neighbourhood,so-called metal-poor (MP) stars, are discovered in our Galaxy andnearby dwarf galaxies. They are intensively studied as the clues
to know the chemical evolution during the structure formation.
This approach is called Galactic archaeology or near-field cosmology. MP stars are classified into carbon-enhanced MP (CEMP) andcarbon-normal MP (CNMP) stars, divided at the boundary conventionally defined as [C/Fe] = 0.7 (Beers & Christlieb 2005; Aoki
et al. 2007).1 CEMP stars are further divided into CEMP-no without the enhancement of neutron-capture elements, and CEMP-r or
CEMP-s with r-process or s-process element enhancement, respectively (Beers & Christlieb 2005).
By recent large observational campaigns,2 we can access thestatistical samples of MP stars. Yoon et al. (2016) report that
 E-mail: chiaki@center.konan-u.ac.jp
1 The ratio between abundances of elements j and k are expressed as [j/k] =log [y(j)/y(k)] − log [y (j)/y (k)] and A(j) = log (j) = 12 + log y(j) foran element j, where y(j) denotes the number fraction of j relative to hydrogen
nuclei.
2 e.g. the HK (Beers, Preston & Shectman 1985, 1992), Hamburg/ESO(Christlieb et al. 2001), SEGUE (Yanny et al. 2009), and LAMOST survey(Cui et al. 2012; Deng et al. 2012).

CEMP stars are apparently subdivided into three groups on the
A(C)–[Fe/H] plane (Fig. 1). While CEMP Group I stars residing in −3.7 < [Fe/H] < −1.2 and 7.0 < A(C) < 9.0 are dominantly CEMP-s stars, Group II (with −5.0 < [Fe/H] < −2.5
and 5.0 < A(C) < 7.0) and Group III (with [Fe/H] < −3.5 and
6.0 < A(C) < 7.5) stars are mainly CEMP-no stars. Since almost all
Group I stars show binary feature, they are considered to have acquired the gas rich with C and n-capture elements from their evolved
companions (Suda et al. 2004). On the other hand, the physical explanation of distinction between Groups II and III stars has not been
made so far.
MP stars with [Fe/H] < −3 including CEMP Groups II and III
stars are particularly called extremely metal-poor (EMP) stars. The
lower limits of their elemental abundances indicate the existenceof the critical metallicity above which their parent clouds become
unstable to fragment into small gas clumps through efficient gas
cooling by heavy elements so that low-mass stars which survive until
the present day are likely to be formed (Bromm & Loeb 2003; Frebel
et al. 2005). Recent theoretical studies have shown that cooling by
dust thermal emission is crucial to form low-mass fragments with
∼0.1 M (Omukai 2000; Schneider et al. 2003).
Marassi et al. (2014) and Chiaki et al. (2015) predict that dust
grains are important commonly for the formation of C-enhanced
EMP (CE-EMP) and C-normal EMP (CN-EMP) stars. They showthat the dominant grain species are carbon and silicate, respectively,C 2017 The Authors
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G. Chiaki, N. Tominaga and T. Nozawa

Figure 1. Carbon abundance A(C) as a function of metallicity [Fe/H] of observed CEMP stars (left-hand panel) and CNMP stars (right-hand panel) retrieved
from SAGA data base (Suda et al. 2008, 2011, 2017; Yamada et al. 2013, http://sagadatabase.jp/). The dashed line represents [C/Fe] = 0.7 as the boundary
between CEMP and CNMP stars (Beers & Christlieb 2005; Aoki et al. 2007). CEMP stars are further divided into three groups indicated by the ellipses in theleft-hand panel (Yoon et al. 2016), and the solid line ([C/Fe] = 2.0) indicates the apparent boundary between Groups II and III. We show the critical carbon
cool /f(equation 2) and iron (equation 4) abundances by red and blue lines, respectively, for various rCcool /fC,C and rSil
Sil,Mg .

and estimate the critical C and Si abundances. However, they resort to theoretical models of grain formation because the propertiesof grains such as radius and condensation efficiency can not bedirectly measured. Further, their analyses are based on the conventional classification of EMP stars, and do not explain the difference
between Groups II and III stars.
In this Letter, we reconsider the classification and formation conditions of EMP stars. From Fig. 1, we point out three interesting
features: (1) no EMP stars have so far been observed in the region of A(C) < 6 and [Fe/H] < −5, (2) Groups III and II stars
are distributed in the regions with high ([C/Fe] > 2) and moderate([C/Fe] < 2) C-enhancement, respectively and (3) the distributionof Group II stars appears continuously connected with CN-EMP
stars.
We derive grain properties of carbon and silicate from the feature(1), and then present a formation condition applicable to every EMP
star. Comparing the contributions of carbon and silicate grains togas cooling, we propose the physically motivated boundary between
EMP stars whose formation could be derived mainly by carbon andsilicate grains. This boundary can simultaneously explain the features (2) and (3). Throughout this Letter, we use the solar abundanceof Asplund et al. (2009) as A (C) = 8.43, A (Mg) = 7.60 andA (Fe) = 7.50.
2 C R I T I C A L E L E M E N TA L A B U N DA N C E S
The critical condition for cloud fragmentation can be described by
the comparison of gas cooling owing to dust thermal emission withgas compressional heating (Schneider et al. 2012). With condensation efficiency fij of a key element j on to a grain species i and acharacteristic grain radius ricool , the fragmentation condition can be
written using the number abundance y(j) as
 3μij fij XHy(j ) > 1.4 × 10−3 cm2 g−1 ,
(1)
cool
4ς
r
i
i
i
where μij denotes the molecular weight of a monomer and ς i is thebulk density of a grain (Chiaki et al. 2015).3 This indicates that,
3 We here consider spherical grains. The radius r cool is defined as r3  /r2 iiicharacterizing the efficiency of gas cooling, where xi = xϕ i (r)dr is the

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once the key element and its abundance y(j) are specified, we canput a constraint on ricool and fij in a form of ricool /fij , which wehereafter call the effective grain radius.
2.1 Critical C abundance and property of carbon grains
We first derive the effective radius rCcool /fC,C for carbon grains.
For carbon grains, the key element is carbon, and μC, C = 12 andς C = 2.23 g cm−3 . Then, from equation (1), we can obtain thecritical carbon abundance above which gas cooling by carbon grainsexceeds gas compressional heating as
 cool
r /fC,C.
(2)
Acr (C) = 5.67 + log C
10 µm
The horizontal red lines in the left-hand panel of Fig. 1 show thecritical carbon abundances for rCcool /fC,C = 1, 10 and 100 µm frombottom to top. CEMP Group III stars are distributed in a range ofA(C) > 6.0 over a wide range of [Fe/H] (−7  [Fe/H]  −4).
Hence, Acr (C) = 6 can be taken as the lower limit of C abundances
for CEMP Group III stars. Then, the effective grain radius is estimated to be rCcool /fC,C = 21.6 µm. Taking the statistical uncertainties into consideration, we here adopt rCcool /fC,C = 10 µm. Below
the horizontal line corresponding to rCcool /fC,C = 10 µm (shaded
region in Fig. 1), carbon dust cooling is inefficient to induce cloudfragmentation, and long-lived low-mass stars are unlikely to form.
Some of CEMP Group II stars have lower carbon abundances thanAcr (C) = 6.0, which is discussed in the subsequent sections.
2.2 Critical Fe abundance and property of silicate grains
Next, we constrain the property of the other major grain species,
silicate. For silicates, we consider enstatite (MgSiO3 ) with its key element being Mg, and μMgSiO3 ,Mg = 100 and ςMgSiO3 = 3.21 g cm−3 .
average of a physical quantity x weighted by the size distribution ϕ i (r) ofa grain species i. Equation (1) is given at the gas density nH = 1014 cm−3and temperature T = 1000 K, where dust cooling is dominant over gas
compressional heating in clouds with [Fe/H] ∼ −5 (Schneider et al. 2012).
XH is the mass fraction of hydrogen nuclei and XH = 0.75 throughout thisLetter.

Classification of EMP stars

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Figure 2. Carbon abundance A(C) as a function of [Fe/H] of Galactic halo MP stars ever observed. The formation of these long-lived, low-mass stars would
be restricted by C and Fe abundances above which gas cooling by carbon and silicate grains exceeds gas compressional heating (equation 5) indicated by the
curve coloured from blue to red with increasing fraction of the carbon grain cooling efficiency. The black line shows the boundary [C/Fe]b = 2.30 (equation 6)
above and below which carbon and silicate grains are dominant coolants for the formation of EMP stars, respectively.

The result is unchanged for forsterite (Mg2 SiO4 ), whose key element is Si. From equation (1), we can calculate the critical condition
where gas cooling by silicate grains overcomes the compressional
gas heating as
 cool
r /fSil,Mg.
(3)[Mg/H]cr = −4.70 + log Sil
0.1 µmWe convert this critical Mg abundance to the critical Fe abundance,
using the average abundance ratio [Mg/Fe] = 0.368 for stars with
[Fe/H] < −1 (from SAGA data base), as cool
r /fSil,Mg.
(4)[Fe/H]cr = −5.07 + log Sil
0.1 µmThe vertical blue lines in the right-hand panel of Fig. 1 indicate
cool/fSil,Mg = 0.01, 0.1 and 1 µm
the critical Fe abundances for rSil
from left to right. To realize the critical abundance [Fe/H]cr = −5.0
suggested by the distribution of CN-EMP stars, the effective grain
cool/fSil,Mg = 0.081 µm is required. We set the fiducial value
radius rSil
cool
/fSil,Mg = 0.1 µm, which isof the effective grain radius as rSil
smaller than that of carbon grains by two orders of magnitude.

The critical condition is shown by the coloured curve in Fig. 2.
The shaded region below the curve can successfully explain theregion where no stars have been observed so far. Also, the figuresuggests that the distribution of CEMP Group II stars shows thelower limit of Fe abundance at [Fe/H] = −5 as that of CN-EMP
stars.
2.4 Boundary between CE-EMP and CN-EMP stars
Equating the first and second terms in the left-hand side ofequation (5), we can define the transition line on which the contributions of carbon and silicate grains to gas cooling are equalas[C/Fe]b = 2.30.

(6)This condition is indicated by the black line in Fig. 2 above which
gas cooling by carbon grain is dominant over that by silicates. The
boundary gives the physical explanation of the distinction between
CEMP Group III and Group II stars.

2.3 Combined criterion for CE-EMP and CN-EMP starformation

3 M O D E L C A L C U L AT I O N S O F G R A I N
P RO P E RT I E S I N P O P I I I S N E J E C TA

In the previous sections, we have considered separately the contributions of carbon and silicate grains to gas cooling, and derived
their effective grain radii. In reality, both the grain species can contribute simultaneously to gas cooling in collapsing clouds. In thiscase, equation (1) is reduced to

We have shown that the effective grain radius of carbon mustbe larger than that of silicate by two orders of magnitude to reproduce the observed distributions of EMP stars. In this section,
we show this difference in grain radius with a dust formation
model. In the early Universe, dust grains are mainly supplied bysupernovae (SNe) arising from first-generation metal-free (PopIII) stars (Todini & Ferrara 2001; Nozawa et al. 2003). Whilethe elemental abundances of CE-EMP stars are well reproducedby faint core-collapse SNe (FSNe) with C enhancement due tolarge fallback of Fe peak elements, those of CN-EMP stars are
reproduced by energetic core-collapse SNe (CCSNe) or hypernovae (HNe) (Umeda & Nomoto 2003; Limongi & Chieffi 2012;

17.5
3.03
y(C) + cooly(Mg) > 1.4 × 10−3 .
rCcool /fC,CrSil /fSil,Mg
cool
Using rCcool /fC,C = 10 µm and rSil
/fSil,Mg = 0.1 µm derived in theprevious sections gives

10[C/H]−2.30 + 10[Fe/H] > 10−5.07 .

(5)

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Figure 4. Maximum grain radius rimax of carbon (left) and silicate (right)
grains as a function of explosion energy ESN with various 56 Ni masses. For
silicate grains, dashed and solid curves show the results with mass fraction
XMg of the key element Mg of 1.0 and 0.1, respectively.

Figure 3. Time evolutions of gas temperature and density (a) with a fixed
56 Ni mass of M(56 Ni) = 10−3 M and (b) with a fixed explosion energyof ESN = 1 × 1051 erg at the mass coordinate where the largest carbon
grains are formed. The circles are plotted at the onset time of carbon grain
formation when T becomes below the condensation temperature (2000 K)
indicated by the black dashed line.

Ishigaki et al. 2014; Marassi et al. 2014; Tominaga, Iwamoto &Nomoto 2014).
To estimate the properties of newly formed dust, we follow the
temporal evolution of temperature T and density ρ of expanding SN
ejecta with radiative transfer calculations including energy deposition from radioactive decay of 56 Ni (Iwamoto et al. 2000). Applying
the approximation formulae of Nozawa & Kozasa (2013), the average grain radius riave (MR ) and condensation efficiency fijave (MR )are calculated at each mass coordinate MR from the concentration
cjon = Xj ρ/mj of a key element j and the cooling time-scale τicool
at the onset time tion of dust formation when T declines down tothe condensation temperature (2000 K and 1500 K for carbon andsilicate grains, respectively). A dominant fraction of grains will beformed at the mass coordinate MRmax , where riave becomes largest because cion marks maximum there. We thus take rimax = riave (MRmax )as the fiducial value of the grain radius. At MRmax , fijave turns tobe ∼1. We take a progenitor model of the SN which reproduces
the chemical composition of HE0557 − 4840 with an intermediate
C-enhancement [C/Fe] = 1.68 (Ishigaki et al. 2014). The masscut is Mcut = 5.65 M and progenitor mass is Mpr = 25 M . The
masses of C and Mg atoms are mC = 12mH and mMg = 24mH , wheremH is the mass of a hydrogen nucleus.
We first see the results for carbon grains. Since carbon grains areformed mainly in the layer rich with C, we set XC = 1.0. Fig. 3 shows
the temporal evolutions of gas temperature and density. With a fixed56
Ni mass of M(56 Ni) = 1 × 10−3 M , temperature and density forhigher explosion energy ESN decline more rapidly due to the higher
expansion rate, and the time tCon (indicated by circles) becomes earlier. With a fixed ESN = 1 × 1051 erg, temperature keeps higher, andtCon becomes later for larger M(56 Ni). Fig. 4 shows the grain radius
rimax as a function of ESN with various M(56 Ni). For each M(56 Ni),
the grain radius is smaller for higher ESN because the gas density
is smaller at tCon by more rapid expansion. For M(56 Ni) < 0.01 M ,MNRASL 472, L115–L119 (2018)

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rimax declines rapidly with ESN  1 × 1051 erg because tion is coincident with the finishing time of the plateau phase when the ejecta
becomes optically thin and the temperature decline suddenly. With
shorter cooling time-scale, the larger number of grain seeds form,
i.e, the radius of each grain becomes smaller.
With the same mass fraction XC = XMg = 1.0, rimax for carbon
and silicate grains are similar for each ESN and M(56 Ni). However,in the formation region of silicate grains, Mg is dominated by O,
and we set the fiducial value as XMg = 0.1, following nucleosynthemax
sis calculations (Tominaga et al. 2014). With XMg = 0.1, the rSil
decreases by an order of magnitude for each ESN and M(56 Ni).
To reproduce the elemental abundance of the most iron-poor
CE-EMP stars such as SMSS J0313 − 6708 (Keller et al. 2014),
ESN ∼ 1051 erg and M(56 Ni)  10−3 M are favoured (Marassi
et al. 2014; Ishigaki et al. 2014). In our calculations,
we estimate rCmax = 34.3 µm with ESN = 1.0 × 1051 erg andM(56 Ni) = 1 × 10−7 M . The abundance ratio of the most metalpoor star SDSS J1029 + 1729 (Caffau et al. 2011) is reproduced by
HN models with ESN ∼ 1052 erg and M(56 Ni) ∼ 0.1 M (Tommax= 0.188 µm with ESN =inaga et al. 2014). We predict rSil
52
56
1.0 × 10 erg, M( Ni) = 0.1 M , and XMg = 0.1. These values
cool/fSil,Mg = 0.1 µm.
are consistent with rCcool /fC,C = 10 µm and rSil
4 DISCUSSION
The observed lower limits of C and Fe abundances of CE-EMP
and CN-EMP stars indicate that these stars form through the fragmentation of their parent clouds by gas cooling owing to thermal
emission of two major grain species, carbon and silicate, respectively. We first derive the grain radius and condensation efficiency
cool/fSil,Mg = 0.1 µm from the lower
as rCcool /fC,C = 10 µm and rSil
limits of C and Fe abundances, respectively. The tendency that carbon grains are larger than silicates is qualitatively explained by oursimple analyses of dust formation. Carbon grains grow more efficiently than silicate because the gas density remains higher at thetime when temperature declines to the condensation temperature
with the smaller ESN and M(56 Ni) favoured for CE-EMP stars, andbecause the mass fraction of C is higher than that of Mg in the dust
formation region.
We can derive the critical condition for EMP star formation as
equation (5), which can well reproduce the region where no stars
have so far been observed as indicated by the shaded region inClassification of EMP stars
Fig. 2. Then, we find that the dominant coolant switches fromcarbon to silicate from above to below the boundary [C/Fe]b = 2.30,
which gives the physically motivated classification of CE-EMP and
CN-EMP stars. This simultaneously explain the discrimination of
CEMP Group II and Group III stars (Yoon et al. 2016). Opposite toGroup III stars, the dominant coolant for the formation of CEMP
Group II stars is silicate grains as CN-EMP stars. Interestingly, thedistribution of Group II stars is continuous with that of CN-EMP
stars as indicated by Fig. 2.
Our estimation of the effective grain radii is based on the observed elemental abundances of EMP stars. Our model presented
in Section 3 predicts the larger values rCcool /fC,C = 34.3 µm andcool/fSil,Mg = 0.188 µm for the fiducial cases. Although we hererSiltake the maximum grain radius at the corresponding mass coordinate MRmax , the mass fraction of smaller grains formed in other mass
coordinates can non-negligible, and the average radius of grains will
be smaller. Marassi et al. (2015) predict the smaller grain radii ofrCcool /fC,C  0.1 µm by their grain formation models in FSN ejecta.
It is still possible that stars with lower elemental abundances, whichis permitted by smaller effective grain radii, are discovered by future
observations. In the current state, although the number of samples in
the Galactic halo is large (∼106 stars), statistics of EMP stars with
[Fe/H] < −3 is still small (Hartwig et al. 2015). As the number
of EMP stars increases by future observations, the accuracy of theestimation of grain property and the boundary between CE-EMP
and CN-EMP stars presented in this Letter will get improved.
AC K N OW L E D G E M E N T S
We thank the referee for the positive comments and suggestions.
GC is supported by Research Fellowships of the Japan Society
for the Promotion of Science (JSPS) for Young Scientists. This
work is supported in part by the Grants-in-Aid for Young Scientists(S: 23224004) and for General Scientists (A: 16H02168,
C: 26400223) by JSPS.
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