inferring the velocity of early massive stars from the ...the long-dead early massive stars are the...

Astronomy & Astrophysics manuscript no. fit_v10 c©ESO 2020January 9, 2020

Inferring the velocity of early massive stars from the abundancesof extremely metal-poor stars.

Arthur Choplin1, 2, Nozomu Tominaga1, 3 and Miho N. Ishigaki4

1 Department of Physics, Faculty of Science and Engineering, Konan University, 8-9-1 Okamoto, Kobe, Hyogo 658-8501, Japane-mail: [email protected]

2 Geneva Observatory, University of Geneva, Maillettes 51, CH-1290 Sauverny, Switzerland3 Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa,

Chiba 277-8583, Japan4 Astronomical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan

Received / Accepted

ABSTRACT

Context. The nature of the early generation of massive stars can be inferred by investigating the origin of the extremely metal-poor(EMP) stars, likely formed from the ejecta of one or a few previous massive stars.Aims. We investigate the rotational properties of early massive stars by comparing the abundance patterns of EMP stars with massivestellar models including rotation.Methods. Low metallicity 20 M massive stellar models with eight initial rotation rates between 0 and 70 % of the critical velocity arecomputed. Explosions with strong fallback are assumed. The ejected material is considered to fit individually the abundance patternsof 272 EMP stars with −4 < [Fe/H] < −3.Results. With increasing initial rotation, the [C/H], [N/H], [O/H], [Na/H], [Mg/H], and [Al/H] ratios in the massive star ejecta aregradually increased (up to ∼ 4 dex) while the 12C/13C ratio is decreased. Among the 272 EMP stars considered, ∼ 40 − 50 % areconsistent with our models. About 60− 70 % of the carbon-enhanced EMP star sample can be reproduced against ∼ 20− 30 % for thecarbon-normal EMP star sample. The abundance patterns of carbon-enhanced EMP stars are preferentially reproduced with a materialcoming from mid to fast rotating massive stars. The overall velocity distribution derived from the best massive star models increasesfrom no rotation to fast rotation. The maximum is reached for massive stars having initial equatorial velocities of ∼ 550− 640 km s−1.Conclusions. Although subject to significant uncertainties, these results suggest that the rotational mixing operating in between the H-burning shell and the He-burning core of early massive stars played an important role in the early chemical enrichment of the Universe.The comparison of the velocity distribution derived from the best massive star models with velocity distributions of nearby OB starssuggests that a greater number of massive fast rotators were present in the early Universe. This may have important consequences forreionization, the first supernovae, or integrated light from high redshift galaxies.

Key words. stars: massive − stars: rotation − stars: interiors − stars: abundances − stars: chemically peculiar − nuclear reactions,nucleosynthesis, abundances

1. Introduction

The long-dead early massive stars are the key objects that syn-thesized the first metals, contributed to cosmic reionization, andproduced the first cosmic explosions (e.g. Tumlinson et al. 2004;Karlsson et al. 2013; Nomoto et al. 2013, and references therein).Their initial masses, rotational velocities, multiplicity, or mag-netic fields were likely the most important parameters that con-trolled their evolution and death (e.g. Yoon & Langer 2005;Heger & Woosley 2010; Maeder & Meynet 2012; Langer 2012).

Different cosmological simulations have suggested that thefirst stars were predominantly massive1 (generally & 20 M, e.g.Abel et al. 2002; Bromm et al. 2002; Bromm & Larson 2004; Hi-rano et al. 2014; Hosokawa et al. 2016), but with a mass distribu-tion possibly extending towards much lower masses (e.g. Clarket al. 2011; Susa 2013; Susa et al. 2014; Stacy et al. 2016). Byrecording the angular momentum of the sink particles falling intothe growing protostar, Stacy et al. (2011) have shown that initialvelocities of 1000 km s−1 or higher can be reached for Population

1 Here massive refers to stars with initial mass greater than 8 M

III (Pop III) stars with Mini ≥ 30 M. Hirano & Bromm (2018)studied the angular momentum transfer in primordial discs in-cluding magnetic fields and suggested that the final rotationalstate of Pop III protostars may exhibit a net bimodality: eitherthe protostar does not rotate at all or it is a fast rotator that isclose to break-up speed.

Observations can greatly help to infer the nature of earlymassive stars, either by trying to catch the most distant galaxiesor transients (e.g. Whalen et al. 2013; Salvaterra 2015; Oeschet al. 2016; Moriya et al. 2019) or by observing the still alivenearby extremely metal-poor (EMP) small mass stars, likelyformed ∼ 10 − 14 Gyr ago (e.g. Hill et al. 2002; Sneden et al.2003; Cayrel et al. 2004; Beers & Christlieb 2005; Norris et al.2013; Frebel & Norris 2015; Starkenburg et al. 2018). The nu-merous surveys of the past few decades progressively revealed apopulation of metal-poor stars, now containing about 500 ob-jects with2 [Fe/H] < −3 (from the SAGA database and JIN-Abase, Suda et al. 2008, 2017; Abohalima & Frebel 2018). Sev-

2 [X/Y] = log10(NX/NY)?−log10(NX/NY) with NX and NY the numberdensity of elements X and Y in the observed star and in the Sun.

Article number, page 1 of 25

arX

iv:1

910.

0136

6v2

[as

tro-

ph.S

R]

8 J

an 2

020

A&A proofs: manuscript no. fit_v10

eral stars with [Fe/H] . −5 have been observed (Christlieb et al.2002; Keller et al. 2014; Bonifacio et al. 2015; Frebel et al.2005, 2015, 2019; Aguado et al. 2018), but no metal-free starswere found. Among the metal-poor stars, many were found tohave a super-solar carbon-to-iron ratio (e.g. Beers & Christlieb2005; Aoki et al. 2007). They are called carbon-enhanced metal-poor (CEMP) stars and are generally defined as having [C/Fe]> 0.7. Their frequency increases with decreasing [Fe/H] to reach∼ 40 % (∼ 80 %) for [Fe/H] < −3 ([Fe/H] < −4, Placco et al.2014b). Even so, 3D/NLTE effects may lead to an overestima-tion of the [C/Fe] ratio and may therefore significantly affect theCEMP fraction (Norris & Yong 2019).

At [Fe/H] & −3, numerous stars show overabundances inboth light elements (e.g. carbon) and heavy elements (e.g. bar-ium), which are generally expected to have been acquired froma now extinct AGB companion during a mass-transfer (or wind-mass-transfer) episode (e.g. Stancliffe & Glebbeek 2008; Bis-terzo et al. 2010, 2012; Lugaro et al. 2012; Abate et al. 2013,2015). This scenario is supported by a large binary fractionamong these stars (Hansen et al. 2016). The enhanced s-processoperating in rotating massive stars may also be at the originof some metal-poor stars enriched in s-elements (Choplin et al.2017b; Banerjee et al. 2019).

Extremely metal-poor stars ([Fe/H] < −3), which are oftenconsidered to be the most pristine objects, generally do not showstrong overabundances in heavy elements. They likely formedfrom a gas cloud that was enriched by one or a few previousmassive stars (e.g. Umeda & Nomoto 2002; Limongi et al. 2003;Meynet et al. 2006; Hirschi 2007; Tominaga et al. 2014; Chiaki& Wise 2019). The surface chemical composition of EMP starsprovides a window on the physical processes and nature of thefirst generation of massive stars. Among the CEMP stars with[Fe/H] < −3, many are CEMP-no stars (CEMP not strongly en-riched in s- or r-process elements), generally defined as having[Ba/Fe] < 0 (Beers & Christlieb 2005).

Comparisons between the chemical composition of EMPstars and ejecta from massive star models lead to various studiesthat investigated the nature of early massive stars and their su-pernovae (SNe), including studies considering mixing and fall-back in massive Pop III stars (e.g. Umeda & Nomoto 2002,2003; Nomoto et al. 2003; Iwamoto et al. 2005; Ishigaki et al.2014), rotating massive stars (e.g. Meynet et al. 2006, 2010;Hirschi 2007; Maeder & Meynet 2014; Takahashi et al. 2014),jet-induced SNe from Pop III 25−40 M stars (Maeda & Nomoto2003; Tominaga 2009; Ezzeddine et al. 2019), proton ingestionevents in the He-shell during late evolutionary stages (Baner-jee et al. 2018; Clarkson et al. 2018), and enrichment by morethan one source (Limongi et al. 2003). No consensus has beenreached yet. The need for multiple kinds of progenitors has beenraised several times (e.g. Yoon et al. 2016; Placco et al. 2016b).In particular, by inspecting the CEMP-no sample morphology inthe A(C)-[Fe/H] diagram, Yoon et al. (2016) divided the CEMP-no sample into two groups and suggested that their existencemay indicate the need for more than one kind of stellar progen-itor. The two groups may also be explained because of two dif-ferent dust-cooling regimes during the EMP star formation (Chi-aki et al. 2017). With the increasing number of metal-poor starsavailable, it is now beginning to be possible to perform extensiveabundance fitting studies between models and metal-poor starsand to infer the characteristics of the early massive star popula-tions. In this way Ishigaki et al. (2018) derived an initial massfunction for Pop III stars, peaking at ∼ 25 M.

In massive stars, rotation may considerably affect the evo-lution and nucleosynthesis (e.g. Heger et al. 2000; Meynet &

Maeder 2000; Brott et al. 2011a; Ekström et al. 2012; Georgyet al. 2013; Langer 2012; Chieffi & Limongi 2013), as well asthe final fate (e.g. Woosley 1993; MacFadyen & Woosley 1999).Nucleosynthesis may be particularly impacted during the He-burning stage: the rotational mixing operating between the He-burning core and H-burning shell triggers exchanges of material,leading a rich nucleosynthesis (e.g. Maeder et al. 2015; Choplinet al. 2016, see also Sect. 2.3). Light elements (mainly from C toAl) and heavy elements (mainly from Fe to Ba, possibly to Pb)are overproduced (e.g. Takahashi et al. 2014; Frischknecht et al.2016; Limongi & Chieffi 2018; Choplin et al. 2018). In particu-lar, if different initial rotation rates are considered, this processis likely able to cover a wide variety of [C/Fe], [N/Fe], [O/Fe],[Na/Fe], [Mg/Fe], and [Al/Fe] ratios. Maeder et al. (2015) pro-posed that this back and forth mixing process could be re-sponsible for the peculiar abundances of CEMP-no stars with[Fe/H] < −2.5. It can be motivated by the fact that the [X/Ca]scatter (or [X/Fe] scatter, which is similar) of EMP stars is of theorder of 3−4 dex for C, N, and O and about 1.5−2.5 dex for Na,Mg, and Al. From Si, the dispersion becomes smaller (Frebel &Norris 2015; Bonifacio et al. 2015).

In this work we investigate how the yields of 20 M mas-sive stars models (also called the source stars) with different ini-tial velocities and experiencing explosions with strong fallbackcompare with the abundance patterns (considering C, N, O, Na,Mg, and Al) of 272 EMP stars in the range −4 < [Fe/H] < −3.The abundance fitting of each of these EMP stars allows us todetermine the characteristics of the best source stars, particu-larly their initial velocity distribution. This distribution is com-pared to distributions based on the observation of nearby OBstars. The mixing processes (dredge-up, thermohaline mixing)that may have altered the initial surface chemical composition ofEMP stars are taken into account.

The paper is organized as follows. In Sect. 2 we discussthe models, especially the interplay between rotation and nucle-osynthesis. In Sect. 3 we introduce the EMP sample and fittingmethod. We present the main results and discuss them in Sect. 4and Sect. 5, respectively.

2. Source star models

2.1. Physical ingredients

The source star models considered here were computed with theGeneva stellar evolution code (e.g. Eggenberger et al. 2008). Wecomputed 20 M models with υini/υcrit = 0, 0.1, 0.2, 0.3, 0.4, 0.5,0.6, and 0.73. An initial mass of 20 M may be considered a rep-resentative mass of a standard massive star population, and mighthave been a typical initial mass during the era of the first stars(e.g. Susa et al. 2014; Ishigaki et al. 2018). The initial sourcestar metallicity was set to Z = 10−5 and the initial metal mixtureis α-enhanced (details can be found in Sect. 2.1 of Frischknechtet al. 2016). The initial abundances are summarized in Table 1.The prescription for radiative mass-loss rates is from Vink et al.(2001) when log Teff ≥ 3.9. The radiative mass loss scales withmetallicity as M ∝ Z0.85. When log Teff < 3.9, the mass-lossrecipe from de Jager et al. (1988) is used. Dshear is from Talon &Zahn (1997) and Dh from Zahn (1992). The efficiency of rota-tional mixing is calibrated such that the surface N/H value at coreH depletion of a 15 M model at solar metallicity with υini = 300

3 The critical velocity υcrit is reached when the gravitational accel-eration is counterbalanced by the centrifugal force. It is expressed asυcrit =

√23

GMRp,c

with Rp,c the polar radius at the critical limit.


A. Choplin et al.: The velocity of early massive stars

km s−1 is enhanced by a factor of 3 compared to its initial sur-face N/H value. These surface enrichments qualitatively agreewith observation of 10 − 20 M rotating stars (e.g. Gies & Lam-bert 1992; Villamariz & Herrero 2005; Hunter et al. 2009).

This study focuses on the light elements which are thoughtto be significantly affected by rotational mixing during the lifeof the star (C, N, O, F, Ne, Na, Mg, and Al; see Introduction).A minimal reaction network containing n, 1H, 3,4He, 12,13,14C,14,15N, 16,17,18O, 18,19F, 20,21,22Ne, 23Na, 24,25,26Mg, 26,27Al, 28Si,32S, 36Ar, 40Ca, 44Ti, 48Cr, 52Fe, and 56Ni is used. It allows usto follow the abundances of the elements of interest togetherwith the reactions that contribute significantly to generate nu-clear energy (e.g. Hirschi et al. 2004; Ekström et al. 2012). Theimportant nuclear reaction rates for this work are from Anguloet al. (1999) for the CNO cycle, except 14N(p, γ)15O, whichis from Mukhamedzhanov et al. (2003). The rates related tothe Ne-Na and Mg-Al cycles are from Iliadis et al. (2001) ex-cept 19F(p, γ)20Ne (Angulo et al. 1999), 20Ne(p, γ)21Na (Anguloet al. 1999), 22Ne(p, γ)23Na (Hale et al. 2002), and 27Al(p, γ)28Si(Cyburt et al. 2010). Other important reactions for the presentwork are 22Ne(α, n)25Mg (Jaeger et al. 2001), 22Ne(α, γ)26Mg(Jaeger et al. 2001), 17O(α, n)20Ne (Angulo et al. 1999), and17O(α, γ)21Ne (Angulo et al. 1999).

The models are computed until the end of the core oxygenburning phase (when the central 16O mass fraction drops be-low 10−4). Table 2 shows the main characteristics of the mod-els, which are labelled vvX, where X refers to the initial rotationrate.

2.2. Explosion with strong fallback

Hydrodynamical calculations of core-collapse supernovae showthat the explosion energy, gravitational potential, and aspheric-ity control the amount of material falling back into the compactobject (Fryer et al. 2007; Moriya et al. 2010). Large fallbackcan occur for low explosion energies, but also for energetic jet-like explosions where the matter around the jet axis is ejectedwhile the matter around the equatorial plane experiences signifi-cant fallback onto the central remnant (Maeda & Nomoto 2003;Tominaga 2009). It has been suggested that the light curve ofSN2008ha could be explained by a 13 M star that experienceda large amount of fallback (Moriya et al. 2010). Low or zerometallicity massive stars may experience a higher degree of fall-back compared to solar metallicity stars because they are morecompact, and consequently might explode with more difficulty(e.g. Woosley et al. 2002). Employing a piston at the edge of theiron-core with E51 = 1.2, Woosley & Weaver (1995) reportedremnant masses of ∼ 2 and ∼ 4 M for a solar and zero metal-licity 20 M model, respectively. The idea of a large fallbackhas also been suggested to account for the abundances of themost metal-poor stars (e.g. Umeda & Nomoto 2002). In partic-ular, Iwamoto et al. (2005) found that the patterns of HE1327-2326 ([Fe/H] = −5.6) and HE0107-5240 ([Fe/H] = −5.2) maybe explained by Pop III 25 M SNe with E51 ∼ 0.7 and with4

Mcut ∼ 6 M (they also assumed mixing at the time of the explo-sion, following Umeda & Nomoto 2002).

In this work, the source stars are supposed to experienceexplosions with strong fallback. Only the layers above the C-burning shell (typically above 4 M for a 20 M) are supposedto be expelled, without having been significantly processed by

4 At the time of the explosion Mcut, the mass cut is the mass coordinatedelimiting the part of the star that is expelled from the part that is lockedinto the remnant.

Table 1. Initial abundances (in mass fraction) of the stellar models. Thelast line gives the ratio of the initial sum of CNO elements in the models,compared to the Sun.

Isotope Mass fraction1H 7.516e-013He 4.123-054He 2.484e-0112C 1.292e-0613C 4.297e-0914N 1.022e-0715N 4.024e-1016O 6.821e-0617O 3.514e-1018O 2.001e-0919F 8.385e-1120Ne 9.205e-0721Ne 7.327e-1022Ne 2.354e-0823Na 4.135e-0924Mg 2.012e-0725Mg 1.030e-0826Mg 1.179e-0827Al 7.694e-0928Si 2.060e-07

(C+N+O) / (C+N+O) 9.444e-04

explosive nucleosynthesis. The EMP stars subsequently formedwith some of this ejecta plus some of the initial background ofmetals (among it the elements from ∼ Si to ∼ Fe) left by one ora few previous source(s), possibly Pop III massive stars.

Although explosions with strong fallback may be a commonphenomena in the early Universe, more standard SNe shouldalso be expected. Considering solely explosions with strong fall-back is likely an important limitation of this study. Consideringvarious kinds of explosions should provide additional solutions(unseen in this study) for reproducing the abundance patterns ofEMP stars. The assumption regarding the explosion made hereallows us to test to what extent rotating models experiencing ex-plosions with strong fallback can reproduce the abundance pat-terns of EMP stars.

2.3. Mixing and nucleosynthesis

During the core H-burning and He-burning phase, the mixinginduced by rotation changes the distribution of the chemical el-ements inside the star. In advanced stages (core C-burning andafter), the burning timescale becomes small compared to the ro-tational mixing timescale so that rotation barely affects the distri-bution of chemical elements. During the core He-burning phase,the rotational mixing triggers exchanges of material between theconvective He-burning core and the convective H-burning shell(Maeder & Meynet 2015; Frischknecht et al. 2016; Choplin et al.2016). In addition, the growing convective He-burning core pro-gressively engulfs the products of H-burning. The main steps ofthis mixing process are summarized below:

1. In the He-burning core, 12C and 16O are synthesized via the3α process and 12C(α, γ)16O.



2 4 6 8 10 12 14 16 18 20

10-2

10-1

100

mas

s. fra

c.

vini/vcrit

1 H

0.00.10.20.3

0.40.50.60.7

2 4 6 8 10 12 14 16 18 20

10-2

10-1

1004 He

2 4 6 8 10 12 14 16 18 20

10-810-710-610-510-410-310-210-1100

12 C

2 4 6 8 10 12 14 16 18 20

10-8

10-7

10-6

10-5

10-4

10-3

mas

s. fra

c.

13 C

2 4 6 8 10 12 14 16 18 20

10-6

10-5

10-4

10-3

10-2

10-1

14 N

2 4 6 8 10 12 14 16 18 20

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

16 O

2 4 6 8 10 12 14 16 18 20

10-9

10-8

10-7

10-6

10-5

10-4

mas

s. fra

c.

17 O

2 4 6 8 10 12 14 16 18 20

10-8

10-7

10-6

10-5

10-4

10-3

10-2

20 Ne

2 4 6 8 10 12 14 16 18 20

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

22 Ne

2 4 6 8 10 12 14 16 18 20

10-8

10-7

10-6

10-5

10-4

mas

s. fra

c.

23 Na

2 4 6 8 10 12 14 16 18 2010-7

10-6

10-5

10-4

24 Mg

2 4 6 8 10 12 14 16 18 2010-9

10-8

10-7

10-6

10-5

10-4

10-3

25 Mg

2 4 6 8 10 12 14 16 18 20Mr [M¯]

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

mas

s. fra

c.

26 Mg

2 4 6 8 10 12 14 16 18 20Mr [M¯]

10-9

10-8

10-7

10-6

10-5

10-4

27 Al

2 4 6 8 10 12 14 16 18 20Mr [M¯]

10-7

10-6

10-5

28 Si

Fig. 1. Internal abundance profiles in mass fraction of the 20 M models with various initial rotation rates, at the end of the core He-burning phase.

2. The abundant 12C and 16O in the He-burning core are pro-gressively mixed into the H-burning shell. It boosts the CNOcycle and creates primary CNO elements, especially 14N and13C.

3. The products of the H-burning shell (among themprimary 13C and 14N) are mixed back into the He-core. From the primary 14N, the reaction chain

14N(α, γ)18F(e+νe)18O(α, γ)22Ne allows the synthesisof primary 22Ne. The reactions 22Ne(α, n) and 22Ne(α, γ)make 25Mg and 26Mg, respectively. The neutrons releasedby the 22Ne(α, n) reaction produce 19F, 23Na, 24Mg, and27Al by 14N(n, γ)15N(α, γ)19F, 22Ne(n, γ)23Ne(e−νe)23Na,23Na(n, γ)24Na(e−νe)24Mg, and 26Mg(n, γ)27Mg(e−νe)27Al,respectively. Free neutrons can also trigger the s-process,



Table 2. Properties of the 20 M source star models: model label (col-umn 1), υini/υcrit (column 2), Ωini/Ωcrit (column 3), initial equatorial ve-locity (column 4), mean equatorial velocity during the MS (column 5),total lifetime (column 6), mass of the model at the end of the evolution(column 7).

Model υini/υcrit Ωini/Ωcrit υini 〈υeq〉MS τtot Mfin

[km/s] [km/s] [Myr] [M]

vv0 0.0 0 0 0 8.94 19.998vv1 0.1 0.15 88 70 9.43 19.998vv2 0.2 0.32 188 146 9.81 19.960vv3 0.3 0.46 276 223 10.07 19.726vv4 0.4 0.69 364 302 10.29 19.625vv5 0.5 0.71 454 384 10.49 19.189vv6 0.6 0.81 547 470 10.65 19.222vv7 0.7 0.90 644 543 11.04 19.764

provided enough seeds, like 56Fe, are present (Pignatariet al. 2008; Frischknecht et al. 2016; Choplin et al. 2018).

4. The newly formed elements in the He-burning core can bemixed again into the H-burning shell. It can boost the Ne-Naand Mg-Al cycles: additional Na and Al can be produced.

Figure 1 shows the results of this mixing process in the20 M models with various initial rotation rates. The chemi-cal profiles are shown at the end of the core He-burning phase.As the initial rotation increases, the chemicals transit more effi-ciently from one burning region to another because of strongerrotational mixing and the convective He-burning core tends togrow more, which also facilitates the exchanges of chemicalsbetween the two burning regions. For high initial rotation rates,however (υini/υcrit & 0.5), the growing of the He-core is limitedby the very active H-burning shell (the high activity is due to thecopious amounts of 12C and 16O entering the shell and boostingthe CNO cycle). This effect limits the efficiency of the mixingprocess for high rotation and makes the production of chemi-cals starting to saturate for υini/υcrit & 0.5 (e.g. the 14N or 22Neprofiles in Fig. 1).

While the Ne-Na cycle is boosted in the H-burning shell ofrotating models (see the peak of 23Na at ∼ 8 M), neither the Mg-Al cycle nor the 27Al(p, γ)28Si reaction is significantly boosted(no similar peak in the H-burning shell) because the temperaturein the H-burning shell (T . 45 MK) is too low to efficientlyactivate these reactions. Moreover, the synthesis of extra Al inthe H-burning shell needs extra Mg, which is only built in theHe-core when T & 220 MK (through an α-capture on 22Ne). Ina 20 M model, this temperature corresponds to the end of thecore He-burning phase. The extra Mg created in the core has thenlittle time to be transported to the H-burning shell and boosts theMg-Al cycle.

2.4. Composition of H- and He-rich layers at the pre-SNstage

H-rich layers

During the evolution of stars, some material is ejected throughstellar winds. Rotation is expected to affect the mass loss ofmassive stars (Maeder 1999; Maeder & Meynet 2000). In these20 M models, however, losses through winds stay small (< 1M, see Table 2). The radiative mass loss–metallicity relation

(M ∝ Z0.85) plays a major role here and prevents significant ra-diative mass loss episodes. The left panel of Fig. 2 shows thechemical composition of the H-rich layers at the end of the evo-lution. It comprises all the material above the bottom of the H-shell (defined where the mass fraction of X(1H) drops below0.01). It includes the wind material. Depending on the model,the bottom of the H-shell is located at a mass coordinate in be-tween 6.3 and 8 M. The typical CNO pattern appears for all themodels (more N, less C and O), but the sum of CNO elementsincreases with rotation, as a result of 12C and 16O having dif-fused to the H-burning shell. Thanks to the extra Ne entering inthe H-shell and boosting the Ne-Na cycle (see Sect. 2.3), [Na/H]spans ∼ 2 dex from the non-rotating to the fast rotating model.The [Mg/H] and [Al/H] ratios do not vary more than 0.5 dex.The log(12C/13C) ratio is close to the CNO equilibrium value of∼ 0.6.

H-rich and He-rich layers

The right panel of Fig. 2 shows the chemical composition of theH- and He-rich layers. All the material above the bottom of theHe-shell (where the mass fraction of X(4He) drops below 0.01)is considered. In this case, the mass cuts are between 3.9 and 5.2M, depending on the model. Compared to the previous case, theadditional ∼ 2 M are H-free, so that it raises the [X/H] valuesslightly (by < 0.5 dex). The CNO pattern is flipped comparedto the ejecta of the H-rich layers only because 14N is depleted,while 12C and 16O are abundant in the region processed by He-burning (Fig. 1). The He-burning products (particularly Ne, Mg,and Al) are boosted compared to the previous case. These prod-ucts also increase with initial rotation as a result of the back-and-forth mixing process (see Sect. 2.3). In the region processedby He-burning, 13C is depleted by (α, n) and (α, γ) reactions sothat the 12C/13C ratio is largely enhanced compared to the casewhere only the H-rich ejecta is considered. Rotation neverthe-less decreases this ratio because of the additional 13C that wassynthesized in the layers processed by H-burning.

2.5. Effect of the mass cut

Figure 3 shows the effect of varying the mass cut Mcut from ∼ 5to ∼ 9 M in the vv4 model. The highest Mcut is located in theH-envelope, the lowest value in the He-shell. The numbers inparentheses indicate the mass fraction of 1H at the mass coor-dinate equal to the indicated Mcut. Varying the mass cut fromthe H- to He-shell flips the CNO pattern. It goes from a ∧-shapeto a ∨-shape pattern: in the H-shell, the effect of CNO cycle isdominant (high N/C and N/O ratios), while in the He-shell, theC and O produced by He-burning dominate so that the C/N andC/O ratios are dramatically increased. While the log(12C/13C) isclose to the CNO equilibrium value (about 0.6) for shallow Mcut,it increases with deeper mass cuts as a results of 13C-depletionand 12C-richness of the layers processed by He-burning. Deepermass cuts also increase [Ne/H] or [Na/H] ratios, for instance, asa result of the addition of He-burning material in the ejecta.

3. Linking EMP stars with their source stars

If they were present, the stars discussed in the previous sectionshould have left their chemical imprints on the next stellar gener-ations. We therefore investigate whether the material processedby rotation may be found in the chemical composition of ob-served EMP stars. For the comparison, the elements C, N, O,



6 7 8 9 10 11 12 13Atomic Number

4

2

0

[X/H

]

H layers

vini/vcrit

ISM

C N O F Ne Na Mg Al 12 C/13 C

0.70.60.50.40.30.20.10.0

1

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

2

0

2

[X/H

]

H + He layers

vini/vcritISM


0.70.60.50.40.30.20.10.0

1

0

1

2

3

4

5

6

7

log(

12C/13

C)

Fig. 2. Integrated [X/H] and log(12C/13C) ratios in the H-rich layers (left panel) and H + He-rich layers (right panel) at the pre-SN stage for the20 M models with different initial rotation rates. The material ejected through winds during the evolution is included. The dashed line shows theinitial source star composition.

Table 3. Number of stars in the considered sample (from the SAGAdatabase, Suda et al. 2008, 2017) having a given abundance available(first row) or having only a limit (second row).

C N O Na Mg Al 12C/13C

Abundance 272 75 35 166 271 248 30Limit 0 54 56 2 0 1 9

Na, Mg, and Al and the 12C/13C ratio are considered becausethey are the elements mostly affected by rotation. The possibleorigin of the heavier elements is discussed in Sect. 5.3.

3.1. Metal-poor star sample

The stars with ≤ −4 [Fe/H] ≤ −3 and with at least threeabundance values determined among C, N, O, Na, Mg, Al,and 12C/13C are selected. This sample comprises 272 stars.The abundance data of the metal-poor stars considered inthis work mostly come from the SAGA database (Suda et al.2008, 2017). The recently observed stars fulfilling the criteriamentioned above were added: G64-12 (Placco et al. 2016a),LAMOSTJ2217+2104 (Aoki et al. 2018), SDSSJ0140+2344,SDSSJ1349+1407 (Bonifacio et al. 2018), SDSSJ0826+6125,SDSSJ1341+4741 (Bandyopadhyay et al. 2018). The individualreferences are given in Appendix A. Table 3 shows the numberof available abundance and limits for the EMP stars considered.

3.2. Internal mixing processes in EMP stars

The link between the EMP star and its source(s) is made moredifficult by the fact that EMP stars themselves may have under-gone internal mixing processes from their birth (e.g. dredge-up,thermohaline mixing, rotation, or atomic diffusion, Richard et al.2002; Charbonnel & Zahn 2007; Stancliffe et al. 2009). Theseprocesses may have caused surface abundance modifications, sothat the abundance of an element derived from observations maybe different to the abundance at the birth of the EMP star.

The first dredge-up and the thermohaline mixing, may be themost important processes. They happen in evolved EMP starsand can decrease the C surface abundance and 12C/13C ratio andincrease the N surface abundance (e.g. Charbonnel 1994; Stan-cliffe et al. 2007; Eggleton et al. 2008; Lagarde et al. 2019). Inthis work, the evolutionary effects on the surface carbon abun-dance were corrected following Placco et al. (2014b), who pro-posed a correction based on stellar models to apply to the car-bon abundance of stars with [Fe/H] < −2. This correction likelyallows the initial surface carbon abundance of metal-poor starsto be recovered. By comparing the Placco et al. (2014b) sam-ple with our sample, we corrected the C abundance of 173 EMPstars. The correction ∆[C/H] applied to the [C/H] ratio variesbetween 0 and 0.77. After correction, the sample comprises 87CEMP stars (EMP stars are considered CEMP if [C/Fe] ≥ 0.7).For N and 12C/13C, no similar correction is available yet. Herewe set the [N/H] and 12C/13C ratios as upper and lower limits,respectively, for the stars on the upper giant branch (log g < 2).These stars may indeed have experienced important modifica-tion of their surface N abundance and 12C/13C ratio5. This as-sumption, and more generally internal mixing processes in EMPstars, is discussed further in Sect. 4.3.3.

We note that most of the CEMP stars considered here be-long to group II (Yoon et al. 2016) because the metallicity rangeconsidered (−4 < [Fe/H] < −3) contains mainly group II stars.Group III stars are found at [Fe/H] . −4, and group I mostly at[Fe/H] & −3 (their figure 1). In our sample, ∼ 8% of the consid-ered CEMP stars have A(C) > 7, where group I stars are found.

3.3. Fitting procedure

To fit the abundances of EMP stars with massive star models,we followed the same procedure described in Heger & Woosley(2010) and Ishigaki et al. (2018), especially for calculating theχ2. Considering N data points, U upper limits, and L lower lim-

5 In our sample, 144 (128) EMP stars have log g < 2 (≥ 2). Amongthe stars with log g ≥ 2, 24 have a determined N abundance, 7 have adetermined 12C/13C ratio and 6 have both a determined N abundanceand 12C/13C ratio.



6 7 8 9 10 11 12 13Atomic Number

6

4

2

0

[X/H

]

8.98(6.3E-01)

7.9(3.8E-03)

7.77(4.1E-05)

7.6(2.8E-06)

7.18(0.0E+00)

4.99(0.0E+00)

ISM


2

1

0

1

2

3

4

5

log(

12C/13

C)

Fig. 3. Effect of the mass cut for the vv4 model. The mass cut (in M)of the corresponding abundance pattern is indicated on the left. Thenumbers in parenthesis indicate the 1H mass fraction in the star at themass coordinate equal to the mass cut.

its, the χ2 can be computed as

χ2 =

N∑i=1

(Di − Mi)2

σ2o,i + σ2

t,i

+

N+U∑i=N+1

(Di − Mi)2

σ2o,i + σ2

t,i

Θ(Mi − Di)

+

N+U+L∑i=N+U+1

(Di − Mi)2

σ2o,i + σ2

t,i

Θ(Di − Mi), (1)

where Di and Mi are the [X/H] and log(12C/13C) ratios derivedfrom observations and predicted by source star models, respec-tively; Θ(x) is the Heaviside function; and σo,i and σt,i are theobservational and theoretical uncertainties. When not available,σo,i is set to σo,i, which is the mean uncertainty of the sample forthe abundance i. Mean uncertainties are 0.18, 0.26, 0.17, 0.12,0.14, and 0.18 dex for [C/H], [N/H], [O/H], [Na/H], [Mg/H], and[Al/H], respectively. The theoretical uncertainties σt,i are set to0.15 for [C/H], [N/H], and [O/H] and 0.3 for [Na/H], [Mg/H],and [Al/H]. Larger uncertainties for Na, Mg, and Al are con-sidered because of the larger uncertainties on the yields of theseelements. The nuclear reaction rates important for the Ne-Na andMg-Al cycles still suffer significant uncertainties that can affectstellar yields (Decressin et al. 2007; Choplin et al. 2016). Theuncertainties associated with (α,γ) or (α,n) reactions operatingin He-burning zones, such as 22Ne(α,γ) or 22Ne(α,n), are alsonon-negligible (e.g. Frischknecht et al. 2012). For log(12C/13C),we set a general sigma value of 0.3 including uncertainties ofmodels and of observations. Theoretical uncertainties are furtherdiscussed in Sect. 4.3.2.

For each EMP star, the minimum χ2 is searched among theeight source star models. For each model the mass cut Mcut andmass of the added interstellar medium (ISM) MISM are left asfree parameters. The Mcut parameter is varied between the bot-tom of the He-shell (located at ∼ 4 − 5 M depending on themodel) and the stellar surface, and MISM is varied between 102

and 106 M. By adding ISM material, we assume some dilu-tion of the source star ejecta with the surrounding ISM. It shouldoccur at the time of the source star explosion. The added ISM

material has the same composition as the initial source star com-position (dashed line in Figs. 2 and 3). The initial ISM composi-tion and its possible impact on our results are further discussedin Sect. 4.1.2.

3.4. Weighting the source star models

As we show in the next section, it happens that for a given EMPstar, more than one of the eight 20 M source star models cangive a reasonable solution. To account for this when deriving, forinstance, the velocity distribution of the best source star models,we associate a weight with each fit, scaling with the goodnessof fit. The goodness of fit is determined thanks to the p-value p,which is directly equal to the weight and can be written as

p(χ2,N − m) = 1 − F(χ2,N − m) = 1 −γ( N−m

2 , χ2

2 )

Γ( N−m2 )

, (2)

with F the χ2 cumulative distribution function, Γ the gammafunction, and γ the lower incomplete gamma function. Here N isthe number of measured abundances for the considered EMP starand m = 2 is the number of free parameters for a given 20 Mmodel (Mcut and MISM). From χ2, N, and m, the reduced χ2 canbe calculated as χ2

ν = χ2/(N − m).Since high χ2 values give negligible weights, the models that

give bad fits are automatically discarded and will not contributeto determining the overall characteristics of the best progenitors(e.g. velocity distribution). Similarly, if no good fit can be foundfor a given EMP star, this EMP star is not considered because ofthe negligible weights of all the source star models.

We note that the weights for given EMP stars are not nor-malized to one. If so, the EMP stars that cannot be fitted cor-rectly (hence having low weights for all source star models) willcontribute similarly to the well fitted EMP stars. However, it ispossible to normalize the weights to one if a threshold χ2

ν,th isfirst set (e.g. χ2

ν,th = 3) so as to discard the EMP stars where noχ2ν < χ

2ν,th can be found. We checked that this alternative method

gives results that are similar to those of the adopted method; theresults are presented in the next section.

4. Results

Figure 4 shows the distribution of χ2 of the best model for the272 star fitted. Two stars with very high χ2 (BS16929-005 andSDSSJ0826+6125 with χ2 = 31 and 58, respectively) are notshown in Fig. 4. The stars that cannot be fitted correctly are dis-cussed further in Sect. 4.4. Tables 4 and 5 give the fraction of fitshaving a χ2 and χ2

ν value below a given threshold, respectively.From Table 4 we see that 60 % (39 %) of the stars have χ2 < 5(χ2 < 3). The CEMP stars show overall better fits than C-normalEMP stars. We also note that the 8 % of CEMP stars with A(C)> 7 (or group I CEMP stars, Yoon et al. 2016) follow a χ2 dis-tribution that is similar to that of the entire CEMP sample. Inparticular, 61 % of them have χ2 < 3.

Figure 14 in Appendix B shows a summary plot of the abun-dance fitting of each of the 272 EMP stars considering each ofthe eight source star models. Figure 15 in Appendix B shows theabundance fitting of all the EMP stars having at least one sourcestar model with χ2

ν < 2. Figure 5 shows the abundance fitting ofseveral EMP stars with χ2

ν < 2. We discuss below some of thesefits individually.



0 5 10 15 20

χ2

0

5

10

15

20

25

30N

Fig. 4. Distribution of the χ2 values for the 272 EMP stars fitted.

Table 4. Fraction of stars with a χ2 value below a given threshold. Re-sults are given for the entire sample (272 stars), for CEMP stars (87stars) and for C-normal EMP stars (185 stars).

χ2 < 10 χ2 < 5 χ2 < 3 χ2 < 2 χ2 < 1

All stars 84 % 60 % 39 % 25 % 11 %CEMP 89 % 77 % 59 % 48 % 30 %C-normal EMP 82 % 52 % 29 % 14 % 3 %

Table 5. Fraction of fits having a χ2ν value (reduced χ2, see text) below a

given threshold. Results are given for the entire sample (272 stars), forCEMP stars (87 stars) and for C-normal EMP stars (185 stars).

χ2ν < 10 χ2

ν < 5 χ2ν < 3 χ2

ν < 2 χ2ν < 1


HE1439-1420

This star is shown in the top left panel. The C and N abundancesof HE1439-1420 are compatible with a ∨-shape CNO pattern,but not with a ∧-shape one. As shown in Figs. 2 and 3, ∨-shapeCNO patterns are characteristics of mass cuts located in the He-shell region. In addition, the high Na and Mg enhancement ofthis star are best explained by fast rotating models that have ex-perienced significant mixing between the H- and He-burning re-gions. The best fit is given by the vv7 model, with Mcut = 5.45M and MISM = 1789 M. The χ2 map for the vv7 model isshown in Fig. 6. The only minimum χ2 is located at the val-ues mentioned previously. In general, it has been checked for theother EMP stars that only one minimum can be found in the Mcut− MISM plane.

HE1150-0428

This star is shown in the top middle panel. The best fit is given bythe vv6 model, with Mcut = 7.46 M and MISM = 100 M. ThisMcut is ∼ 0.4 M below the bottom of the hydrogen envelope. A

deeper Mcut will give a more ∨−shape pattern for CNO, while ashallower Mcut will give a more ∧-shape pattern. HE1150-0428,having [C/H] ∼ [N/H] therefore requires a Mcut around the bot-tom of the H-envelope, which is the region where the CNO pat-tern is flipping from a ∧-shape to a ∨-shape.

BD-18_5550

The high [Mg/H] of this star (top right panel) requires both fastrotation and a deep mass cut. The best model is vv6, with Mcut =4.74 and MISM = 50941 M.

CS29502-092

This star (shown in the middle left panel) is evolved, withlog g < 2. Consequently, the [N/H] and 12C/13C are set asupper and lower limits respectively (see Sect. 3.2). In this case,the good source star models have similar characteristics tothose in the previous case (BD-18_5550). The hypothesis ofnon-efficient internal mixing processes in EMP stars, whichmeans that the [N/H] and 12C/13C ratios should not be set aslimits in evolved stars, is investigated in Sect. 4.3.3.

4.1. Characteristics of the best source star models

We now derive the Mcut, MISM, and velocity distribution of thebest source star models. The following analysis determines theability of the eight models to fit the entire EMP star sample. Ourapproach may be seen as statistical: for a given EMP star andsource star, the weight attributed to the fit (Sect. 3.4) can be seenas the likelihood of this source star being the true source of thisspecific EMP star.

In the case of HE1439-1420, the weights associated with theχ2 and χ2

ν values shown in the top left panel of Fig. 5 are asfollows:

– 0.92 for the vv7 model, (χ2, χ2ν) = (0.17, 0.09);





– 4.2 × 10−3 for the vv2 model, (χ2, χ2ν) = (10.98, 5.49);

– 1.4 × 10−6 for the vv1 model, (χ2, χ2ν) = (26.93, 13.47);

– 1.4 × 10−7 for the vv0 model, (χ2, χ2ν) = (31.49, 15.75).

4.1.1. Mass cut distribution

Figure 7 (top panel) shows the weighted Mcut distribution of thesource star models. The distribution is normalized to 1. The twopeaks in the mass cut distribution correspond to the bottom ofthe H-shell (∼ 8 M) and the bottom of the He-burning shell(∼ 5 M). Around these two mass coordinates, the stellar chemi-cal composition is diverse and therefore a wide variety of chem-ical patterns, needed to account for the wide variety of EMP starchemical pattern, can be produced. We note that the best so-lutions for the CEMP stars (red distribution) are preferentiallyfound for deeper Mcut in the layers processed by He-burningwhere C, Na, Mg, and Al are abundant (cf. Figs. 2 and 3).

Finding most of the mass cuts at the bottom of the H-shelland He-shell may be physically motivated by the fact that theenergy required to unbind the material above a given mass cutshows jumps at these locations (Fig. 7, middle and bottom pan-els). By peaking at ∼ 5 and ∼ 8 M, the derivative of EUB reveals



6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: HE1439-1420Teff =6056 K logg =3.8

vv7 (χ2 ,χ 2ν ) = (0.17,0.09)

vv5 (χ2 ,χ 2ν ) = (0.53,0.27)

vv6 (χ2 ,χ 2ν ) = (0.56,0.28)

vv4 (χ2 ,χ 2ν ) = (1.07,0.53)

vv3 (χ2 ,χ 2ν ) = (3.63,1.82)

vv2 (χ2 ,χ 2ν ) = (10.98,5.49)

vv1 (χ2 ,χ 2ν ) = (26.93,13.47)

vv0 (χ2 ,χ 2ν ) = (31.49,15.75)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: HE1150-0428Teff =5200 K logg =2.5

vv6 (χ2 ,χ 2ν ) = (0.19,0.1)

vv7 (χ2 ,χ 2ν ) = (1.01,0.51)

vv5 (χ2 ,χ 2ν ) = (1.42,0.71)

vv4 (χ2 ,χ 2ν ) = (3.9,1.95)

vv3 (χ2 ,χ 2ν ) = (14.2,7.1)

vv2 (χ2 ,χ 2ν ) = (42.8,21.4)

vv1 (χ2 ,χ 2ν ) = (89.39,44.69)

vv0 (χ2 ,χ 2ν ) = (107.22,53.61)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: BD-18_5550Teff =4660 K logg =1.05

vv6 (χ2 ,χ 2ν ) = (1.74,0.87)

vv7 (χ2 ,χ 2ν ) = (2.28,1.14)

vv4 (χ2 ,χ 2ν ) = (4.36,2.18)

vv5 (χ2 ,χ 2ν ) = (4.56,2.28)

vv3 (χ2 ,χ 2ν ) = (5.38,2.69)

vv1 (χ2 ,χ 2ν ) = (5.53,2.76)

vv2 (χ2 ,χ 2ν ) = (5.76,2.88)

vv0 (χ2 ,χ 2ν ) = (5.94,2.97)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS29502-092Teff =4820 K logg =1.5

vv6 (χ2 ,χ 2ν ) = (0.54,0.18)

vv7 (χ2 ,χ 2ν ) = (1.08,0.36)

vv4 (χ2 ,χ 2ν ) = (1.94,0.65)

vv5 (χ2 ,χ 2ν ) = (2.23,0.74)

vv3 (χ2 ,χ 2ν ) = (2.63,0.88)

vv2 (χ2 ,χ 2ν ) = (3.68,1.23)

vv1 (χ2 ,χ 2ν ) = (5.0,1.67)

vv0 (χ2 ,χ 2ν ) = (5.77,1.92)

0

1

2

3lo

g(12

C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS22960-010Teff =5280 K logg =4.0

vv6 (χ2 ,χ 2ν ) = (2.4,1.2)

vv7 (χ2 ,χ 2ν ) = (2.84,1.42)

vv1 (χ2 ,χ 2ν ) = (5.12,2.56)

vv0 (χ2 ,χ 2ν ) = (5.28,2.64)

vv5 (χ2 ,χ 2ν ) = (5.39,2.69)

vv2 (χ2 ,χ 2ν ) = (5.48,2.74)

vv4 (χ2 ,χ 2ν ) = (5.5,2.75)

vv3 (χ2 ,χ 2ν ) = (5.54,2.77)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: SDSSJ0212+0137Teff =6333 K logg =4.0

vv2 (χ2 ,χ 2ν ) = (2.41,1.21)

vv3 (χ2 ,χ 2ν ) = (2.7,1.35)

vv1 (χ2 ,χ 2ν ) = (2.71,1.36)

vv0 (χ2 ,χ 2ν ) = (2.76,1.38)

vv4 (χ2 ,χ 2ν ) = (2.91,1.46)

vv6 (χ2 ,χ 2ν ) = (2.99,1.49)

vv5 (χ2 ,χ 2ν ) = (3.38,1.69)

vv7 (χ2 ,χ 2ν ) = (4.15,2.07)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE1357-0123Teff =4600 K logg =1.05

vv5 (χ2 ,χ 2ν ) = (0.55,0.27)

vv6 (χ2 ,χ 2ν ) = (0.96,0.48)

vv4 (χ2 ,χ 2ν ) = (1.02,0.51)

vv7 (χ2 ,χ 2ν ) = (1.06,0.53)

vv3 (χ2 ,χ 2ν ) = (1.57,0.78)

vv2 (χ2 ,χ 2ν ) = (1.78,0.89)

vv1 (χ2 ,χ 2ν ) = (2.16,1.08)

vv0 (χ2 ,χ 2ν ) = (2.45,1.22)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(12

C/13

C)

6 7 8 9 10 11 12 13Atomic Number

5

4

3

2

1

[X/H

]


: SMSSJ200654.42Teff =5395 K logg =2.95

vv6 (χ2 ,χ 2ν ) = (2.11,1.06)

vv7 (χ2 ,χ 2ν ) = (2.39,1.2)

vv4 (χ2 ,χ 2ν ) = (2.86,1.43)

vv3 (χ2 ,χ 2ν ) = (2.87,1.43)

vv2 (χ2 ,χ 2ν ) = (2.96,1.48)

vv5 (χ2 ,χ 2ν ) = (3.04,1.52)

vv1 (χ2 ,χ 2ν ) = (3.14,1.57)

vv0 (χ2 ,χ 2ν ) = (3.37,1.68)

1

0

1

2

3

log(12

C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: CS29498-043Teff =4440 K logg =0.5

vv6 (χ2 ,χ 2ν ) = (3.39,1.13)

vv7 (χ2 ,χ 2ν ) = (4.07,1.36)

vv4 (χ2 ,χ 2ν ) = (7.44,2.48)

vv5 (χ2 ,χ 2ν ) = (7.48,2.49)

vv3 (χ2 ,χ 2ν ) = (9.46,3.15)

vv2 (χ2 ,χ 2ν ) = (12.35,4.12)

vv1 (χ2 ,χ 2ν ) = (21.25,7.08)

vv0 (χ2 ,χ 2ν ) = (23.88,7.96)

0

1

2

3

4

log(12

C/13

C)

Fig. 5. Examples of EMP stars having at least one source star model with χ2ν < 2 (χ2 . 3). Red and green circles denote CEMP ([C/Fe] > 0.7) and

C-normal EMP stars, respectively. For each EMP star, the best fit for each of the 20 M models is shown, ranked by increasing χ2. For evolvedEMP stars (log g < 2), [N/H] and log(12C13C) are shown as light red and green symbols and are considered upper and lower limits, respectively.When available, the correction on the C abundance from Placco et al. (2014b) is taken into account. In this case, the [C/H] ratio before (after)correction is shown by a light (normal) red or green symbol. When available, the observational uncertainty is shown by a black bar. If it is notavailable, the mean observational uncertainty of the EMP sample (Sect. 3.3) is shown as a grey bar.

these jumps. The jump at ∼ 8 M is smaller for slow rotatingmodels (especially vv0 and vv1) because these models do notfully enter the red super giant (RSG) phase (Fig. 8), where thestellar radius expands significantly. On the contrary, since thefaster rotating models enter the RSG phase, their envelopes ex-pand dramatically and become loosely bound. Overall, we mayexpect a clustering of the mass cuts around ∼ 5 and ∼ 8 M be-cause the binding energy of most models significantly increasesbelow these mass coordinates, making these deeper layers moredifficult to expel.

4.1.2. MISM distribution

Figure 9 shows the weighted distribution of MISM, the massof added ISM. The distribution is normalized to 1. The over-all blue distribution peaks around low MISM values. Among thebest source star models (with χ2 < 3), 59 % have 102 < MISM <103 M and 73 % have 102 < MISM < 104 M. For such MISMvalues, the contribution of ISM is generally small compared tothe source star contribution. For CEMP stars, it is more equallydistributed. It can be understood together with the mass cut dis-tribution: the good solutions for CEMP stars are generally found

at deep mass cuts; it therefore requires significant dilution withISM to not overestimate the CEMP star abundances.

In most cases, even with large MISM, the source star mate-rial still dominates. For instance, BD-18_5550 (Fig. 5, top rightpanel) is best fitted by the vv6 model with (χ2, χ2

ν) = (1.74, 0.87),Mcut = 4.74 M, and MISM = 5.1 × 104 M. This MISM valuecorresponds to ∼ 0.07 M of carbon. In the source star ejectathere is ∼ 0.59 M of carbon6. Hence, the resulting carbon con-tent reflects more source star material than ISM material. WhenMcut ∼ 8 M (i.e. around the second peak, Fig. 7), less carbonis ejected from the source star. The star BS16920-017 is best fitby the vv5 model with (χ2, χ2

ν) = (1.69, 0.84), Mcut = 7.99 Mand MISM = 102 M. In this case the carbon mass from the stellarejecta and the ISM are similar, about 10−4 M. However, the totalamount of metals is higher in the stellar ejecta (∼ 3.2×10−3 M)compared to the added ISM material (∼ 9.6 × 10−4 M). Thisis mainly because there is more nitrogen in the stellar ejecta(∼ 2.5 × 10−3 M) than in the added ISM (∼ 10−5 M). Thestellar ejecta is enriched in nitrogen because of the operation of

6 Even if the mass of carbon is high, the resulting [C/H] ratio may below, as a result of the large amount of added hydrogen.



102 103 104 105

MISM [M¯]

5

6

7

8

9

10M

cut [M

¯]

0.5

2.04.0

7.0

10.0

15.0

20.0

Fig. 6. χ2 contour map for the vv7 model, considering the fit of HE1439-1420 (the axis shows the two free parameters Mcut and MISM). The num-bers associated with the contours give the χ2 values. The minimum χ2 isfound for Mcut = 5.45 M and MISM = 1789 M. These values producethe black pattern shown in the top left panel of Fig. 5.

the CNO cycle, which was boosted by the progressive arrival of12C and 16O from the He-burning core.

Generally, apart from the most outer source star layers, themodel loses memory of its initial chemical composition as evo-lution proceeds. The overproduction of C, N, O, Na, Mg, and Alin the source star is mainly due to the primary channel, whichmeans that they were synthesized from the initial H and He con-tent, not the initial metal content. Consequently, and also be-cause the source star material generally dominates over the ISMmaterial, the results should not depend critically on the initialmetal mixture considered.

4.1.3. Velocity distribution

Figure 10 shows the weighted υini/υcrit distribution of the sourcestar models. The distribution is normalized to 1. There is a cleardifference between the distribution derived from the C-normaland CEMP stars. For C-normal stars the amount of good fits iscomparable, whatever the initial rotation rate. It gives a rather flatυini/υcrit distribution; instead, for CEMP stars the ability to findgood fits globally increases from non-rotation to fast rotation bya factor of ∼ 6 − 7. This difference is due to the fact that C-normal stars generally have low [X/H] ratios, which can oftenbe reproduced by any source star models. It eventually providessimilar weights to all the source star models. The CEMP starsare enriched in carbon and also very often in N, O, Na, Mg,and Al, whose production increases with the initial source starrotation. While a large C or O abundance can be achieved inevery source star model (Fig. 2, right panel), a large N, Na, Mg orAl abundance is preferentially obtained in fast rotating models.It gives higher weights to rotating models, hence the differencebetween the red and green distribution in Fig. 10.

The overall υini/υcrit distribution follows a trend in be-tween the C-normal EMP and CEMP distributions. The num-ber of good fits increases by a factor of ∼ 3 from no rota-tion to fast rotation. For indicative purposes, three fits of theυini/υcrit distribution are shown in Fig. 10. The grey fit is ofthe form ax + b, with (a, b) = (0.192, 0.058). The blue fit isa fourth-degree polynomial:

∑4n=0 anxn with (a0, a1, a2, a3, a4) =

(0.064, 0.31,−1.71, 4.91,−3.90). The red fit is the sum of a nor-

0 2 4 6 8 10 12 14 16 18 20Mcut [M¯]

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Nor

mal

ized

fre

quen

cy

allCEMP

0 2 4 6 8 10 12 14 16 18 201048

1049

1050

1051

EU

B [

erg]

0 2 4 6 8 10 12 14 16 18 20Mcut [M¯]

1050

1051

1052dE

UB /

dM

cut

vv0vv1vv2vv3

vv4vv5vv6vv7

Fig. 7. Top panel: Distribution of the source stars Mcut values derivedfrom the CEMP star sample (red) and the entire sample (blue). Middlepanel : Energy required to unbind the source star material above theconsidered Mcut. It is computed as EUB(Mcut) =

∫ Mfin

McutGMr/r dMr with

Mfin the final source star mass (see Table 2). Bottom panel : Derivativeof EUB as a function of Mcut. The shaded regions show the approximateunexplored Mcut region (below the bottom of the He-shell).

mal distribution and a skew normal distribution. It is of the form

α g(x; a0, b0) + β f (x; a1, b1, c1), (3)

where

g(x; a, b) = e−(x−a)2/b2(4)

and

f (x; a, b, c) = g(x; a, b)[1 + er f

(c

x − ab

)]. (5)

The coefficients in Eq. 3 are (α, β, a0, b0, a1, b1, c1) =(0.14, 3.50 × 10−2, 5.77 × 10−1, 6.41 × 10−1, 5.42 × 10−1, 2.44 ×10−1, 6.0). Although the red fit has the smallest residuals, wecannot exclude the other fits, which also provide reasonableagreements to the distribution.

4.2. Impact on the individual elements on the fitting

In order to check which chemical element(s) can have the largestimpact in determining the best EMP source stars, we first in-spected two individual stars (CS29498-043 and CS29502-092,



3.63.84.04.24.44.6log (Teff [K])

4.6

4.8

5.0

5.2

5.4

log

(L/L

¯)

20s020s120s220s3

20s420s520s620s7

Fig. 8. Tracks of the models in the Hertzsprung–Russell diagram. Thecircles denote the endpoints of the evolution.

102 103 104 105 106

MISM [M¯]

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Nor

mal

ized

fre

quen

cy

allCEMP

Fig. 9. Distribution of the MISM values derived from the CEMP sample(red) and the entire sample (blue).

shown in Fig. 5) which have all seven abundances determined7.We fitted these stars while removing each time one of the sevenelements from the fit. Overall, the fits are similar and the rankingof the source star models remains the same, except when remov-ing Mg from the fit. Without Mg, the best fits for these two starstend to be slower rotators. This shows that Mg may be an im-portant element for constraining the rotation of the EMP sourcestars.

To check further, we performed the fitting analysis againwhile removing each time one of the seven elements from theanalysis. When removed, an element was not considered to fitany of the EMP stars. Removing either N, O, or 12C/13C didnot affect significantly the distributions shown in Figs. 7, 9, and10. On the contrary, C and Mg (Na and Al to a smaller extent)mostly determine the shape of the distributions. This is mainlydue to the fact that the number of stars with a measured N, O,or 12C/13C ratio is low compared to the number of stars havinga C, Na, Mg, or Al abundance (see Table 3). In addition, somestars with a measured N or 12C/13C ratio have log g < 2 so that

7 However, these stars are evolved with log g < 2 so that [N/H] and12C/13C are set as upper and lower limits, respectively.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.00

0.05

0.10

0.15

0.20

0.25

Nor

mal

ized

fre

quen

cy

allCEMPC-normal EMP

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7vini/vcrit

0.020.000.020.04

Res

.Fig. 10. Distribution of the source stars υini/υcrit values derived from theCEMP sample (red), the C-normal EMP sample (green), and the entiresample (blue). Three fits of the distribution are shown (red, blue, andgrey curves; see text for details) together with their associated residuals(bottom panel).

only limits were considered (see Sect. 3.2). Also, the observa-tional uncertainties σo for N are on average higher than for C,Na, Mg, and Al (see Sect. 3.3). Overall, it gives less weight tothe N abundance compared to other abundances. In the end, Cand Mg (Na and Al to a smaller extent) have the highest impacton the derived distributions.

4.3. Robustness of the fitting analysis

4.3.1. Size of the abundance data

The amount of abundance data available varies from one EMPstar to another. To check the robustness of our results against thenumber of abundance constraints, we performed the fitting anal-ysis again by selecting only the EMP stars having at least fivemeasured abundances. While 119 EMP stars have at least fiveabundances or limits, only 38 have at least five determined abun-dances. Considering only these 38 stars for the analysis gives asimilar increasing trend to that seen in Fig. 10, and a similar dou-ble peaked mass cut distribution (Fig. 7). Compared to Fig. 9,the MISM distribution is more equally distributed between 102

and ∼ 105 M. These overall similar results suggest that the de-rived distributions are robust against the number of abundanceconstraints.

4.3.2. Varying the theoretical uncertainties

The chemical yields of stellar models depend on processes suchas convection, nuclear reaction rates, or the physics of rotationfor instance. These processes contain uncertainties that cannot beestimated easily (see also discussion in Sect. 5.5). In this work,the model uncertainties σt,i were treated approximately and setto fixed values (see Sect. 3.3).

As a simple (and limited) approach to investigate the im-pact of uncertainties on the results, we performed the previous



Table 6. Same as Table 4, but considering very inefficient internal mix-ing processes in EMP stars (see text).

χ2ν < 10 χ2

ν < 5 χ2ν < 3 χ2

ν < 2 χ2ν < 1


analysis while changing the σt,i. We found that increasing theσt,i gives a similar increasing trend for the υini/υcrit distribution(Fig. 10), but progressively flattens the distribution. This occursbecause with larger uncertainties, the source stars models thathad high χ2 values (mostly non-rotating or slow rotating mod-els) now have lower χ2 values and therefore greater weights. Itincreases the contribution of these models. For instance, settingσt,i = 0.2 for [C/H], [N/H], and [O/H] (instead of 0.15) andσt,i = 0.4 for [Na/H], [Mg/H], and [Al/H] (instead of 0.3) givesa contrast (ratio of the highest υini/υcrit frequency to the lowestυini/υcrit frequency) of 2.3, against 3.0 in the standard case. In-creasing σt,i again to 0.25 for C, N, and O and 0.5 for Na, Mg,and Al gives a contrast of 1.9. Overall, the specific slope (orshape) of the υini/υcrit depends on the adopted uncertainties, butthe dependance likely stays modest.

4.3.3. Internal mixing in EMP stars

The efficiency of the internal mixing processes in low mass starsis still discussed, particularly thermohaline mixing (e.g. Denis-senkov & Merryfield 2011; Traxler et al. 2011; Wachlin et al.2014; Sengupta & Garaud 2018). If these processes were veryefficient in EMP stars, we should see a clear separation betweenthe C, N, and 12C/13C abundances of evolved and unevolvedEMP stars, but this is not the case (Choplin et al. 2017a). Asa test, we did the analysis again, assuming inefficient internalmixing processes in EMP stars (i.e. their C, N, and 12C/13C abun-dances did not change since their birth). In this case the carboncorrection from Placco et al. (2014b) was not considered and theN abundance and 12C/13C ratio were not considered as limits ifthe EMP star was evolved (log g < 2). This new analysis slightlydecreases the number of good fits (Table 6) because additionalconstraints were added (in the evolved EMP stars, N and 12C/13Care now data points and not limits). The υini/υcrit distribution isbarely affected. The maximum change in the distribution shownin Fig. 10 is about 4 %. This shows that, based on the current un-derstanding on internal mixing processes (mainly dredge-up andthermohaline mixing), the efficiency of these processes, for thecurrent sample of EMP stars, may not impact much the resultspresented here.

We also carried out the analysis again while considering onlythe not-so-evolved EMP stars because the abundances of evolvedEMP stars suffer additional uncertainties, and thus their inclu-sion in the analysis may reduce its robustness. Among the 272EMP stars, we selected the 128 EMP stars having log g ≥ 2. Theυini/υcrit, Mcut and MISM distributions were found to be compa-rable to the distributions derived from the entire sample. In par-ticular, the overall υini/υcrit distribution is very similar to that ofFig. 10.

4.4. EMP stars with high χ2

Stars with [Na, Mg, Al / C] & 0

The shared feature of about 70 % of the EMP stars having ahigh χ2 is a relatively high [Mg/C] ratio (a high [Na/C] or [Al/C]ratio to a lesser extent), which cannot be achieved with the con-sidered assumptions (see the five first panels of Fig. 11). In thesource star models considered here, [Mg/C] < 0 (Fig. 2), exceptin the H-rich layers of non-rotating or slow rotating models (e.g.the black pattern in the left panel of Fig. 2), but in this case,the low [C/H] and [Mg/H] ratios generally cannot account forthe EMP star abundances. During the advanced stages of evo-lution and explosion, the most inner stellar layers are enrichedin C, O, Na, Mg, Al, and heavier elements until the Fe-group(e.g. Thielemann et al. 1996; Woosley et al. 2002; Nomoto et al.2006). Higher [Mg/C] ratios could be obtained in deeper sourcestar layers. This EMP star group with high χ2 and high [Mg/C]ratios may indicate the need for a different source star material,likely originating from deeper layers and possibly processed byexplosive nucleosynthesis.

Stars with very low [X/H] ratios

Some other EMP stars (∼ 20) have at least one very low [X/H]ratio, below the ISM values considered here (e.g. CS22897-008with a low [Al/H] ratio; see Fig. 11, middle right panel). Nosolution can give such low values. Zero-metallicity source starmodels may provide better solutions. A more complete study in-cluding source stars spanning a range of different initial metal-licities will be addressed in a future work.

Stars with [O/C] > 0

Several EMP stars (∼ 5 − 10) have very high [O/C] ratios (e.g.HE0130-1749, Fig. 11, bottom left panel). In most of the cases,the source star models predict [O/C] ≤ 0. Since HE0130-1749 isevolved (log g = 1.6), the initial [C/H] was likely higher than theobserved value. However, the [O/C] ratio after the Placco et al.(2014a) correction is still well above 0. If the internal mixingprocesses were much more efficient in HE0130-1749, we mightexpect a higher [C/H] ratio, which would improve the fit.

Other stars with high χ2

The other problematic EMP stars are generally specific cases.The unevolved star CS22958-042 has a low 12C/13C (Fig. 11,bottom centre panel) that can only be reproduced in the H-richlayers of source stars (Fig. 2). However, these H-rich layers have[N/C] ∼ 1 − 2, while CS22958-042 has [N/C] ∼ 0. Producingboth a low [N/C] with a low 12C/13C is challenging for thesemodels. A numerical experiment was carried out in Choplin et al.(2017a) in order to try improving the fit for such stars. This pe-culiar abundance trend can be reproduced if a late mixing eventis included in the source star, occurring between the hydrogen-and helium-burning shell, shortly before the end of the sourcestar evolution. In the EMP star sample, only a few stars have ameasured C, N, and 12C/13C ratio together. Moreover, some ofthese stars are evolved and may have undergone important mod-ifications of these abundances. More N abundances and 12C/13Cratio measurements in rather unevolved stars are required to fur-ther test the idea of a late mixing event in the source star.

Finally, HE1456+0230 (bottom right panel) has a high[C/H], [N/H] together with [N/C] > 0. This is consistent with



6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS22954-004Teff =5810 K logg =3.55

vv6 (χ2 ,χ 2ν ) = (5.47,2.74)

vv7 (χ2 ,χ 2ν ) = (5.78,2.89)

vv4 (χ2 ,χ 2ν ) = (7.78,3.89)

vv5 (χ2 ,χ 2ν ) = (7.91,3.96)

vv3 (χ2 ,χ 2ν ) = (8.13,4.06)

vv2 (χ2 ,χ 2ν ) = (8.8,4.4)

vv1 (χ2 ,χ 2ν ) = (9.73,4.87)

vv0 (χ2 ,χ 2ν ) = (10.5,5.25)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS22957-013Teff =4620 K logg =0.95

vv6 (χ2 ,χ 2ν ) = (11.49,5.74)

vv7 (χ2 ,χ 2ν ) = (11.9,5.95)

vv1 (χ2 ,χ 2ν ) = (13.24,6.62)

vv0 (χ2 ,χ 2ν ) = (13.32,6.66)

vv4 (χ2 ,χ 2ν ) = (13.6,6.8)

vv5 (χ2 ,χ 2ν ) = (13.65,6.82)

vv3 (χ2 ,χ 2ν ) = (14.11,7.05)

vv2 (χ2 ,χ 2ν ) = (14.16,7.08)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS22958-083Teff =4900 K logg =1.75

vv6 (χ2 ,χ 2ν ) = (6.13,3.06)

vv7 (χ2 ,χ 2ν ) = (6.8,3.4)

vv4 (χ2 ,χ 2ν ) = (11.19,5.59)

vv5 (χ2 ,χ 2ν ) = (11.24,5.62)

vv2 (χ2 ,χ 2ν ) = (12.68,6.34)

vv3 (χ2 ,χ 2ν ) = (13.08,6.54)

vv1 (χ2 ,χ 2ν ) = (13.51,6.75)

vv0 (χ2 ,χ 2ν ) = (14.19,7.1)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS29493-090Teff =4700 K logg =1.3

vv6 (χ2 ,χ 2ν ) = (19.4,6.47)

vv7 (χ2 ,χ 2ν ) = (21.81,7.27)

vv5 (χ2 ,χ 2ν ) = (30.05,10.02)

vv4 (χ2 ,χ 2ν ) = (30.07,10.02)

vv3 (χ2 ,χ 2ν ) = (36.54,12.18)

vv2 (χ2 ,χ 2ν ) = (43.86,14.62)

vv1 (χ2 ,χ 2ν ) = (49.9,16.63)

vv0 (χ2 ,χ 2ν ) = (53.26,17.75)

0

1

2

3lo

g(12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS22941-017Teff =5070 K logg =2.2

vv6 (χ2 ,χ 2ν ) = (7.87,3.94)

vv7 (χ2 ,χ 2ν ) = (8.25,4.12)

vv1 (χ2 ,χ 2ν ) = (8.52,4.26)

vv2 (χ2 ,χ 2ν ) = (8.67,4.34)

vv0 (χ2 ,χ 2ν ) = (9.02,4.51)

vv5 (χ2 ,χ 2ν ) = (9.06,4.53)

vv4 (χ2 ,χ 2ν ) = (9.46,4.73)

vv3 (χ2 ,χ 2ν ) = (9.72,4.86)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

5

4

3

2

1

[X/H

]


: CS22897-008Teff =4550 K logg =0.7

vv2 (χ2 ,χ 2ν ) = (5.75,2.87)

vv0 (χ2 ,χ 2ν ) = (5.75,2.87)

vv1 (χ2 ,χ 2ν ) = (5.75,2.87)

vv3 (χ2 ,χ 2ν ) = (5.8,2.9)

vv4 (χ2 ,χ 2ν ) = (5.97,2.99)

vv5 (χ2 ,χ 2ν ) = (6.12,3.06)

vv6 (χ2 ,χ 2ν ) = (6.25,3.12)

vv7 (χ2 ,χ 2ν ) = (6.42,3.21)

1

0

1

2

3

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: HE0130-1749Teff =4820 K logg =1.6

vv7 (χ2 ,χ 2ν ) = (22.25,7.42)

vv6 (χ2 ,χ 2ν ) = (25.56,8.52)

vv4 (χ2 ,χ 2ν ) = (26.05,8.68)

vv5 (χ2 ,χ 2ν ) = (26.29,8.76)

vv3 (χ2 ,χ 2ν ) = (26.71,8.9)

vv2 (χ2 ,χ 2ν ) = (31.84,10.61)

vv1 (χ2 ,χ 2ν ) = (40.2,13.4)

vv0 (χ2 ,χ 2ν ) = (48.26,16.09)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: CS22958-042Teff =5760 K logg =3.55

vv6 (χ2 ,χ 2ν ) = (8.2,2.73)

vv5 (χ2 ,χ 2ν ) = (13.72,4.57)

vv7 (χ2 ,χ 2ν ) = (14.14,4.71)

vv4 (χ2 ,χ 2ν ) = (19.97,6.66)

vv3 (χ2 ,χ 2ν ) = (33.39,11.13)

vv2 (χ2 ,χ 2ν ) = (71.2,23.73)

vv1 (χ2 ,χ 2ν ) = (128.08,42.69)

vv0 (χ2 ,χ 2ν ) = (141.18,47.06)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]C N O F Ne Na Mg Al 12 C/13 C

: HE1456+0230Teff =5664 K logg =2.2

vv5 (χ2 ,χ 2ν ) = (8.38,2.79)

vv6 (χ2 ,χ 2ν ) = (9.68,3.23)

vv7 (χ2 ,χ 2ν ) = (10.72,3.57)

vv4 (χ2 ,χ 2ν ) = (11.3,3.77)

vv3 (χ2 ,χ 2ν ) = (19.89,6.63)

vv2 (χ2 ,χ 2ν ) = (44.06,14.69)

vv1 (χ2 ,χ 2ν ) = (78.1,26.03)

vv0 (χ2 ,χ 2ν ) = (88.49,29.5)

0

1

2

3

4

log(

12C/13

C)

Fig. 11. Same as Fig. 5, but for EMP stars with χ2ν > 2 (χ2 > 5).

material processed by H-burning of a rotating source star. How-ever, in such material, [Na/H] is high, which is not the case forHE1456+0230. Generally, our models predict that a high [N/H]with [N/C] > 0 should be accompanied with some Na enhance-ments, together with a low 12C/13C ratio.

5. Discussions

5.1. CEMP and C-normal EMP stars, and source star matterejection

While 64 % (40 %) of the CEMP stars have χ2ν < 2 (χ2

ν < 1),only 26 % (5 %) of C-normal EMP stars have χ2

ν < 2 (χ2ν < 1, Ta-

ble 5). This important difference between CEMP and C-normalEMP stars suggests that the assumptions made in this studyare adequate for most of the CEMP stars, but are not suitablefor a large fraction of C-normal EMP stars. In particular, it islikely that the assumption of an explosion with strong fallback(Sect. 2.2) plays a major role and is more suitable for CEMP thanC-normal EMP stars. Different kinds of SNe (e.g. more stan-dard core collapse SNe), that could also have existed in the earlyUniverse, may be predominantly responsible for the abundancesof C-normal EMP stars. On the contrary, the great fraction ofCEMP stars can be explained by source stars that experienced anexplosion with strong fallback. We note that the idea of strongfallback was already associated with CEMP stars based on thefact that they have high [C/Fe] ratios and that, in the massivesource star, C is located in shallower layers than Fe (e.g. Umeda

& Nomoto 2003). Similar conclusions are derived here withoutconsidering Fe abundances.

5.2. Comparison with the velocity of nearby OB stars

5.2.1. 〈υeq〉MS distributions

It is worth comparing the derived velocity distribution (Fig. 10)to distributions based on the observation of solar or near-solarmetallicity massive stars. Figure 12 shows the distribution of〈υeq〉MS, the mean velocity during the main sequence (MS), forour source star models (the 〈υeq〉MS values are reported in Ta-ble 2). These values are representative of υeq at any stage ofthe MS because of the modest variation of υeq during the MS.This is shown by the grey segment at the top of Fig. 12 thatrepresents the υeq range during the MS for the vv6 model. Thethree fits in Fig. 12 are the same as in Fig. 10 (see Sect. 4.1.3for details), but adapted to the new x-axis. The parametersare now (a, b) = (2.46 × 10−4, 5.94 × 10−2) for the grey fit;(a0, a1, a2, a3, a4) = (6.40×10−2, 4.14×10−4,−2.84×10−6, 1.02×10−8,−1.04×10−11) for the blue fit; and (α, β, a0, b0, a1, b1, c1) =(0.14, 3.5 × 10−2, 4.5 × 102, 5.0 × 102, 4.2 × 102, 1.8 × 102, 6.0)for the red fit.

The dashed distribution labelled H+2006 shows the equato-rial velocity distribution reported in Huang & Gies (2006), basedon the observation of 496 presumably single OB-type stars ob-served in 19 different Galactic open clusters. The dashed dis-tribution labelled Ra+2013 shows the distribution reported in



Ramírez-Agudelo et al. (2013), based on the observation of 216presumably single O-type stars observed in the 30 Doradus re-gion of the Large Magellanic Cloud. The OB star samples span arange of spectral types which likely correspond to a range of evo-lutionary stages during the MS. As a first-order comparison, weconsider here that the velocity distributions of these two OB starsamples are representative of 〈υeq〉MS (x-axis of Fig. 12). Thismay be a reasonable assumption since these two OB star sampleslikely contain objects with masses mostly below 30−40 M andthe surface equatorial velocity of solar metallicity models withMini . 32 M does not vary strongly during the MS (Ekströmet al. 2012, especially their Fig. 10). The black segment at thetop of Fig. 12 illustrates this by showing the range of υeq dur-ing the MS for a 20 M solar metallicity model computed atυini/υcrit = 0.3.

The H+2006 and Ra+2013 distributions peak at 200 and 100km s−1. Whether the distribution derived from EMP stars peaksat ∼ 500 km s−1 or would still increase toward higher velocitiescannot be determined. In any case, a higher fraction of fast ro-tators and a flatter distribution can be noticed, compared to thedistributions derived from observations. We note that while thecomparison is made through 〈υeq〉MS, the velocity differences arelikely significant because the variations in υeq during the MS aremodest compared to the peak difference (see the two segmentsat the top of Fig. 12).

5.2.2. Two different metallicity regimes

The H+2006 and Ra+2013 distributions are based on OB stars,which are either in open clusters (−0.5 < [Fe/H] < +0.5 in mostof the cases, e.g. Paunzen et al. 2010; Heiter et al. 2014; Ne-topil et al. 2016) or in the 30 Doradus region (with metallic-ity ∼ 0.6 Z Lebouteiller et al. 2008). This work investigates amuch lower metallicity range, sub-solar by a factor of 103 − 104.Low metallicity stars are less metal-rich so that they are lessopaque and more compact. As a consequence, for a given angu-lar momentum content, they tend rotate faster than solar metal-licity stars (e.g. Maeder & Meynet 2001). Figure 13 shows themodels of Table 2 (blue curve) together with the same modelscomputed at solar metallicity (red curve). For a given initial an-gular momentum content LZAMS, 〈υeq〉MS is indeed higher at lowmetallicity. The increasing fraction of fast rotators at low metal-licity is supported by observations of rotating massive stars indifferent metallicity environments (Maeder et al. 1999; Martayanet al. 2007; Hunter et al. 2008; however, the metallicity regimein these studies is not comparable to the very low metallicityregime investigated here).

Figure 13 also shows that the higher fraction of fast rota-tors in the distribution derived from EMP stars might not beunderstood solely as a result of the physics of rotating massivestars. According to the additional solar metallicity models wehave computed, the peaks of the distributions of Huang & Gies(2006) and Ramírez-Agudelo et al. (2013) correspond to an ini-tial angular momentum of ∼ 1.5 − 3 × 1052 g cm2 s−1 (red cir-cles in Fig. 13). The distribution derived in this work peaks at∼ 4 − 5 × 1052 g cm2 s−1 (blue circles). This might indicate thatlow metallicity massive stars were born with more angular mo-mentum. It might suggest that the removal of angular momen-tum during massive star formation was less efficient in the earlyUniverse. This may happen if the magnetic braking during starformation is rather inefficient (Hirano & Bromm 2018).

0 100 200 300 400 500 600 700 8000.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Nor

mal

ized

fre

quen

cy

H+2006

Ra+2013

0 100 200 300 400 500 600 700 800⟨veq

⟩MS [km s−1 ]

0.020.000.020.04

Res

.Fig. 12. Distribution of the mean equatorial velocity during the MS forthe EMP source star models. The three fits are the same as in Fig. 10, butadapted to the new x-axis (see text for details). The dashed black dis-tributions show two equatorial velocity distributions reported in Huang& Gies (2006, H+2006) and Ramírez-Agudelo et al. (2013, Ra+2013),based on the observation of Galactic and LMC O-type and B-type stars(see text for details). The segments at the top show the υeq range duringthe MS for the vv6 model (grey) and for a 20 M model computed atsolar metallicity with υini/υcrit = 0.3 (black).

0 1 2 3 4 5LZAMS [1052 g cm2 s−1 ]

0

100

200

300

400

500

600

⟨ v eq⟩ MS [

km s−

1]

H+2006 (peak)

Ra+2013 (peak)

vv6

vv7

Z=10−5

Z=Z¯

Fig. 13. Mean equatorial velocity during the MS as a function of LZAMS,the total angular momentum content at the ZAMS. The two curves show20 M models computed at solar metallicity (red) and at Z = 10−5 (blue,the models of Table 2). The two peaks of the Huang & Gies (2006,H+2006) and Ramírez-Agudelo et al. (2013, Ra+2013) velocity distri-butions are indicated, together with the vv6 and vv7 models.

5.3. Origin of trans-iron elements

Most metal-poor stars having [Fe/H] < −3 do not show strongenhancements in trans-iron elements. In our sample, 4 stars have[Sr/Fe] > 1, 14 have [Ba/Fe] > 1, and 7 have [Eu/Fe] > 1. One



possible origin of these elements (or at least some of them) couldbe due to the s-process operating in the massive source stars,mainly during the core He-burning stage (e.g. Cameron 1960;Peters 1968; Couch et al. 1974; Lamb et al. 1977; Langer et al.1989; Raiteri et al. 1991). To produce trans-iron elements, thisprocess requires some initial amount of heavy seeds (e.g. Fe) tostart with because the neutron flux is too weak to reach trans-ironelements starting from light seeds. Consequently, at zero metal-licity, an almost null amount of trans-iron elements is expected.The standard s-process in non-rotating massive stars is likely in-efficient below Z ∼ 10−4 (Prantzos et al. 1990). However, it hasbeen shown that rotation can enhance the neutron flux and there-fore boosts the s-process (e.g. Pignatari et al. 2008; Frischknechtet al. 2012; Choplin et al. 2018; Limongi & Chieffi 2018; Baner-jee et al. 2019). This can lead to a significant production of trans-iron elements even at low metallicity. In what proportions thisprocess can produce light (e.g. Sr) and heavy (e.g. Pb) trans-iron elements is still uncertain. The inclusion of the s-process inour analysis will be the object of a future work. Other processesor sources may also have contributed to the early enrichmentof trans-iron elements, such as AGB stars (e.g. Herwig 2004;Cristallo et al. 2009), jet-like explosions driven by magneto-rotational instabilities (e.g. Winteler et al. 2012; Nishimura et al.2015), or neutron star mergers (e.g. Thielemann et al. 2017).

5.4. Initial source star masses

The back and forth mixing process likely operates more effi-ciently in < 60 M models compared to higher masses mod-els (Choplin et al. 2018), one reason being that higher massstars have shorter lifetimes hence there is less time for the backand forth mixing process to operate. On the other hand, be-cause higher mass stars have more massive H-shells and He-cores, their mass yields can be higher. Moreover, strong H–Heshell interactions can occur in some models and can largely im-pact the nucleosynthesis (e.g. Ekström et al. 2008). The massdependency of yields is then complex and it generally variesnon-monotonically with initial mass (e.g. Hirschi 2007; Ekströmet al. 2008; Yoon et al. 2012; Takahashi et al. 2014). Withouta detailed study, it is therefore not possible to predict how ourresults will depend on the initial source star mass. It is likely,however, that EMP stars with high [Na, Mg, Al/H] ratios maybe better reproduced by ∼ 20 M than ∼ 60 M models becausean overproduction of Na, Mg, or Al requires enough time for theback and forth mixing to operate (Sect. 2.3). The shorter coreHe-burning stage of higher mass stars8 may prevent a signifi-cant overproduction of Na, Mg, or Al through the back and forthmixing process.

5.5. Rotational mixing uncertainties

Although we investigate the impact of uncertainties inSect. 4.3.2, we employ a limited approach that cannot fully treatthe strong stellar model uncertainties, especially those linked tothe rotational mixing. In rotating models, the transport of chem-ical elements is governed by different diffusion coefficients (e.g.horizontal turbulence or shear mixing). Depending on the pre-scription used for these coefficients (e.g. Zahn 1992; Mathis et al.2004; Talon & Zahn 1997; Maeder 1997; Maeder et al. 2013) theproduction of chemical elements (especially N) can vary signif-icantly (Meynet et al. 2013).

8 The duration of the core He-burning stage of a Pop III 20 M is abouttwice as long as a Pop III 85 M (Ekström et al. 2008).

Thanks to asteroseismic observations, it has also been shownthat current low mass stellar models likely miss an angular mo-mentum transport process (e.g. Cantiello et al. 2014; Eggen-berger et al. 2017). This additional process may also be missingin massive stars. The nature and efficiency of this process is ac-tively discussed (e.g. Eggenberger et al. 2019; Fuller et al. 2019).If added in the present models, it may provide different chemi-cal yields. Brott et al. (2011b) also suggested that an additionalmixing process should be included in massive stars to accountfor the observed population of slow rotating massive stars withhigh surface nitrogen abundances. The results of this work aresubject to important model uncertainties that cannot be fully ac-counted for with simple approaches, such as the method used inSect. 4.3.2.

6. Summary and conclusions

In this work, we have investigated whether the peculiar chemi-cal signature of long-dead early massive stars including rotationmay be found in the observed extremely metal-poor stars. Wecomputed 20 M models at metallicity Z = 10−5 with eight ini-tial rotation rates (0 < υini/υcrit < 0.7).

The rotational mixing operating between the He-burningcore and H-burning shell affects the abundances of light ele-ments from C to Al. At the pre-SN stage, the material abovethe C-burning shell (Mr & 4 − 5 M) shows a variable chemi-cal composition that strongly depends on the initial rotation. Inthe H-rich layers, the [C/H], [N/H], [F/H], and [Na/H] ratios areincreased by ∼ 1 − 2 dex from the non-rotating to the fast ro-tating case. In the H + He-rich layers, the [N/H], [F/H], [Ne/H],[Na/H], [Mg/H], and [Al/H] ratios are increased by ∼ 2 − 4 dexfrom the non-rotating to the fast rotating case.

We compared the chemical composition of this materialwith the abundances of EMP stars with −4 < [Fe/H] < −3.We assumed that the massive stars experienced an explosionwith strong fallback. Among the 272 EMP stars considered,∼ 40 − 50 % were found to have an abundance pattern con-sistent with our massive source star models. About 60 − 70 %(20 − 30 %) of the CEMP (C-normal EMP) stars can be reason-ably well reproduced. In addition, while the abundance patternsof C-normal stars are roughly equally well reproduced by non-rotating and rotating source stars, the patterns of CEMP stars arebetter explained by fast rotators.

The velocity distribution of the best source star modelsreaches a maximum at υini/υcrit = 0.6 − 0.7 (corresponding toinitial equatorial velocities of ∼ 550−640 km s−1). Compared tothe velocity distributions derived from the observation of nearbyOB stars, our distribution is flatter and suggests a greater amountof massive fast rotators in the early Universe. The stellar evolu-tion effects (such as the higher compactness of low metallicitystars) may not be sufficient to explain the observed differences.Our results suggest that the initial angular momentum content ofearly massive stars might have been higher than for solar metal-licity massive stars. The possibly higher fraction of fast rotatorsat low metallicity may have important consequences for the SNtypes (and rates) from early massive stars, the integrated light ofhigh redshift galaxies and the contribution of early massive starsto reionization.

Caution when using these results is required because of thelimiting assumptions made here, especially the explosions withstrong fallback (Sect. 2.2). Our results appear to be particu-larly sensitive to the Mg source star yield (Sect. 4.2), whichcould change significantly if considering different kind of ex-plosions. As already suggested in the past (e.g. Meynet et al.



2010; Maeder et al. 2015; Choplin et al. 2017a), the 12C/13Cratio and N abundance should be among the best elements toprobe the mixing process(es) at work in early massive stars. Con-sequently, more 12C/13C and N measurements (preferentially innon-evolved EMP stars) are desirable to better probe these pro-cesses. Finally, caution is also required because of the strongstellar model uncertainties, particularly on the physics of rota-tional mixing (Sect. 5.5).Acknowledgements. The authors thank an anonymous referee for the construc-tive and helpful comments. A.C. acknowledges funding from the Swiss NationalScience Foundation under grant P2GEP2_184492.

ReferencesAbate, C., Pols, O. R., Izzard, R. G., Mohamed, S. S., & de Mink, S. E. 2013,

A&A, 552, A26Abate, C., Pols, O. R., Karakas, A. I., & Izzard, R. G. 2015, A&A, 576, A118Abel, T., Bryan, G. L., & Norman, M. L. 2002, Science, 295, 93Abohalima, A. & Frebel, A. 2018, ApJS, 238, 36Aguado, D. S., Allende Prieto, C., González Hernández, J. I., et al. 2016, A&A,

593, A10Aguado, D. S., Allende Prieto, C., González Hernández, J. I., & Rebolo, R. 2018,

ApJ, 854, L34Allen, D. M., Ryan, S. G., Rossi, S., Beers, T. C., & Tsangarides, S. A. 2012,

A&A, 548, A34Andrievsky, S. M., Spite, M., Korotin, S. A., et al. 2010, A&A, 509, A88Andrievsky, S. M., Spite, M., Korotin, S. A., et al. 2007, A&A, 464, 1081Andrievsky, S. M., Spite, M., Korotin, S. A., et al. 2008, A&A, 481, 481Angulo, C., Arnould, M., Rayet, M., et al. 1999, Nuclear Physics A, 656, 3Aoki, W. 2010, in IAU Symposium, Vol. 265, IAU Symposium, ed. K. Cunha,

M. Spite, & B. Barbuy, 111–116Aoki, W., Barklem, P. S., Beers, T. C., et al. 2009, ApJ, 698, 1803Aoki, W., Beers, T. C., Christlieb, N., et al. 2007, ApJ, 655, 492Aoki, W., Beers, T. C., Lee, Y. S., et al. 2013, AJ, 145, 13Aoki, W., Beers, T. C., Sivarani, T., et al. 2008, ApJ, 678, 1351Aoki, W., Honda, S., Beers, T. C., et al. 2005, ApJ, 632, 611Aoki, W., Matsuno, T., Honda, S., et al. 2018, PASJ, 70, 94Bandyopadhyay, A., Sivarani, T., Susmitha, A., et al. 2018, ApJ, 859, 114Banerjee, P., Heger, A., & Qian, Y.-Z. 2019, arXiv e-printsBanerjee, P., Qian, Y.-Z., & Heger, A. 2018, ApJ, 865, 120Barklem, P. S., Christlieb, N., Beers, T. C., et al. 2005, A&A, 439, 129Beers, T. C. & Christlieb, N. 2005, ARA&A, 43, 531Behara, N. T., Bonifacio, P., Ludwig, H.-G., et al. 2010, A&A, 513, A72Bisterzo, S., Gallino, R., Straniero, O., Cristallo, S., & Käppeler, F. 2010, MN-

RAS, 404, 1529Bisterzo, S., Gallino, R., Straniero, O., Cristallo, S., & Käppeler, F. 2012, MN-

RAS, 422, 849Boesgaard, A. M., Rich, J. A., Levesque, E. M., & Bowler, B. P. 2011, ApJ, 743,

140Bonifacio, P., Caffau, E., Spite, M., et al. 2015, A&A, 579, A28Bonifacio, P., Caffau, E., Spite, M., et al. 2018, A&A, 612, A65Bonifacio, P., Molaro, P., Sivarani, T., et al. 2007, A&A, 462, 851Bonifacio, P., Spite, M., Cayrel, R., et al. 2009, A&A, 501, 519Bromm, V., Coppi, P. S., & Larson, R. B. 2002, ApJ, 564, 23Bromm, V. & Larson, R. B. 2004, ARA&A, 42, 79Brott, I., de Mink, S. E., Cantiello, M., et al. 2011a, A&A, 530, A115Brott, I., Evans, C. J., Hunter, I., et al. 2011b, A&A, 530, A116Cameron, A. G. W. 1960, AJ, 65, 485Cantiello, M., Mankovich, C., Bildsten, L., Christensen-Dalsgaard, J., & Paxton,

B. 2014, ApJ, 788, 93Cayrel, R., Depagne, E., Spite, M., et al. 2004, A&A, 416, 1117Charbonnel, C. 1994, A&A, 282, 811Charbonnel, C. & Zahn, J.-P. 2007, A&A, 467, L15Chiaki, G., Tominaga, N., & Nozawa, T. 2017, MNRAS, 472, L115Chiaki, G. & Wise, J. H. 2019, MNRAS, 482, 3933Chieffi, A. & Limongi, M. 2013, ApJ, 764, 21Choplin, A., Ekström, S., Meynet, G., et al. 2017a, A&A, 605, A63Choplin, A., Hirschi, R., Meynet, G., & Ekström, S. 2017b, A&A, 607, L3Choplin, A., Hirschi, R., Meynet, G., et al. 2018, A&A, 618, A133Choplin, A., Maeder, A., Meynet, G., & Chiappini, C. 2016, A&A, 593, A36Christlieb, N., Bessell, M. S., Beers, T. C., et al. 2002, Nature, 419, 904Clark, P. C., Glover, S. C. O., Klessen, R. S., & Bromm, V. 2011, ApJ, 727, 110Clarkson, O., Herwig, F., & Pignatari, M. 2018, MNRAS, 474, L37Cohen, J. G., Christlieb, N., Thompson, I., et al. 2013, ApJ, 778, 56Cohen, J. G., McWilliam, A., Shectman, S., et al. 2006, AJ, 132, 137Couch, R. G., Schmiedekamp, A. B., & Arnett, W. D. 1974, ApJ, 190, 95

Cristallo, S., Straniero, O., Gallino, R., et al. 2009, ApJ, 696, 797Cyburt, R. H., Amthor, A. M., Ferguson, R., et al. 2010, ApJS, 189, 240de Jager, C., Nieuwenhuijzen, H., & van der Hucht, K. A. 1988, A&AS, 72, 259Decressin, T., Meynet, G., Charbonnel, C., Prantzos, N., & Ekström, S. 2007,

A&A, 464, 1029Denissenkov, P. A. & Merryfield, W. J. 2011, ApJ, 727, L8Eggenberger, P., Deheuvels, S., Miglio, A., et al. 2019, A&A, 621, A66Eggenberger, P., Lagarde, N., Miglio, A., et al. 2017, A&A, 599, A18Eggenberger, P., Meynet, G., Maeder, A., et al. 2008, Ap&SS, 316, 43Eggleton, P. P., Dearborn, D. S. P., & Lattanzio, J. C. 2008, ApJ, 677, 581Ekström, S., Georgy, C., Eggenberger, P., et al. 2012, A&A, 537, A146Ekström, S., Meynet, G., Chiappini, C., Hirschi, R., & Maeder, A. 2008, A&A,

489, 685Ezzeddine, R., Frebel, A., Roederer, I. U., et al. 2019, ApJ, 876, 97Frebel, A., Aoki, W., Christlieb, N., et al. 2005, in IAU Symposium, Vol. 228,

From Lithium to Uranium: Elemental Tracers of Early Cosmic Evolution, ed.V. Hill, P. Francois, & F. Primas, 207–212

Frebel, A., Chiti, A., Ji, A. P., Jacobson, H. R., & Placco, V. M. 2015, ApJ, 810,L27

Frebel, A., Ji, A. P., Ezzeddine, R., et al. 2019, ApJ, 871, 146Frebel, A. & Norris, J. E. 2015, ARA&A, 53, 631Frebel, A., Norris, J. E., Aoki, W., et al. 2007, ApJ, 658, 534Frischknecht, U., Hirschi, R., Pignatari, M., et al. 2016, MNRAS, 456, 1803Frischknecht, U., Hirschi, R., & Thielemann, F.-K. 2012, A&A, 538, L2Fryer, C. L., Hungerford, A. L., & Young, P. A. 2007, ApJ, 662, L55Fuller, J., Piro, A. L., & Jermyn, A. S. 2019, MNRAS, 485, 3661Georgy, C., Ekström, S., Eggenberger, P., et al. 2013, A&A, 558, A103Gies, D. R. & Lambert, D. L. 1992, ApJ, 387, 673Hale, S. E., Champagne, A. E., Iliadis, C., et al. 2002, Phys. Rev. C, 65, 015801Hansen, T., Hansen, C. J., Christlieb, N., et al. 2015, ApJ, 807, 173Hansen, T., Hansen, C. J., Christlieb, N., et al. 2014, ApJ, 787, 162Hansen, T. T., Andersen, J., Nordström, B., et al. 2016, A&A, 588, A3Heger, A., Langer, N., & Woosley, S. E. 2000, ApJ, 528, 368Heger, A. & Woosley, S. E. 2010, ApJ, 724, 341Heiter, U., Soubiran, C., Netopil, M., & Paunzen, E. 2014, A&A, 561, A93Herwig, F. 2004, ApJ, 605, 425Hill, V., Plez, B., Cayrel, R., et al. 2002, A&A, 387, 560Hirano, S. & Bromm, V. 2018, MNRAS, 476, 3964Hirano, S., Hosokawa, T., Yoshida, N., et al. 2014, ApJ, 781, 60Hirschi, R. 2007, A&A, 461, 571Hirschi, R., Meynet, G., & Maeder, A. 2004, A&A, 425, 649Hollek, J. K., Frebel, A., Roederer, I. U., et al. 2011, ApJ, 742, 54Honda, S., Aoki, W., Beers, T. C., & Takada-Hidai, M. 2011, ApJ, 730, 77Honda, S., Aoki, W., Kajino, T., et al. 2004, ApJ, 607, 474Hosokawa, T., Hirano, S., Kuiper, R., et al. 2016, ApJ, 824, 119Huang, W. & Gies, D. R. 2006, ApJ, 648, 580Hunter, I., Brott, I., Langer, N., et al. 2009, A&A, 496, 841Hunter, I., Brott, I., Lennon, D. J., et al. 2008, ApJ, 676, L29Iliadis, C., D’Auria, J. M., Starrfield, S., Thompson, W. J., & Wiescher, M. 2001,

ApJS, 134, 151Ishigaki, M. N., Tominaga, N., Kobayashi, C., & Nomoto, K. 2014, ApJ, 792,

L32Ishigaki, M. N., Tominaga, N., Kobayashi, C., & Nomoto, K. 2018, ApJ, 857, 46Iwamoto, N., Umeda, H., Tominaga, N., Nomoto, K., & Maeda, K. 2005, Sci-

ence, 309, 451Jacobson, H. R., Keller, S., Frebel, A., et al. 2015, ApJ, 807, 171Jaeger, M., Kunz, R., Mayer, A., et al. 2001, Physical Review Letters, 87, 202501Karlsson, T., Bromm, V., & Bland-Hawthorn, J. 2013, Reviews of Modern

Physics, 85, 809Keller, S. C., Bessell, M. S., Frebel, A., et al. 2014, Nature, 506, 463Lagarde, N., Reylé, C., Robin, A. C., et al. 2019, A&A, 621, A24Lai, D. K., Bolte, M., Johnson, J. A., et al. 2008, ApJ, 681, 1524Lai, D. K., Johnson, J. A., Bolte, M., & Lucatello, S. 2007, ApJ, 667, 1185Lamb, S. A., Howard, W. M., Truran, J. W., & Iben, Jr., I. 1977, ApJ, 217, 213Langer, N. 2012, ARA&A, 50, 107Langer, N., Arcoragi, J.-P., & Arnould, M. 1989, A&A, 210, 187Lebouteiller, V., Bernard-Salas, J., Brandl, B., et al. 2008, ApJ, 680, 398Li, H., Aoki, W., Zhao, G., et al. 2015, PASJ, 67, 84Limongi, M. & Chieffi, A. 2018, ApJS, 237, 13Limongi, M., Chieffi, A., & Bonifacio, P. 2003, ApJ, 594, L123Lugaro, M., Karakas, A. I., Stancliffe, R. J., & Rijs, C. 2012, ApJ, 747, 2MacFadyen, A. I. & Woosley, S. E. 1999, ApJ, 524, 262Maeda, K. & Nomoto, K. 2003, ApJ, 598, 1163Maeder, A. 1997, A&A, 321, 134Maeder, A. 1999, A&A, 347, 185Maeder, A., Grebel, E. K., & Mermilliod, J.-C. 1999, A&A, 346, 459Maeder, A. & Meynet, G. 2000, ARA&A, 38, 143Maeder, A. & Meynet, G. 2001, A&A, 373, 555Maeder, A. & Meynet, G. 2012, Reviews of Modern Physics, 84, 25Maeder, A. & Meynet, G. 2014, ApJ, 793, 123



Maeder, A. & Meynet, G. 2015, A&A, 580, A32Maeder, A., Meynet, G., & Chiappini, C. 2015, A&A, 576, A56Maeder, A., Meynet, G., Lagarde, N., & Charbonnel, C. 2013, A&A, 553, A1Martayan, C., Frémat, Y., Hubert, A.-M., et al. 2007, A&A, 462, 683Masseron, T., Johnson, J. A., Lucatello, S., et al. 2012, ApJ, 751, 14Masseron, T., van Eck, S., Famaey, B., et al. 2006, A&A, 455, 1059Mathis, S., Palacios, A., & Zahn, J.-P. 2004, A&A, 425, 243Matsuno, T., Aoki, W., Beers, T. C., Lee, Y. S., & Honda, S. 2017, AJ, 154, 52Meynet, G., Ekström, S., & Maeder, A. 2006, A&A, 447, 623Meynet, G., Ekstrom, S., Maeder, A., et al. 2013, in Lecture Notes in Physics,

Berlin Springer Verlag, Vol. 865, Lecture Notes in Physics, Berlin SpringerVerlag, ed. M. Goupil, K. Belkacem, C. Neiner, F. Lignières, & J. J. Green,3–642

Meynet, G., Hirschi, R., Ekstrom, S., et al. 2010, A&A, 521, A30Meynet, G. & Maeder, A. 2000, A&A, 361, 101Moriya, T., Tominaga, N., Tanaka, M., et al. 2010, ApJ, 719, 1445Moriya, T. J., Tanaka, M., Yasuda, N., et al. 2019, ApJS, 241, 16Mukhamedzhanov, A. M., Bém, P., Brown, B. A., et al. 2003, Phys. Rev. C, 67,

065804Netopil, M., Paunzen, E., Heiter, U., & Soubiran, C. 2016, A&A, 585, A150Nishimura, N., Takiwaki, T., & Thielemann, F.-K. 2015, ApJ, 810, 109Nomoto, K., Kobayashi, C., & Tominaga, N. 2013, ARA&A, 51, 457Nomoto, K., Maeda, K., Umeda, H., et al. 2003, in IAU Symposium, Vol. 212,

A Massive Star Odyssey: From Main Sequence to Supernova, ed. K. van derHucht, A. Herrero, & C. Esteban, 395

Nomoto, K., Tominaga, N., Umeda, H., Kobayashi, C., & Maeda, K. 2006, Nu-clear Physics A, 777, 424

Norris, J. E. & Yong, D. 2019, ApJ, 879, 37Norris, J. E., Yong, D., Bessell, M. S., et al. 2013, ApJ, 762, 28Oesch, P. A., Brammer, G., van Dokkum, P. G., et al. 2016, ApJ, 819, 129Paunzen, E., Heiter, U., Netopil, M., & Soubiran, C. 2010, A&A, 517, A32Peters, J. G. 1968, ApJ, 154, 225Pignatari, M., Gallino, R., Meynet, G., et al. 2008, ApJ, 687, L95Placco, V. M., Beers, T. C., Reggiani, H., & Meléndez, J. 2016a, ApJ, 829, L24Placco, V. M., Frebel, A., Beers, T. C., et al. 2014a, ApJ, 781, 40Placco, V. M., Frebel, A., Beers, T. C., & Stancliffe, R. J. 2014b, ApJ, 797, 21Placco, V. M., Frebel, A., Beers, T. C., et al. 2016b, ApJ, 833, 21Placco, V. M., Frebel, A., Lee, Y. S., et al. 2015, ApJ, 809, 136Prantzos, N., Hashimoto, M., & Nomoto, K. 1990, A&A, 234, 211Preston, G. W., Sneden, C., Thompson, I. B., Shectman, S. A., & Burley, G. S.

2006, AJ, 132, 85Raiteri, C. M., Busso, M., Gallino, R., Picchio, G., & Pulone, L. 1991, ApJ, 367,

228Ramírez-Agudelo, O. H., Simón-Díaz, S., Sana, H., et al. 2013, A&A, 560, A29Ren, J., Christlieb, N., & Zhao, G. 2012, Research in Astronomy and Astro-

physics, 12, 1637Richard, O., Michaud, G., Richer, J., et al. 2002, ApJ, 568, 979Roederer, I. U., Kratz, K.-L., Frebel, A., et al. 2009, ApJ, 698, 1963Roederer, I. U., Preston, G. W., Thompson, I. B., Shectman, S. A., & Sneden, C.

2014a, ApJ, 784, 158Roederer, I. U., Preston, G. W., Thompson, I. B., et al. 2014b, AJ, 147, 136Salvaterra, R. 2015, Journal of High Energy Astrophysics, 7, 35Sbordone, L., Bonifacio, P., Caffau, E., et al. 2010, A&A, 522, A26Sengupta, S. & Garaud, P. 2018, ApJ, 862, 136Siqueira Mello, C., Hill, V., Barbuy, B., et al. 2014, A&A, 565, A93Sivarani, T., Beers, T. C., Bonifacio, P., et al. 2006, A&A, 459, 125Sneden, C., Cowan, J. J., Lawler, J. E., et al. 2003, ApJ, 591, 936Spite, M., Caffau, E., Bonifacio, P., et al. 2013, A&A, 552, A107Spite, M., Cayrel, R., Hill, V., et al. 2006, A&A, 455, 291Spite, M., Cayrel, R., Plez, B., et al. 2005, A&A, 430, 655Spite, M., Spite, F., Bonifacio, P., et al. 2014, A&A, 571, A40Stacy, A., Bromm, V., & Lee, A. T. 2016, MNRAS, 462, 1307Stacy, A., Bromm, V., & Loeb, A. 2011, MNRAS, 413, 543Stancliffe, R. J., Church, R. P., Angelou, G. C., & Lattanzio, J. C. 2009, MNRAS,

396, 2313Stancliffe, R. J. & Glebbeek, E. 2008, MNRAS, 389, 1828Stancliffe, R. J., Glebbeek, E., Izzard, R. G., & Pols, O. R. 2007, A&A, 464, L57Starkenburg, E., Aguado, D. S., Bonifacio, P., et al. 2018, MNRAS, 481, 3838Suda, T., Hidaka, J., Aoki, W., et al. 2017, PASJ, 69, 76Suda, T., Katsuta, Y., Yamada, S., et al. 2008, PASJ, 60, 1159Susa, H. 2013, ApJ, 773, 185Susa, H., Hasegawa, K., & Tominaga, N. 2014, ApJ, 792, 32Susmitha Rani, A., Sivarani, T., Beers, T. C., et al. 2016, MNRAS, 458, 2648Takahashi, K., Umeda, H., & Yoshida, T. 2014, ApJ, 794, 40Talon, S. & Zahn, J.-P. 1997, A&A, 317, 749Thielemann, F.-K., Eichler, M., Panov, I. V., & Wehmeyer, B. 2017, Annual

Review of Nuclear and Particle Science, 67, 253Thielemann, F.-K., Nomoto, K., & Hashimoto, M.-A. 1996, ApJ, 460, 408Tominaga, N. 2009, ApJ, 690, 526Tominaga, N., Iwamoto, N., & Nomoto, K. 2014, ApJ, 785, 98

Traxler, A., Garaud, P., & Stellmach, S. 2011, ApJ, 728, L29Tumlinson, J., Venkatesan, A., & Shull, J. M. 2004, ApJ, 612, 602Umeda, H. & Nomoto, K. 2002, ApJ, 565, 385Umeda, H. & Nomoto, K. 2003, Nature, 422, 871Venn, K. A., Irwin, M., Shetrone, M. D., et al. 2004, AJ, 128, 1177Villamariz, M. R. & Herrero, A. 2005, A&A, 442, 263Vink, J. S., de Koter, A., & Lamers, H. J. G. L. M. 2001, A&A, 369, 574Wachlin, F. C., Vauclair, S., & Althaus, L. G. 2014, A&A, 570, A58Whalen, D. J., Fryer, C. L., Holz, D. E., et al. 2013, ApJ, 762, L6Winteler, C., Käppeli, R., Perego, A., et al. 2012, ApJ, 750, L22Woosley, S. E. 1993, ApJ, 405, 273Woosley, S. E., Heger, A., & Weaver, T. A. 2002, Reviews of Modern Physics,

74, 1015Woosley, S. E. & Weaver, T. A. 1995, ApJS, 101, 181Yong, D., Norris, J. E., Bessell, M. S., et al. 2013, ApJ, 762, 26Yoon, J., Beers, T. C., Placco, V. M., et al. 2016, ApJ, 833, 20Yoon, S.-C., Dierks, A., & Langer, N. 2012, A&A, 542, A113Yoon, S.-C. & Langer, N. 2005, A&A, 443, 643Zahn, J.-P. 1992, A&A, 265, 115Zhang, L., Karlsson, T., Christlieb, N., et al. 2011, A&A, 528, A92

Appendix A

Individual references for the considered stars include Jacobsonet al. (2015), Roederer et al. (2014b), Andrievsky et al. (2007),Hollek et al. (2011), Spite et al. (2006), Bonifacio et al. (2007),Bonifacio et al. (2009), Lai et al. (2008), Spite et al. (2005), Co-hen et al. (2013), Honda et al. (2004), Lai et al. (2007), An-drievsky et al. (2010), Andrievsky et al. (2008), Cayrel et al.(2004), Honda et al. (2011), Allen et al. (2012), Zhang et al.(2011), Barklem et al. (2005), Roederer et al. (2014a), Roed-erer et al. (2009), Venn et al. (2004), Aoki et al. (2009), Sbor-done et al. (2010), Preston et al. (2006), Masseron et al. (2012),Spite et al. (2014), Aoki et al. (2005), Sivarani et al. (2006),Siqueira Mello et al. (2014), Masseron et al. (2006), Boesgaardet al. (2011), Placco et al. (2016a), Ren et al. (2012), Placcoet al. (2014a), Hansen et al. (2015), Hansen et al. (2014), Yonget al. (2013), Aoki et al. (2007), Frebel et al. (2007), Cohen et al.(2006), Li et al. (2015), Li et al. (2015), Matsuno et al. (2017),Aoki et al. (2018), Aoki et al. (2008), Aoki et al. (2013), Boni-facio et al. (2018), Bonifacio et al. (2015), Bandyopadhyay et al.(2018), Matsuno et al. (2017), Behara et al. (2010), Spite et al.(2013), Placco et al. (2015), Aguado et al. (2016), Susmitha Raniet al. (2016), Aoki (2010).

Appendix B



vv0

vv1

vv2

vv3

vv4

vv5

vv6

vv7

2MASSJ020318602MASSJ10242264

BD-18_5550BD-20_6008

BS16076-006BS16080-054BS16084-160BS16467-062BS16469-075BS16477-003BS16550-087BS16920-017BS16928-053BS16929-005BS16968-061BS16981-009CS22166-016CS22169-035CS22172-002CS22183-031CS22185-007CS22186-023CS22189-009CS22873-072CS22873-128CS22873-166CS22877-001CS22877-011CS22878-002CS22878-101CS22879-012CS22879-094CS22880-067CS22880-086CS22888-031CS22891-209CS22891-221CS22892-052CS22893-010CS22894-019CS22897-008CS22898-047CS22941-017CS22942-002CS22942-035CS22943-137CS22944-032CS22945-031CS22948-066CS22949-030CS22949-048CS22952-015CS22953-003CS22953-037CS22954-004CS22955-174CS22956-050CS22956-114CS22957-013CS22957-022CS22957-027CS22958-042CS22958-083CS22960-010CS22960-029CS22960-048CS22960-053CS22964-183CS22965-016CS22965-054CS22966-011CS22968-001CS22968-014CS22968-029CS29491-053CS29493-090CS29498-043CS29502-042CS29502-092CS29504-006CS29506-090CS29516-024CS29527-015CS29528-041CS30308-035CS30312-044CS30312-059CS30314-067CS30315-029CS30322-023CS30325-094CS30339-015CS30339-073CS30492-016CS30492-110CS31072-118CS31082-001

G190-15G206-34G64-12G64-37

HD126587HD200654HD237846HD340279HD88609

HE0005-0002HE0008-3842HE0009-6039HE0011-0035HE0013-0257HE0013-0522

HE0015+0048HE0017-4346HE0017-4838HE0037-0348HE0037-2657HE0039-4154HE0044-2459HE0048-6408HE0056-3022HE0102-0633HE0103-0357HE0104-4007HE0104-5300HE0130-1749HE0131-2740HE0132-2439HE0134-1519HE0139-2826HE0146-1548HE0157-3335HE0240-6105HE0243-5238HE0251-3216

HE0302-3417A

vv0

vv1

vv2

vv3

vv4

vv5

vv6

vv7

HE0305-5442HE0312-5200

HE0316+0214HE0323-4529

HE0324+0152AHE0336-2412HE0344-0243HE0353-6024HE0401-0138HE0401-3835HE0411-5725

HE0420+0123AHE0432-0923

HE0432-1005AHE0440-1049HE0450-4705HE0450-4902HE0454-4758HE0547-4539HE1005-1439HE1029-0546HE1054-0059HE1116-0634HE1124-2335HE1148-0037HE1150-0428HE1201-1512HE1214-1819HE1246-1344HE1249-3121

HE1252+0044HE1258-1317

HE1300+0157HE1300-0641HE1300-0642HE1300-2431HE1311-0131HE1317-0407

HE1320+0139HE1320-1339HE1338-0052HE1347-1025HE1351-1049HE1356-0622HE1357-0123HE1410-0004HE1419-1759HE1422-0818HE1439-1420

HE1456+0230HE1506-0113HE2123-0329HE2138-0314HE2139-1851HE2141-3741HE2204-4034HE2216-0621HE2217-4053HE2228-3806HE2233-4724HE2238-0131HE2249-1704

HE2302-2154AHE2304-4153HE2314-1554HE2318-1621HE2323-6549HE2331-7155HE2333-1358HE2357-0701

LAMOSTJ0006+10LAMOSTJ0126+01LAMOSTJ0326+02LAMOSTJ110901.LAMOSTJ141002.

LAMOSTJ1626+17LAMOSTJ2217+21

SDSS0126+06SDSSJ0002+2928SDSSJ0126+0607SDSSJ0140+2344SDSSJ0212+0137SDSSJ0259+0057SDSSJ0351+1026SDSSJ0723+3637SDSSJ0826+6125SDSSJ1036+1212SDSSJ1143+2020SDSSJ1204+1201SDSSJ1245-0738SDSSJ1322+0123SDSSJ1341+4741SDSSJ134338.67SDSSJ1349-0229

SDSSJ1349+1407SDSSJ1422+0031SDSSJ142441.87SDSSJ142441.88

SDSSJ1613+5309SDSSJ170339.60

SDSSJ1746+2455SMSSJ002148.06SMSSJ004037.56SMSSJ005953.98SMSSJ010332.63SMSSJ010651.91SMSSJ010839.58SMSSJ015941.53SMSSJ022410.38SMSSJ022423.27SMSSJ023147.96SMSSJ024643.28SMSSJ024858.41SMSSJ031556.09SMSSJ032132.29SMSSJ033005.90SMSSJ040148.04SMSSJ051008.62SMSSJ063447.15SMSSJ065014.40SMSSJ085924.06SMSSJ093209.41SMSSJ094029.05SMSSJ123246.06SMSSJ125804.65SMSSJ143511.34SMSSJ173823.36SMSSJ183246.49SMSSJ184825.29SMSSJ190549.33SMSSJ190931.13SMSSJ200228.85SMSSJ200654.42SMSSJ215805.81SMSSJ225851.25SMSSJ230013.16

1

2

3

4

5

6

7

8

9

>10χ

2

Fig. 14. Summary plot of the abundance fitting of the 272 EMP stars with the eight source star models. For a given EMP star (y-axis label) and agiven source star model (x-axis label), the colour indicates the best χ2 found.



6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: BD-18_5550Teff =4660 K logg =1.05

vv6 (χ2 ,χ 2ν ) = (1.74,0.87)

vv7 (χ2 ,χ 2ν ) = (2.28,1.14)

vv4 (χ2 ,χ 2ν ) = (4.36,2.18)

vv5 (χ2 ,χ 2ν ) = (4.56,2.28)

vv3 (χ2 ,χ 2ν ) = (5.38,2.69)

vv1 (χ2 ,χ 2ν ) = (5.53,2.76)

vv2 (χ2 ,χ 2ν ) = (5.76,2.88)

vv0 (χ2 ,χ 2ν ) = (5.94,2.97)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

[X/H

]


: BS16076-006Teff =5199 K logg =3.0

vv2 (χ2 ,χ 2ν ) = (0.6,0.6)

vv1 (χ2 ,χ 2ν ) = (0.6,0.6)

vv0 (χ2 ,χ 2ν ) = (0.62,0.62)

vv3 (χ2 ,χ 2ν ) = (0.66,0.66)

vv4 (χ2 ,χ 2ν ) = (0.68,0.68)

vv5 (χ2 ,χ 2ν ) = (0.82,0.82)

vv6 (χ2 ,χ 2ν ) = (0.84,0.84)

vv7 (χ2 ,χ 2ν ) = (0.85,0.85)

0.5

0.0

0.5

1.0

1.5

2.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

[X/H

]


: BS16084-160Teff =4728 K logg =1.26

vv6 (χ2 ,χ 2ν ) = (3.19,1.06)

vv7 (χ2 ,χ 2ν ) = (3.67,1.22)

vv2 (χ2 ,χ 2ν ) = (3.88,1.29)

vv5 (χ2 ,χ 2ν ) = (4.06,1.35)

vv4 (χ2 ,χ 2ν ) = (4.3,1.43)

vv1 (χ2 ,χ 2ν ) = (4.33,1.44)

vv3 (χ2 ,χ 2ν ) = (4.63,1.54)

vv0 (χ2 ,χ 2ν ) = (4.73,1.58)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: BS16467-062Teff =5364 K logg =3.0

vv6 (χ2 ,χ 2ν ) = (0.16,0.08)

vv7 (χ2 ,χ 2ν ) = (0.18,0.09)

vv3 (χ2 ,χ 2ν ) = (0.2,0.1)

vv1 (χ2 ,χ 2ν ) = (0.2,0.1)

vv2 (χ2 ,χ 2ν ) = (0.2,0.1)

vv0 (χ2 ,χ 2ν ) = (0.2,0.1)

vv4 (χ2 ,χ 2ν ) = (0.22,0.11)

vv5 (χ2 ,χ 2ν ) = (0.23,0.11)

0

1

2

3lo

g(12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

[X/H

]


: BS16477-003Teff =4919 K logg =2.02

vv6 (χ2 ,χ 2ν ) = (2.49,1.24)

vv7 (χ2 ,χ 2ν ) = (2.94,1.47)

vv4 (χ2 ,χ 2ν ) = (3.82,1.91)

vv5 (χ2 ,χ 2ν ) = (4.02,2.01)

vv3 (χ2 ,χ 2ν ) = (4.5,2.25)

vv2 (χ2 ,χ 2ν ) = (5.09,2.54)

vv1 (χ2 ,χ 2ν ) = (5.23,2.61)

vv0 (χ2 ,χ 2ν ) = (5.24,2.62)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: BS16920-017Teff =4760 K logg =1.2

vv5 (χ2 ,χ 2ν ) = (1.69,0.84)

vv6 (χ2 ,χ 2ν ) = (2.07,1.03)

vv7 (χ2 ,χ 2ν ) = (2.17,1.09)

vv4 (χ2 ,χ 2ν ) = (3.72,1.86)

vv3 (χ2 ,χ 2ν ) = (5.02,2.51)

vv2 (χ2 ,χ 2ν ) = (5.4,2.7)

vv1 (χ2 ,χ 2ν ) = (6.01,3.01)

vv0 (χ2 ,χ 2ν ) = (6.51,3.25)

0

1

2

3

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: BS16981-009Teff =5259 K logg =2.92

vv6 (χ2 ,χ 2ν ) = (1.84,1.84)

vv7 (χ2 ,χ 2ν ) = (2.15,2.15)

vv5 (χ2 ,χ 2ν ) = (2.83,2.83)

vv1 (χ2 ,χ 2ν ) = (2.84,2.84)

vv3 (χ2 ,χ 2ν ) = (2.84,2.84)

vv2 (χ2 ,χ 2ν ) = (2.85,2.85)

vv4 (χ2 ,χ 2ν ) = (2.85,2.85)

vv0 (χ2 ,χ 2ν ) = (2.96,2.96)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

1

[X/H

]


: CS22873-072Teff =6030 K logg =3.7

vv6 (χ2 ,χ 2ν ) = (1.86,0.93)

vv7 (χ2 ,χ 2ν ) = (2.59,1.29)

vv4 (χ2 ,χ 2ν ) = (4.06,2.03)

vv5 (χ2 ,χ 2ν ) = (4.31,2.16)

vv3 (χ2 ,χ 2ν ) = (4.51,2.25)

vv2 (χ2 ,χ 2ν ) = (4.79,2.4)

vv1 (χ2 ,χ 2ν ) = (5.19,2.6)

vv0 (χ2 ,χ 2ν ) = (5.58,2.79)

0

1

2

3

4

5

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H


: CS22877-001Teff =4790 K logg =1.45

vv3 (χ2 ,χ 2ν ) = (1.61,0.81)

vv4 (χ2 ,χ 2ν ) = (1.71,0.86)

vv2 (χ2 ,χ 2ν ) = (1.93,0.97)

vv6 (χ2 ,χ 2ν ) = (2.6,1.3)

vv5 (χ2 ,χ 2ν ) = (2.65,1.32)

vv1 (χ2 ,χ 2ν ) = (2.74,1.37)

vv7 (χ2 ,χ 2ν ) = (3.01,1.5)

vv0 (χ2 ,χ 2ν ) = (3.45,1.73)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

5

4

3

2

1

0

1

[X/H

]


: CS22888-031Teff =5810 K logg =3.5

vv3 (χ2 ,χ 2ν ) = (2.38,1.19)

vv4 (χ2 ,χ 2ν ) = (2.42,1.21)

vv2 (χ2 ,χ 2ν ) = (2.43,1.21)

vv6 (χ2 ,χ 2ν ) = (2.44,1.22)

vv7 (χ2 ,χ 2ν ) = (2.51,1.25)

vv5 (χ2 ,χ 2ν ) = (2.51,1.25)

vv1 (χ2 ,χ 2ν ) = (2.55,1.28)

vv0 (χ2 ,χ 2ν ) = (2.73,1.36)

1

0

1

2

3

4

5

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS22891-209Teff =4620 K logg =0.95

vv4 (χ2 ,χ 2ν ) = (3.48,1.74)

vv7 (χ2 ,χ 2ν ) = (3.72,1.86)

vv6 (χ2 ,χ 2ν ) = (3.73,1.86)

vv5 (χ2 ,χ 2ν ) = (3.92,1.96)

vv3 (χ2 ,χ 2ν ) = (3.93,1.97)

vv2 (χ2 ,χ 2ν ) = (4.16,2.08)

vv1 (χ2 ,χ 2ν ) = (4.63,2.32)

vv0 (χ2 ,χ 2ν ) = (5.05,2.52)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS22891-221Teff =5290 K logg =2.8

vv6 (χ2 ,χ 2ν ) = (3.21,1.61)

vv7 (χ2 ,χ 2ν ) = (3.52,1.76)

vv4 (χ2 ,χ 2ν ) = (4.02,2.01)

vv3 (χ2 ,χ 2ν ) = (4.08,2.04)

vv2 (χ2 ,χ 2ν ) = (4.16,2.08)

vv1 (χ2 ,χ 2ν ) = (4.31,2.16)

vv5 (χ2 ,χ 2ν ) = (4.33,2.17)

vv0 (χ2 ,χ 2ν ) = (4.62,2.31)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS22892-052Teff =4690 K logg =1.15

vv6 (χ2 ,χ 2ν ) = (0.16,0.08)

vv7 (χ2 ,χ 2ν ) = (0.6,0.3)

vv4 (χ2 ,χ 2ν ) = (1.93,0.96)

vv5 (χ2 ,χ 2ν ) = (2.13,1.06)

vv3 (χ2 ,χ 2ν ) = (3.13,1.57)

vv2 (χ2 ,χ 2ν ) = (4.14,2.07)

vv1 (χ2 ,χ 2ν ) = (4.93,2.47)

vv0 (χ2 ,χ 2ν ) = (5.48,2.74)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

5

4

3

2

[X/H

]


: CS22942-002Teff =5010 K logg =2.0

vv3 (χ2 ,χ 2ν ) = (3.7,1.85)

vv2 (χ2 ,χ 2ν ) = (3.71,1.85)

vv4 (χ2 ,χ 2ν ) = (3.71,1.86)

vv1 (χ2 ,χ 2ν ) = (3.73,1.86)

vv5 (χ2 ,χ 2ν ) = (3.99,1.99)

vv6 (χ2 ,χ 2ν ) = (4.02,2.01)

vv7 (χ2 ,χ 2ν ) = (4.03,2.02)

vv0 (χ2 ,χ 2ν ) = (4.1,2.05)

1.0

0.5

0.0

0.5

1.0

1.5

2.0

2.5

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS22948-066Teff =4830 K logg =1.55

vv4 (χ2 ,χ 2ν ) = (3.84,1.92)

vv3 (χ2 ,χ 2ν ) = (4.13,2.07)

vv5 (χ2 ,χ 2ν ) = (4.28,2.14)

vv2 (χ2 ,χ 2ν ) = (4.31,2.16)

vv1 (χ2 ,χ 2ν ) = (4.69,2.34)

vv6 (χ2 ,χ 2ν ) = (4.8,2.4)

vv7 (χ2 ,χ 2ν ) = (4.96,2.48)

vv0 (χ2 ,χ 2ν ) = (5.05,2.52)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/13

C)

Fig. 15. EMP stars having at least one source star model with χ2ν < 2. Red and green circles denote CEMP ([C/Fe] > 0.7) and C-normal EMP

stars, respectively. For evolved EMP stars (log g < 2), [N/H] and log(12C13C) are shown as light red or green symbols and are considered upperand lower limits, respectively. When available, the correction on the C abundance from Placco et al. (2014b) is taken into account. In this case, the[C/H] ratio before (after) correction is shown by a light (normal) red or green symbol. When available, the observational uncertainty is shown bya black bar. If it is not available, the mean observational uncertainty of the EMP sample (Sect. 3.3) is shown as a grey bar.



6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: CS22949-030Teff =5890 K logg =3.6

vv6 (χ2 ,χ 2ν ) = (4.98,1.66)

vv7 (χ2 ,χ 2ν ) = (6.17,2.06)

vv5 (χ2 ,χ 2ν ) = (7.79,2.6)

vv4 (χ2 ,χ 2ν ) = (9.2,3.07)

vv3 (χ2 ,χ 2ν ) = (11.07,3.69)

vv2 (χ2 ,χ 2ν ) = (12.53,4.18)

vv1 (χ2 ,χ 2ν ) = (15.2,5.07)

vv0 (χ2 ,χ 2ν ) = (16.13,5.38)

0

1

2

3

4

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS22960-010Teff =5280 K logg =4.0

vv6 (χ2 ,χ 2ν ) = (2.4,1.2)

vv7 (χ2 ,χ 2ν ) = (2.84,1.42)

vv1 (χ2 ,χ 2ν ) = (5.12,2.56)

vv0 (χ2 ,χ 2ν ) = (5.28,2.64)

vv5 (χ2 ,χ 2ν ) = (5.39,2.69)

vv2 (χ2 ,χ 2ν ) = (5.48,2.74)

vv4 (χ2 ,χ 2ν ) = (5.5,2.75)

vv3 (χ2 ,χ 2ν ) = (5.54,2.77)

0

1

2

3

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS22964-183Teff =6010 K logg =3.65

vv6 (χ2 ,χ 2ν ) = (0.68,0.68)

vv7 (χ2 ,χ 2ν ) = (0.85,0.85)

vv4 (χ2 ,χ 2ν ) = (1.16,1.16)

vv5 (χ2 ,χ 2ν ) = (1.31,1.31)

vv3 (χ2 ,χ 2ν ) = (1.36,1.36)

vv2 (χ2 ,χ 2ν ) = (1.49,1.49)

vv1 (χ2 ,χ 2ν ) = (1.49,1.49)

vv0 (χ2 ,χ 2ν ) = (1.58,1.58)

0

1

2

3

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: CS22965-054Teff =6050 K logg =3.7

vv7 (χ2 ,χ 2ν ) = (2.36,0.79)

vv6 (χ2 ,χ 2ν ) = (2.38,0.79)

vv5 (χ2 ,χ 2ν ) = (2.58,0.86)

vv4 (χ2 ,χ 2ν ) = (3.84,1.28)

vv3 (χ2 ,χ 2ν ) = (5.57,1.86)

vv2 (χ2 ,χ 2ν ) = (7.26,2.42)

vv1 (χ2 ,χ 2ν ) = (10.29,3.43)

vv0 (χ2 ,χ 2ν ) = (11.12,3.71)

0

1

2

3

4lo

g(12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS22966-011Teff =6204 K logg =4.75

vv6 (χ2 ,χ 2ν ) = (3.92,1.96)

vv7 (χ2 ,χ 2ν ) = (4.06,2.03)

vv4 (χ2 ,χ 2ν ) = (5.47,2.74)

vv5 (χ2 ,χ 2ν ) = (5.53,2.77)

vv3 (χ2 ,χ 2ν ) = (6.1,3.05)

vv2 (χ2 ,χ 2ν ) = (6.37,3.19)

vv1 (χ2 ,χ 2ν ) = (6.79,3.39)

vv0 (χ2 ,χ 2ν ) = (7.16,3.58)

0

1

2

3

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: CS22968-001Teff =5940 K logg =3.65

vv6 (χ2 ,χ 2ν ) = (3.67,1.84)

vv7 (χ2 ,χ 2ν ) = (4.2,2.1)

vv5 (χ2 ,χ 2ν ) = (4.77,2.39)

vv4 (χ2 ,χ 2ν ) = (5.23,2.61)

vv3 (χ2 ,χ 2ν ) = (6.55,3.28)

vv2 (χ2 ,χ 2ν ) = (6.98,3.49)

vv1 (χ2 ,χ 2ν ) = (7.66,3.83)

vv0 (χ2 ,χ 2ν ) = (8.22,4.11)

0

1

2

3

4

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: CS29498-043Teff =4440 K logg =0.5

vv6 (χ2 ,χ 2ν ) = (3.39,1.13)

vv7 (χ2 ,χ 2ν ) = (4.07,1.36)

vv4 (χ2 ,χ 2ν ) = (7.44,2.48)

vv5 (χ2 ,χ 2ν ) = (7.48,2.49)

vv3 (χ2 ,χ 2ν ) = (9.46,3.15)

vv2 (χ2 ,χ 2ν ) = (12.35,4.12)

vv1 (χ2 ,χ 2ν ) = (21.25,7.08)

vv0 (χ2 ,χ 2ν ) = (23.88,7.96)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

[X/H

]


: CS29502-042Teff =5100 K logg =2.5

vv6 (χ2 ,χ 2ν ) = (5.42,1.81)

vv7 (χ2 ,χ 2ν ) = (5.51,1.84)

vv5 (χ2 ,χ 2ν ) = (6.03,2.01)

vv4 (χ2 ,χ 2ν ) = (6.03,2.01)

vv1 (χ2 ,χ 2ν ) = (6.11,2.04)

vv0 (χ2 ,χ 2ν ) = (6.11,2.04)

vv3 (χ2 ,χ 2ν ) = (6.11,2.04)

vv2 (χ2 ,χ 2ν ) = (6.15,2.05)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H


: CS29502-092Teff =4820 K logg =1.5

vv6 (χ2 ,χ 2ν ) = (0.54,0.18)

vv7 (χ2 ,χ 2ν ) = (1.08,0.36)

vv4 (χ2 ,χ 2ν ) = (1.94,0.65)

vv5 (χ2 ,χ 2ν ) = (2.23,0.74)

vv3 (χ2 ,χ 2ν ) = (2.63,0.88)

vv2 (χ2 ,χ 2ν ) = (3.68,1.23)

vv1 (χ2 ,χ 2ν ) = (5.0,1.67)

vv0 (χ2 ,χ 2ν ) = (5.77,1.92)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: CS29504-006Teff =6150 K logg =3.7

vv6 (χ2 ,χ 2ν ) = (0.39,0.39)

vv7 (χ2 ,χ 2ν ) = (0.74,0.74)

vv4 (χ2 ,χ 2ν ) = (0.98,0.98)

vv5 (χ2 ,χ 2ν ) = (1.46,1.46)

vv3 (χ2 ,χ 2ν ) = (1.74,1.74)

vv2 (χ2 ,χ 2ν ) = (2.8,2.8)

vv1 (χ2 ,χ 2ν ) = (3.97,3.97)

vv0 (χ2 ,χ 2ν ) = (4.12,4.12)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS29527-015Teff =6242 K logg =4.0

vv3 (χ2 ,χ 2ν ) = (1.42,0.71)

vv2 (χ2 ,χ 2ν ) = (1.47,0.73)

vv1 (χ2 ,χ 2ν ) = (1.47,0.73)

vv7 (χ2 ,χ 2ν ) = (1.48,0.74)

vv0 (χ2 ,χ 2ν ) = (1.5,0.75)

vv6 (χ2 ,χ 2ν ) = (1.54,0.77)

vv4 (χ2 ,χ 2ν ) = (1.64,0.82)

vv5 (χ2 ,χ 2ν ) = (1.66,0.83)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: CS30314-067Teff =4320 K logg =0.5

vv6 (χ2 ,χ 2ν ) = (0.85,0.43)

vv7 (χ2 ,χ 2ν ) = (1.27,0.63)

vv4 (χ2 ,χ 2ν ) = (3.02,1.51)

vv5 (χ2 ,χ 2ν ) = (3.18,1.59)

vv3 (χ2 ,χ 2ν ) = (3.8,1.9)

vv2 (χ2 ,χ 2ν ) = (4.22,2.11)

vv1 (χ2 ,χ 2ν ) = (4.98,2.49)

vv0 (χ2 ,χ 2ν ) = (5.4,2.7)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

[X/H

]


: CS30315-029Teff =4570 K logg =0.99

vv6 (χ2 ,χ 2ν ) = (1.53,1.53)

vv7 (χ2 ,χ 2ν ) = (1.82,1.82)

vv1 (χ2 ,χ 2ν ) = (2.57,2.57)

vv2 (χ2 ,χ 2ν ) = (2.58,2.58)

vv4 (χ2 ,χ 2ν ) = (2.63,2.63)

vv5 (χ2 ,χ 2ν ) = (2.69,2.69)

vv0 (χ2 ,χ 2ν ) = (2.7,2.7)

vv3 (χ2 ,χ 2ν ) = (2.76,2.76)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

1

[X/H

]


: G206-34Teff =5930 K logg =3.6

vv6 (χ2 ,χ 2ν ) = (2.25,1.12)

vv7 (χ2 ,χ 2ν ) = (2.56,1.28)

vv5 (χ2 ,χ 2ν ) = (3.78,1.89)

vv4 (χ2 ,χ 2ν ) = (4.06,2.03)

vv3 (χ2 ,χ 2ν ) = (4.38,2.19)

vv2 (χ2 ,χ 2ν ) = (4.95,2.47)

vv1 (χ2 ,χ 2ν ) = (5.85,2.93)

vv0 (χ2 ,χ 2ν ) = (6.73,3.36)

0

1

2

3

4

5

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: G64-12Teff =6463 K logg =4.26

vv7 (χ2 ,χ 2ν ) = (1.7,0.57)

vv6 (χ2 ,χ 2ν ) = (1.85,0.62)

vv4 (χ2 ,χ 2ν ) = (4.18,1.39)

vv5 (χ2 ,χ 2ν ) = (4.51,1.5)

vv3 (χ2 ,χ 2ν ) = (5.36,1.79)

vv2 (χ2 ,χ 2ν ) = (7.98,2.66)

vv1 (χ2 ,χ 2ν ) = (11.58,3.86)

vv0 (χ2 ,χ 2ν ) = (15.45,5.15)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0lo

g(12

C/13

C)

Fig. 15. Continued.



6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: G64-37Teff =6570 K logg =4.4

vv6 (χ2 ,χ 2ν ) = (0.59,0.2)

vv7 (χ2 ,χ 2ν ) = (1.11,0.37)

vv4 (χ2 ,χ 2ν ) = (3.11,1.04)

vv5 (χ2 ,χ 2ν ) = (3.49,1.16)

vv3 (χ2 ,χ 2ν ) = (4.33,1.44)

vv2 (χ2 ,χ 2ν ) = (6.77,2.26)

vv1 (χ2 ,χ 2ν ) = (10.18,3.39)

vv0 (χ2 ,χ 2ν ) = (13.72,4.57)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HD237846Teff =4730 K logg =1.3

vv7 (χ2 ,χ 2ν ) = (2.49,1.24)

vv6 (χ2 ,χ 2ν ) = (2.5,1.25)

vv4 (χ2 ,χ 2ν ) = (4.74,2.37)

vv5 (χ2 ,χ 2ν ) = (5.07,2.53)

vv3 (χ2 ,χ 2ν ) = (5.4,2.7)

vv2 (χ2 ,χ 2ν ) = (6.74,3.37)

vv1 (χ2 ,χ 2ν ) = (8.99,4.5)

vv0 (χ2 ,χ 2ν ) = (11.45,5.73)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

1

[X/H

]


: HD340279Teff =5950 K logg =3.65

vv6 (χ2 ,χ 2ν ) = (1.32,1.32)

vv7 (χ2 ,χ 2ν ) = (1.7,1.7)

vv4 (χ2 ,χ 2ν ) = (2.88,2.88)

vv5 (χ2 ,χ 2ν ) = (2.97,2.97)

vv1 (χ2 ,χ 2ν ) = (3.0,3.0)

vv3 (χ2 ,χ 2ν ) = (3.0,3.0)

vv2 (χ2 ,χ 2ν ) = (3.01,3.01)

vv0 (χ2 ,χ 2ν ) = (3.15,3.15)

0

1

2

3

4

5

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0009-6039Teff =5250 K logg =2.7

vv7 (χ2 ,χ 2ν ) = (1.02,0.51)

vv5 (χ2 ,χ 2ν ) = (1.02,0.51)

vv6 (χ2 ,χ 2ν ) = (1.02,0.51)

vv4 (χ2 ,χ 2ν ) = (1.09,0.54)

vv3 (χ2 ,χ 2ν ) = (1.49,0.75)

vv2 (χ2 ,χ 2ν ) = (1.63,0.82)

vv1 (χ2 ,χ 2ν ) = (1.9,0.95)

vv0 (χ2 ,χ 2ν ) = (2.09,1.04)

0

1

2

3lo

g(12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0015+0048Teff =4600 K logg =0.9

vv6 (χ2 ,χ 2ν ) = (0.94,0.94)

vv7 (χ2 ,χ 2ν ) = (1.19,1.19)

vv4 (χ2 ,χ 2ν ) = (5.21,5.21)

vv5 (χ2 ,χ 2ν ) = (5.56,5.56)

vv3 (χ2 ,χ 2ν ) = (6.83,6.83)

vv2 (χ2 ,χ 2ν ) = (8.17,8.17)

vv1 (χ2 ,χ 2ν ) = (8.93,8.93)

vv0 (χ2 ,χ 2ν ) = (9.26,9.26)

0

1

2

3

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

1

[X/H

]


: HE0017-4346Teff =6198 K logg =3.8

vv5 (χ2 ,χ 2ν ) = (0.06,0.03)

vv4 (χ2 ,χ 2ν ) = (0.53,0.27)

vv6 (χ2 ,χ 2ν ) = (0.56,0.28)

vv7 (χ2 ,χ 2ν ) = (1.08,0.54)

vv3 (χ2 ,χ 2ν ) = (1.84,0.92)

vv2 (χ2 ,χ 2ν ) = (9.5,4.75)

vv1 (χ2 ,χ 2ν ) = (39.5,19.75)

vv0 (χ2 ,χ 2ν ) = (57.94,28.97)

0

1

2

3

4

5

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0017-4838Teff =5149 K logg =2.23

vv3 (χ2 ,χ 2ν ) = (1.93,1.93)

vv1 (χ2 ,χ 2ν ) = (1.94,1.94)

vv2 (χ2 ,χ 2ν ) = (1.94,1.94)

vv4 (χ2 ,χ 2ν ) = (1.94,1.94)

vv5 (χ2 ,χ 2ν ) = (1.94,1.94)

vv6 (χ2 ,χ 2ν ) = (1.96,1.96)

vv0 (χ2 ,χ 2ν ) = (2.02,2.02)

vv7 (χ2 ,χ 2ν ) = (2.03,2.03)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0037-2657Teff =4982 K logg =2.21

vv6 (χ2 ,χ 2ν ) = (1.78,1.78)

vv7 (χ2 ,χ 2ν ) = (1.9,1.9)

vv2 (χ2 ,χ 2ν ) = (1.95,1.95)

vv3 (χ2 ,χ 2ν ) = (1.95,1.95)

vv1 (χ2 ,χ 2ν ) = (1.95,1.95)

vv5 (χ2 ,χ 2ν ) = (1.95,1.95)

vv4 (χ2 ,χ 2ν ) = (1.96,1.96)

vv0 (χ2 ,χ 2ν ) = (2.04,2.04)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H


: HE0102-0633Teff =6012 K logg =3.7

vv6 (χ2 ,χ 2ν ) = (1.18,1.18)

vv7 (χ2 ,χ 2ν ) = (1.38,1.38)

vv4 (χ2 ,χ 2ν ) = (4.49,4.49)

vv5 (χ2 ,χ 2ν ) = (4.73,4.73)

vv3 (χ2 ,χ 2ν ) = (5.41,5.41)

vv2 (χ2 ,χ 2ν ) = (6.08,6.08)

vv1 (χ2 ,χ 2ν ) = (6.18,6.18)

vv0 (χ2 ,χ 2ν ) = (6.38,6.38)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0103-0357Teff =5406 K logg =3.2

vv6 (χ2 ,χ 2ν ) = (2.33,1.17)

vv7 (χ2 ,χ 2ν ) = (2.74,1.37)

vv4 (χ2 ,χ 2ν ) = (5.23,2.61)

vv5 (χ2 ,χ 2ν ) = (5.37,2.69)

vv3 (χ2 ,χ 2ν ) = (6.64,3.32)

vv1 (χ2 ,χ 2ν ) = (6.76,3.38)

vv0 (χ2 ,χ 2ν ) = (7.06,3.53)

vv2 (χ2 ,χ 2ν ) = (7.52,3.76)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0104-5300Teff =4732 K logg =1.43

vv6 (χ2 ,χ 2ν ) = (1.34,1.34)

vv7 (χ2 ,χ 2ν ) = (1.48,1.48)

vv3 (χ2 ,χ 2ν ) = (1.63,1.63)

vv2 (χ2 ,χ 2ν ) = (1.63,1.63)

vv5 (χ2 ,χ 2ν ) = (1.63,1.63)

vv4 (χ2 ,χ 2ν ) = (1.63,1.63)

vv1 (χ2 ,χ 2ν ) = (1.64,1.64)

vv0 (χ2 ,χ 2ν ) = (1.7,1.7)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0132-2439Teff =5294 K logg =2.75

vv2 (χ2 ,χ 2ν ) = (0.29,0.1)

vv7 (χ2 ,χ 2ν ) = (0.35,0.12)

vv6 (χ2 ,χ 2ν ) = (0.36,0.12)

vv5 (χ2 ,χ 2ν ) = (0.38,0.13)

vv4 (χ2 ,χ 2ν ) = (0.47,0.16)

vv3 (χ2 ,χ 2ν ) = (0.55,0.18)

vv1 (χ2 ,χ 2ν ) = (3.97,1.32)

vv0 (χ2 ,χ 2ν ) = (6.03,2.01)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0240-6105Teff =4720 K logg =1.26

vv6 (χ2 ,χ 2ν ) = (1.46,1.46)

vv7 (χ2 ,χ 2ν ) = (1.6,1.6)

vv1 (χ2 ,χ 2ν ) = (1.72,1.72)

vv3 (χ2 ,χ 2ν ) = (1.72,1.72)

vv5 (χ2 ,χ 2ν ) = (1.73,1.73)

vv2 (χ2 ,χ 2ν ) = (1.73,1.73)

vv4 (χ2 ,χ 2ν ) = (1.74,1.74)

vv0 (χ2 ,χ 2ν ) = (1.85,1.85)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: HE0251-3216Teff =5750 K logg =3.7

vv5 (χ2 ,χ 2ν ) = (0.39,0.19)

vv7 (χ2 ,χ 2ν ) = (0.75,0.37)

vv4 (χ2 ,χ 2ν ) = (1.38,0.69)

vv6 (χ2 ,χ 2ν ) = (1.39,0.69)

vv3 (χ2 ,χ 2ν ) = (2.91,1.46)

vv2 (χ2 ,χ 2ν ) = (8.11,4.06)

vv1 (χ2 ,χ 2ν ) = (24.82,12.41)

vv0 (χ2 ,χ 2ν ) = (31.54,15.77)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0305-5442Teff =4904 K logg =1.7

vv6 (χ2 ,χ 2ν ) = (0.94,0.47)

vv7 (χ2 ,χ 2ν ) = (0.99,0.5)

vv3 (χ2 ,χ 2ν ) = (1.35,0.68)

vv2 (χ2 ,χ 2ν ) = (1.36,0.68)

vv1 (χ2 ,χ 2ν ) = (1.42,0.71)

vv4 (χ2 ,χ 2ν ) = (1.44,0.72)

vv5 (χ2 ,χ 2ν ) = (1.45,0.73)

vv0 (χ2 ,χ 2ν ) = (1.56,0.78)

0

1

2

3lo

g(12

C/13

C)

Fig. 15. Continued.



6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0312-5200Teff =5204 K logg =2.6

vv5 (χ2 ,χ 2ν ) = (2.68,1.34)

vv7 (χ2 ,χ 2ν ) = (2.69,1.34)

vv6 (χ2 ,χ 2ν ) = (2.73,1.37)

vv4 (χ2 ,χ 2ν ) = (4.41,2.21)

vv3 (χ2 ,χ 2ν ) = (5.85,2.92)

vv2 (χ2 ,χ 2ν ) = (6.15,3.08)

vv1 (χ2 ,χ 2ν ) = (6.73,3.36)

vv0 (χ2 ,χ 2ν ) = (7.18,3.59)

0

1

2

3

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0323-4529Teff =5127 K logg =2.51

vv6 (χ2 ,χ 2ν ) = (1.99,1.99)

vv7 (χ2 ,χ 2ν ) = (2.34,2.34)

vv5 (χ2 ,χ 2ν ) = (3.18,3.18)

vv3 (χ2 ,χ 2ν ) = (3.19,3.19)

vv1 (χ2 ,χ 2ν ) = (3.2,3.2)

vv2 (χ2 ,χ 2ν ) = (3.2,3.2)

vv4 (χ2 ,χ 2ν ) = (3.21,3.21)

vv0 (χ2 ,χ 2ν ) = (3.34,3.34)

0

1

2

3

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0353-6024Teff =5320 K logg =3.15

vv6 (χ2 ,χ 2ν ) = (1.08,1.08)

vv7 (χ2 ,χ 2ν ) = (1.26,1.26)

vv5 (χ2 ,χ 2ν ) = (1.53,1.53)

vv3 (χ2 ,χ 2ν ) = (1.53,1.53)

vv2 (χ2 ,χ 2ν ) = (1.54,1.54)

vv1 (χ2 ,χ 2ν ) = (1.54,1.54)

vv4 (χ2 ,χ 2ν ) = (1.54,1.54)

vv0 (χ2 ,χ 2ν ) = (1.62,1.62)

0

1

2

3

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0401-3835Teff =5458 K logg =3.2

vv7 (χ2 ,χ 2ν ) = (1.1,0.55)

vv6 (χ2 ,χ 2ν ) = (1.26,0.63)

vv5 (χ2 ,χ 2ν ) = (3.24,1.62)

vv4 (χ2 ,χ 2ν ) = (3.42,1.71)

vv3 (χ2 ,χ 2ν ) = (5.32,2.66)

vv2 (χ2 ,χ 2ν ) = (6.79,3.39)

vv1 (χ2 ,χ 2ν ) = (8.04,4.02)

vv0 (χ2 ,χ 2ν ) = (8.72,4.36)

0

1

2

3lo

g(12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0411-5725Teff =5000 K logg =2.1

vv6 (χ2 ,χ 2ν ) = (3.6,1.8)

vv7 (χ2 ,χ 2ν ) = (3.84,1.92)

vv4 (χ2 ,χ 2ν ) = (4.99,2.5)

vv5 (χ2 ,χ 2ν ) = (5.01,2.5)

vv3 (χ2 ,χ 2ν ) = (5.62,2.81)

vv2 (χ2 ,χ 2ν ) = (5.84,2.92)

vv1 (χ2 ,χ 2ν ) = (6.18,3.09)

vv0 (χ2 ,χ 2ν ) = (6.53,3.26)

0

1

2

3

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE0450-4705Teff =5429 K logg =3.34

vv6 (χ2 ,χ 2ν ) = (0.34,0.34)

vv7 (χ2 ,χ 2ν ) = (0.58,0.58)

vv4 (χ2 ,χ 2ν ) = (1.44,1.44)

vv5 (χ2 ,χ 2ν ) = (1.61,1.61)

vv3 (χ2 ,χ 2ν ) = (1.76,1.76)

vv1 (χ2 ,χ 2ν ) = (2.01,2.01)

vv2 (χ2 ,χ 2ν ) = (2.01,2.01)

vv0 (χ2 ,χ 2ν ) = (2.11,2.11)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

1

[X/H

]


: HE0450-4902Teff =6300 K logg =4.5

vv7 (χ2 ,χ 2ν ) = (3.02,1.01)

vv5 (χ2 ,χ 2ν ) = (4.3,1.43)

vv6 (χ2 ,χ 2ν ) = (4.65,1.55)

vv4 (χ2 ,χ 2ν ) = (5.3,1.77)

vv3 (χ2 ,χ 2ν ) = (7.65,2.55)

vv2 (χ2 ,χ 2ν ) = (19.96,6.65)

vv1 (χ2 ,χ 2ν ) = (41.04,13.68)

vv0 (χ2 ,χ 2ν ) = (47.86,15.95)

0

1

2

3

4

5

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

[X/H

]


: HE0454-4758Teff =5140 K logg =2.4

vv1 (χ2 ,χ 2ν ) = (4.64,1.55)

vv0 (χ2 ,χ 2ν ) = (4.66,1.55)

vv7 (χ2 ,χ 2ν ) = (4.92,1.64)

vv6 (χ2 ,χ 2ν ) = (4.96,1.65)

vv5 (χ2 ,χ 2ν ) = (5.03,1.68)

vv2 (χ2 ,χ 2ν ) = (5.05,1.68)

vv4 (χ2 ,χ 2ν ) = (5.07,1.69)

vv3 (χ2 ,χ 2ν ) = (5.1,1.7)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H


: HE0547-4539Teff =5152 K logg =2.59

vv6 (χ2 ,χ 2ν ) = (1.27,1.27)

vv7 (χ2 ,χ 2ν ) = (1.62,1.62)

vv4 (χ2 ,χ 2ν ) = (2.45,2.45)

vv5 (χ2 ,χ 2ν ) = (2.57,2.57)

vv3 (χ2 ,χ 2ν ) = (2.6,2.6)

vv1 (χ2 ,χ 2ν ) = (2.61,2.61)

vv2 (χ2 ,χ 2ν ) = (2.61,2.61)

vv0 (χ2 ,χ 2ν ) = (2.72,2.72)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: HE1005-1439Teff =5000 K logg =1.9

vv6 (χ2 ,χ 2ν ) = (0.01,0.01)

vv4 (χ2 ,χ 2ν ) = (0.11,0.11)

vv7 (χ2 ,χ 2ν ) = (0.14,0.14)

vv5 (χ2 ,χ 2ν ) = (0.15,0.15)

vv3 (χ2 ,χ 2ν ) = (1.27,1.27)

vv2 (χ2 ,χ 2ν ) = (6.23,6.23)

vv1 (χ2 ,χ 2ν ) = (19.68,19.68)

vv0 (χ2 ,χ 2ν ) = (25.19,25.19)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

[X/H

]


: HE1054-0059Teff =4601 K logg =1.19

vv1 (χ2 ,χ 2ν ) = (1.27,1.27)

vv2 (χ2 ,χ 2ν ) = (1.27,1.27)

vv3 (χ2 ,χ 2ν ) = (1.27,1.27)

vv4 (χ2 ,χ 2ν ) = (1.28,1.28)

vv0 (χ2 ,χ 2ν ) = (1.34,1.34)

vv5 (χ2 ,χ 2ν ) = (1.48,1.48)

vv6 (χ2 ,χ 2ν ) = (1.5,1.5)

vv7 (χ2 ,χ 2ν ) = (1.5,1.5)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE1124-2335Teff =4870 K logg =1.65

vv6 (χ2 ,χ 2ν ) = (2.47,1.24)

vv7 (χ2 ,χ 2ν ) = (2.89,1.45)

vv4 (χ2 ,χ 2ν ) = (4.5,2.25)

vv5 (χ2 ,χ 2ν ) = (4.61,2.3)

vv1 (χ2 ,χ 2ν ) = (5.03,2.51)

vv0 (χ2 ,χ 2ν ) = (5.16,2.58)

vv3 (χ2 ,χ 2ν ) = (5.24,2.62)

vv2 (χ2 ,χ 2ν ) = (5.6,2.8)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

5

4

3

2

1

[X/H

]


: HE1148-0037Teff =5990 K logg =3.7

vv4 (χ2 ,χ 2ν ) = (3.53,1.76)

vv5 (χ2 ,χ 2ν ) = (3.65,1.82)

vv6 (χ2 ,χ 2ν ) = (3.66,1.83)

vv7 (χ2 ,χ 2ν ) = (3.66,1.83)

vv3 (χ2 ,χ 2ν ) = (3.84,1.92)

vv2 (χ2 ,χ 2ν ) = (4.01,2.01)

vv1 (χ2 ,χ 2ν ) = (4.34,2.17)

vv0 (χ2 ,χ 2ν ) = (4.57,2.28)

1

0

1

2

3

log(12

C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: HE1150-0428Teff =5200 K logg =2.5

vv6 (χ2 ,χ 2ν ) = (0.19,0.1)

vv7 (χ2 ,χ 2ν ) = (1.01,0.51)

vv5 (χ2 ,χ 2ν ) = (1.42,0.71)

vv4 (χ2 ,χ 2ν ) = (3.9,1.95)

vv3 (χ2 ,χ 2ν ) = (14.2,7.1)

vv2 (χ2 ,χ 2ν ) = (42.8,21.4)

vv1 (χ2 ,χ 2ν ) = (89.39,44.69)

vv0 (χ2 ,χ 2ν ) = (107.22,53.61)

0

1

2

3

4

log(12

C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: HE1249-3121Teff =5373 K logg =3.4

vv3 (χ2 ,χ 2ν ) = (0.35,0.35)

vv4 (χ2 ,χ 2ν ) = (0.4,0.4)

vv6 (χ2 ,χ 2ν ) = (0.48,0.48)

vv7 (χ2 ,χ 2ν ) = (0.58,0.58)

vv5 (χ2 ,χ 2ν ) = (0.61,0.61)

vv2 (χ2 ,χ 2ν ) = (0.65,0.65)

vv1 (χ2 ,χ 2ν ) = (1.42,1.42)

vv0 (χ2 ,χ 2ν ) = (1.51,1.51)

0

1

2

3

4lo

g(12

C/13

C)

Fig. 15. Continued.



6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE1252+0044Teff =5296 K logg =2.98

vv6 (χ2 ,χ 2ν ) = (1.86,1.86)

vv7 (χ2 ,χ 2ν ) = (2.2,2.2)

vv5 (χ2 ,χ 2ν ) = (3.01,3.01)

vv1 (χ2 ,χ 2ν ) = (3.03,3.03)

vv3 (χ2 ,χ 2ν ) = (3.03,3.03)

vv4 (χ2 ,χ 2ν ) = (3.04,3.04)

vv2 (χ2 ,χ 2ν ) = (3.04,3.04)

vv0 (χ2 ,χ 2ν ) = (3.18,3.18)

0

1

2

3

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE1300+0157Teff =5550 K logg =3.3

vv3 (χ2 ,χ 2ν ) = (4.34,1.45)

vv7 (χ2 ,χ 2ν ) = (4.81,1.6)

vv4 (χ2 ,χ 2ν ) = (5.05,1.68)

vv5 (χ2 ,χ 2ν ) = (5.12,1.71)

vv2 (χ2 ,χ 2ν ) = (5.52,1.84)

vv6 (χ2 ,χ 2ν ) = (6.36,2.12)

vv1 (χ2 ,χ 2ν ) = (8.36,2.79)

vv0 (χ2 ,χ 2ν ) = (11.77,3.92)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE1320+0139Teff =5200 K logg =2.6

vv4 (χ2 ,χ 2ν ) = (0.04,0.02)

vv3 (χ2 ,χ 2ν ) = (0.04,0.02)

vv5 (χ2 ,χ 2ν ) = (0.04,0.02)

vv6 (χ2 ,χ 2ν ) = (0.04,0.02)

vv7 (χ2 ,χ 2ν ) = (0.04,0.02)

vv2 (χ2 ,χ 2ν ) = (0.04,0.02)

vv1 (χ2 ,χ 2ν ) = (0.07,0.04)

vv0 (χ2 ,χ 2ν ) = (0.12,0.06)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: HE1338-0052Teff =5856 K logg =3.7

vv7 (χ2 ,χ 2ν ) = (0.61,0.61)

vv6 (χ2 ,χ 2ν ) = (1.24,1.24)

vv5 (χ2 ,χ 2ν ) = (3.63,3.63)

vv4 (χ2 ,χ 2ν ) = (3.69,3.69)

vv3 (χ2 ,χ 2ν ) = (5.46,5.46)

vv2 (χ2 ,χ 2ν ) = (7.19,7.19)

vv1 (χ2 ,χ 2ν ) = (8.9,8.9)

vv0 (χ2 ,χ 2ν ) = (9.1,9.1)

0

1

2

3

4

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE1347-1025Teff =5195 K logg =2.5

vv2 (χ2 ,χ 2ν ) = (1.7,0.85)

vv3 (χ2 ,χ 2ν ) = (1.7,0.85)

vv1 (χ2 ,χ 2ν ) = (1.74,0.87)

vv4 (χ2 ,χ 2ν ) = (1.8,0.9)

vv0 (χ2 ,χ 2ν ) = (1.85,0.93)

vv5 (χ2 ,χ 2ν ) = (1.88,0.94)

vv7 (χ2 ,χ 2ν ) = (1.89,0.95)

vv6 (χ2 ,χ 2ν ) = (1.89,0.95)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

5

4

3

2

1

0

[X/H

]


: HE1351-1049Teff =5204 K logg =2.85

vv3 (χ2 ,χ 2ν ) = (1.32,1.32)

vv4 (χ2 ,χ 2ν ) = (1.39,1.39)

vv2 (χ2 ,χ 2ν ) = (1.46,1.46)

vv6 (χ2 ,χ 2ν ) = (1.47,1.47)

vv7 (χ2 ,χ 2ν ) = (1.52,1.52)

vv5 (χ2 ,χ 2ν ) = (1.52,1.52)

vv1 (χ2 ,χ 2ν ) = (1.59,1.59)

vv0 (χ2 ,χ 2ν ) = (1.66,1.66)

1

0

1

2

3

4

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE1357-0123Teff =4600 K logg =1.05

vv5 (χ2 ,χ 2ν ) = (0.55,0.27)

vv6 (χ2 ,χ 2ν ) = (0.96,0.48)

vv4 (χ2 ,χ 2ν ) = (1.02,0.51)

vv7 (χ2 ,χ 2ν ) = (1.06,0.53)

vv3 (χ2 ,χ 2ν ) = (1.57,0.78)

vv2 (χ2 ,χ 2ν ) = (1.78,0.89)

vv1 (χ2 ,χ 2ν ) = (2.16,1.08)

vv0 (χ2 ,χ 2ν ) = (2.45,1.22)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: HE1410-0004Teff =5605 K logg =3.5

vv6 (χ2 ,χ 2ν ) = (3.9,1.95)

vv4 (χ2 ,χ 2ν ) = (5.35,2.67)

vv7 (χ2 ,χ 2ν ) = (5.77,2.88)

vv5 (χ2 ,χ 2ν ) = (6.0,3.0)

vv3 (χ2 ,χ 2ν ) = (6.54,3.27)

vv2 (χ2 ,χ 2ν ) = (8.63,4.32)

vv1 (χ2 ,χ 2ν ) = (13.44,6.72)

vv0 (χ2 ,χ 2ν ) = (18.1,9.05)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H


: HE1439-1420Teff =6056 K logg =3.8

vv7 (χ2 ,χ 2ν ) = (0.17,0.09)

vv5 (χ2 ,χ 2ν ) = (0.53,0.27)

vv6 (χ2 ,χ 2ν ) = (0.56,0.28)

vv4 (χ2 ,χ 2ν ) = (1.07,0.53)

vv3 (χ2 ,χ 2ν ) = (3.63,1.82)

vv2 (χ2 ,χ 2ν ) = (10.98,5.49)

vv1 (χ2 ,χ 2ν ) = (26.93,13.47)

vv0 (χ2 ,χ 2ν ) = (31.49,15.75)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE2123-0329Teff =4725 K logg =1.15

vv6 (χ2 ,χ 2ν ) = (1.17,1.17)

vv7 (χ2 ,χ 2ν ) = (1.78,1.78)

vv4 (χ2 ,χ 2ν ) = (4.58,4.58)

vv5 (χ2 ,χ 2ν ) = (4.93,4.93)

vv3 (χ2 ,χ 2ν ) = (5.39,5.39)

vv1 (χ2 ,χ 2ν ) = (5.92,5.92)

vv2 (χ2 ,χ 2ν ) = (5.93,5.93)

vv0 (χ2 ,χ 2ν ) = (6.12,6.12)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE2138-0314Teff =5015 K logg =1.9

vv6 (χ2 ,χ 2ν ) = (1.94,1.94)

vv7 (χ2 ,χ 2ν ) = (2.49,2.49)

vv4 (χ2 ,χ 2ν ) = (3.99,3.99)

vv5 (χ2 ,χ 2ν ) = (4.16,4.16)

vv3 (χ2 ,χ 2ν ) = (4.21,4.21)

vv1 (χ2 ,χ 2ν ) = (4.21,4.21)

vv2 (χ2 ,χ 2ν ) = (4.22,4.22)

vv0 (χ2 ,χ 2ν ) = (4.39,4.39)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE2141-3741Teff =4945 K logg =1.0

vv6 (χ2 ,χ 2ν ) = (2.72,1.36)

vv7 (χ2 ,χ 2ν ) = (3.19,1.6)

vv4 (χ2 ,χ 2ν ) = (5.58,2.79)

vv5 (χ2 ,χ 2ν ) = (5.6,2.8)

vv2 (χ2 ,χ 2ν ) = (7.19,3.59)

vv3 (χ2 ,χ 2ν ) = (7.26,3.63)

vv1 (χ2 ,χ 2ν ) = (7.95,3.98)

vv0 (χ2 ,χ 2ν ) = (8.54,4.27)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: HE2204-4034Teff =6114 K logg =3.8

vv7 (χ2 ,χ 2ν ) = (1.06,0.53)

vv6 (χ2 ,χ 2ν ) = (1.24,0.62)

vv4 (χ2 ,χ 2ν ) = (3.95,1.98)

vv5 (χ2 ,χ 2ν ) = (4.05,2.03)

vv3 (χ2 ,χ 2ν ) = (5.76,2.88)

vv2 (χ2 ,χ 2ν ) = (8.29,4.15)

vv1 (χ2 ,χ 2ν ) = (9.64,4.82)

vv0 (χ2 ,χ 2ν ) = (10.37,5.19)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE2216-0621Teff =4671 K logg =1.27

vv3 (χ2 ,χ 2ν ) = (1.5,1.5)

vv2 (χ2 ,χ 2ν ) = (1.5,1.5)

vv1 (χ2 ,χ 2ν ) = (1.51,1.51)

vv4 (χ2 ,χ 2ν ) = (1.51,1.51)

vv5 (χ2 ,χ 2ν ) = (1.51,1.51)

vv6 (χ2 ,χ 2ν ) = (1.58,1.58)

vv0 (χ2 ,χ 2ν ) = (1.61,1.61)

vv7 (χ2 ,χ 2ν ) = (1.63,1.63)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE2233-4724Teff =4360 K logg =0.4

vv5 (χ2 ,χ 2ν ) = (2.47,1.23)

vv6 (χ2 ,χ 2ν ) = (3.56,1.78)

vv7 (χ2 ,χ 2ν ) = (3.76,1.88)

vv4 (χ2 ,χ 2ν ) = (4.98,2.49)

vv3 (χ2 ,χ 2ν ) = (6.09,3.04)

vv2 (χ2 ,χ 2ν ) = (6.48,3.24)

vv1 (χ2 ,χ 2ν ) = (7.24,3.62)

vv0 (χ2 ,χ 2ν ) = (7.81,3.9)

0

1

2

3

log(

12C/13

C)

Fig. 15. Continued.



6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE2304-4153Teff =4663 K logg =1.01

vv6 (χ2 ,χ 2ν ) = (1.66,1.66)

vv7 (χ2 ,χ 2ν ) = (1.82,1.82)

vv5 (χ2 ,χ 2ν ) = (2.16,2.16)

vv1 (χ2 ,χ 2ν ) = (2.16,2.16)

vv3 (χ2 ,χ 2ν ) = (2.17,2.17)

vv2 (χ2 ,χ 2ν ) = (2.17,2.17)

vv4 (χ2 ,χ 2ν ) = (2.17,2.17)

vv0 (χ2 ,χ 2ν ) = (2.26,2.26)

0

1

2

3

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: HE2331-7155Teff =4900 K logg =1.5

vv6 (χ2 ,χ 2ν ) = (3.22,1.61)

vv7 (χ2 ,χ 2ν ) = (3.97,1.99)

vv4 (χ2 ,χ 2ν ) = (6.26,3.13)

vv5 (χ2 ,χ 2ν ) = (6.56,3.28)

vv3 (χ2 ,χ 2ν ) = (7.01,3.51)

vv2 (χ2 ,χ 2ν ) = (7.3,3.65)

vv1 (χ2 ,χ 2ν ) = (7.64,3.82)

vv0 (χ2 ,χ 2ν ) = (8.0,4.0)

0

1

2

3

4

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: HE2357-0701Teff =5142 K logg =2.4

vv7 (χ2 ,χ 2ν ) = (4.33,1.44)

vv6 (χ2 ,χ 2ν ) = (4.71,1.57)

vv5 (χ2 ,χ 2ν ) = (5.02,1.67)

vv2 (χ2 ,χ 2ν ) = (5.68,1.89)

vv4 (χ2 ,χ 2ν ) = (5.73,1.91)

vv3 (χ2 ,χ 2ν ) = (6.04,2.01)

vv1 (χ2 ,χ 2ν ) = (12.04,4.01)

vv0 (χ2 ,χ 2ν ) = (14.88,4.96)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: LAMOSTJ141002.Teff =6169 K logg =4.21

vv6 (χ2 ,χ 2ν ) = (1.16,1.16)

vv7 (χ2 ,χ 2ν ) = (1.63,1.63)

vv4 (χ2 ,χ 2ν ) = (6.86,6.86)

vv5 (χ2 ,χ 2ν ) = (7.72,7.72)

vv3 (χ2 ,χ 2ν ) = (11.39,11.39)

vv2 (χ2 ,χ 2ν ) = (19.55,19.55)

vv1 (χ2 ,χ 2ν ) = (23.13,23.13)

vv0 (χ2 ,χ 2ν ) = (24.57,24.57)

0

1

2

3

4

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: LAMOSTJ1626+17Teff =5930 K logg =3.6

vv6 (χ2 ,χ 2ν ) = (0.99,0.5)

vv7 (χ2 ,χ 2ν ) = (1.24,0.62)

vv4 (χ2 ,χ 2ν ) = (3.98,1.99)

vv5 (χ2 ,χ 2ν ) = (4.17,2.08)

vv3 (χ2 ,χ 2ν ) = (5.63,2.82)

vv2 (χ2 ,χ 2ν ) = (6.46,3.23)

vv1 (χ2 ,χ 2ν ) = (7.28,3.64)

vv0 (χ2 ,χ 2ν ) = (7.82,3.91)

0

1

2

3

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

1

[X/H

]


: SDSS0126+06Teff =6600 K logg =4.1

vv2 (χ2 ,χ 2ν ) = (0.16,0.16)

vv3 (χ2 ,χ 2ν ) = (0.69,0.69)

vv5 (χ2 ,χ 2ν ) = (2.19,2.19)

vv4 (χ2 ,χ 2ν ) = (2.34,2.34)

vv7 (χ2 ,χ 2ν ) = (3.27,3.27)

vv6 (χ2 ,χ 2ν ) = (3.52,3.52)

vv1 (χ2 ,χ 2ν ) = (8.71,8.71)

vv0 (χ2 ,χ 2ν ) = (17.26,17.26)

0

1

2

3

4

5

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: SDSSJ0002+2928Teff =6150 K logg =4.0

vv5 (χ2 ,χ 2ν ) = (0.08,0.08)

vv4 (χ2 ,χ 2ν ) = (0.14,0.14)

vv3 (χ2 ,χ 2ν ) = (0.16,0.16)

vv6 (χ2 ,χ 2ν ) = (0.5,0.5)

vv7 (χ2 ,χ 2ν ) = (0.92,0.92)

vv2 (χ2 ,χ 2ν ) = (2.87,2.87)

vv1 (χ2 ,χ 2ν ) = (11.65,11.65)

vv0 (χ2 ,χ 2ν ) = (16.37,16.37)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

1

[X/H

]


: SDSSJ0126+0607Teff =6900 K logg =4.0

vv2 (χ2 ,χ 2ν ) = (0.44,0.44)

vv3 (χ2 ,χ 2ν ) = (0.68,0.68)

vv5 (χ2 ,χ 2ν ) = (2.3,2.3)

vv4 (χ2 ,χ 2ν ) = (2.57,2.57)

vv6 (χ2 ,χ 2ν ) = (3.83,3.83)

vv7 (χ2 ,χ 2ν ) = (3.9,3.9)

vv1 (χ2 ,χ 2ν ) = (15.88,15.88)

vv0 (χ2 ,χ 2ν ) = (26.69,26.69)

0

1

2

3

4

5

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

5

4

3

2

1

[X/H


: SDSSJ0140+2344Teff =5848 K logg =4.0

vv0 (χ2 ,χ 2ν ) = (3.81,1.9)

vv1 (χ2 ,χ 2ν ) = (3.85,1.93)

vv2 (χ2 ,χ 2ν ) = (4.19,2.09)

vv3 (χ2 ,χ 2ν ) = (5.34,2.67)

vv4 (χ2 ,χ 2ν ) = (6.85,3.43)

vv5 (χ2 ,χ 2ν ) = (6.86,3.43)

vv7 (χ2 ,χ 2ν ) = (7.89,3.95)

vv6 (χ2 ,χ 2ν ) = (8.11,4.06)

1

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: SDSSJ0212+0137Teff =6333 K logg =4.0

vv2 (χ2 ,χ 2ν ) = (2.41,1.21)

vv3 (χ2 ,χ 2ν ) = (2.7,1.35)

vv1 (χ2 ,χ 2ν ) = (2.71,1.36)

vv0 (χ2 ,χ 2ν ) = (2.76,1.38)

vv4 (χ2 ,χ 2ν ) = (2.91,1.46)

vv6 (χ2 ,χ 2ν ) = (2.99,1.49)

vv5 (χ2 ,χ 2ν ) = (3.38,1.69)

vv7 (χ2 ,χ 2ν ) = (4.15,2.07)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: SDSSJ0259+0057Teff =4550 K logg =5.0

vv5 (χ2 ,χ 2ν ) = (1.45,1.45)

vv6 (χ2 ,χ 2ν ) = (2.27,2.27)

vv4 (χ2 ,χ 2ν ) = (2.4,2.4)

vv7 (χ2 ,χ 2ν ) = (2.42,2.42)

vv3 (χ2 ,χ 2ν ) = (2.99,2.99)

vv2 (χ2 ,χ 2ν ) = (3.22,3.22)

vv1 (χ2 ,χ 2ν ) = (3.65,3.65)

vv0 (χ2 ,χ 2ν ) = (4.0,4.0)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: SDSSJ0351+1026Teff =5450 K logg =3.6

vv6 (χ2 ,χ 2ν ) = (1.07,1.07)

vv7 (χ2 ,χ 2ν ) = (1.37,1.37)

vv4 (χ2 ,χ 2ν ) = (2.99,2.99)

vv5 (χ2 ,χ 2ν ) = (3.39,3.39)

vv3 (χ2 ,χ 2ν ) = (3.47,3.47)

vv2 (χ2 ,χ 2ν ) = (4.95,4.95)

vv1 (χ2 ,χ 2ν ) = (5.99,5.99)

vv0 (χ2 ,χ 2ν ) = (6.35,6.35)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: SDSSJ0723+3637Teff =5150 K logg =2.2

vv3 (χ2 ,χ 2ν ) = (0.3,0.3)

vv2 (χ2 ,χ 2ν ) = (0.58,0.58)

vv4 (χ2 ,χ 2ν ) = (1.2,1.2)

vv5 (χ2 ,χ 2ν ) = (1.25,1.25)

vv1 (χ2 ,χ 2ν ) = (1.28,1.28)

vv0 (χ2 ,χ 2ν ) = (1.58,1.58)

vv7 (χ2 ,χ 2ν ) = (2.11,2.11)

vv6 (χ2 ,χ 2ν ) = (2.28,2.28)

0

1

2

3

log(12

C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: SDSSJ1036+1212Teff =5502 K logg =3.74

vv7 (χ2 ,χ 2ν ) = (0.2,0.1)

vv6 (χ2 ,χ 2ν ) = (0.5,0.25)

vv5 (χ2 ,χ 2ν ) = (0.86,0.43)

vv4 (χ2 ,χ 2ν ) = (1.77,0.89)

vv3 (χ2 ,χ 2ν ) = (2.5,1.25)

vv2 (χ2 ,χ 2ν ) = (4.76,2.38)

vv1 (χ2 ,χ 2ν ) = (15.64,7.82)

vv0 (χ2 ,χ 2ν ) = (19.67,9.83)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(12

C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

1

[X/H

]


: SDSSJ1245-0738Teff =6110 K logg =2.5

vv3 (χ2 ,χ 2ν ) = (1.08,0.54)

vv5 (χ2 ,χ 2ν ) = (2.76,1.38)

vv4 (χ2 ,χ 2ν ) = (3.08,1.54)

vv2 (χ2 ,χ 2ν ) = (3.82,1.91)

vv6 (χ2 ,χ 2ν ) = (4.99,2.49)

vv7 (χ2 ,χ 2ν ) = (7.4,3.7)

vv1 (χ2 ,χ 2ν ) = (23.94,11.97)

vv0 (χ2 ,χ 2ν ) = (38.29,19.15)

0

1

2

3

4

5lo

g(12

C/13

C)

Fig. 15. Continued.



6 7 8 9 10 11 12 13Atomic Number

4

3

2

[X/H

]


: SDSSJ134338.67Teff =5620 K logg =3.44

vv0 (χ2 ,χ 2ν ) = (3.68,1.84)

vv1 (χ2 ,χ 2ν ) = (3.68,1.84)

vv2 (χ2 ,χ 2ν ) = (3.68,1.84)

vv7 (χ2 ,χ 2ν ) = (3.7,1.85)

vv6 (χ2 ,χ 2ν ) = (3.7,1.85)

vv3 (χ2 ,χ 2ν ) = (3.71,1.86)

vv5 (χ2 ,χ 2ν ) = (3.76,1.88)

vv4 (χ2 ,χ 2ν ) = (3.77,1.89)

0.5

0.0

0.5

1.0

1.5

2.0

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

1

[X/H

]


: SDSSJ1349-0229Teff =6200 K logg =4.0

vv6 (χ2 ,χ 2ν ) = (0.16,0.16)

vv4 (χ2 ,χ 2ν ) = (0.51,0.51)

vv5 (χ2 ,χ 2ν ) = (0.61,0.61)

vv7 (χ2 ,χ 2ν ) = (1.42,1.42)

vv3 (χ2 ,χ 2ν ) = (2.22,2.22)

vv2 (χ2 ,χ 2ν ) = (8.66,8.66)

vv1 (χ2 ,χ 2ν ) = (30.27,30.27)

vv0 (χ2 ,χ 2ν ) = (44.59,44.59)

0

1

2

3

4

5

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: SDSSJ1349+1407Teff =6112 K logg =4.0

vv6 (χ2 ,χ 2ν ) = (1.87,0.93)

vv7 (χ2 ,χ 2ν ) = (3.08,1.54)

vv4 (χ2 ,χ 2ν ) = (5.11,2.56)

vv5 (χ2 ,χ 2ν ) = (6.17,3.08)

vv3 (χ2 ,χ 2ν ) = (7.55,3.78)

vv2 (χ2 ,χ 2ν ) = (13.64,6.82)

vv1 (χ2 ,χ 2ν ) = (18.68,9.34)

vv0 (χ2 ,χ 2ν ) = (19.98,9.99)

0

1

2

3

4

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: SDSSJ1422+0031Teff =5200 K logg =2.2

vv6 (χ2 ,χ 2ν ) = (0.04,0.04)

vv7 (χ2 ,χ 2ν ) = (0.26,0.26)

vv4 (χ2 ,χ 2ν ) = (3.19,3.19)

vv5 (χ2 ,χ 2ν ) = (3.9,3.9)

vv3 (χ2 ,χ 2ν ) = (5.6,5.6)

vv2 (χ2 ,χ 2ν ) = (11.06,11.06)

vv1 (χ2 ,χ 2ν ) = (17.31,17.31)

vv0 (χ2 ,χ 2ν ) = (18.61,18.61)

0

1

2

3

4

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: SDSSJ142441.87Teff =6088 K logg =4.34

vv6 (χ2 ,χ 2ν ) = (0.65,0.65)

vv7 (χ2 ,χ 2ν ) = (1.14,1.14)

vv4 (χ2 ,χ 2ν ) = (6.28,6.28)

vv5 (χ2 ,χ 2ν ) = (7.23,7.23)

vv3 (χ2 ,χ 2ν ) = (10.66,10.66)

vv2 (χ2 ,χ 2ν ) = (19.38,19.38)

vv1 (χ2 ,χ 2ν ) = (25.29,25.29)

vv0 (χ2 ,χ 2ν ) = (26.92,26.92)

0

1

2

3

4

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: SDSSJ1613+5309Teff =5350 K logg =2.1

vv7 (χ2 ,χ 2ν ) = (0.01,0.01)

vv6 (χ2 ,χ 2ν ) = (0.01,0.01)

vv4 (χ2 ,χ 2ν ) = (1.05,1.05)

vv5 (χ2 ,χ 2ν ) = (1.4,1.4)

vv3 (χ2 ,χ 2ν ) = (2.69,2.69)

vv2 (χ2 ,χ 2ν ) = (6.99,6.99)

vv1 (χ2 ,χ 2ν ) = (12.07,12.07)

vv0 (χ2 ,χ 2ν ) = (13.39,13.39)

0

1

2

3

4

log(

12C/1

3C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: SDSSJ170339.60Teff =5100 K logg =4.8

vv4 (χ2 ,χ 2ν ) = (1.43,1.43)

vv5 (χ2 ,χ 2ν ) = (1.62,1.62)

vv7 (χ2 ,χ 2ν ) = (1.63,1.63)

vv6 (χ2 ,χ 2ν ) = (1.65,1.65)

vv3 (χ2 ,χ 2ν ) = (1.69,1.69)

vv2 (χ2 ,χ 2ν ) = (1.8,1.8)

vv1 (χ2 ,χ 2ν ) = (2.01,2.01)

vv0 (χ2 ,χ 2ν ) = (2.25,2.25)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

0

[X/H

]


: SDSSJ1746+2455Teff =5350 K logg =2.6

vv6 (χ2 ,χ 2ν ) = (1.46,1.46)

vv7 (χ2 ,χ 2ν ) = (1.76,1.76)

vv5 (χ2 ,χ 2ν ) = (4.34,4.34)

vv4 (χ2 ,χ 2ν ) = (4.53,4.53)

vv3 (χ2 ,χ 2ν ) = (6.78,6.78)

vv2 (χ2 ,χ 2ν ) = (8.43,8.43)

vv1 (χ2 ,χ 2ν ) = (9.58,9.58)

vv0 (χ2 ,χ 2ν ) = (10.17,10.17)

0

1

2

3

4

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

5

4

3

2

1

[X/H


: SMSSJ023147.96Teff =4720 K logg =1.05

vv3 (χ2 ,χ 2ν ) = (2.65,1.32)

vv2 (χ2 ,χ 2ν ) = (2.66,1.33)

vv1 (χ2 ,χ 2ν ) = (2.73,1.37)

vv4 (χ2 ,χ 2ν ) = (2.74,1.37)

vv5 (χ2 ,χ 2ν ) = (2.86,1.43)

vv7 (χ2 ,χ 2ν ) = (2.87,1.43)

vv6 (χ2 ,χ 2ν ) = (2.87,1.44)

vv0 (χ2 ,χ 2ν ) = (2.88,1.44)

1

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

5

4

3

2

1

[X/H

]


: SMSSJ024858.41Teff =4977 K logg =1.6

vv1 (χ2 ,χ 2ν ) = (3.89,1.94)

vv2 (χ2 ,χ 2ν ) = (3.91,1.96)

vv0 (χ2 ,χ 2ν ) = (3.95,1.98)

vv3 (χ2 ,χ 2ν ) = (3.96,1.98)

vv6 (χ2 ,χ 2ν ) = (3.98,1.99)

vv7 (χ2 ,χ 2ν ) = (4.04,2.02)

vv4 (χ2 ,χ 2ν ) = (4.06,2.03)

vv5 (χ2 ,χ 2ν ) = (4.1,2.05)

1

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: SMSSJ125804.65Teff =5040 K logg =1.8

vv6 (χ2 ,χ 2ν ) = (3.4,1.7)

vv5 (χ2 ,χ 2ν ) = (3.42,1.71)

vv7 (χ2 ,χ 2ν ) = (3.45,1.73)

vv4 (χ2 ,χ 2ν ) = (5.97,2.99)

vv3 (χ2 ,χ 2ν ) = (7.79,3.9)

vv2 (χ2 ,χ 2ν ) = (8.22,4.11)

vv1 (χ2 ,χ 2ν ) = (8.98,4.49)

vv0 (χ2 ,χ 2ν ) = (9.57,4.78)

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

5

4

3

2

1

[X/H

]


: SMSSJ173823.36Teff =4558 K logg =0.75

vv5 (χ2 ,χ 2ν ) = (2.14,1.07)

vv6 (χ2 ,χ 2ν ) = (2.29,1.14)

vv7 (χ2 ,χ 2ν ) = (2.39,1.2)

vv4 (χ2 ,χ 2ν ) = (4.48,2.24)

vv3 (χ2 ,χ 2ν ) = (6.01,3.0)

vv2 (χ2 ,χ 2ν ) = (6.42,3.21)

vv1 (χ2 ,χ 2ν ) = (7.11,3.55)

vv0 (χ2 ,χ 2ν ) = (7.63,3.82)

1

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

4

3

2

1

[X/H

]


: SMSSJ184825.29Teff =4518 K logg =0.75

vv4 (χ2 ,χ 2ν ) = (1.98,0.99)

vv5 (χ2 ,χ 2ν ) = (2.01,1.01)

vv3 (χ2 ,χ 2ν ) = (2.36,1.18)

vv2 (χ2 ,χ 2ν ) = (2.55,1.28)

vv6 (χ2 ,χ 2ν ) = (2.69,1.35)

vv7 (χ2 ,χ 2ν ) = (2.85,1.42)

vv1 (χ2 ,χ 2ν ) = (2.95,1.48)

vv0 (χ2 ,χ 2ν ) = (3.3,1.65)

0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

5

4

3

2

1

[X/H

]


: SMSSJ200654.42Teff =5395 K logg =2.95

vv6 (χ2 ,χ 2ν ) = (2.11,1.06)

vv7 (χ2 ,χ 2ν ) = (2.39,1.2)

vv4 (χ2 ,χ 2ν ) = (2.86,1.43)

vv3 (χ2 ,χ 2ν ) = (2.87,1.43)

vv2 (χ2 ,χ 2ν ) = (2.96,1.48)

vv5 (χ2 ,χ 2ν ) = (3.04,1.52)

vv1 (χ2 ,χ 2ν ) = (3.14,1.57)

vv0 (χ2 ,χ 2ν ) = (3.37,1.68)

1

0

1

2

3

log(

12C/13

C)

6 7 8 9 10 11 12 13Atomic Number

5

4

3

2

1

[X/H

]


: SMSSJ225851.25Teff =4612 K logg =0.8

vv4 (χ2 ,χ 2ν ) = (2.33,1.16)

vv5 (χ2 ,χ 2ν ) = (2.33,1.16)

vv6 (χ2 ,χ 2ν ) = (2.34,1.17)

vv7 (χ2 ,χ 2ν ) = (2.35,1.18)

vv3 (χ2 ,χ 2ν ) = (2.58,1.29)

vv2 (χ2 ,χ 2ν ) = (2.69,1.35)

vv1 (χ2 ,χ 2ν ) = (2.92,1.46)

vv0 (χ2 ,χ 2ν ) = (3.08,1.54)

1

0

1

2

3lo

g(12

C/13

C)

Fig. 15. Continued.


inferring the velocity of early massive stars from the ...the long-dead early massive stars are the...

Documents