Non-LTE abundances of Mg and K in extremely metal-poor stars and the evolution of [O/Mg], [Na/Mg], [Al/Mg] and [K/Mg] in the Milky Way

0.44 MB·English

by  S. M. Andrievsky

1 Astronomy
(DOI:willbeinsertedbyhandlater) &
(cid:13)c ESO2010 Astrophysics
Non-LTE abundances of Mg and K in extremely metal-poor stars
and the evolution of [O/Mg], [Na/Mg], [Al/Mg] and [K/Mg] in the
⋆
Milky Way.
S.M.Andrievsky1,2,M.Spite1,S.A.Korotin2,F.Spite1,P.Bonifacio1,3,4,R.Cayrel1,P.Franc¸ois1,andV.Hill5
1 GEPI, Observatoire de Paris, CNRS, Universite´ Paris Diderot; F-92125 Meudon Cedex, France, e-mail :
[email protected]
2 Department of Astronomy and Astronomical Observatory, Odessa National University, Isaac Newton Institute of Chile, Odessa
0 branch,ShevchenkoPark,65014Odessa,Ukraine,e-mail:[email protected]
1 3 CIFISTMarieCurieExcellenceTeam
0 4 IstitutoNazionalediAstrofisica,OsservatorioAstronomicodiTrieste,ViaTiepolo11,I-34143Trieste,Italy
2 5 ObservatoiredelaCotedAzur,CNRSUMR6202,BP4229,06304NiceCedex4,France

n
a
J
ABSTRACT
8

Aims.LTEabundancesoflightelementsinextremelymetal-poor(EMP)starshavebeenpreviouslyderivedfromhighqualityspectra.
]
A Newderivations,freefromtheNLTEeffects,willbetterconstrainthemodelsoftheGalacticchemicalevolutionandtheyieldsofthe
veryfirstsupernovae.
G Methods.TheNLTEprofilesofthemagnesiumandpotassiumlineshavebeencomputedinasampleof53extremelymetal-poorstars
. withamodifiedversionoftheprogramMULTIandadjustedtotheobservedlinesinordertoderivetheabundancesoftheseelements.
h
Results.The NLTE corrections for magnesium and potassium are in good agreement with the works found in the literature. The
p
abundances are slightly changed, reaching a better precision: the scatter around the mean of the abundance ratios has decreased.
- Magnesiummaybeusedwithconfidenceasreferenceelement.TogetherwithpreviouslydeterminedNLTEabundancesofsodium
o
andaluminum,thenewratiosaredisplayed,forcomparison,alongthetheoreticaltrendsproposedbysomemodelsofthechemical
r
t evolutionoftheGalaxy,usingdifferentmodelsofsupernovae.
s
a Keywords.Galaxy:abundances–Galaxy:halo–Galaxy:evolution–Stars:abundances–Stars:mixing–Stars:Supernovae
[

1
v 1. Introduction sive nucleosynthesis, mixing and fallback episodes and possi-
7 blelateSNIacontributions.Magnesiumis,inprinciple,abetter
0 In the frame of the ESO Large Program ”First stars, first nu-
choicesince thiselementis mainlyformedin massive SNe, its
2 cleosynthesis” Cayrel et al. (2004) and Bonifacio et al. (2007,
productionisdominatedbyhydrostaticcarbonburning,anditis
1 2009)havestudiedanhomogeneoussampleofextremelymetal-
lessaffectedbyexplosiveburningandfallback(e.g.Woosley&
1. poorgiantsandturnoffstars.Foraboutfiftystars,mostofthem Weaver,1995).Amongothers,Shigeyama& Tsujimoto(1998)
0 with [Fe/H] < −3, they determine the abundances of the ele- recommendedMgratherthanFeasareferenceelement,follow-
0 ments from C to Zn, especially of the light metals Na, Mg, Al
ingthesamelogic.
1 andK,intheearlyGalaxy.TheseabundancesarebasedonLTE
Cayrel et al. (2004) have recognised this too and have ac-
: computationsoftheequivalentwidthsorofthelineprofiles.
v cordingly used magnesium as a reference element to compare
Aftersodiumandaluminum(Andrievskyetal.,2007,2008)
i the observed ratios [X/Mg] to the ejecta of the massive super-
X wepresentherenon-LTEdeterminationsofthemagnesiumand
novaeinthelastpartofthepaper.Butitappearedthatunexpect-
r potassiumabundancesbycomparisonoftheobservedandcom-
a putedlineprofilesandwediscusstheevolutionoftheabundance edlytherelations[X/Mg]vs. [Mg/H]weremorescatteredthan
thecorrespondingrelations[X/Fe]vs.[Fe/H].Also,inBonifacio
ratios [O/Mg], [Na/Mg], [Al/Mg] and [K/Mg] in the Galaxy.
etal.(2009),themeanvalueof[Mg/Fe]differedsignificantlyin
Recently,Takedaetal.(2009)havecomputedthenon-LTEabun-
giantandturnoffstars.Asaconsequencewesuspectedthatboth
danceofpotassiuminthesamesampleofEMPstars,basedon
theunexpectedbehaviourofthescatteroftheratios[X/Mg]and
the equivalentwidths of the potassium lines given in Cayrel et
thedifferentbehaviourofdwarfsandgiantscouldbedueatleast
al.(2004).Wecompareourresultswiththeirdeterminations.
partlytotheneglectofthedeparturesfromLTE.
InCayreletal.(2004)andBonifacioetal.(2007,2009),iron
-InSect. 2wepresentthecharacteristicsoftheatomicmodels
had beenfirst chosenas the main tracer ofthe chemicalevolu-
usedforthenon-LTEcomputations.
tion of the Galaxy. It had also been noted however,thatiron is
-InSect.3arepresentedthemainparametersoftheanalysis.
perhapsnotthebestchoicesincethereareseveralprocessesthat
-InSect.4wediscusstheratios[Mg/Fe]and[K/Fe]intheearly
affect the yield of iron : Si burning in massive SNe II, explo-
Galaxy, and we compare the ratios [O/Mg], [Na/Mg], [Al/Mg]
⋆ BasedonobservationsobtainedwiththeESOVeryLargeTelescope and [K/Mg] at low metallicity to the predictions of the ejecta
at Paranal Observatory (Large Programme ”First Stars”, ID 165.N- ofsupernovae/hypernovae.Finallyforacompletehalo-diskpic-
0276;P.I.:R.Cayrel. ture we havealso addedthe NLTE determinationsofthe abun-
2 Andrievsky:RelativeabundancesoflightmetalsinEMPstars
dancesofNa,Mg,AlandKinthediskfromthe”Gehrenteam” 2. AtomicmodelsandNLTEcalculations
(Gehrenetal.2004,2006,Mashonkinaetal.2008,andZhanget
al.2006),tostudytheevolutionoftheseratiosintheGalaxyand 2.1.Magnesium
tocomparethistothepredictionsofthemodelsofthechemical
The atomic model of magnesium used in this work is essen-
evolutionoftheGalaxy.
tially the same as the onedescribed in Mishenina et al. (2004).
Thismodelconsistsof84levelsof Mgi,12levelsof Mgiiand
the ground level of Mgiii (Martin & Zalubas, 1980, Biemont
&Brault1986).Withinthedescribedsystemthetransitionsbe-
tween the 59 first levels of Mgi and the ground level of Mgii
have been considered. The detailed structure of the multiplets
was ignored and each LS multiplet was considered as a sin-
gleterm.Thefinestructurewastakenintoaccountonlyforthe
3s3p3P0level(moredetailsinMisheninaetal.2004).
2.2.Potassium
Our model of the Ki atom is based on the model of Bruls et
al.(1992).Inourimplementationweconsideredindetailallthe
transitionsbetweenthefirst20levelsofthe Ki andtheground
level of the Kii. For the level 4p2P we took into account the
finesplitting.Theotherlevelswereconsideredassinglelevels.
Fifteen additional levels of Ki and 7 levels of Kii were used
to allow the conservation of the number of particles. The level
energiesare taken from Sugar& Corliss (1985). The oscillator
strengthsofthebound-boundtransitionsaretakenfromWieseet
al. (1969) as well as Biemont & Grevesse (1973). For the res-
onancetransitionswe useddata fromMorton(1991). Thetotal
numberofbound-boundtransitionsconsideredindetailis62.
Photoionization cross-sections from the ground level of
potassiumwere reportedby Rahman-Attiaet al. (1986). Forp-
levelswe tookionizationcross-sectionspublishedbyAymaret
al. (1976). For 2S, 2D, 2F levels the cross-sections calculated
withthehelpofquantumdefectmethod(Hofsaess,1979)were
used.Fortheotherlevels,weusedthehydrogen-likeapproxima-
tion.Theelectroncollisionalrateswereestimatedwiththehelp
oftheVanRegemorter(1962)formula,whileAllen’s(1973)for-
mulawasusedforforbiddentransitions.Thecollisionalioniza-
tionfromthegroundlevelwasdescribedusingthecorrespond-
ingformulafromSobelmanetal.(1981).Fortheotherlevelswe
usedSeaton’s(1962)formula.Totakeintoaccountcollisionsof
potassiumatomswithhydrogenatomsweappliedtheformulaof
Steenbock&Holweger(1984)withacorrectingfactorequalto
Fig.1. Profile fittingof the magnesiumlinesin the solar spec- 0.05.AsimilarcorrectingfactorwasusedbyZhangetal.(2006).
trum. Theprincipaldifferencebetweenthe LTE andNLTE-based
abundancesiscausedbyanover-recombinationonthefirstlevel
of the Ki atom in the atmospheres of the late-type stars. This
leads to an increase of the equivalent widths of the Ki 766.5
and769.9nmlines, andasa consequencethe LTE abundances
are overestimated.Detailed discussion of this effect is given in
Ivanova&Shymansky(2000).
2.2.1. Fitofthesolarspectrum
To verifyouradoptedatomicmodelsofmagnesiumandpotas-
siumwehavecarriedoutthecomputationoftheNLTEsynthetic
profiles of several magnesium and potassium lines. The Solar
Flux Atlas of Kurucz (1984) in the visual and infra red range
wasusedforthispurpose.
Fig.2.Profilefittingofthepotassiumlinesinthesolarspectrum. The NLTE profiles have been determined with the help of
themodified”MULTI”codeofCarlsson(1986).Themodifica-
tions are described in Korotin et al. (1999), they include opac-
itysourcesfromATLAS9(Kurucz1992).TheKurucz’s(1996)
Andrievsky:RelativeabundancesoflightmetalsinEMPstars 3
modelofthesolaratmospherehasbeenusedinthesecomputa- 3.4.NLTEabundances
tions.
To compute NLTE profiles of the magnesium and potassium
The damping constants have been taken from the Vienna
lines, we have used Kurucz’s models (ATLAS9) without over-
AtomicLineDataBase(VALD,Piskunovetal.,1995).Thecor-
shooting(Kurucz1993).Wehavecheckedonsometypicalstars
rection ∆logC found by Mishenina et al. (2004) has been ap-
6 that the use of MARCS models (Gustafsson et al., 2008) as in
plied for the computation of the magnesium lines. The NLTE
Cayreletal.(2004)wouldnotmakeasignificantdifference.
profiles of the Mg I lines computed with log(Mg/H) = 7.57
The NLTE correctionsdepend on the effective temperature
agree well with the solar spectrum (see Fig. 1 in good agree-
and gravity of the model, as well as on the elementabundance
mentwiththedeterminationsofGrevesse&Sauval(2000),and
itself. The latter circumstance strongly suggests that the abun-
of Shimanskaya (2000) who found log(Mg/H) = 7.58. The
⊙
dances must be derived individually for each star using com-
potassium lines are also well reproduced by our calculations
plete NLTE computation. The use of published NLTE correc-
(see Fig. 2) with a potassium abundancelog(K/H) = 5.11,in
⊙
tions as a function T and logg can introduce some errors in
goodagreementwiththevalueadoptedbyZhangetal.(2006), eff
the derivedabundancesif the abundancesare different.For ex-
andveryclosetothemeteoriticpotassiumabundance(Lodders,
ample in metal-poorstars in the range −2.0 < [Fe/H] < −3.0
2003).
the NLTE corrections for the potassium abundance are within
the range 0.2-0.5 dex. But in the extremely metal-poor stars
([Fe/H] < −3.0) the potassium line is very weak (the equiva-
3. Analysisofthestarsample
lent width of the 7699 Å line is always less than 25 mÅ and
3.1.Sampleofstars.Observationsandreduction often less than 10 mÅ); the line is thus formed rather deeply
in the atmosphere where collisions are important and finally
The sample of stars and the observationaldata are the same as
the NLTE correction at these metallicities is small. As a con-
discussed in Cayrel et al. (2004). The observations were per-
sequence,the use of a uniformNLTE correction(computedby
formedwiththehighresolutionspectrographUVESattheVLT
Ivanova&Shymanskyforametallicityof-2.0),hasledCayrel
(Dekkeret al., 2000). The resolvingpowerin the regionof the
et al. (2004) to underestimatethe potassium abundanceat very
magnesiumlinesisR ≈ 45,000anditisR ≈ 41,000inthere-
lowmetallicity.
gionofthepotassiumlines.TheS/Nratioisgenerally≈120/pix
withabout5pixelsperresolutionelement.Inthisregionofthe
potassiumlines,residualfringeslimittheprecisionofthemea-
1.0
surementsandinmostofthestarsalinewithanequivalentwidth 1.0
0.9
lessthan3mÅ cannotbedetected. X
LU 0.8
The spectra have been reduced using the UVES context F
(Ballesteretal.2000). TIVE 0.9 00..67
A
EL 0.5
R
0.4
3.2.Atmosphericparameters 0.8
0.3
TheparametersoftheatmosphereofthestarsT ,logg,v and BS 16968-61 0.2 BS 16968-61
eff t
[Fe/H]aregiveninTable1,andarequotedfromtheLTEanaly- 0.7 0.1
sesofCayreletal.(2004)andBonifacioetal.(2007,2009).An 5528.0 5528.5 5529.05183.0 5183.5 5184.0
”m”inthelastcolumnofthetablemeansthattheatmosphereof λ(A) λ(A)
thestar(giant)hasbeenfound”mixed”withthedeephydrogen 1.0 1.0
burninglayerbySpiteetal.(2005,2006a).Forthedetermination X0.9 0.9
oftherelativeLTEandNLTEabundances,weadoptedinthista- FLU0.8 0.8
blethesolarvalueslog(Mg/H)⊙ = 7.58andlog(K/H)⊙ = 5.12 TIVE 00..67 00..67
following Grevesse & Sauval (2000) for a better homogeneity A
EL0.5 0.5
withthepreviousLTEdeterminations(Cayreletal.2004). R
0.4 0.4
0.3 0.3
HD186478 HD186478
0.2 0.2
3.3.LTEabundancesofKandMg
0.1 0.1
Asacomparison,wegiveinTable1newabundancesofmagne- 5528.0 5528.5 5529.0 5183.0 5183.5 5184.0 5184.5
sium and potassium computedwith the LTE hypothesis.These λ(A) λ(A)
new determinationshave been obtained by fitting the synthetic
spectrawiththeobservedprofiles.
Fig.3. Magnesium. Profile fitting for two metal-poor stars
For the abundance of potassium the result is sometimes
with different effective temperature, with similar metallicity
slightlydifferentfromthevaluepublishedinCayreletal.(2004)
:[Fe/H]≈−2.8.Oneisaturnoffstar(BS16968-61),theothera
because,forexample,adifferentpositionofthecontinuumhas
giant(HD186478).TheMgabundancewasvariedby0.10dex
beenadopted.
(dottedlines).
However,the difference is larger for magnesium.In Cayrel
etal.(2004)theequivalentwidthsofmagnesiumlinesingiants
have been often underestimated:the lines are often strong and
the wings hadbeen neglected.Thiserror hasbeen correctedin The profile fitting for two metal-poor stars is displayed in
Bonifacioetal.(2009).Thecorrectionisnegligibleforthemost Fig.3and4.TheNLTEmagnesiumandpotassiumabundances
magnesium-poor giants, but in in the other (less Mg-poor) gi- inourprogramstarsarelistedinTable1.Inthistable,wegive
ants,thedifferenceisabout0.15dex. alsoasacomparisontheabundanceoftheseelementscomputed
4 Andrievsky:RelativeabundancesoflightmetalsinEMPstars
Table 1.Adoptedmodelandpotassiumabundanceforoursampleofstars.Inthelastcolumnthelettermindicatesthatthegiant
hasbeenfound“mixed”(seetext).
T log v LTE NLTE NLTE NLTE LTENLTENLTE NLTE
eff t
star (K) g (kms−1)[Fe/H] ǫ(Mg)ǫ(Mg)[Mg/H][Mg/Fe] ǫ(K) ǫ(K) [K/H][K/Fe]Rem
GIANTS
01 HD2796 4950 1.5 2.1 -2.47 5.54 5.74 -1.84 0.63 3.25 2.90 -2.22 0.25 m
02 HD122563 4600 1.1 2.0 -2.82 5.29 5.39 -2.19 0.63 2.78 2.57 -2.55 0.27 m
03 HD186478 4700 1.3 2.0 -2.59 5.55 5.72 -1.86 0.73 3.10 2.85 -2.27 0.32 m
04 BD+17:3248 5250 1.4 1.5 -2.07 6.00 6.19 -1.39 0.68 3.77 3.35 -1.77 0.30 m
05 BD-18:5550 4750 1.4 1.8 -3.06 4.99 5.14 -2.44 0.62 2.63 2.45 -2.67 0.39
06 CD-38:245 4800 1.5 2.2 -4.19 3.66 4.02 -3.56 0.63 - - - - m
07 BS16467-062 5200 2.5 1.6 -3.77 3.95 4.24 -3.34 0.43 1.85 1.70 -3.42 0.35
08 BS16477-003 4900 1.7 1.8 -3.36 4.76 4.86 -2.72 0.64 2.30 2.04 -3.08 0.28
09 BS17569-49 4700 1.2 1.9 -2.88 5.36 5.47 -2.11 0.77 2.84 2.59 -2.53 0.35 m
10 CS22169-035 4700 1.2 2.2 -3.04 4.76 4.92 -2.66 0.38 2.55 2.37 -2.75 0.29 m
11 CS22172-002 4800 1.3 2.2 -3.86 3.89 4.19 -3.39 0.47 1.85 1.67 -3.45 0.41
12 CS22186-025 4900 1.5 2.0 -3.00 5.05 5.19 -2.39 0.61 2.68 2.47 -2.65 0.35 m
13 CS22189-009 4900 1.7 1.9 -3.49 4.29 4.47 -3.11 0.38 2.20 2.06 -3.06 0.43
14 CS22873-055 4550 0.7 2.2 -2.99 5.11 5.24 -2.34 0.65 2.60 2.39 -2.73 0.26 m
15 CS22873-166 4550 0.9 2.1 -2.97 5.27 5.44 -2.14 0.83 2.71 2.52 -2.60 0.37 m
16 CS22878-101 4800 1.3 2.0 -3.25 4.85 5.02 -2.56 0.69 2.35 2.16 -2.96 0.29 m
17 CS22885-096 5050 2.6 1.8 -3.78 4.13 4.39 -3.19 0.59 1.80 1.72 -3.40 0.38
18 CS22891-209 4700 1.0 2.1 -3.29 4.76 4.89 -2.69 0.60 2.35 2.15 -2.97 0.32 m
19 CS22892-052* 4850 1.6 1.9 -3.03 4.90 5.06 -2.52 0.51 2.55 2.34 -2.78 0.25
20 CS22896-154 5250 2.7 1.2 -2.69 5.22 5.52 -2.06 0.63 2.88 2.62 -2.50 0.19
21 CS22897-008 4900 1.7 2.0 -3.41 4.54 4.75 -2.83 0.58 2.20 2.02 -3.10 0.31
22 CS22948-066 5100 1.8 2.0 -3.14 4.81 4.99 -2.59 0.55 2.55 2.37 -2.75 0.39 m
23 CS22949-037* 4900 1.5 1.8 -3.97 5.07 5.16 -2.42 1.55 1.50 1.32 -3.80 0.17 m
24 CS22952-015 4800 1.3 2.1 -3.43 4.20 4.51 -3.07 0.36 2.15 1.99 -3.13 0.30 m
25 CS22953-003 5100 2.3 1.7 -2.84 5.03 5.24 -2.34 0.50 2.60 2.42 -2.70 0.14
26 CS22956-050 4900 1.7 1.8 -3.33 4.59 4.99 -2.59 0.74 2.20 2.09 -3.03 0.30
27 CS22966-057 5300 2.2 1.4 -2.62 5.39 5.69 -1.89 0.73 2.95 2.77 -2.35 0.27
28 CS22968-014 4850 1.7 1.9 -3.56 4.27 4.54 -3.04 0.52 1.83 1.77 -3.35 0.21
29 CS29491-053 4700 1.3 2.0 -3.04 5.09 5.24 -2.34 0.70 2.69 2.42 -2.70 0.34 m
30 CS29495-041 4800 1.5 1.8 -2.82 5.23 5.49 -2.09 0.73 2.91 2.63 -2.49 0.33
31 CS29502-042 5100 2.5 1.5 -3.19 4.74 5.06 -2.52 0.67 2.26 2.07 -3.05 0.14
32 CS29516-024 4650 1.2 1.7 -3.06 5.25 5.34 -2.24 0.82 - - - -
33 CS29518-051 5200 2.6 1.4 -2.69 5.27 5.56 -1.02 0.67 2.94 2.67 -2.45 0.24 m
34 CS30325-094 4950 2.0 1.5 -3.30 4.81 5.04 -2.54 0.76 2.65 2.42 -2.70 0.60
35 CS31082-001 4825 1.5 1.8 -2.91 5.21 5.49 -2.09 0.82 2.80 2.47 -2.65 0.26
TURNOFF
1 BS16023–046 6360 4.5 1.4 -2.97 4.67 4.97 -2.61 0.36
2 BS16968–061 6040 3.8 1.5 -3.05 4.82 5.12 -2.46 0.59
3 BS17570–063 6240 4.8 0.5 -2.92 4.74 5.06 -2.52 0.40
4 CS22177–009 6260 4.5 1.2 -3.10 4.70 5.11 -2.47 0.63
5 CS22888–031 6150 5.0 0.5 -3.28 4.51 5.04 -2.54 0.74
6 CS22948–093 6360 4.3 1.2 -3.43 4.33 4.72 -2.86 0.57
7 CS22953–037 6360 4.3 1.4 -2.89 5.05 5.34 -2.24 0.65
8 CS22965–054 6090 3.8 1.4 -3.04 4.79 5.16 -2.42 0.62
9 CS22966–011 6200 4.8 1.1 -3.07 4.72 5.01 -2.57 0.50
10 CS29499–060 6320 4.0 1.5 -2.70 5.07 5.44 -2.14 0.56
11 CS29506–007 6270 4.0 1.7 -2.91 4.95 5.33 -2.25 0.66
12 CS29506–090 6300 4.3 1.4 -2.83 5.02 5.36 -2.22 0.61
13 CS29518–020 6240 4.5 1.7 -2.77 4.87 5.31 -2.27 0.50
14 CS29518–043 6430 4.3 1.3 -3.24 4.57 4.94 -2.64 0.60
15 CS29527–015 6240 4.0 1.6 -3.55 4.46 4.86 -2.72 0.83
16 CS30301–024 6330 4.0 1.6 -2.75 5.11 5.33 -2.25 0.50
17 CS30339–069 6240 4.0 1.3 -3.08 4.68 5.04 -2.54 0.54
18 CS31061–032 6410 4.3 1.4 -2.58 5.22 5.44 -2.14 0.44
*Anasteriskafterthenameofthestarmeansthatthestariscarbon-rich.
independently with the LTE approximation (and without any
correction).Thepotassiumabundancecanbecomputedonlyin
giantstars,thelinesarenotvisibleintheturnoffstars.
Andrievsky:RelativeabundancesoflightmetalsinEMPstars 5
X1.0 1.0
U
L
F
E
V
TI0.9 0.9
A
L
E
R
0.8 0.8
CS 22953-003 HD 122563
0.7 0.7
7698.5 7699.0 7699.5 7698.5 7699.0 7699.5
λ(A) λ(A)
Fig.4.Potassium.Profilefittingfortwometal-poorgiants,both
with[Fe/H]≈−2.8butwithdifferenteffectivetemperature.The
best-fitKabundancewasvariedby0.05dex.
4. Discussion
4.1.Abundanceofmagnesiumandpotassiumintheearly
Galaxy
As recalled in Cayrel et al. (2004), Mg is formed during hy-
drostatic carbonburningandexplosiveneonburning,K during
explosiveoxygenburning;theirabundancesarethereforerelated
totheimportanceofboththehydrostaticandexplosivephases.
InFig.5wecomparetheLTEabundancesofmagnesiumin
our sample of EMP dwarfs and giants (Bonifacio et al., 2009) Fig.6. [K/Fe]vs.[Fe/H]intheearlyGalaxy.Opencircles(red
with the new NLTEdeterminations.The carbon-richandpecu- andblue)standfor”mixed”and”unmixed”giantsrespectively
liarstarCS22949-037hasbeendiscarded. (seeSpiteetal.2005,2006a).Thepotassiumabundancecannot
bemeasuredintheturnoffstars,thelinesaretooweak.
Thetrendof the [Mg/Fe]ratio vs. metallicity atlow metal-
licity is not changed, it remains a plateau. But the scatter of
[Mg/Fe] is smaller when NLTE effects are taken into account:
0.13fromNLTEcomputationsand0.16fromLTEcomputation.
The difference between dwarfs and giants is strongly reduced
and is notsignificant anymore. The mean value of [Mg/Fe] in
theinterval−4<[Fe/H]<−2.5isnow+0.61dex(itwas+0.34
fromLTE computations).Thisvalueof [Mg/Fe]isnowsimilar
to the mean value of [O/Fe] previously deduced (Cayrel et al.
2004) from the forbidden oxygen line (not sensitive to NLTE
effects).
For the determination of the mean value of the ratios
[Mg/Fe], their trend and their scatter around the trend, the
carbon-richstarCS22949-037(showingalsostrongabundance
anomalies of light elements) has been discarded. The star has
been as well excludedfrom all computationsand/orfiguresre-
latedtoMgabundances.
When NLTE is taken into account, the values of the abun-
danceratios[K/Fe]areslightlydecreased.Thescatterof[K/Fe]
isalsoslightlysmaller.Themeanvalueof[K/Fe]intheinterval
−4<[Fe/H]<−2.5isabout+0.33dex.Thisvalueisveryclose
to the value found by Takeda et al. (2009). We have checked
thatthesmalldifferencesbetweenthetwodeterminationsreflect
the fact that we have determined the potassium abundance by
Fig.5. [Mg/Fe]vs.[Fe/H]intheearlyGalaxy.Opencircles(red a direct fit of the profiles whereas Takeda et al. have used the
andblue)standfor”mixed”and”unmixed”giants(seeSpiteet equivalentwidthsgiveninCayreletal.(2004).
al.2005,2006a,2006b),blackfilledsymbolsforturnoffstars. Wehaveestimatedstarbystartheerroron[K/Fe]inoursam-
ple of stars. This error is dominated by the measurementerror
(equivalentwidthorprofile)anditincreasessignificantlywhen
themetallicitydecreases:atlowmetallicitythepotassiumlines
6 Andrievsky:RelativeabundancesoflightmetalsinEMPstars
becomesveryweak(lessthan10mÅandoftenlessthan5mÅ)
inaregionwheretheS/Nratioisonlyabout100andwherethe
positionofthecontinuumisnotveryprecisebecauseofresidual
fringes.Inconsequence,asshowninourFig.6wedonotcon-
firm the suggestionof Takeda et al. (2009) of ”a marginalsign
ofdeclinetowardafurtherlower[Fe/H]”.
It is interesting to note that the K-rich star CS 30325-94
(LTE,see Cayreletal. 2004) remainsK-rich(andwitha small
error)intheNLTEanalysis(seeFig.6)anditisalsoSc-rich.In
thestellarsampleofZhang&Zhao(2005),themostpotassium-
rich star HD 195636 (with [Fe/H]=–3.3, and [K/Fe]=+1.35)
is also very scandium-rich. The production of these elements
is not unanimously ascribed to definite sites; there could be
a link between the formation processes of these elements in Fig.7. Abundance of O, Na, Al, and K relative to Mg in the
massive stars. However,the scandium-richstars are notalways early Galaxy. The abundances of all these elements have been
potassium-rich(seeforexampleCS22885-096inoursample). computedtaking into accountthe NLTE effect. Since the mea-
suredoxygenlinesareforbiddenlinestheyarefreefromNLTE
effects.
4.2.AbundancesofOandlightmetalsrelativetoMginthe
earlyGalaxy
Oxygen:
ThemagnesiumabundanceslistedinTable1canbeusedasa 4.3.Comparisontothepredictionsoftheejectaof
normalizationfactorforotherelements.Itisinterestingtocom- supernovae
pute the ratio [O/Mg] using this new NLTE value of the mag-
nesium abundance : since the abundance of oxygen has been It is interesting to compare the abundance ratios [O/Mg],
determinedfromtheforbiddenoxygenline,is freefromNLTE [Na/Mg], [Al/Mg] and [K/Mg] to the predictions of the ejecta
effects.ThecorrespondingplotsareshowninFig.7. ofmetal-poorsupernovaeorhypernovae.InFig.8theobserved
ratios are compared to the predictions of Woosley & Weaver
Sodium:
(1995),ofHeger&Woosley(2008,2002),ofChieffi&Limongi
AsfoundinAndrievskyetal. (2007),the”mixed”starsare
(2003), and Kobayashi et al. for supernovae and hypernovae
oftenenrichedinsodium.Thisreflectsaninternalmixinginside
(Kobayashietal.,2006).
these giant stars. Thereforethe mixed stars should not be used
to determine the ratio [Na/Mg] in the early Galaxy. Note that
the star CS 22952-15(a mixedstar with [Fe/H]=–3.43)is very
sodium-rich, but its ratio [Al/Fe] is normal (see Andrievsky et
al., 2008). However its ratio [Al/Mg] is also rather high. The
explanationisthatthismixedstarisNa-richandMg-poor.
Meanvalueandscatter:
SincetheabundancesofO,Na,AlandKrelativetoMgare
ratherflatintheircentralpart,wecandefineameanvalueinthis
centralinterval,say−3.6<[Fe/H]< −2.5.Themeanvaluesof
theseflatpartsare:
[O/Mg] ≈ 0.1, [Na/Mg] ≈ −0.8, [Al/Mg] ≈ −0.7 and
[K/Mg]≈−0.3.
For the same sample of stars in the same intervalof metal-
licity(−3.6 < [Fe/H] < −2.5),thescatteraroundthemeancan
alsobecomputed,thevaluesare:
σ = 0.18 but σ = 0.20, σ = 0.12 but
[O/Fe] [O/Mg] [Na/Fe]
σ = 0.14,σ = 0.11,σ = 0.11,σ = 0.09
[Na/Mg] [Al/Fe] [Al/Mg] [K/Fe]
butσ =0.15.
[K/Mg] Fig.8. Comparisonof the new abundanceratiosto the predic-
ThelargescatterfoundforO,isduetothereducednumber
tionsofsupernovaeorhypernovae.
ofmeasurements.
The valuesof the scatter obtainedfor the NLTE abundance
ratios are lower than for the LTE abundances. However, it ap-
pearsthat,asalreadyobservedinLTE(Cayreletal.,2004),the The quantity of potassium ejected is generally underesti-
scatter of the abundance ratios is larger when Mg is chosen as mated by the models of supernovae. The best agreement is
thereferenceelementinsteadofFe.Alisanexception. obtained by the predictions of Heger & Woosley (2008) with
Thisfactissurprising:itwouldhavebeenexpectedthatthe the hypotheses B and D (see the paper), although the abun-
abundancesof Na and K producedby (mainlyhydrostatic)nu- dance of sodium and aluminum are in this case a little overes-
clearprocesses(similartothoseproducingMg)wouldbearmore timated. The ratio Al/Mg is also well representedin the model
resemblance to the Mg abundance than to the Fe abundance of Chieffi & Limongi (2003). Unfortunately there are no pre-
(producedquitedifferently);thescatterof[Na/Mg]and[K/Mg] dictions for the abundance of O, Na and K in this model. The
wouldthenbesmallerthanthescatterof[Na/Fe]and[K/Fe],but modelsofKobayashietal.(2006)(supernovaeandhypernovae
theobservationsshowthecontrary. withZ=0.0)seemalsoabletorepresenttherelativeabundances
Andrievsky:RelativeabundancesoflightmetalsinEMPstars 7
ofO,Na,MgandAl,buthereagaintheproductionofpotassium
isstronglyunderestimated.
4.4.Variationof[O/Mg],[Na/Mg],[Al/Mg]and[K/Mg]inthe
Galaxy
InFig.9wepresentthevariationof[O/Mg],[Na/Mg],[Al/Mg]
and[K/Mg]intheGalaxyasafunctionof[Mg/H]whereNa,Al,
Mg and K have been computed taking into account the NLTE
effects (the oxygenabundancededucedfromforbiddenlines is
notaffectedbydeparturefromLTE).
As already noted,[Mg/H]should be a better indexof time,
since magnesiumis only formedin massive SN II with a short
lifetime,unlikeironformedinSNIIorSNIofvariousmasses.
WehaveaddedinthefigurethedeterminationsofGehrenet
al. (2004, 2006), ofMashonkinaetal. (2008), andZhanget al.
(2006) in the Galactic disk and halo. All these determinations
havebeendoneincludingtheNLTEeffectsonthelineprofiles.
As seen in Fig. 9, the abundance ratios [Na/Mg], [Al/Mg]
and[K/Mg]intheGalaxydecreasewith[Mg/H]from[Mg/H]=
0 to [Mg/H]=–2, then are almost constant between [Mg/H]=–
2 and [Mg/H]=–2.8,and finally, at lower metallicity, the ratios
[Na/Mg],[Al/Mg],and[K/Mg]andmaybealso[O/Mg]seemto
increase when [Mg/H] decreases. (The error on [O/Mg] in the
two mostmagnesium-poorstars islargeandthusthistendency
isnotfirmlyestablishedforoxygen.)
In Fig. 9 the evolutions of the abundance ratios [O/Mg],
[Na/Mg], [Al/Mg] and [K/Mg] in the Galaxy are also drawn,
followingKobayashietal.(2006),Franc¸oisetal.(2004)andfor
NaandAl,Goswami&Prantzos(2000).
Kobayashietal. use newnucleosynthesisyieldscalculated,
from Z = 0 to Z = Z , for supernovae and hypernovae. With
⊙
these new yields, the general trend of O, Na and Al is rather
wellreproduced,butnotthebehaviourofpotassium.Theunder-
productionofpotassiuminthemodelsofsupernovaehasalreay
been pointed out by Samland (1998). To solve this problem as
well as the underproduction of Si and Sc, Umeda & Nomoto
(2005)haveproposedtointroduceamodelofsupernovawhere
thedensityisassumedtobereduced(duringtheexplosiveburn-
ing)toincreasethefreezeout.
The predictions of Franc¸ois et al. (2004) are based on the Fig.9. Variation of [O/Mg], [Na/Mg], [Al/Mg], [K/Mg] vs.
yields of Woosley & Weaver (1995). For a better fit of the ob- [Mg/H] in the Galaxy. The red and blue open circles repre-
servations they had to systematically increase the production sent our measurements for mixed and unmixed giants (see the
of K by a factor of 8. In the computations of Kobayashi et al. electronic version of A&A for a color version of this figure),
(2006)theratio[O/Mg]remainsstableatverylowmetalliciticty. the large black dots represent the turnoff stars of our sample
Contrary to that, Fanc¸ois et al. (2004) predict an increase of and the small black dots are from Gehren et al. (2004, 2006),
[O/Mg]whenthemetallicitydecreasesfor[Mg/H]<−2.5.The Mashonkinaetal. (2008), andZhanget al. (2006), forthe disk
measurementof[O/Mg]inthetwomostmetal-poorstarsinthe andhalostars.ThethinsolidlineisthepredictionofFranc¸oiset
Fig. 9 is unfortunately too uncertain (one is clearly an upper al.(2004)forOandKandofCescuttietal.(privatecommunica-
limit)toenabletochooseoneofthetwomodels. tion)forNaandMg.Thedasheddottedlinesarethepredicitions
For Na and Al we give the predictions of Goswami & ofGoswami&Prantzos(2000)forNaandAl.Thesepredictions
Prantzos(2000),andofCescuttietal.(privatecommunication). arebased(withoccasionaladjustments)onthemodelsofsuper-
Thesepredictionsare,asinFranc¸oisetal.(2004),basedonthe novaeejectaofWoosley&Weaver(1995).Thethicksolidlines
yieldsofWoosley&Weaver (1995) buttheyieldsoflowmass arethepredictionsofKobayashietal.(2006)based(withoutad-
andintermediatemassstarshavebeenadjusted.LikeKobayashi justments)onnewmodelsofsupernovaeandhypernovae.
et al. (2006), they predict a decrease of [Na/Mg] and [Al/Mg]
when[Mg/H]decreases,buttheagreementwiththeobservations
isbetterwhenthemodelofKobayashietal.isadopted.
AbundancesofMgandK:
5. Conclusion
The NLTE correction for magnesium is in accord with the
ThespectraoftheEMPstars,(programmeFirstStars)analysed correctioncomputedbyGehrenandcollaborators(2004,2006)
previously(Cayreletal.2004)inLTEhavebeenreanalysedhere inlessmetal-poorstars.TheMgabundanceinthegiantsisraised
forMgandK,takingintoaccountthedeparturesofLTE. by a factor of about 2 and the NLTE abundance of Mg is the
8 Andrievsky:RelativeabundancesoflightmetalsinEMPstars
sameingiantsandindwarfs.TheO/Mgratioisnearlysolar(the Bonifacio,P.,SpiteM.,CayrelR.,HillV.,etal.2009acceptedtoA&A(arXiv
precisionoftheOabundanceishoweverratherlow). 0903.4174).
The NLTE abundance of potassium, computed by adjuste- BrulsJ.H.,RuttenR.J.,ShchukinaN.1992,A&A265,237
CarlssonM.1986,UppsalaObs.Rep.33
mentofobservedandcomputedprofiles,hasbeencomparedto
CayrelR.,DepagneE.,SpiteM.,HillV.,SpiteF.,Franc¸oisP.,PlezB.,Beers
the work of Takeda et al. (2009). The agreement is generally T.C.,PrimasF.,AndersenJ.,BarbuyB.,BonifacioP.,MolaroP.,Nordstro¨m
verygood.When differencesdo occur,theyarise fromthe fact B.2004,A&A416,1117(“FirstStarsV”)
thatTakedaetal.usedtheequivalentwidthsgiveninCayreletal. ChieffiA.,LimongiM.2003intheESOastrophysicssymposia:FromTwilight
to Highlight: The physics of Supernovae, ed. W. Hillebrandt & B.
(2004)whilewefittedthecomputedprofilesdirectlytotheob-
Leibundgut,p.367
servedspectra.(Therearesometimesslightdifferencesinthepo-
ChenY.Q.,NissenP.E.,ZhaoG.,ZhangH.W.,BenoniT.2000,A&AS141,491
sitionofthecontinuum.)TheNLTEcorrectionforthepotassium DekkerH.,D’OdoricoS.,KauferA.,etal.2000inOpticalandIRTelescopes
lines is smaller in the more metal-poorstars, (as already noted InstrumentationandDetectors,edsI.Masanori&A.F.MorwoodProc.SPIE
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DrawinH.-W.1961,ZPhy164,513
abundance had been roughly corrected for NLTE (by applying
DrawinH.-W.1968,ZPhy211,404
uniformlyacorrectionof–0.35dex):thepotassiumabundances Franc¸oisP,MatteucciF.,CayrelR.,SpiteM.,SpiteF.,ChiappiniC.2004,A&A
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GehrenT.,ShiJ.R.,ZhangH.W.etal.2006,A&A451,1065
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