NLTE determination of the sodium abundance in a homogeneous sample of extremely metal-poor stars

0.29 MB·English

by  S. M. Andrievsky

1 Astronomy
(DOI:willbeinsertedbyhandlater) &
(cid:13)c ESO2008 Astrophysics
NLTE determination of the sodium abundance in a homogeneous
sample of extremely metal-poor stars
S.M.Andrievsky1,2,M.Spite1,S.A.Korotin2,F.Spite1,P.Bonifacio1,3,R.Cayrel1,
V.Hill1,andP.Franc¸ois1
1 GEPI,CNRSUMR8111,ObservatoiredeParis-Meudon,F-92125MeudonCedex,France
7
2 DepartmentofAstronomyandAstronomicalObservatory,OdessaNationalUniversity,ShevchenkoPark,65014Odessa,Ukraine
0
3 CIFISTMarieCurieExcellenceTeam
0
2

n
ABSTRACT
a
J
Context.Abundanceratiosinextremelymetal-poor(EMP)starsareagoodindicationofthechemicalcompositionofthegasintheearliest
9
phasesoftheGalaxyevolution.IthadbeenfoundfromanLTEanalysisthatatlowmetallicity,andincontrastwithmostoftheotherelements,

2 thescatterof[Na/Fe]versus[Fe/H]wassurprisinglylargeandthat,ingiants,[Na/Fe]decreasedwithmetallicity.
v Aims.Sinceitiswellknownthattheformationofsodiumlinesisverysensitivetonon-LTEeffects,tofirmlyestablishthebehaviourofthe
9 sodiumabundanceintheearlyGalaxy,wehaveusedhighqualityobservationsofasampleofEMPstarsobtainedwithUVESattheVLT,and
9 wehavetakenintoaccountthenon-LTElineformationofsodium.
1 Methods.The profiles of the two resonant sodium D lines (only these sodium lines are detectable in the spectra of EMP stars) have been
1 computedinasampleof54EMPgiantsandturn-offstars(33ofthemwith[Fe/H]<−3.0)withamodifiedversionofthecodeMULTI,and
0 comparedtotheobservedspectra.
7
Results.Withthesenewdeterminationsintherange−4<[Fe/H]<−2.5,both[Na/Fe]and[Na/Mg]arealmostconstantwithalowscatter.
0
In the turn-off stars and ”unmixed” giants (located in the low RGB): [Na/Fe]=−0.21±0.13 or [Na/Mg]=−0.45±0.16. These values
/
h are in good agreement with the recent determinations of [Na/Fe] and [Na/Mg] in nearby metal-poor stars. Moreover we confirm that all
p the sodium-rich stars are ”mixed” stars (i.e., giants located after the bump, which have undergone an extra mixing). None of the turn-off
- starsissodium-rich.Asaconsequenceitisprobablethatthesodiumenhancementobservedinsomemixedgiantsistheresultofadeepmixing.
o
r
t
s
a Keywords. Line:Formation–Line:Profiles–Stars:Abundances–Stars:Mixing–Stars:Supernovae–Galaxyevolution
:
v
i
X
1. Introduction Such abundance ratios as [α/Fe], [Na, Al/Fe], and others can
r bederivedfromhigh-resolutionspectraandthencomparedto
a
Duringthelastdecadetheinterestintheextremelymetal-poor
theSNeIIyieldprediction.InparticularinCayreletal.(2004)
(EMP)galacticstarshassignificantlyincreased.Thesestars,in
andinBonifacioetal.(2006),ahomogeneoussampleofEMP
fact,arereservoirsoftheprimordialGalacticmaterialthatwas
stars has been studied: 35 giants and 18 turn-off stars (39 of
only slightly polluted by nuclides producedin SNe II (by the
themwith[Fe/H]≤−3).IthasbeenshownthatintheseEMP
firstgenerationofmassivestars).Thus,elementalabundances
stars the scatter of the abundanc e ratios at metallicity below
providedbymetal-pooroldstars,andespeciallyabundancera-
–3.0 dex is generally very small and comparable to the mea-
tios, are of the highest importance for the testing of the SN
surementerrors.Buttherearesomeexceptions,andoneofthe
theoreticalmodels,theiryields,andfinallyforconstrainingthe
most striking cases is [Na/Fe], which varies from star to star
initialmassfunctionslopeintheearlyGalaxyandunderstand-
byafactorclosetoten.IntheseEMPstars,onlytheresonance
ingitsformationhistoryandearlyevolution.
linesofNa(D1andD2)arevisible,andtheselinesareknown
Withtheadventoflargeaperturetelescopes,thepreciseel- to be very sensitive to NLTE effects (e.g., Mashonkina et al.
emental abundances in these faint objects became available. 1993;Baumu¨lleretal.1998).
Sendoffprintrequeststo:M.Spite In Cayrel et al. (2004) and Spite et al. (2005) the sodium
e-mail:[email protected] abundance has been calculated under the LTE hypothesis.
2 Andrievskyetal.:NLTEdeterminationoftheSodiumabundance
ing power of 43000 in the region of the D lines and a typi-
cal S/N ratio per pixel of ∼ 200; they have been reduced us-
ing the UVES context (Ballester et al. 2000) within MIDAS.
Stellar parameters (effective temperature, surface gravity, mi-
croturbulentvelocity,and metallicity) for each star have been
takenfromCayreletal.(2004)andBonifacioetal.(2006).
3. Methodofanalysis
Toderivethesodiumabundanceintheprogramstars,weper-
formanNLTEanalysisofthetworesonantsodiumD1andD2
lines(onlytheselinesareseeninthespectraoftheEMPstars)
Fig.1.[Na/Fe]vs.[Fe/H]foranhomogeneoussampleofEMP usingamodifiedversionoftheMULTIcode(Carlsson1986).
stars(Cayreletal.2004;Bonifacioetal.2006):dwarfs(black These modifications are described in Korotin et al. (1999ab).
dots), low RGB stars (grey dots), and upper RGB stars (open To more adequately calculate the continuous opacity taking
circles). The abundance of Na is deduced from the D lines into account the absorption produced by the great number of
throughanLTEanalysis.Asamean,theratio[Na/Fe]islower spectral lines, the additional opacity sources from ATLAS9
in turn-off stars (black dots) than in RGB stars and is also (Kurucz 1992) are included. Simultaneous solution of the ra-
lowerinlowerRGBstars(greydots)thaninupperRGBstars diative transfer and statistical equilibrium equations are ob-
(opencircles).Thisgraphsuggestsavariationofthecomputed tainedusingtheapproximationofacompletefrequencyredis-
sodiumabundancewiththegravity,whichcouldbetheconse- tributionforallthesodiumlines.Atmospheremodelsofappro-
quenceofanNLTEeffect. priatemetallicityareinterpolatedinKurucz’sgridofstellarat-
mospheremodels(microturbulentvelocity2kms−1,α=1.25).
ThismodifiedcodehasalreadybeenusedforNLTEabundance
determinationofcarbon,oxygen,andsodiuminstarsofdiffer-
Later,asaveryfirstapproximation,auniformcorrectionLTE- enttypes(see,e.g.,Korotinetal.1999ab;Korotin&Mishenina
NLTE of –0.5 dex, extrapolated in the table of Baumu¨ller 1999;Andrievskyetal.2001;Andrievskyetal.2002,andref-
et al. (1998) for log g = 2, was applied to all the giants. erencestherein).
The scatter of the relation [Na/Fe] versus [Fe/H] in giants We employ the modified model of the sodium atom (first
was then very large, and [Na/Fe] was decreasing with the consideredbySakhibullin1987)thatconsistsof27energylev-
metallicity in contrast to the turn-off stars (Spite et al., 2005) elsofNaIatomsinadditiontothegroundleveloftheNaIIion.
where the ratio [Na/Fe] was almost constant in the interval The fine splitting has been taken into accountonly for the 3p
−3.5<[Fe/H]<−2.5. level. This enables one to calculate the sodium doublet more
In Fig. 1 we show the relation [Na/Fe] vs. [Fe/H] for our precisely. The radiative transitions between the first 20 levels
sampleofdwarfsandgiantswithoutanyNLTEcorrection.The of Na I and the ground level of Na II are considered, while
lower RGB stars (below the bump, see Spite et al. 2006) and transitions between the other levels are used for the particle
theupperRGBstars(abovethebump)havebeenplottedwith number conservation. Linearization includes 46 b−b and 20
differentsymbols.Inthe mean,thedwarfshavealowervalue b − f transitions. Radiative rates for 34 transitions are fixed.
of [Na/Fe] than the giants, and the lower RGB stars a lower Photoionization rates were taken from TOPBASE. Collisions
value of [Na/Fe] than the upper RGB stars. This variation of withelectrons,aswellaswithhydrogenatoms,havebeenin-
[Na/Fe]withthegravityofthestarsuggeststhat,asexpected, cluded.
non-LTE effects are very pronounced on the Na D lines, and Figure2showsthebehaviourofthedeparturecoefficients
that as a consequence it is important to carefully take them of Na I for dwarfs and giants of different metallicities. It is
into account. In this paper we present new determinations of clearlyseenthatwithintheregionoftheline-formationinthe
thesodiumabundanceinthesampleofEMPstarsofCayrelet atmosphere, the lower levels of the Na I atom are overpopu-
al.(2004)andBonifacioetal.(2006)throughacarefulNLTE lated, leading to a larger opacity in D1,2 lines compared to
analysis,andwediscussthenewtrendsobtained. the pure LTE case, and therefore to larger equivalent widths
of these lines. This means that NLTE abundance corrections
willbenegative.
2. Thestarsample
To find the relative-to-solar sodium abundance, we com-
The spectraused here havebeenpresentedin detailin Cayrel puted NLTE sodium abundance in the Sun. This was done
etal.(2004)andBonifacioetal.(2006).Theobservationswere withthefollowinglines:4496.05,4982.81,5148.84,5682.63,
performedwith the ESO VLT andits highresolutionspectro- 5688.20, 5889.95, 5895.92, 6154.22, 6160.75, 8183.25,
graphUVES (Dekkeret al. 2000).The spectra have a resolv- 8194.82,and 12679.14Å. Their profiles were extracted from
Andrievskyetal.:NLTEdeterminationoftheSodiumabundance 3
Log bi00..12 3s Teff = 6000 K [ FLeo/gH g] == -4 4 000...246 3s Teff = 6000 K [ FLeo/gH ]g = = - 4 2 RELATIVE FLUX00001.....67890 00001.....67890
4p 3p 3p 0.5 0.5
0.0 0.0 4p 0.4 BD+17 3248 0.4
5s 3d 0.3 0.3
4s -0.2 5s3d 4s 0.2 5889.5 5890.0 5890.5 λ(A) 0.2 5895.5 5896.0 5896.5 λ(A)
-0.1
-0.4 E FLUX01..90 01..90
-0.2 V
-4 -3 -2 -1Log τ50000 -4 -3 -2 -1Log τ05000 RELATI00..78 00..78
0.6 0.6
bi0.4 Teff = 5200 K Log g = 1.5 0.6 Teff = 5200 K Log g = 1.5 0.5 BS16477-003 0.5
Log 0.2 3s [Fe/H] = - 4 0.4 3s [Fe/H] = - 2 0.4 5889.5 5890.0 5890.5 λ(A) 0.4 5895.5 5896.0 5896.5 λ(A)
4p 0.2 4p 3p X1.0 1.0
5s U
-00..20 33dp 4s --000...420 5s 4s3d RELATIVE FL000...789 000...789
0.6 CS29499-60 0.6
-0.6
-0.4
0.5 0.5
5889.5 5890.0 5890.5 λ(A) 5895.5 5896.0 5896.5 λ(A)
-4 -3 -2 -1 0 -4 -3 -2 -1 0
Log τ5000 Log τ5000 X1.0 1.0
U
E FL0.9 0.9
Fig.2.Departurecoefficientsinatmospheresofdwarfsandgi- ATIV0.8 0.8
antsofthedifferentmetallicities. EL
R0.7 0.7
BS17570-63
0.6 0.6
UX1.0 1.0 0.5 5889.5 5890.0 5890.5 λ(A) 0.5 5895.5 5896.0 5896.5 λ(A)
E FL0.9 0.9
TIV0.8 0.8 Fig.4. Best fit between observed (dots) and calculated
A
REL0.7 0.7 (solid line) profiles of the Na D1 (5889.95Å) and D2
0.6 0.6 (5895.92Å)lines,forsomeprogramstars.
0.5 BS16477-003 0.5
0.4 5889.5 5890.0 5890.5 λ(A) 0.4 5895.5 5896.0 5896.5 λ(A)
Fig.3. The observed spectra of the D1 and D2 lines (dots) Fig. 3). Figure 4 shows the best fitting between observedand
in BS 16477-003 are compared to the theoretical profiles calculated profilesfor some EMP giantsand dwarfs. In Table
computed for the best-fit Na abundance +0.10 and – 0.10 1theparametersofthemodels(Teff,loggandvt)whichhave
(solidlines). been used and the new sodium abundancein logarithmǫ(Na)
(forǫ(H)=12)aregivenforeachstar.Thestellarratios[Na/H]
havebeencomputedassumingǫ(Na) =6.25(seeSect.3).
⊙
the Kurucz et al. (1984) solar flux spectrum. Similarly to Three stars in our sample are very peculiar carbon-
the stellar spectra analysis, to derive the NLTE sodium abun- rich stars: CS 22892-52 (Sneden et al. 1996, 2000, 2003),
dance in the Sun, we used the solar atmosphere model from CS 22949-37 (Norris et al. 2001; Depagne et al. 2002), and
the Kurucz’s grid and the solar microturbulent velocity rec- CS 29528-41 (Sivarani et al. 2006). The models we used for
ommended by Maltby et al. (1986). Our NLTE solar sodium theNLTEcomputationsdonottakethecarbonenhancementin
abundance is ǫ(Na)⊙ =6.25±0.04, in agreement with the these stars into accountand thus the sodium abundancecom-
valuefoundbyBaumu¨lleretal.(1998):ǫ(Na)⊙ =6.30±0.03, putedheremustbeconsideredasverypreliminary.Thesestars
and Mashonkina et al. (2000): ǫ(Na)⊙ = 6.20. The value arenottakenintoaccountinthediscussion.
ǫ(Na)⊙ =6.25 will be used later, as a reference to determine InFig.5wepresentanestimateofthedifferenceinsodium
[Na/H].
abundanceobtainedwhenLTEorNLTEprofilesoftheDlines
areusedalongtheRed GiantBranchoftheHRdiagram.The
computationshavebeendoneforasetoftemperaturesbetween
4. Results
6500K(turn-offstars)to4500K(upperRGBstars)andmetal-
New sodiumabundanceshavebeendeducedfromNLTEpro- licities from−2.5to −4.0(Table2). Foreach temperaturethe
files of the D lines for our sample of EMP stars. Typical un- gravity has been deduced from the isochrones of Kim et al.
certaintyinthederivedsodiumabundanceisabout±0.05(see (2002) for 14 Gyr, [α/Fe]=+0.6, [Fe/H] = −3.7and − 2.7
4 Andrievskyetal.:NLTEdeterminationoftheSodiumabundance
Table 1. Model parameters and NLTE sodium abundance in our sample of stars. The three stars marked with an asterisk are
carbon-richstars.An”m”inthelastcolumndenotesthemixedgiantsfollowingSpiteetal.(2005).
Star T , K log g v,kms−1 [Fe/H] ǫ(Na) [Na/H] [Na/Fe] Rem
eff t
Turnoffstars
BS16023–046 6360 4.5 1.4 –2.97 3.33 –2.92 +0.05
BS16968–061 6040 3.8 1.5 –3.05 2.80 –3.45 –0.40
BS17570–063 6240 4.8 0.5 –2.92 3.12 –3.13 –0.21
CS22177–009 6260 4.5 1.2 –3.10 2.95 –3.30 –0.20
CS22888–031 6150 5.0 0.5 –3.28 2.70 –3.55 –0.25
CS22948–093 6360 4.3 1.2 –3.43 2.44 –3.81 –0.51
CS22953–037 6360 4.3 1.4 –2.89 2.90 –3.35 –0.46
CS22965–054 6090 3.8 1.4 –3.04 3.10 –3.15 –0.11
CS22966–011 6200 4.8 1.1 –3.07 2.95 –3.30 –0.23
CS29499–060 6320 4.0 1.5 –2.70 3.23 –3.02 –0.32
CS29506–007 6270 4.0 1.7 –2.91 3.15 –3.10 –0.19
CS29506–090 6300 4.3 1.4 –2.83 3.40 –2.85 –0.02
CS29518–020 6240 4.5 1.7 –2.77 3.20 –3.05 –0.25
CS29518–043 6430 4.3 1.3 –3.24 2.75 –3.50 –0.30
CS29527–015 6240 4.0 1.6 –3.55 2.50 –3.75 –0.20
CS29528–041* 6170 4.0 1.3 –3.06 3.85 –2.40 +0.66
CS30301–024 6330 4.0 1.6 –2.75 3.30 –2.95 –0.20
CS30339–069 6240 4.0 1.3 –3.08 3.00 –3.25 –0.17
CS31061–032 6410 4.3 1.4 –2.58 3.50 –2.75 –0.17
Giants
HD2796 4950 1.5 2.1 –2.47 3.65 –2.60 –0.13 m
HD122563 4600 1.1 2.0 –2.82 3.20 –3.05 –0.23 m
HD186478 4700 1.3 2.0 –2.59 3.45 –2.80 –0.21 m
BD+17:3248 5250 1.4 1.5 –2.07 4.44 –1.81 +0.26 m
BD–18:5550 4750 1.4 1.8 –3.06 2.90 –3.35 –0.29
CD–38:245 4800 1.5 2.2 –4.19 2.15 –4.10 +0.09 m
BS16467–062 5200 2.5 1.6 –3.77 2.38 –3.87 –0.10
BS16477–003 4900 1.7 1.8 –3.36 2.80 –3.45 –0.09
BS17569–049 4700 1.2 1.9 –2.88 3.25 –3.00 –0.12 m
CS22169–035 4700 1.2 2.2 –3.04 3.30 –2.95 +0.09 m
CS22172–002 4800 1.3 2.2 –3.86 2.15 –4.10 –0.24
CS22186–025 4900 1.5 2.0 –3.00 3.15 –3.10 –0.10 m
CS22189–009 4900 1.7 1.9 –3.49 2.47 –3.78 –0.29
CS22873–055 4550 0.7 2.2 –2.99 3.40 –2.85 +0.14 m
CS22873–166 4550 0.9 2.1 –2.97 3.20 –3.05 –0.08 m
CS22878–101 4800 1.3 2.0 –3.25 2.95 –3.30 –0.05 m
CS22885–096 5050 2.6 1.8 –3.78 2.50 –3.75 +0.03
CS22891–209 4700 1.0 2.1 –3.29 3.10 –3.15 +0.14 m
CS22892–052* 4850 1.6 1.9 –3.03 3.00 –3.25 –0.22
CS22896–154 5250 2.7 1.2 –2.69 3.47 –2.78 –0.09
CS22897–008 4900 1.7 2.0 –3.41 2.69 –3.56 –0.15
CS22948–066 5100 1.8 2.0 –3.14 2.97 –3.28 –0.14 m
CS22949–037* 4900 1.5 1.8 –3.97 3.85 –2.40 +1.57 m
CS22952–015 4800 1.3 2.1 –3.43 3.33 –2.92 +0.51 m
CS22953–003 5100 2.3 1.7 –2.84 3.20 –3.05 –0.21
CS22956–050 4900 1.7 1.8 –3.33 4.30 –1.95 --
CS22966–057 5300 2.2 1.4 –2.62 3.60 –2.65 –0.03
CS22968–014 4850 1.7 1.9 –3.56 2.35 –3.90 –0.34
CS29491–053 4700 1.3 2.0 –3.04 3.05 –3.20 –0.16 m
CS29495–041 4800 1.5 1.8 –2.82 3.22 –3.03 –0.21
CS29502–042 5100 2.5 1.5 –3.19 2.63 –3.62 –0.43
CS29516–024 4650 1.2 1.7 –3.06 3.05 –3.20 –0.14
CS29518–051 5200 2.6 1.4 –2.69 3.40 –2.85 –0.16 m
CS30325–094 4950 2.0 1.5 –3.30 2.84 –3.41 –0.11
CS31082–001 4825 1.5 1.8 –2.91 3.30 –2.95 –0.04
Andrievskyetal.:NLTEdeterminationoftheSodiumabundance 5
Table 2. Abundance corrections (ǫ(NLTE)−ǫ(LTE)) for the
D1andD2lines.
[M/H] -2.5 -3.0 -3.5 -4.0
Teff=4500logg=0.8
EW corr EW corr EW corr EW corr
D1 182-0.48 138-0.63 107-0.44 81 -0.24
D2 161-0.54 122-0.52 93 -0.32 66 -0.14
Teff=4600logg=1.0
D1 167-0.62 - - - - - -
D2 149-0.60 - - - - - -
Teff=4750logg=1.4
D1 151-0.65 124-0.53 100-0.34 74 -0.13
D2 135-0.58 110-0.41 85 -0.20 57 -0.08
Teff=5000logg=2.0
D1 142-0.59 115-0.44 91 -0.24 63 -0.08
D2 126-0.52 100-0.31 75 -0.14 45 -0.06
Teff=5250logg=2.7
D1 137-0.56 108-0.39 82 -0.19 52 -0.06
D2 119-0.47 92 -0.28 64 -0.12 34 -0.06
Teff=5550logg=3.3
D1 122-0.49 95 -0.32 67 -0.14 38 -0.06
Fig.5.IndividualcorrectionapplyingtoanLTEanalysisofthe
D2 105-0.38 79 -0.22 49 -0.09 23 -0.06
NaD1andD2linesalongtheRGB, formetal-poorstarswith
−4.0<[Fe/H]<−2.5andthehypothesisthat[Na/Fe]=0. Teff=6000logg=3.7
D1 101-0.39 75 -0.22 45 -0.10 21 -0.06
D2 85 -0.28 57 -0.13 29 -0.08 12 -0.06
Teff=6350logg=4.1
withtheclassicalformula:
D1 88 -0.34 61 -0.18 32 -0.09 13 -0.06
D2 72 -0.23 43 -0.12 19 -0.08 7 -0.06
logL/L =logM/M +4logT /T −logg/g
⊙ ⊙ eff eff,⊙ ⊙
5. Discussion
For this set of models, the LTE profiles have been com-
5.1.Mixingeffectsingiantstars
putedwiththehypothesisthat[Na/H]=[Fe/H](i.e.,[Na/Fe]=
0),andthenfittedbyNLTEprofilesthatenabledthederivation InFig.7wepresenttheNLTEvaluesof[Na/Fe]foroursample
of the appropriate NLTE corrections. A first cause of uncer- ofstarsasafunctionof[Fe/H](thecarbon-richstarshavebeen
taintyisthattheshapesofLTEandNLTEprofilesareslightly omitted).ThesymbolsarethesameasinFig1.Dwarfsandgi-
different,butthe correctionmainlydependson the equivalent antsnowlieinthesamelocus,andthetrendofthe[Na/Fe]ra-
widthofthe sodiumlines,as canbeseen in Fig.6. Asa con- tio,intherange−4.0<[Fe/H]<−2.5,isflat.Themeanvalue
sequence,thecorrectionsgivenin Table2 canbeusedonlyif of[Na/Fe]iscloseto–0.2.
theequivalentwidthofthelinesissimilarto thatgiveninthe A few stars appear to be ”Na-rich” with [Na/Fe]>+0.1.
table. If there is a strong anomaly of the sodium abundance Allthesestarsbelong,followingSpiteetal.(2006),totheclass
in the star, it is better to deduce the correction from the Fig. ofthe”mixedstars”.Theypresentthecharacteristicsofamix-
6 (or to directly compute the non-LTE profile of the line as ing with the H-burningshell, low abundanceof carboncorre-
it has been done for the stars of our sample). Takeda et al. lated with a high abundance of nitrogen, and a low value of
(2003)havemadeafirstattempttocomputethenon-LTEcor- the 12C/13C ratio close to the equilibriumvalue.However,all
rection of the sodium abundance in a large metallicity range themixedstarsarenotNa-rich.Letusremarkthatallthestars
(−4.0<[Fe/H]<+0.4). We havecheckedthatinourdomain foundherewith [Na/Fe]>+0.1were alreadysuspected from
ofmetallicity([Fe/H]<−2.5)thereisarathergoodagreement LTEcomputations,tobeNa-rich.Allofthem,butBD17:3248,
withtheircomputations. havealsobeenfoundtobealuminumrich,andfromtheirpo-
6 Andrievskyetal.:NLTEdeterminationoftheSodiumabundance
Fig.7. [Na/Fe] vs. [Fe/H] for the sample of EMP stars. The
symbolsarethesameasinFig.1.Thesodiumabundancehas
been computed in NLTE with a modified version of the pro-
gram of Carlsson. The trend of the [Na/Fe] ratio is flat in the
region −4.0<[Fe/H]<−2.5, and there is a good agreement
betweentheabundancesofthegiantsandturn-offstars.Allthe
starswith[Na/Fe]>0.1havebeenfoundtobeextra-mixed,in
Spiteetal.(2005).
LTEeffects.InFig.8wecomparetheratio[Na/Fe]inourEMP
Fig.6.Individualcorrectionsplottedasafunctionoftheequiv- starsandinthesampleofGehrenetal.(2006);unfortunately,
alentwidthsofthelinesforthedifferentmodelsgiveninTable we haveno star in commonto checktheinfluenceof system-
2. The solid line represents the corrections for models with aticeffects,buttheyhaveonestarinourdomainofmetallicity
[Fe/H]=-2.5, the dashed lines models with [Fe/H]=-3.0, the (G64-12 with [Fe/H]=–3.1), and this star falls exactly in the
dotted-dashed lines models with [Fe/H]=-3.5, and the dotted middleofoursampleinFig.8.
linesmodelswith[Fe/H]=-4.0.Forasameequivalentwidthof Sodium has only one (stable) isotope, 23Na, which is
the D lines the correction little depends on the parameters of mainly produced in the carbon burning process operating in-
themodels sidemassivestars.AsnotedbyWoosley&Weaver(1995)the
resulting amount of sodium nuclei in the SN ejecta is sensi-
tivetotheexcessofneutrons,thereforeitsproductionissome-
sition in the HR diagram they could be AGB stars (see also whatmetaldependent,butintheearlyGalaxy(verylowmetal
Johnson(2002),andBond(1980)forBD17:3248).Noneofthe content)thiselementproductionshouldbethesameasforthe
turn-off stars or ”unmixed”giants are sodium rich. As a con- primary elements. There were several attempts to incorporate
sequence the sodium rich stars are suspected to have suffered theobservedsodiumabundanceinthediscandhalostarsinto
a mixing between the atmosphere and the H-burning shell, a Galacticevolutionarymodels.Onecanmentionheretheworks
mixing deep enough to bring the products of the Ne-Na cy- of Timmes et al. (1995), Samland (1998), and Goswami &
cletothesurface.WhenonlyEMPdwarfsandunmixedgiants Prantzos(2000).Alltheabove-mentionedmodelsarebasedon
are taken into account, we find that [Na/Fe]=−0.21±0.13 the Woosley & Weaver (1995) yields from massive stars, but
or[Na/Mg]=−0.45±0.16;thestar-to-starvariationbecomes use different initial-mass functions, star formation rates, and
smallandcomparabletowhatisobtainedfortheotherelements othermodelspecifications,whichcanexplaintheslightdiffer-
(seeCayreletal.2004). encesinthepredictions.
InFig.8ourobservationsandthoseofGehrenetal.(2006)
5.2.Comparisonwiththenearbymetal-poorstars, arecomparedtothepredictionsofTimmesetal.(1995).These
authors predict a local minimum around [Fe/H] = –1.5 with
andthepredictionofthemodelsofgalactic
subsequent increasing of [Na/Fe] as the metallicity decreases
chemicalevolution
to[Fe/H]=–3.Thepredictionsfortwodifferentvaluesofthe
RecentlyGehrenetal.(2006)havecomputedthesodiumabun- ironyieldsfrommassivestars(whichdependonthemasscutin
danceinasampleof55nearbymetal-poorstars,mostofthem themassivesupernovae)arerepresentedinthefigure.Between
belongingtothethinorthickGalacticdiscandsomeofthemto modelsT(A)andT(B),the massofironejectedbySN IIdif-
thehalo.Theyhaveverycarefullytakenintoaccountthenon- fers by a factor of two. At a metallicity higher than [Fe/H]=
Andrievskyetal.:NLTEdeterminationoftheSodiumabundance 7
Fig.8.[Na/Fe]vs.[Fe/H]forthesampleofEMPstars(Cayrel Fig.9. [Na/Mg] vs. [Fe/H] for the sample of EMP stars and
et al. 2004; Spite et al. 2005 ), dwarfs (black dots), unmixed the nearby metal-poor stars studied by Gehren et al. (2006).
giants(greydots), andthe nearbymetal-poorstars studied by Symbols are the same as in Fig. 8. The dashed line repre-
Gehrenet al. (2006) (open triangles).The dashed lines repre- sents the prediction of the model of Timmes et al. (1995).
sentthepredictionsoftwomodelsofTimmesetal.(1995)that (The [Na/Mg] ratio is independent of the mass cut at vari-
differbythequantityofironejectedbymassivestarsandthus ance with [Na/Fe] and the predictions are reduced to a sin-
bythepositionofthemasscut. gle curve). It can be seen in the figure that in the interval
−4<[Fe/H]<−2.8 [Na/Mg] is constant. However, a slight
increase of [Na/Mg] when the metallicity decreases (from
[Na/Mg]= –0.5 at [Fe/H]=–3. to [Na/Mg]= –0.3 at [Fe/H]=–
–3, there is a rather good agreement with the predictions of
4.)cannotbeexcluded.
themodelT(A),whichsupposesthesmallestvalueoftheiron
yieldsfrommassivestars,andsuchanagreementisgenerally
foundfortheotherelements(seeCayreletal.2004).
Incontrastwith[Na/Fe],theratio[Na/Mg]isindependent the distribution of EMP stars in the [Na/Mg] or [Al/Mg] ver-
ofthemasscut.InFig.9wepresent[Na/Mg]asafunctionof sus [Mg/H] plane. The observed trends and the scatter of the
[Fe/H]foroursampleofEMPstarsandthesampleofGehren observations are mainly based on the work of McWilliam et
et al. (2006). (We neglected the NLTE effects on the magne- al. (1995). This sample contains several mixed giants which
sium lines that are not supposed to be very important). The explain the very large scatter of [Na/Mg] and [Al/Mg] they
agreementisrathergoodfor[Fe/H]>−3. observed at low metallicity. Such a scatter, which is an im-
Timmes et al. (1995) do not predict the behaviour of portant point in the definition of the model of Tsujimoto et
[Na/Fe]or[Na/Mg]for[Fe/H]<−3.Fromourmeasurements, al. (2002), is not observed in the unmixed stars of our sam-
[Na/Fe]and[Na/Mg]becomeflat:therelativeabundancesare ple(dwarfsand”unmixed”giants)andthusdoesnotprobably
independent of the metallicity. However, a slight increase of reflectascatterinthepristinematerial.LetusnotethatCohen
[Na/Mg]whenthemetallicitydecreases(from[Na/Mg]=–0.5 et al. (2004), who studied a sample of turnoff stars in the in-
at[Fe/H]=–3.to[Na/Mg]=–0.3at[Fe/H]=–4.)cannotbeex- terval−3.6<[Fe/H]<−2.2,alsofoundaverysmallscatterof
cluded. [Al/Mg].Theprecise determinationof[Al/Mg]in oursample
ofstarsfromnon-LTEsyntheticprofilesisinprogress.
Samland (1998) has considered the chemical evolution of
many elements and found that the expected distribution of
[Na/Fe] vs. [Fe/H] in the extreme metallicity region from
6. Conclusion
[Fe/H] = –4 to –2.5 is almost independent of [Fe/H], and
the mean [Na/Fe] value equals approximately –0.2. This was NLTE abundances of sodium have been derived for
not supported by observations available at that time, but is a sample of extremely metal-poor dwarfs and giants us-
in good agreement with our observations. Qualitatively the ing high-resolution spectra obtained with VLT. Both sub-
sameconclusionwasreachedbyGoswami&Prantzos(2000). samples of dwarfs and unmixed giants now have the
According to their model, [Na/Fe] must be almost constant same mean [Na/Fe] or [Na/Mg] values, within the standard
within this metallicity interval and equal approximately –0.5, errors: [Na/Fe]=−0.21±0.13 or [Na/Mg]=−0.45±0.16.
butthisissignificantlylowerthanwhatisgivenbyourcalcu- However,aslightincreaseof[Na/Mg]atlowmetallicity,(from
lations. [Na/Mg]= –0.5 at [Fe/H]=–3. to [Na/Mg]= –0.3 [Fe/H]=–4.)
RecentlyTsujimotoetal.(2002)havealsoinvestigatedthe cannotbeexcluded.
chemicalevolution of sodium and aluminum duringthe early •Inthedomain−4<[Fe/H]<−2.5,thegiantsofoursam-
epochsoftheGalaxy.Theyhaveusedamodelthatreproduces pledonotexhibitanysystematicdependenceof[Na/Fe]upon
8 Andrievskyetal.:NLTEdeterminationoftheSodiumabundance
[Fe/H], contrary to the preliminary findings of Cayrel et al. GoswamiA.,PrantzosN.,2000,A&A359,191
(2004). This effect was a consequence of a coarse treatment JohnsonJ.A.,2002,ApJ139,219
of the non-LTEeffects: in Cayrel et al. (2004) the LTE abun- KimY.-C.,DemarqueP.,YiS.K.,AlexanderD.R.,2002, ApJS143,
danceshadbeenuniformelycorrectedby–0.5dex.Infact,the 499
KorotinS.A.,AndrievskyS.M.,LuckR.E.,1999a,A&A351,168
non-LTEcorrectionstrongly dependson the equivalentwidth
Korotin S.A., Andrievsky S.M., Kostynchuk L.Yu., 1999b, Ap&SS
ofthesodiumlinesandthusisgenerallysmalleratlowermetal-
260,531
licity. (When the lines are smaller they formdeeperin the at-
KorotinS.A.,MisheninaT.V.,1999,ARep43,533
mosphere where, in particular, collisions are more important
KuruczR.,1992,RMxAA23,45
andthusnon-LTEcorrectionsaresmaller.)
KuruczR.L.,FurenlidI.,BraultJ.,TestermanL.,1984,NationalSolar
•Amongthegiantstars,the”mixed”giants(starsthathave Observatory,Atlas,Sunspot,NewMexico
undergone an extra-mixing between the atmosphere and the MaltbyP.,AvrettE.H.,CarlssonM.,Kjeldseth-MoeO.,KuruczR.L.,
H-burningshell following Spite et al. 2005), often presentan LoeserR.,1986,ApJ306,284
overabundanceofNa.Itissuggestedthatinthesestars,mate- MashonkinaL.I.,SakhibullinN.A.,ShimanskijV.V.,1993,ARep37,
rialprocessedinNe-Nacycleinthehothydrogenburningshell 192
hasbeenbroughttothesurface.FromtheirpositionintheHR MashonkinaL.I.,ShimanskiiV.V.,SakhibullinN.A.,2000,ARep44,
790
diagram,someofthesestarscouldbeAGBstars.
McWilliam A., Preston G.W., Sneden C., Searle L., 1995, AJ 109,
• Qualitatively, our observational result on sodium distri-
2757
butionin themetallicityregion[Fe/H]from–4to–2.5agrees
Mishenina T.V., Kovtyukh V.V., Korotin S.A., Soubiran C., 2003,
withpredictionsofmodelselaboratedbySamland(1998)and
ARep47,422
Goswami & Prantzos (2000). Both models produce the al-
NorrisJ.E.,RyanS.G.,BeersT.C.,2001,ApJ561,1034
most constant [Na/Fe] value in the region of extreme metal- SamlandM.,1998,ApJ496,155
poorstars.Inparticular,theSamland’smodelgivesanaverage SivaraniT.,BeersT.C.,BonifacioP.,MolaroP.,etal.2006,(submitted
[Na/Fe] value that approximately equals –0.2, and this value toA&A)
appearstobeinquantitaviveagreementwithourestimateofthe SnedenC.,McWilliamA.,PrestonG.W.,etal.,1996,ApJ467,819
mean relative-to-iron sodium abundance in the early Galaxy. SnedenC.,CowanJ.J.,IvansI.I.,etal.,2000,ApJ533,L139
ThemodelofTimmesetal.(1995)alsoagreeswithourobser- SnedenC.,CowanJ.J.,LawlerJ.E.,IvansI.I.,BurlesS.,BeersT.C.,
PrimasF.,HillV.,etal.,2003,ApJ591,936
vationsaround[Fe/H]=–3.Inqualitativeagreement,themodel
SpiteM.,CayrelR.,PlezB.,HillV.,F.Spite,E.Depagneetal.,2005,
of Goswami & Prantzos predicts a slightly too low relative
A&A430,655
sodiumabundanceforextremelymetal-poorstars.
Spite M., Bonifacio P., Cayrel R., Hill V., Francois P., Spite F.
et al., 2005 in the Proceedings of the IAU symposium 228
Acknowledgements. SMA kindly acknowledges the C.N.R.S./INSU
”FromlithiumtoUranium:ElementalTracersofEarlyChemical
forfinancialsupportandtheParis-MeudonObservatoireforitshospi-
Evolution”,V.Hill,P.Franc¸ois,&F.Primaseds.,p.185
talityduringhisproductivestayinMeudon.
SpiteM.,CayrelR.,HillV.,SpiteF.,FrancoisP.,PlezB.,Bonifacio
P., Molaro P., Depagne E. et al., 2006, A&A (in press), astro-
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