The chemical composition of red giants in 47 Tucanae. II. Magnesium isotopes and pollution scenarios

0.69 MB·

by  A. O. Thygesen

Astronomy&Astrophysicsmanuscriptno.47Tuc_paper2_v8 (cid:13)cESO2016
February2,2016
The chemical composition of red giants in 47 Tucanae. II.
Magnesium isotopes and pollution scenarios (cid:63)
A.O.Thygesen1,2,L.Sbordone3,4,2,H.-G.Ludwig2,P.Ventura5,D.Yong6,R.Collet6,N.Christlieb2,J.Melendez7,
andS.Zaggia8
1 CaliforniaInstituteofTechnology,1200E.CaliforniaBlvd.,MC249-17,Pasadena,CA91125,USA.
2 ZentrumfürAstronomiederUniversitätHeidelberg,Landessternwarte,Königstuhl12,69117Heidelberg,Germany.
3 MillenniumInstituteofAstrophysics,Chile.
4 PontificiaUniversidadCatólicadeChile,Av.VicuñaMackenna4860,782-0436Macul,Santiago,Chile.
5 INAF-OsservatorioAstronomicodiRoma,ViaFrascati33,I-00040MontePorzioCatone,Italy.
6 6 ResearchSchoolofAstronomyandAstrophysics,AustralianNationalUniversity,Canberra,ACT0200,Australia.
1 7 DepartamentodeAstronomiadoIAG/USP,UniversidadedeSãoPaulo,ruadoMãtao1226,05508-900,SãoPaulo,SP,Brasil.
0 8 INAF-OsservatorioAstronomicodiPadova,Vicolodell’Osservatorio5,35122Padova,Italy.
2
Received01-062015;Accepted25-012016
n
a
J ABSTRACT

0
3 Context.Thephenomenonofmultiplepopulationsinglobularclustersisstillfarfromunderstood,withseveralproposedmechanisms
toexplaintheobservedbehaviour.Thestudyofelementalandisotopicabundancepatternsarecrucialforinvestigatingthedifferences
] amongcandidatepollutionmechanisms.
R Aims.Wederivemagnesiumisotopicratiosfor13starsintheglobularcluster47Tucanae(NGC104)toprovidenew,detailedinfor-
S mationaboutthenucleosynthesisthathasoccurredwithinthecluster.Forthefirsttime,theimpactof3Dmodelstellaratmospheres
onthederivedMgisotopicratiosisinvestigated.
.
h Methods. Usingbothtailored1Datmosphericmodelsand3Dhydrodynamicalmodels,wederivemagnesiumisotopicratiosfrom
p fourfeaturesofMgHnear5135Åin13giantsnearthetipoftheRGB,usinghighsignal-to-noise,high-resolutionspectra.
- Results.Wederivethemagnesiumisotopicratiosforallstarsandfindnosignificantoffsetoftheisotopicdistributionbetweenthe
o
pristineandthepollutedpopulations.Furthermore,wedonotdetectanystatisticallysignificantdifferencesinthespreadintheMg
r
t isotopesineitherpopulation.NotrendswerefoundbetweentheMgisotopesand[Al/Fe].Theinclusionof3Datmosphereshasa
s significantimpactonthederived25Mg/24Mgratio,increasingitbyafactorofupto2.5,comparedto1D.The26Mg/24Mgratio,onthe
a
otherhand,essentiallyremainsunchanged.
[
Conclusions.Weconfirmtheresultsseenfromotherglobularclusters,wherenostrongvariationintheisotopicratiosisobserved
1 betweenstellarpopulations,forobservedrangesin[Al/Fe].WeseenoevidenceforanysignificantactivationoftheMg-Alburning
v chain.Theuseof3Datmospherescausesanincreaseofafactorofupto2.5inthefractionof25Mg,resolvingpartofthediscrepancy
8 betweentheobservedisotopicfractionandthepredictionsfrompollutionmodels.
5
Keywords. globularclusters:individual:47Tucanae-stars:abundances-stars:fundamentalparameters-methods:observational-
0
techniques:spectroscopic
0
0
.
2
1. Introduction Ventura&D’Antona2009;Karakas2010),fast-rotatingmassive
0
stars(FRMS,Decressinetal.2007),massiveinteractingbinaries
6Themultiplepopulationphenomenoninglobularclusters(GCs)
1 (de Mink et al. 2009), early disk accretion on low-mass proto-
isatthepresentnotunderstoodwell.Essentially,allwell-studied
: stars (Bastian et al. 2013), or supermassive stars (Denissenkov
vGCs are found to harbour a pristine population of stars with a
& Hartwick 2014). All of these candidates can, with the right
icomposition similar to field stars at the same metallicity, and
X assumptions, explain parts of the observed behaviour, but each
one or more polluted populations, which show anomalies in
candidatestruggleswithitsownsetofproblems,andnosingle
rthelightelementabundances.Theonlyknownexceptionisthe
a pollutercanexplaintheobservedbehaviourinfull(Bastianetal.
GC Ruprecht 106 (Villanova et al. 2013), which appears to be
2015).
a single stellar population. Whereas it is observationally well-
established that most, if not all, GCs show variations in the
A large part of the observational constraints on the polluter
light elements (He, C, N, O, Na, sometimes Mg and Al, see
candidates comes from elemental abundance studies. Here, the
e.g. Gratton et al. 2012), the mechanism responsible for these
presenceoftheNa-Oanti-correlation,aswellastheoccasional
variations has not yet been determined. A number of different
Mg-Alanti-correlation,givesinsightintotheburningconditions
candidates for this pollution has been proposed, namely AGB
that must have occurred in the polluters. The magnitude of the
stars (e.g. Cottrell & Da Costa 1981; Denissenkov et al. 1997;
variations also gives clues to the amount of processed material
Sendoffprintrequeststo:A.O.Thygesen thatneedsincorporationinthepollutedpopulationofstars,and
(cid:63) BasedonobservationsmadewiththeESOVeryLargeTelescopeat thedegreeofdilutionwithpristinegas.However,evenwiththe
ParanalObservatory,Chile(Programmes084.B-0810and086.B-0237). ever-increasing number of GC stars with accurately measured
Articlenumber,page1of22
A&Aproofs:manuscriptno.47Tuc_paper2_v8
abundances, no consensus has been reached on the full expla- changes are well outside the total range of reaction rates deter-
nation of the observed trends. Thus, it is necessary to try and minedfromnuclearphysics,whichspanslessthanoneorderof
provide additional diagnostics that can be used to constrain the magnitude,fortherelevanttemperatures(Longlandetal.2010).
natureofthepolluters. Using standard reaction rates, the FRMS provide a net produc-
The measurement of Mg isotopes may provide additional tionofMg,mainlyintheformof24Mg,sothiswouldalsoresult
piecesofinformation,supplementingwhatcanbeinferredfrom inamodificationoftheisotopicratios.However,fromthemod-
abundanceratios.Inmoststarstheisotopicdistributionisdomi- els one would expect a correlation between Mg and Al, which
natedby24Mg,whichismainlyproducedintypeIIsupernovae, againcontradictstheobservations.
althoughsomeproductioncanalsohappeninAGBstars(Waller- It has been shown by Prantzos et al. (2007) that the con-
steinetal.1997).Theamountofthetwoheavyisotopes,25Mg ditions required to activate the Mg-Al burning chain can be
and26Mg,istypicallysignificantlyless,withthesolarvaluebe- reached in the center of massive stars, but only at the very end
ing 79:10:11, given as percentage 24Mg:25Mg:26Mg. The pro- of their main sequence evolution. There exist no known mech-
ductionofheavyMgisotopesisrathercomplex,andcanoccur anism for transporting the processed material to the surface of
in multiple sites. In the context of variations of the Mg and Al thestar,andreleaseitinaslowfashionsothatitcanberetained
abundances, one possible mechanism is AGB stars undergoing withintheclusteratthisstageofthestellarevolution.Rather,at
hot bottom burning (HBB), which will alter the distribution of this point, the mass loss is dominated by a fast wind, which a
theMgisotopes.Thisprocessisverysensitivetotheconditions typical GC will have difficult to retain (Decressin et al. 2007).
in the nuclear burning zone, more so than just the bulk abun- Finallywenotethatalsothesupermassivestars(Denissenkov&
dances (see e.g. Karakas & Lattanzio 2003). Thus, when pos- Hartwick 2014) reach the appropriate conditions for activating
sible to measure magnesium isotopes in GC stars, these mea- the Mg-Al chain, but these models rely on some very particu-
surements can be used to yield detailed information about the larconditions,andrequiresmoreexplorationbeforetheycanbe
polluters,comparedtowhatelementalabundancescandeliver. appliedtoGCsinfull.
Obtainingspectraofaqualitywheretheisotopicdistribution The GC 47 Tucanae is known to harbour at least two pop-
can be measured is observationally challenging, because it re- ulations of stars, making itself known both through splittings
quires very high resolution spectra (> 80000), combined with of stellar sequences in the colour-magnitude diagram (Ander-
exquisite signal-to-noise (≥ 150). Such measurements only ex- son et al. 2009; Milone et al. 2012), and through light element
istforafewGCs,startingwiththepioneeringworkofShetrone abundance variations (e.g. Cottrell & Da Costa 1981; Briley
(1996), who used the observed variations in heavy isotopes to et al. 1996; Alves-Brito et al. 2005; Koch & McWilliam 2008;
rule out deep mixing as the cause of the abundance variations Corderoetal.2014;Thygesenetal.2014).Mostpronouncedis
in the GC M13. This provided a strong argument for the case the anti-correlation between Na and O, but also a variation in
of abundance variations being present already in the gas that [Al/Fe]isobserved.Eventhough,duetoitsproximity,47Tucis
formedthepollutedgenerationofstars,thenowcommonlyac- exceptionallywell-studied,agoodunderstandingofitschemical
ceptedinternalpollutionscenario.MeasurementsofMgisotopic evolutionhistoryisstilllacking.Venturaetal.(2014)proposed
ratios have also been carried out for NGC6752 (Yong et al. a pollution scenario based on AGB stars as the main source of
2003a), M13 (Shetrone 1996; Yong et al. 2006), M71 (Melén- pollution.Theywereabletoexplainalargepartoftheobserved
dez&Cohen2009;Yongetal.2006)andωCentauri(DaCosta abundance variations, but as recently argued by Bastian et al.
etal.2013). (2015), none of the polluter candidates are able to explain the
In all cases, a correlation has been observed between the fullrangeofobservedabundancevariations.
amountofheavyMgisotopesand[Al/Fe],whichbecomespar- InthispaperweaddmeasurementsofMgisotopesin13stars
ticularly evident when the [Al/Fe] enhancement reaches values to the chemical inventory of the cluster. This is a continuation
≥ 0.5 dex. In the context of AGB stars, production of heavy of Thygesen et al. (2014), hereafter Paper 1, where we derived
Mg isotopes requires adopting the maximum values consistent stellarparametersandabundancesforabroadrangeofelements
withnuclearphysicsforthe25Mg(p,γ)26Alreaction(Ventura& for the same sample of stars. By also adding measurements of
D’Antona2008,2011;Venturaetal.2011).Themodelsalsopre- theMgisotopes,wecaninvestigatethecandidatepolluterseven
dictthatmostoftheinitial24Mgisconvertedto25Mg.Anexperi- further.
mentalmodelbyVenturaetal.(2011),wheretheprotoncapture
on 25Mg is increased by a factor of two, is required to explain
themostextreme[Al/Fe]enrichments,andalsoreducesthefinal 2. Observations
amountof25Mg.However,themodelsstillpredicta25Mg/24Mg
TheobservationsforthisprojectwereobtainedwiththeUVES
ratiothatissignificantlyhigherthanthe26Mg/24Mgratio,which
spectrograph (Dekker et al. 2000) equipped with Image-Slicer
is in contrast to the observations. Karakas et al. (2006) on the
#3, mounted on the ESO VLT on Cerro Paranal, Chile. Each
other hand, achieves 26Mg/24Mg ratios higher than 25Mg/24Mg
spectrumhasaresolutionofR = 110000andreachedasignal-
in their models, but their adopted reaction rates also result in a
to-noise of ∼150 at the position of the MgH features, which is
net production of Mg, which is in contrast to the Mg-Al anti-
requiredforaccuratedeterminationofthedistributionofmagne-
correlationseeninanumberofGCs.Asimilarbehaviourisalso
siumisotopes.Thetargetswerechosenfromtheclustercolour-
observed for the most massive models in the computations of
magnitude diagram such that members of both the pristine and
Fishlocketal.(2014).
pollutedpopulationwereincluded.WereferthereadertoPaper
The FRMS are also able to process some Mg, which re-
1forfurtherdetailsabouttheobservationsanddatareduction.
sults in a production of Al, at the expense of 24Mg. However,
thisrequiresthatthenuclearreactionratesforprotoncaptureon
24Mgareartificiallyincreasedbythreeordersofmagnitude(De-
3. Analysis
cressinetal.2007).Thismodificationisalsorequiredtorepro-
ducetheMgisotopicdistributioninthecaseofNGC6752,which The isotopic shifts of the atomic lines of Mg are much smaller
Decressin et al. (2007) use for model comparison. Such drastic than the natural broadening of the spectral lines, so in order to
Articlenumber,page2of22
A.O.Thygesenetal.:Thechemicalcompositionof47TucII
measuretheisotopicmixture,onehastoutilisemolecularlines the isotopic ratios with temperature when inspecting the indi-
ofmagnesiumhydride(MgH).Weusethefeaturesfromtheelec- vidual results from the 5134.6Å and 5140.2Å features. These
tronic A-X transitions around 5135Å, where the isotopic shifts trendswerenotpresentwhenthestrongC lineswereincluded
2
areobservedasanasymmetryintheredwingofthedominating in the line list. As such, the complete removal of the C lines
2
24MgHfeature. amountstoovercompensating.Rather,theculpritC linesdoap-
2
peartobepresent,butlikelytheirlog(gf)valuesaretoohigh.
From this exercise, we also identified a previously unused
3.1. Lineselection
MgH molecular feature at 5135.1Å that is also not sensi-
Traditionally, three molecular MgH features are used for the tive to the C abundances (Fig. 1). If we exclude the 5140Å
derivationofmagnesiumisotopes(McWilliam&Lambert1988) feature for Arcturus, we find the percentage distribution of
at: 24Mg:25Mg:26Mg=82.3:9.0:8.7,iftakenasastraightaverage.If
weinsteaddoaweightedmean,likeadoptedforthe47Tucstars
– 5134.6Å,whichisablendofthe0−0Q (23)and0−0R (11) (seelater)wefind82.0:9.8:8.2.Finally,ifweincludethe5140Å
1 2
electronictransitions. feature(butdepleteCbyanadditional0.1dex,comparedtothe
– 5138.7Å,whichisablendofthe0−0Q (22)and1−1Q (14) valuequotedinSnedenetal.2014),wearriveat83.6:9.2:7.2for
1 2
electronictransitions. the distribution of the isotopes. This is in good agreement with
– 5140.2Å,whichisablendofthe0−0R (10)and1−1R (14) the values found by McWilliam & Lambert (1988), who found
1 2
electronictransitions. 82:9:9; and Hinkle et al. (2013) who reported 80:10:10. Keep-
inginmindthedifferencesinlinelistsandanalysismethods,we
AlloftheMgHfeaturesmentionedabove,sufferfromblends considerthisagreementsatisfactory.
with both atomic lines and molecular lines of C , CN and CH. In order to use the 5134.6Å and 5140.2Å features to de-
2
However, it is believed that these three features are suffering rive Mg isotopic ratios, information about the C abundance is
theleastfromblends,comparedtootherMgHtransitionsinthe required.Meléndez&Cohen(2009)andYongetal.(2003a)use
vicinity. twodifferentregionstoestimatetheCabundanceintheirsam-
Compared to previous investigations of Mg isotopic ratios, pleofgiants,namelyaC featureat5136Å,andtheC features
2 2
we used new, updated line positions and level energies taken around5635Å.Inoursampleofstars,wecannotderiveanuseful
from Shayesteh & Bernath (2011) for 24MgH and from Hinkle Cmeasurefromthe5136Åfeature,butwewereabletousethe
et al. (2013) for 25MgH and 26MgH, where all previous studies 5635Åregion,althoughtheC featureswereveryweak.While
2
have been using the pioneering work of Bernath et al. (1985). thisregionshowsmultipleblendsfromothermolecularspecies,
The changes in line position between our data and the work of it can be used to give an indication of the C abundance in our
Bernath et al. (1985) were typically small, so this did not have stars. The lines are already very weak, and are not sensitive to
a strong impact on the derived results, compared to employing strong C depletion. As such, our derived values should only be
thelinelistusedinearlierworks.ForCHweusedlineinforma- taken as upper limits on the C abundance. As can be seen in
tionfromMasseronetal.(2014),whereasforC weuseBrooke
2 Fig.1,the5134.6Åand5140.2ÅMgHfeaturesareverysensi-
etal.(2013),andSnedenetal.(2014)togetherwithBrookeetal.
tivetotheCabundance,butnonetheless,forour47Tucstars,we
(2014)forCN.Fortheatomicblends,weusedthelineinforma-
areabletofitthesetwofeatureswiththeCabundanceestimated
tionfromversion3oftheGaia-ESOsurveylinelist(Heiteretal.
fromtheC transitionsinthe5635Åregion.
2
inpreparation),withafewlinesaddedfromtheVALDdatabase
However, keeping in mind the result from the test on Arc-
(Kupka et al. 2000). We include atomic blends from Ti, V, Cr,
turus, even with a correct C abundance, the isotopic ratios de-
Fe, Co, Y, Nb, Mo, Ce and Pr. We used the elemental abun-
rived from these two features should not be considered as re-
dancesmeasuredinPaperIwhereavailable.Incaseswherethe
liable as what can be derived from the 5135.1Å and 5138.7Å
elemental abundances could not be measured, we used scaled
features, which do not show such sensitivity. In particular the
solarvalues.
measurements from the 5140.2Å feature will likely underesti-
We checked our line list against a spectrum of Arcturus,
matethetrueamountoftheheavyisotopes.
whichisadmittedlymoremetal-rich,anditwasfoundthatafew
WhencalculatingtheaverageMgisotopicfractions,weonly
C lines came out very strong in the synthesis, when Arcturus
2
was fitted with the stellar parameters from Ramírez & Allende give half weight to the results from the 5134.6Å and 5140.2Å
Prieto(2011),usingtheCabundancefromSnedenetal.(2014). features, although we were able to fit the features with similar
Thispointstowardseitherproblemswiththelog(gf)values,the isotopicfractionstothe5135.1Åand5138.7Åfeaturesinmost
presence of 3D effects on selected C lines, or mis-identified cases.Thiswasdoneforallstarsinthesample,duetothelikely
2
lines. This issue is particularly evident for the region around log(gf)problemsdiscussedabove.Fullweightwasgiventothe
5140Å. In Arcturus, the MgH feature present here, cannot be 5135.1Åand5138.7Åfeatures.
fitusingtheCabundancefromSnedenetal.(2014),butrequires Since also the abundance of nitrogen is known to exhibit
additionaldepletion,evenifthe25Mgand26Mgcomponentsare strong variations in GCs, this may affect the shape of the MgH
removed entirely. The overly strong C lines in Arcturus in the regions as well, as blends of CN are also included in our line
2
5140Åregionaresooverestimatedthatamuchbetterfitisob- list.However,asillustratedinFig.2,evena1dexvariationofN
tainedbysimplyremovingthemfromthesyntheses.Conversely, doesnotinfluencethelineshapes.Thus,wedonotconsiderthe
wefoundthatthisisnotadvisableinthecaseofourstars. unknownnitrogenabundancetobeanissueforouranalysis.
WhiletheC linesaretoostrong,atleastforstarsasmetal- In principle, also blends of TiO could influence our results.
2
rich as Arcturus, they are also temperature-sensitive, increas- Wetestedthisbycalculatingasynthesisforallfourfeatures,us-
ing with strength with temperature, for the temperature range ingallknowntransitionsofTiOfromPlez(1998).Weincluded
considered here. If the C lines in question were left out when linesofallstableTiisotopesandusedthesolarisotopicmixture.
2
analysingour47Tucsample,thisresultedinaspurioustrendof Thiswasdoneforourcooleststar(star5265),wheretheforma-
Articlenumber,page3of22
A&Aproofs:manuscriptno.47Tuc_paper2_v8
24MgH25MgH26MgH 24MgH25MgH26MgH
1.2 1.2
Best fit, [C/Fe]=−0.3
[C/Fe]=0.0
1.0 [C/Fe]=−0.6 1.0
x 0.8 x 0.8
u u
s. fl s. fl
e e
R 0.6 R 0.6
0.4 0.4
0.2 0.2
5134.2 5134.4 5134.6 5134.8 5135.0 5134.6 5134.8 5135.0 5135.2 5135.4
Wavelength [Å] Wavelength [Å]
24MgH25MgH26MgH 24MgH25MgH26MgH
1.2 1.2
1.0 1.0
x 0.8 x 0.8
u u
s. fl s. fl
e e
R 0.6 R 0.6
0.4 0.4
0.2 0.2
5138.4 5138.6 5138.8 5139.0 5139.2 5139.8 5140.0 5140.2 5140.4 5140.6
Wavelength [Å] Wavelength [Å]
Fig.1:SynthesisofthefourMgHfeaturesusedtoderivetheisotopicfractionsofMginstar5265.Theredlineshowsthesynthesis
usingbestfitting[C/Fe]value,whereasthedashedlinesshowthechangeofthelineshapewhenthe[C/Fe]ischangedby±0.3dex
aroundthisvalue.
tionofTiOmoleculesshouldbemostpronounced.Includingthe in Meléndez & Cohen (2009), we revisited our broadening, by
TiO features had negligible impact on the line shapes, and we synthesizing Fe I lines at 6056.0, 6078.5, 6096.7, 6120.2 and
discardedtheminthesynthesisforallremainingstars. 6151.6Å. The broadening derived from these lines were sub-
sequently adopted, assuming a Gaussian broadening profile for
eachstar,representingtheinstrumentalresolution,macroturbu-
3.2. MgisotopeswithMOOG
lenceandrotationalbroadeningasawhole.
We synthesised the MgH features using the 2013 version of EventhoughtheisotopicsplittingsoftheMgHfeaturesare
theMOOGspectralsynthesiscode(Sneden1973;Sobecketal. small, it is immediately evident that all three isotopic compo-
2011;Snedenetal.2012),forour1Danalysis.Weusedthesame nents are required to produce a satisfactory match between the
ATLAS12 models as for the abundance analysis in Paper 1 as observed spectra and the syntheses. This is illustrated in Fig. 3
the basis for our syntheses. Initially a 20Å piece of the spec- whereweshowthebest-fittingsynthesesforthe5135.07Åfea-
trumwassynthesisedinordertosetthecontinuumlevel.Using ture in star 5265, including various isotopic components of the
thisnormalisation,wedeterminedtheinitialbestfittingisotopic MgHfeature.Inallcasesare24Mg+25Mg+26Mgkeptconstant.
mixture by eye, where we varied both the isotopic mixture and Onlythesynthesiswithallthreecomponentsprovideasatisfac-
theabundanceofMg,untilasatisfactoryfitwasachieved.This toryfittotheobservedspectrum.
was done individually for each of the considered regions. The Using our by-eye fits as a first estimate of the isotopic ra-
isotopicmixturevariationswereaccomplishedbyadjustingthe tios, we refined the synthesis, determining the best fit by doing
log(gf)-value of the molecular transition so that the fractional aχ2-minimisationbetweentheobservedspectrumandagridof
strength of each isotopic component corresponded to the frac- synthetic spectra following the method of Yong et al. (2003a).
tional abundance of that isotope. With the quality of the obser- This was done iteratively, in each step varying the isotopic ra-
vations available here, variations as small as 3% for 25Mg and tios25,26Mg/24Mgandtotalmagnesiumabundance.Initially,we
26Mgcaneasilybedistinguishedbyeye.TheabundanceofMg explored a large parameter space, but for the final result we
is a free parameter in the fits, and is solely used to adjust the adopted a finer sampling to refine our results. Each of the four
overall strength of the MgH features. Following the procedure MgH features used was fitted independently. As an example,
Articlenumber,page4of22
A.O.Thygesenetal.:Thechemicalcompositionof47TucII
24MgH25MgH26MgH 24MgH25MgH26MgH
1.2 1.2
Best fit, [N/Fe]=0.0
[N/Fe]=+0.5
1.0 [N/Fe]=−0.5 1.0
x 0.8 x 0.8
u u
s. fl s. fl
e e
R 0.6 R 0.6
0.4 0.4
0.2 0.2
5134.2 5134.4 5134.6 5134.8 5135.0 5134.6 5134.8 5135.0 5135.2 5135.4
Wavelength [Å] Wavelength [Å]
24MgH25MgH26MgH 24MgH25MgH26MgH
1.2 1.2
1.0 1.0
x 0.8 x 0.8
u u
s. fl s. fl
e e
R 0.6 R 0.6
0.4 0.4
0.2 0.2
5138.4 5138.6 5138.8 5139.0 5139.2 5139.8 5140.0 5140.2 5140.4 5140.6
Wavelength [Å] Wavelength [Å]
Fig.2:SynthesisofthefourMgHfeaturesusedtoderivetheisotopicfractionsofMginstar5265.Theredlineshowsthesynthesis
usingthescaledsolar[N/Fe],whereasthedashedlinesshowthechangeofthelineshapewhenthe[N/Fe]ischangedby±0.5dex
aroundthisvalue.
24MgH 25MgH 26MgH
identthatthefittedratiosaredetectionsatleastatthe3σlevel,
1.0 forboththe25Mg/24Mgand26Mg/24Mgratios.
Intotal,morethan1300differentsyntheseswerecalculated
in each iteration for each feature. The differences between the
0.8 isotopicfractionsfoundbyeye,comparedtotheχ2-fittingwere
ux small,typically1%butneverhigherthan3%.Thefinalisotopic
m. fl mixturefromthismethodisgivenasaweightedmeanofthein-
Nor 0.6 dividualresults,withfullweightgiventothe5135Åand5138Å
features. We only gave half weight to the results from the fea-
All isotopes tures at 5134Å and 5140Å, which suffered from C molecular
0.4 24MgH 2
24MgH+25MgH blends.
24MgH+26MgH
5134.8 5134.9 5135.0 5135.1 5135.2 5135.3 5135.4 3.3. MgisotopeswithCO5BOLD/Linfor3D
Wavelength [Å]
Fig.3:1Dsynthesesofthe5135.07ÅMgHfeaturefordifferent WhenderivingtheMgisotopicratiosfromthelineasymmetries
in the MgH features it is important to take into account all po-
isotopic components. The central wavelength of each isotopic
tentialeffectsthatcouldcreatesuchasymmetries.Blendingwith
transitionisindicatedwithverticallines.
other atomic and molecular lines is one effect that could cause
discrepanciesintheobservedisotopicratios,asdiscussedabove.
Alsotheconvectivemotionsofgasinthestellaratmospheresare
knowntocauselineasymmetries(seee.g.Dravins1982).Con-
wepresentthebest-fittingsyntheses,aswellascurvesshowing vection is an intrinsically multi-dimensional phenomenon and
∆χ2 = χ2 −χ2 forallfourfeaturesinthestar4794inFigs.4 cannotbemodelledin1D.IntheATLAS12models,convection
min
and5.Here,wetake∆χ2 =1asthe1σfittingprecision.Itisev- isapproximatedbythemixing-lengthformulation,andtheusual
Articlenumber,page5of22
A&Aproofs:manuscriptno.47Tuc_paper2_v8
1.0 1.0
0.8 0.8
x x
u u
m. fl 0.6 m. fl 0.6
or or
N N
0.4 0.4
0.2 0.2
5134.4 5134.5 5134.6 5134.7 5134.8 5134.8 5134.9 5135.0 5135.1 5135.2 5135.3 5135.4 5135.5
Wavelength [Å] Wavelength [Å]
10 10
8 8
6 6
χ2 χ2
∆ ∆
4 4
2 2
0 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.09 0.10 0.11 0.12 0.13 0.14 0.15
25Mg/24Mg 25Mg/24Mg
10 10
8 8
6 6
χ2 χ2
∆ ∆
4 4
2 2
0 0
0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.07 0.08 0.09 0.10 0.11 0.12 0.13
26Mg/24Mg 26Mg/24Mg
(a)MgH5134Å (b)MgH5135Å
Fig.4:Linefitsandχ2distributionsforthefittedisotopicratiosforthe5124Åand5135ÅMgHfeaturesinstar4794.Thepositions
oftheMgHtransitionsareindicatedinthetopplots.Vertical,magentalinesshowbest-fittingvaluesintheχ2plots..Thereddashed
linesindicatethe1σfittingprecision.
macro-andmicro-turbulencequantitiesareusedtoparametrise Table1:ModelparametersforourCO5BOLD3Dmodels.
large-andsmall-scalegasmotionsrespectively.
ID Teff logg [Fe/H] [α/Fe] modeltime
HiMet 3970K 1.50 −0.50 +0.2 1472h
3.3.1. Modelsetup LoMet 4040K 1.50 −1.00 +0.4 1111h
Three-dimensional,hydrodynamicalatmospheresdonotrelyon
the mixing-length theory (MLT) approximation or similar ap-
proximatedescriptionsfortreatingconvectiveenergytransport,
noronmicro-/macro-turbulenceparametersforthemodellingof entropy. Hence why the 3D model Teff is not the same in the
convectivebroadeningofspectrallines.WeusedtheCO5BOLD twocases.Wedidnotcalculate3Dmodelsforourmoreevolved
atmosphericcode(Freytagetal.2012)tocalculatetwobox-in-a- giants, since the horizontal temperature fluctuations become so
star3DLTEmodels.Wecalculatedmodelswithparametersrep- largeinthesemodelsthattheradiativetransfercodebreaksdown
resentative for the less evolved stars in our sample. The model and provides unphysical results. In addition, the box-in-a-star
parametersarelistedinTable1.In3Datmospheremodels,Teff approximationischallengedforlowgravitymodels.Rectifying
isnotacontrolparameterasinthe1Dcase.Rather,itisanout- these problems would be a major theoretical undertaking, well
come of the simulation, indirectly controlled by the inflowing beyondthescopeofthispaper.
Articlenumber,page6of22
A.O.Thygesenetal.:Thechemicalcompositionof47TucII
1.0 1.0
0.8 0.8
x x
u u
m. fl 0.6 m. fl 0.6
or or
N N
0.4 0.4
0.2 0.2
5138.5 5138.6 5138.7 5138.8 5138.9 5139.0 5140.0 5140.1 5140.2 5140.3 5140.4 5140.5
Wavelength [Å] Wavelength [Å]
10 10
8 8
6 6
χ2 χ2
∆ ∆
4 4
2 2
0 0
−0.02 −0.01 0.00 0.01 0.02 0.03 0.04 −0.02 −0.01 0.00 0.01 0.02 0.03 0.04
25Mg/24Mg 25Mg/24Mg
10 10
8 8
6 6
χ2 χ2
∆ ∆
4 4
2 2
0 0
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.08 0.09 0.10 0.11 0.12 0.13 0.14
26Mg/24Mg 26Mg/24Mg
(a)MgH5138Å (b)MgH5140Å
Fig.5:AsFig.4,butforthe5138Åand5140Åfeatures.
One of the main results of 3D hydrodynamical modelling aturefluctuations,ratherthanchangesintheoverallatmospheric
ofstellaratmospheres,isthepredictionofaverageatmospheric structure.
temperature stratifications that are in general significantly dif-
ferentfromtheonespredictedbytraditional1Dmodels.Thisis
particularlyevidentforthelowestmetallicities(e.g.Colletetal. 3.3.2. 3Dsynthesis
2007),whereanetcoolingeffectismanifestedin3D.InFig.6
With the models computed, we selected 20 model snapshots,
weplottheaveragethermalstructureofthetwo3Dmodelsto-
getherwiththestructureoftheATLAS12models(α =1.25), with near-equidistant time steps as a basis for the spectral syn-
and two reference LHD (Caffau & Ludwig 2007)M1LDT models thesis.Thesewereselectedsuchthattheycoverednearlythefull
(α = 0.5),whicharecalculatedwiththesameinputphysics modeltime,togivegoodtemporalcoverage.Sincetheconvec-
MLT tive motions are responsible for a large part of the line asym-
astheCO5BOLDmodels.Alsoindicatedarethemeantemper-
metries, the snapshots should ideally be sampled so that they
aturefluctuationsinour3Dmodels.Asisevident,atthemetal-
representuncorrelatedconvectivepatternsinthesimulation.By
licities treated here, the average thermal structure of the photo-
computingtheauto-correlationbetweenthehorizontal,grayin-
spheres in the 3D models are nearly identical to the equivalent
tensitiesforallourmodelinstances,wecangaininsightintothe
1D models. On the other hand, the convection still causes sig-
typicallifetimeofaconvectivecell.Havingcomputedtheauto-
nificantvariationinthethermalstructureofour3Dmodel.The
similarity of the average structures implies that differences be- correlation, we performed a spline interpolation for a range of
modeltimes,sothatoursnapshottimestepwasincluded.From
tweenthe1Dand3Dsynthesisaremostlyrelatedtothetemper-
this, the value of the auto-correlation between two consecutive
Articlenumber,page7of22
A&Aproofs:manuscriptno.47Tuc_paper2_v8
3D 3D
8000 1D LHD 8000 1D LHD
ATLAS12 ATLAS12
7000 7000
6000 6000
T T
5000 5000
4000 4000
3000 3000
−5 −4 −3 −2 −1 0 1 2 −5 −4 −3 −2 −1 0 1 2
log(τ ) log(τ )
Ross Ross
Fig. 6: Average thermal structure of the 3D models (solid line), the equivalent 1D ATLAS12 (triple dot-dash), and LHD (dash)
models.TheredlinesindicatetheRMSvariationofthetemperatureinthe3Dmodels.Leftpanel:HiMet,right:LoMet.
< 0.21 in steps of 0.03. The isotopic fraction of 24Mg was cal-
culatedas24Mg= 1.0−25Mg−26Mg.Therelativestrengthofthe
1.0
isotopiccomponentsoftheMgHlinesweresetbyadjustingtheir
log(gf) value. Similar to the 1D syntheses, the Mg abundance
wasusedtoadjusttheMgHfeaturestrengths.Weusedanabun-
0.8
dance mixture identical to the mixture used in the model com-
putationasastartingpointofoursyntheses,asstatedinTable1.
ation 0.6 ThelinelistisidenticaltowhatwasusedinMOOG.
el
orr Duetothevelocityfieldsintheatmospheresofthe3Dmod-
utoc 0.4 els, lines synthesised in 3D will exhibit a small velocity shift,
A
relative to an equivalent 1D synthesis. To account for this, we
synthesised a single 24MgH line in both 1D and 3D and cross-
0.2 correlated the two spectra to determine the velocity shift. This
gaveshiftsof0.26kms−1and0.38kms−1forthe[Fe/H]=−0.50
and −1.00 models, respectively. By synthesizing only a single
0.0
line,webypasspotentiallydifferentbehaviourofline-blendsbe-
0 50 100 150 200 250 300 tween1Dand3D,whichcouldmimicanoverallvelocityshift.
∆ t [h]
Before performing any analysis, we shifted the 3D spectra by
thisamount,tobeasconsistentwiththe1Danalysisaspossible.
Fig. 7: Auto-correlation of the horizontal grey intensity for the
Itwas,however,foundthatsomeadditionalvelocityshiftswere
HiMetmodel.Theblue,dashedline,showsthevalueforthetime
neededforsomefeatures,whichwasalsothecaseforour1Dfits.
stepbetweentwoconsecutivesnapshots.
The synthesis of the single 24MgH transition also revealed that
3Deffectsintroducedaweaklineasymmetry(Fig.8),whichis
expectedalsotobepresentforthetwoheavyMgHcomponents
time steps could readily be determined. This showed that there
ofthefeature.Thiscanexplainpartofthedifferentlineshapes
istypicallya13%correlationbetweenourindividualsnapshots
(Fig. 7), which is sufficiently uncorrelated for our purpose. We between1Dand3D.
After shifting the spectra, the final 3D spectrum was con-
note that the time axis is truncated, so that the decrease in the
volvedwiththeinstrumentalprofileofUVEStoyieldthebroad-
auto-correlation is visible. The total length of the simulation is
significantlylongerthanindicatedinthefigure(∼1400h). ened spectrum. We assumed a Gaussian profile. In the absence
ofstrongrotation,thisshouldaccountforalltheline-broadening
Furthermore,weensuredthatthemeanTeff,andRMSscatter present in the observed spectra, because the effects of micro-
of the Teff in our snapshot selection was nearly identical to the
andmacroturbulencearisesasanaturalconsequenceofthegas
Teff andRMSfoundfromthecompletemodelgrid.Thisrepre-
motions in the 3D models. Because this work deals with cool,
sentsacompromisebetweencomputationaltimeandmodelcov-
evolved giants, we consider them non-rotating for all practical
erage,sothatthetemperaturevariationsfromthe3Dmodelare
purposes, and did not impose any additional broadening to the
keptintactinthespectralsynthesis.Foreachsnapshotwecalcu-
latedthefull3DradiativetransferusingtheLinfor3Dcode1,to spectra. This is further justified by the similarity of the Vmacro
measurementsreportedinPaper1.Withthesynthesescalculated
yieldtheemergentspectrum.Thesnapshotsynthesesweresub-
forbothmodels,weperformedasimple,linearinterpolationin
sequently averaged and normalised, to yield the final, synthetic
metallicitybetweenthespectra,tomatchtheobservedmetallic-
spectra.
itiesofourstars.Thegridofsynthesesweresubsequentlygiven
For each 3D model, we calculated a grid of syntheses with
−0.50 < ∆[Mg/H]< 0.50, in steps of 0.2, relative to the input asinputtotheFitprofilecode,describedbelow,tofittheob-
servedspectra.
mixture. The isotopic fractions of the heavy Mg isotopes were
varied between 0 < frac(25Mg) < 0.21 and 0 < frac(26Mg) Due to the issues with the C2 blends discussed earlier, we
choseonlytocalculate3Dsynthesisforthe5135Åand5138Å
1 http://www.aip.de/Members/msteffen/linfor3d features, which do not suffer from strong carbon blends. If we
Articlenumber,page8of22
A.O.Thygesenetal.:Thechemicalcompositionof47TucII
Whetherthisisthecasealsoforthetworemainingfeaturescan-
notbejudgedfromthisexercise,andwillrequireresolvingthe
1.0 issuewiththeC blendinglines,asdiscussedearlier.
2
0.8 3.3.3. Fittingthe3DsyntheseswithFitprofile
x
u
m. fl The software used for the 1D fitting of the MgH features us-
Nor 0.6 ingMOOGcalculatesspectralsynthesisonthefly,whichisnot
feasibletodoin3D,wherethecomputationaloverheadsaresig-
nificantlyhigher.Thus,forthepurposeofdeterminingthebest-
0.4 3D fitting 3D synthetic profile we developed the multi-parametric
1D
fitting code Fitprofile, which uses a pre-computed grid of
5138.5 5138.6 5138.7 5138.8 5138.9 5139.0 syntheses. Before applying to our 3D synthesis, we tested that
Wavelength the1Dsynthesisprovidednear-identicalresultstoour1Dfitting
routinesusingMOOG.
Fig. 8: Comparison of the syntheses of the 5138Å feature for Fitprofilesharesmuchofthegeneralinnerworkingsand
24MgH.Notethelineasymmetryintheredwing.Thesyntheses a relevant amount of code with the automated parameter deter-
havebeenscaledtohavethesameoverallstrength. mination and abundance analysis code MyGIsFOS (Sbordone
et al. 2014). As MyGIsFOS it is written in Fortran 90 (with
Intel extensions) and uses the CERN function minimisation li-
weretosynthesisealsothe5134Åfeaturesand5140Åfeatures, braryMINUIT(James&Roos1975;Lazzaro&Moneta2010)
it would require adding an extra dimension to our parameter as χ2 minimisation engine. The Fitprofile code was devel-
space for the syntheses, namely C abundance variations. Since oped to provide a flexible line-fitting tool that could both per-
we are already varying the Mg abundance, and the fractions of form simple, general purpose line fitting for single lines, and
24,25,26Mg, it would become very computationally expensive to moresophisticatedmulti-parameter,multi-regionfittingsuchas
alsoincludevariationsinthecarbonabundance. theoneneededforthepresentstudy.Fitprofilewasusedal-
In Figs. 9, 10 the effects of the 3D atmospheres are illus- readyinPaper1,toderiveabundancesfromelementswithlines
trated. Three different syntheses are shown. A full 3D synthe- thatshowedhyperfinesplittings.
sis,asynthesisusingthehorizontallyaveraged3Dtemperature Fitprofile reads in a grid of synthetic spectra varying in
structure(<3D>),andfinallyasynthesisusinga1Datmosphere up to four parameters, an observed spectrum against which the
calculated with the same input physics as the 3D model. The fit is to be performed, and a list of spectral regions to be used
HiMet and LoMet syntheses both have the same Mg-depletion inthefit.Twotypesofregionsareaccepted:pseudo-continuum
(-0.10dex)relativetotheinputmixture.Asisevident,boththe regions are used to pseudo-normalise the observed spectrum as
strength of the features, as well as the line shapes, change be- wellasthesyntheticgrid,andtodeterminetheS/Nratio,while
tween 1D and 3D. Whereas some differences can be observed fitting regions define the spectral ranges over which the actual
between 1D and <3D>, it is clear that in this case, one needs fitting is performed. We used the same fitting regions for each
thefullinformationfromthe3Dsynthesistocapturethediffer- featureasinthe1Dcase.
ences between 1D and 3D. This underlines that the main rea- Theup-to-fourparametersvaryinginthegridcanrepresent
son for the different behaviour of the MgH features is related any quantity varying from one spectrum to another in the syn-
to the temperature fluctuations and not changes in the average thetic grid. Any number of them can be fitted, or kept fixed to
thermalstructure.Interestingly,Ramírezetal.(2008)foundthat an user-chosen value. In the case of the present work, for in-
the overall strength of the MgH features were increasing when stance,theprovidedgridparametersweresettototalMgabun-
3D atmospheres were applied to a K-dwarf model, where we, dance, 25Mg fraction and 26Mg fraction (and all were fitted),
ontheotherhandfindthatthefeaturesaredecreasingslightlyin while the fourth parameter was not used. From this, the 24Mg
strength,relativetoastandard1Dsynthesis. fractioncouldeasilybecalculated.Thegridmustbeequispaced
Naturally, both the MgH lines and the lines of the blending andrectangularinanyparameteritcontains.
species will feel the effect of the 3D model atmospheres, and If the user provides pseudo-normalisation regions, they are
itisthusinterestingtoinspectwhethertheresultingchangesin usedtolocallyestimatetheS/Nandapseudo-continuumspline
thelineasymmetriesaremainlyduetoeffectsontheMgHfea- thatisusedtopseudo-normalisethesyntheticgridandobserved
turesthemselves,orduetotheblendingspeciesrespondingdif- spectrum.Bothquantitiesareestimatedasconstantifonesingle
ferentlyto1Dand3Datmospheres.InFig.11weplotsyntheses pseudo-continuum interval was provided, as a linear interpola-
ofallfourMgHbandsforourlow-metallicitymodel,notinclud- tion if two pseudo-continua are given, and as a spline for three
ing any blending lines. The syntheses have been normalised to ormorepseudo-continua.Bothquantitiescanbekeptfixed,pro-
have the same strength of the 24MgH feature, and the 1D syn- vidingapre-normalisedspectrumandanestimationofS/N.Due
theses have been broadened to match the intrinsic broadening tothelackofsuitablecontinuumregionsintheimmediatevicin-
fromthe3Dsyntheses.Thenormalisationtothesamestrength, ity of the MgH bands, we used pre-normalised spectra with a
allowsforabettercomparisonoflineasymmetries,butwenote S/N estimate for our fitting. The normalisation was identical to
that without the normalisation, the MgH bands are weaker in whatwasusedinMOOG.
3D, compared to 1D, as also seen for the syntheses, including Fitting regions can be contiguous or not. A contiguous re-
allblendingspecies.Itisclearthattheeffectof3DontheMgH gion is, for instance, a typical spectral region covering a spec-
transitionsthemselvesarerathersmallandmostpronouncedfor tral line one wants to fit. A non-contiguous region is called in
the5135Åfeature.Thus,thisillustratesthatthedifferenceswe Fitprofilea“regiongroup”,asitis,indeed,agroupofcon-
findbetween1Dand3Dhaveasignificantcontributionfromthe tiguousregionsthatarefittedasone,i.e.asingleχ2iscomputed
blending species, at least for the 5135Å and 5138Å features. forallthepixelscontainedinthecontiguousregionscomposing
Articlenumber,page9of22
A&Aproofs:manuscriptno.47Tuc_paper2_v8
24MgH 25MgH 26MgH 24MgH 25MgH 26MgH
4040/1.50/−1.00 3970/1.50/−0.50
1.0 1.0
0.8 0.8
x x
u u
el. fl 0.6 el. fl 0.6
R R
0.4 Full 3D 0.4 Full 3D
<3D> <3D>
1D LHD 1D LHD
0.2 0.2
5134.8 5135.0 5135.2 5135.4 5134.8 5135.0 5135.2 5135.4
Wavelength [Å] Wavelength [Å]
Fig.9:SynthesesoftheMgHfeatureat5135.07Å.Shownisthefull3Dsynthesis(solid),the<3D>synthesis(dashed)andthe1D
LHDsynthesis(dot-dashed).IndicatedisalsothecentralpositionofeachoftheMgHcomponents.Left:LoMet,right:HiMet.
24MgH25MgH26MgH 24MgH25MgH26MgH
4040/1.50/−1.00 3970/1.50/−0.50
1.0 Full 3D 1.0 Full 3D
<3D> <3D>
1D LHD 1D LHD
0.8
0.8
x x
u u
el. fl 0.6 el. fl 0.6
R R
0.4
0.4
0.2
0.2
5138.4 5138.6 5138.8 5139.0 5138.4 5138.6 5138.8 5139.0
Wavelength [Å] Wavelength [Å]
Fig.10:AsFig.9,butfortheMgHfeatureat5138.71Å.ThisfeatureisablendoftwoMgHtransitions,indicatedwithsolidand
dashedverticallines.
1.0
0.8
x
u
m. fl
0.6
r
o
N
0.4
Full 3D
<3D>
1D 3970/1.5/−1.0
0.2
5134.2 5134.4 5134.6 5134.8 5134.8 5135.0 5135.2 5135.4 5138.4 5138.6 5138.8 5139.0 5140.0 5140.2 5140.4 5140.6
Wavelength
Fig.11:SynthesesofonlytheMgHtransitionsforallfourfeaturesused.Solidline:Full3D,dashedline:<3D>,anddot-dashed
line:1D.Allsyntheseshavebeennormalisedtosame24MgHstrength.
Articlenumber,page10of22