Determination of robust metallicities for metal-rich red giant branch stars

3.2 MB·

by  C. Liu

Astronomy&Astrophysicsmanuscriptno. NGC6528 (cid:13)cESO2017
January24,2017
Determination of robust metallicities for metal-rich red giant
branch stars (cid:63)
An application to the globular cluster NGC6528
C.Liu1,2,G.Ruchti1,S.Feltzing1,andF.Primas3
1 LundObservatory,DepartmentofAstronomyandTheoreticalPhysics,Box43,SE–22100Lund,Sweden
e-mail:[cheng, greg, sofia]@astro.lu.se
2 KeyLabofOpticalAstronomy,NationalAstronomicalObservatories,ChineseAcademyofSciences,A20DatunRoad,Chaoyang,
7 Beijing100012,China
1 3 EuropeanSouthernObservatory,D-85748Garching,Germany
0 e-mail:[email protected]
2
Received05May2016;accepted05January2017

n
a
J ABSTRACT

2
Context. ThestudyoftheMilkyWayreliesonourabilitytointerpretthelightfromstarscorrectly. Withtheadventoftheastro-
2
metricESAmissionGaiawewillenteranewerawherethestudyoftheMilkyWaycanbeundertakenonmuchlargerscalesthan

currentlypossible. Inparticularwewillbeabletoobtainfull3Dspacemotionsofredgiantstarsatlargedistances. Thiscallsfor
]
A areinvestigationofhowreliablywecandetermine,e.g.,ironabundancesinsuchstarsandhowwelltheyreproducethoseofdwarf
stars.
G
Aims. Hereweexplorerobustwaystodeterminetheironcontentofmetal-richgiantstars. Weaimtounderstandwhatbiasesand
. shortcomingswidelyappliedmethodssufferfrom.
h
Methods. In this study we are mainly concerned with standard methods to analyse stellar spectra. This includes the analysis of
p
individuallinestodeterminestellarparameters,analysisofthebroadwingsofcertainlines(e.g.,Hαandcalciumlines)todetermine
o- effectivetemperatureandsurfacegravityforthestars.
r Results. ForNGC6528wefindthat[Fe/H]=+0.04dexwithascatterofσ = 0.07dex,whichgivesanerrorinthederivedmean
t abundanceof0.02dex.
as Conclusions. Our work has two important conclusions for analysis of metal-rich red giant branch stars. 1) For spectra with S/N
[ belowabout35perreducedpixel[Fe/H]becometoohigh,2)DeterminationofTeff usingthewingsoftheHαlineresultsin[Fe/H]
valuesabout0.1dexhigherthanifexcitationalequilibriumisused.ThelastconclusionisperhapsnotsurprisingasweexpectNLTE

1 effecttobecomemoreprominentincoolerstarsandwecannotusethethewingsoftheHαlinetodetermineTeffforthecoolstarsin
v oursample.Wethereforerecommendthatinstudiesofmetal-richredgiantstarscareneedstobetakentoobtainsufficientcalibration
2 datainordertobeabletoalsousethecoolerstars.
3
1 Keywords. Galaxy:bulge–globularclusters:individual:NGC6528–stars:atmospheres–stars:fundamentalparameters
6
0
1.1. Introduction rich giants, such as those seen in the Galactic bulge and old,
0 metal-rich globular clusters. We are interested in providing a
Theanalysisofspectraofredgiantbranchstarsisproblematic.
7 better understanding of the influence on the derived iron abun-
1Asweprogressalongtheredgiantbranchupwards,tocoolerand dancefromthesignal-to-noiseratio(S/N)intheanalysedspectra
:lowergravitystarsanumberofphenomenastartappearingmore andanyinfluenceonthemethodusedtodeterminetheotherstel-
v
iandmorestronglyinthespectra. Inparticular,theatomiclines larparameters,e.g.,Teff andlogg,onthefinalironabundance.
Xgetstronger,causingmoreblendsandthecooleratmospheresal-
lowfortheformationofmoleculessuchasTiO,CN,andMgH Whyisthisinteresting? ThestudyoftheMilkyWayhasin
r
aresulting in strong molecular features. This makes it progres- thelastcoupleofdecadesbecomeamajorareainastrophysics.
sivelymoreandmoredifficulttofind(ordefine)thecontinuum Thisisduetotwoinfluentialastrometricmissions: thepastHip-
inthespectrum. Asmanymethodsrelyontheidentificationof parcosmission(Perrymanetal.1997)andthecurrentGaiamis-
thecontinuum,thiscausesaproblem. sion (Brown 2013; Perryman et al. 2001, where the first paper
Ourmainaimwiththepresentinvestigationistostudyhow describestheconceptbehindtheGaiaproposaltotheEuropean
wecan,inarobustway,determinetheironabundanceformetal- SpaceAgencyandthesecondpapergivesanoverviewof,Gaia
justbeforelaunch).TheHipparcoscatalogueenabledanewtype
(cid:63) BasedonobservationsmadewiththeESO/VLT,atParanalObser- of studies with determination of accurate velocities and ages
for samples consisting of many hundreds of stars near the sun
vatory, under programme 067.B-0382(A) and on data obtained from
the ESO Science Archive Facility under programme 065.L-0340(A), (e.g., Adibekyan et al. 2013, 2012; Bensby et al. 2004, 2014;
067.D-0489(A), and 077.B-0327(A) and from the Keck Observatory Fuhrmann2011;Soubiran&Girard2005). Thesestudieswere
ArchiveunderprogrammeC53HandC19H. doneonFandGdwarfstars.However,Gaiawillprovidedataof
Articlenumber,page1of25
Table1.BasicdataforNGC6528 archives. Inthearchivewefoundspectraof34starsthatarepo-
tentialmembersofNGC6528. Ofthese12havebeenobserved
R.A. Dec. (m-M) E(B-V)
by UVES on VLT in stand-alone mode, 20 with UVES as part
180449.64 –300322.6 16.17 0.54
of FLAMES observations, and 2 stars had been observed with
HIRESonKECK.Table2listsbasicinformationaboutthestars
the same quality as Hipparcos for a significantly larger volume andobservations. Thereisnooverlapbetweentheobservations
oftheMilkyWay,reachingallthewayintotheGalacticbulge. fromthedifferentprogrammes. Belowwedescribethedifferent
But,thestarsavailableforspectroscopicworkwill(astoday)be data-setsinsomedetail.
the red giant branch stars as these are intrinsically sufficiently
bright to be possible to observe with current instrumentation at
Stars observed with UVES: Our starting data-set consists of
adistanceof8kpc. Theonlyoptiontoobtainspectrafordwarf
observations of seven stars carried out in 2001 at the VLT 8-
starsintheGalacticbulgeiscurrentlytotakeadvantageofmi-
mtelescopeusingtheUVESspectrograph(Dekkeretal.2000)
crolensing events (e.g., Bensby et al. 2013). This is, however,
under our program 067.B-0382(A) (PI: S. Feltzing). The stars
notanoptionifwewanttostudylargesamples. Thusitremains
wereselectedasmembersofNGC6528basedonapropermo-
importanttostudyhowwebestcandeterminestellarparameters
tionstudyusinghigh-resolutionimagesandVIphotometryfrom
andelementalabundancesofevolvedredgiantstarsinarobust
HST (see Feltzing & Johnson 2002). In the ESO archive we
manner. Thispaperdealswiththistopic.
found an additional five stars observed with UVES from pro-
The spectroscopic and photometric data Gaia benchmark
gramme 065.L-0340(A) and 067.D-0489(A) (PI: D. Minniti).
stars and stars in the metal-rich globular cluster NGC6528 are
Thesewereallobservedin2000and2001,respectively.
presented in Sect. 2. Our basic tools and linelist are described
Theresolutionoftheobservationsis45000or55000inthe
inSect.3. Todeterminestellarparametersforredgiantsweex-
redarm(480–680nm)dependingontheslitwidthused(0.8”or
ploredifferentmethodsandtestthemonthebenchmarkstarsin
1.0”). The observations were all done using the standard setup
Sect. 4. In Sect. 5 we apply our analysis to stars in NGC6528
580 with CD #3. The exposures have been split in order to al-
and discuss problems in the analysis. In Sect. 6, we determine
low for the removal of cosmic ray hits. The data were reduced
[Fe/H] for NGC6528. Section 7 provides our conclusions and
usingtheUVESpipeline(Ballesteretal.2000),includingbias,
discussesfuturedevelopments.
inter-orderbackgroundsubtraction, flatfieldcorrection, extrac-
tion, and wavelength calibration. All the echelle orders were
thenmergedintoa1Dspectrumforeachexposure.
2. Descriptionofdata
In the archive we found 20 stars which are potential mem-
2.1. Spectra bers of NGC 6528 from program 077.B-0327(A) (PI: M. Zoc-
cali)whichwasobservedin2006.
2.1.1. Benchmarkstars
The multi-object optical spectrograph FLAMES (Pasquini
In order to work out the best analysis techniques for metal- etal.2002)hastwoparts,onebeingFLAMES-UVESwhichhas
rich cool giant stars we make use of spectra of stars with well- 8roboticfiberswhichfeedtheUVESspectrographatVLT.The
determined stellar parameters, the so called Gaia benchmark spectrahaveR∼47000andtheobservationsweredonewiththe
stars (Heiteret al. 2015a). Thesehave a wealthof high quality setup centred at 580 nm (wavelength coverage: 480–680 nm).
data available, in particular they have interferrometric observa- WereducedtherawframesusingtheFLAMES-UVESpipeline
tionsenablingadirectdeterminationoftheirradiiandeffective in a standard way. After all the recipes, which include creat-
temperatures(Teff). Asweareinterestedinmetal-richstars,we ing a master bias and the master slit flat-field frame, determin-
selectedtenredgiantswhichhaveironabundancesgreaterthan ingthefiberordertable,thewavelengthsolution,andextracting
–0.55dex(Jofréetal.2014). Thetenstars,whichhaveTeff sim- the science frame, of the pipeline have been executed we sub-
ilar to the star’s of NGC6528, are Arcturus, µLeo, HD107328, tracttheskybackgroundspectrumfromthestellarspectra. For
βGem,(cid:15)Vir,ξHya,αCet,γSge,αTau,andβAra. Theirreference FLAMES-UVEStheskybackgroundisusuallyobservedbyone
valuesforthestellarparametersarelistedinTable 3. fiber placed in an empty part of the sky. With the sky back-
The fifteen spectra with high S/N (> 250) were taken from ground removed, we shifted the sky-subtracted spectra to a he-
theESOarchiveandfromobservationsdonewithNARVAL.The liocentric reference frame making use of the packages RVSAO
spectrafromtheESOarchiveconsistofobservationstakenwith andDOPCORwithinIRAF1.
UVES (Dekker et al. 2000) and HARPS (Mayor et al. 2003). To improve the S/N, we co-added all the UVES spectra of
TheNARVALspectraarefurtherdescribedinBlanco-Cuaresma thesamestarintoasinglespectrum.TheaverageS/Nofthefinal
etal.(2014),whichalsogivesdetailsonhowtoretrievethespec- co-addedspectrumforeachstarwasestimatedbymakinguseof
tra from their archive. It should be noted that five stars, µLeo, the SPLOT task within IRAF at three short wavelength regions
βGem, ξHya, αCet, and γSge, have one spectrum each, while (574.4 − 574.7nm, 604.7 − 606.3nm, and 606.8 − 607.6nm).
the rest of stars have two spectra observed in different instru- TheS/Nisgreaterthan30perpixelformostofthespectra(see
ments. For example, the star Arcturus was observed with the Table2).
NARVAL and UVES spectrographs, while βAra was observed
withtheHARPSandUVESspectrographs.
Stars observed with HIRES: We collected spectra of two red
horizontal branch stars (3014 and 3025) from the Keck Obser-
2.1.2. StarsinNGC6528 vatoryarchive. TheobservationsweretakenwithHIRES(Vogt
The basis for our study of stars in NGC6528 is our own ob- 1 IRAFisdistributedbytheNationalOpticalAstronomyObservatory,
servations of 7 stars that were observed in 2001. In order to whichisoperatedbytheAssociationofUniversitiesforResearchinAs-
have a statistically significant sample of spectra of red giant tronomy(AURA)undercooperativeagreementwiththeNationalSci-
starsinNGC6528wefurthersearchedtheESOandtheKECK enceFundation.
Articlenumber,page2of25
C.Liu etal.:Determinationofrobustmetallicitiesformetal-richredgiantbranchstars
etal.1994)atKeckIundertheprogrammeC53HandC19H(PI:
J.Cohen)in1999and2000,respectively. 5
4
Since the HIRES detector is not large enough to yield full
spectralcoverage,thereisagap(1.0−6.0nm)betweenanytwo 3
echelleorders. TherawspectrawerereducedusingtheMAKEE
2 package. Itdeterminesthepositionofeachechelleorder, de- 2
finestheobjectandbackgroundextractionboundaries,optimally
) 1
extractsaspectrumforeachorder,andcomputewavelengthcal- /s
m
ibrationsnon-interactively. k 0
(
Weco-addedthespectraofeachstarintoonespectrum. The ∆vr -1
measuredmeanS/Noftheco-addedspectrawasestimatedinthe
-2
samewayasfortheUVESspectra(Table2).
-3
-4
2.2. AdditionaldataforNGC6528
-5
-150 -100 -50 0 50 100 150 200
2.2.1. Photometry vr(com. spectra)(km/s)
Fig.1. Comparisonofradialvelocitiesforthestarsderivedfromthe
In order to estimate good starting values for Teff for our stars combinedspectrumandfromtheindividualspectraseparatelyandthen
wemakeuseofcolour-temperature-metallicityrelations. Tothis averaged (see Sect.2.2.3). The x-axis shows the value derived from
end we collected near-infrared photometric data from 2MASS the combined spectra whilst the y-axis shows the difference between
(Cutri et al. 2003) and VVV (VISTA Variables in Via Lactea) v determinedinthetwoways. Theerror-barsforthedifferenceisthe
r
(Minnitietal.2010). coaddederrorsestimatedfromIRAF(forthecombinedspectra)andthe
σaroundthemeanfortheindependentmeasures. Errorsonthex-axis
The survey area of VVV is fully imaged in five photomet- aretoosmalltobeseen.
ric bands: Z,Y,J,H,K and 2MASS has imaging in J,H,K .
s s
VVV goes about 4 magnitutes deeper than 2MASS. However,
the larger telescope aperture of VISTA results in saturation for
the brightest stars. The saturation magnitude in the VVV pho-
tometryoccursatK <12. Wethereforeadopt2MASSphotom-
s
etryforstarsbrighterthan12maginK andwerequirethatthe 2.2.3. Radialvelocities
s
photometric quality flag is AAA, i.e. the best quality. For all
otherstarsweuseVISTAphotometry.
Radial velocities (v) with respect to the Sun were derived us-
r
There is a very small offset between the zero-points of the ing the RVSAO package within IRAF. The XCSAO task cross-
VVVand2MASScatalogs. Toensurethatallphotometryison correlates a template spectrum with the observed spectrum and
thesamesystemwehavechosentotransfertheVVVphotometry reportsthevelocitydifferencebetweenthetwo. Hereweuseda
ontothe2MASSphotometricsystemasthisisthesystemmost template spectrum from the radial velocity standard star (cid:15) Peg.
commonly used in the available temperature calibrations. The The resolution of the spectrum is similar to that for the spectra
followingzero-pointoffsetshavebeenapplied: (J −J )= ofoursamplespectra.
2mass vvv
0.029; (H − H ) = −0.039; (K − K ) = −0.028
2mass vvv s,2mass s,vvv
(Gonzalezetal.2011). Eachofourstarshavemorethanoneobservation(Table2).
The spectra are often taken at different nights and sometimes
evenmonthsapart. Thisallowsustoderivev intwoways,en-
r
2.2.2. Reddening ablingatestofthequalityofourresults. Firstweextractedall
spectraandcorrectedthemforEarth’smotioninordertoco-add
them. Radialvelocitieswerethendeterminedusingthesecom-
ReddeningisimportantfortheinitialestimateofTeff,butitcan binedspectra. Intheotherapproachwederivedtheradialveloc-
alsobeofinterestwhendiscussingthepropertiesofthecluster.
ityforeachobservationindividually. Theseindividualmeasure-
Here we make use of the recent reddening maps by Gonzalez
mentswerethenaveragedandthescatteraroundthemeanwas
etal.(2011,2012)toestimatethereddeningtowardsourstars.
calculated. Typically, the scatter around the mean radial veloc-
As the maximum sky resolution of the reddening map is ities is less than 0.50 km s−1. We find that the two approaches
2(cid:48), we assumed that the stars are subject to the same redden- giveverysimilarresults(compareFig.1).
ing within a 4(cid:48) × 4(cid:48) box. The observed targets are spread in
a relatively large area, the total coverage of the dereddened re- Forunknownreasons,weareunabletorecovertheradialve-
gion is 28(cid:48) ×28(cid:48) consisting of 49 boxes of 4(cid:48) ×4(cid:48). The mean locities determined by Carretta et al. (2001) for star 3014 and
extinction,A ,andcolourexcess,E(J−K ),arecalculatedus- 3025. Our results are about 50 km s−1 larger than the values
Ks s
ing BEAM3 which uses the extinction law from Cardelli et al. givenbythem. Asfarasweunderstandweareusingthesame
(1989). TheadoptedcoefficientsforJ,H,andK (inthe2MASS spectra and same reduction software. In Table 2 we list the
s
passbands)are:A =1.692E(J−K ),A =1.054E(J−K ),A value from Carretta et al. (2001). Apart from this difference
=0.689E(J−K ).JWhereA =0.6s89E(HB−V). ThederedsdeneKds ourderivedvelocitiesagreewellwiththoseintheliterature(see
s Ks
magnitudesofJ,H,andK arelistedinTable2. Sect.2.3).
s
Articlenumber,page3of25
Tsantakietal.(2013),DenHartogetal.(2014),andthelinelist
12 compiledfortheGaia-ESOsurvey(Heiteretal.,inprep.andref-
12
erencestherein)(seealso,Heiteretal.2015b). Inparticular,we
10
10 stars 8 selected90Feiand16Feiilines. Allourlineswereexamined
of 6 in the spectra of the Sun and ξHya. ξHya is a relatively cool
mber 4 and metal-rich star with stellar parameters similar to those in
s 8 Nu 2 oursampleofstarsinNGC6528andstarsintheGalacticbulge
r
sta 0190 200 210 220 230 (comparevaluesinTable4). Firstly,thesetwospectrawereused
of 6 vr(com.spectra)(km/s) tocheckthatthelinesarecleanandpossibletoanalyseinmetal-
r richgiantstars. Secondly,theequivalentwidth(EW)oflinesin
e
mb the two stars were measured. Because the strong lines are sen-
u sitive to the selection of the microturbulent velocity (Fulbright
N 4
etal.2006)andmightsufferfromtheeffectsofimpropermodel-
ingoftheouterlayersinstellaratmospheremodels(McWilliam
2 et al. 1995), all lines with EWs higher than 130 mÅ were re-
movedfromourlinelist.
0 Ascoolandmetal-richstarshavemoremolecularlinesthan
-150 -100 -50 0 50 100 150 200 250 warmerstars,wemakeanextrachecktomakesurethatourlines
vr(com. spectra)(km/s) arenotblendedbymolecules. Forthischeck,weusedthespec-
trumsyntheticprogram(seedescribedin 3.2)andthecomplete
Fig. 2. Distribution of measured heliocentric radial velocities for
VALD(Kupkaetal.1999,2000,seealsoreferencesinthedata-
our program stars. The inset in the top-left corner shows a zoom-in
base) line list containing all metal and molecular lines to com-
high-lightingthevelocitydistributionoftheclustermembersfittedbya
Gaussian.Theredcrossindicatesthemean(212.1kms−1)andstandard puteasyntheticspectrum. Togenerateaspectrumofacooland
deviation(4.2kms−1)oftheradialvelocityfortheclustermembers. metal-rich giant, the typical stellar parameters (Teff = 4500 K,
logg=2.0,[Fe/H]=+0.1dex)wereinterpolatedintheMARCS
model atmospheres (Gustafsson et al. 2008). We examined all
the lines by eye and found that most of them are free of TiO,
2.3. Membership
CN, C2, and MgH within 0.2 mÅ of the center of the Fe line.
Membership of globular clusters for individual stars is com- SixteenFelinesmightsufferaweakcontaminationfromtheCN
monly determined using radial velocities (e.g., Simmerer et al. lines. This suggests that our final measured stellar parameters
2013) or proper motions relative to the background and fore- andabundanceshouldnothavealargesystematicerrorscaused
ground stars (e.g., Zoccali et al. 2001). NGC6528 has a ra- bytheblendingofmolecularlines.
dialvelocityof∼210kms−1 (Carrettaetal.2001;Zoccalietal. The oscillator strength (loggf) for the Hα line is adopted
2004)andapropermotionrelativetothebackgroundbulgepop- from the VALD database. The atomic data for the Cai lines
ulationof< l >=0.006and< b >=0.044arcsecpercentury are taken from Smith & Raggett (1981), apart from the loggf
(Feltzing&Johnson2002).Thismeansthatradialvelocityisthe values for Cai 612.2 and 616.2nm, which are from Aldenius
bestwaytodeterminemembershipforthiscluster. Usingmea- etal.(2009).
surements from the luminous stars in globular clusters, as well Thefulllistoflines,includingreferencestoatomicdata,can
as their integrated spectra, Pryor & Meylan (1993) determined befoundintheon-lineAppendixB(TableB.1).
thevelocitydispersionsformanyglobularclusters. Theyfound
thattypicalvelocitydispersionsinglobularclustersislessthan
10kms−1. 3.2. Spectralanlaysis–SME
Figure2showsthedistributionofradialvelocitiesforallour
WeuseSpectroscopyMadeEasy(SME,Valenti&Fischer2005;
stars. There is a clustering of stars just above 200kms−1. To
Valenti&Piskunov1996)todeterminethestellarparametersby
findthemeanvelocityandvelocitydispersionofNGC6528,we
comparing synthetic spectra with observed spectra. SME uses
started by considering stars with a radial velocity in the range
theLevenberg-Marquardt(LM)algorithmtooptimizestellarpa-
155−240kms−1. For these we calculated the mean and stan-
rametersbyfittingobservedspectrawithsyntheticspectra. The
darddeviation(σ)oftheradialvelocity. Wethenproceededto
LMalgorithmcombinesgradientsearchandlinearizationmeth-
exclude stars more than 3σ from the mean value and the mean
ods to determine parameter values that yield a chi-square (χ2)
and σ were re-calculated. This procedure was iterated until no
valueclosetotheminimum. Stellarparametersandatomicline
more stars could be excluded with a 3σ-clipping. This left 26
data are required to generate a synthetic spectrum. In addition
stars for which we found a mean velocity of 212.1 km s−1 and
to specified narrow wavelength segments of the observed spec-
σ = 4.2 km s−1. Our velocity dispersion is in good agreement
trum, SME requires line masks in order to compare with syn-
withthevalueof4.0kms−1measuredbyCarrettaetal.(2001).
thetic spectrum and determine velocity shifts, and continuum
masks that are used to normalize the spectral segments. The
homogeneous segments and masks are created to fit all of our
3. Linelistandanalysistool
solarsiblingcandidates.
3.1. Linelist SME needs input values for Teff, logg, [Fe/H], microtur-
bulence (v ), macroturbulence (v ), and rotational velocity
Toassemblethelinelistwemadeuseofseveralsources.Foriron mic mac
(vsini). Given initial stellar parameters, the model atmospheres
we selected 106 clean lines between 470 nm and 690 nm from
areinterpolatedintheprecomputedMARCSmodelatmosphere
2 http://www.astro.caltech.edu/tb/ipac_staff/tab/makee/index.html grid,whichhasstandardcompositionofelementalabundances.
3 http://mill.astro.puc.cl/BEAM/calculator.php WethenconfiguredSMEtofiteachstellarspectrumbyadjust-
Articlenumber,page4of25
C.Liu etal.:Determinationofrobustmetallicitiesformetal-richredgiantbranchstars
This comparison shows that our line data and method of
0.3
analysing the iron lines (assuming all other parameters to be
FeI+FeII
FeI known) is fully compatible with those in Jofré et al. (2014)
0.2 FeII
whohasestablishedthereferencevaluesfortheGaiabenchmark
0.1 stars.
H]r 0
/
Fe
−[-0.1 4. Lookingforarobustmethodtodetermine[Fe/H]
H]x formetal-richredgiantstarsfromopticalspectra
/-0.2
Fe
[
-0.3 4.1. Methodstoderiveeffectivetemperature
-0.4 Effectivetemperaturescanbederivedfromstellarspectrausing
severalmethods. Feiisthemostcommonionintermsoflines
-0.5 intheopticalspectrum. AslinesarisingfromtheFeiionhavea
3800 4000 4200 4400 4600 4800 5000 5200
Teff,r widerangeoflinestrengthsaswellasexcitationpotentialsitisin
principlestraightforwardtodetermineTeff forthestarbyrequir-
Fig. 3. Test of the ability of our linelist to reproduce the reference ing Fei lines with differing excitation potentials to produce the
[Fe/H]fortheGaiabenchmarkstars. They-axisshowsthedifference sameironabundances(e.g.,Edvardssonetal.1993). Thisanal-
betweenthevaluewederive,usingthereferenceTeff andloggbutour ysisrestsontheassumptionoflocalthermalequilibrium(LTE).
ownlinelistandSME,andthereferencevalue. Wederived[Fe/H]in
However, several studies suggest that this assumption does not
three ways: using both Fei and Feii lines (blue filled squares), using
necessarilyhold(e.g.,Fuhrmann1998;Mashonkinaetal.2011;
onlyFeilines(redfilledcircles),andusingonlyFeiilines(blackfilled
Ruchti et al. 2013; Thévenin & Idiart 1999). Recently, NLTE
triangles). The stars can be identified using the Teff values which are calculations, e.g., from Bergemann et al. (2012), have been in-
givenonthex-axis.Forsomeofthestarswehavemorethanonespec-
trum.Resultsforbothareshownintheplot. cludedintosomestudies(e.g.,Ruchtietal.2013). However,at
solarmetallicitiesthedifferencebetweenLTEandNLTEresults
for Fei tend to be very small for metal-rich stars (Ruchti et al.
2013)andwecanthusneglectthemhere. Determinationofthe
ingthefreeparameters(seeSect.4). Theconvergenceis(likely) ironabundanceisaby-productwhenTeff isderivedinthisway
speedier if we start with realistic initial values. However, it anderrorsintheTeff andironabundancemustcorrelate.
shouldbenotedthatSMEiscapableofconvergingtothecorrect AnothermethodtoderiveTeff istousethestronghydrogen
valuesalsoifwestartfrominitialvaluesthatarefarofffromthe lines present in stellar spectra as these lines change rapidly in
correct ones (Daniel Adén, priv.comm., tests for the Gaia-ESO strength as a function of Teff. These lines also have no grav-
Survey). ity dependence in cool stars. Most commonly, Teff is derived
from the synthesis of the extended wings of the Hα and Hβ
lines(e.g.,Barklemetal.2002;Ruchtietal.2013). Thismake
3.2.1. Canourlinelistreproduce[Fe/H]forstarswithknown themveryusefulfordeterminingthetemperatureforstarswith
metallicites? Teff < 8000K(Gray2005). Withthismethodironmustbede-
terminedindependentlyandhencetheerrorsarenotcorrelated.
Beforestartingourinvestigation,wefirstcheckedhowwellour
set-upandlinelistreproducesthereferencevaluesfor[Fe/H]for Another approach is to use line-depth ratios to derive Teff
(Gray 1994). One advantage of using line-depth ratios is that
thebenchmarkstars.
these do not depend on the metallicity of the star. In the visi-
To this end we analysed the spectra fixing Teff and logg to blespectralrange,unblendedSi,Ti,V,Cr,FeandNiline-depth
therecommendedvalues(Table3).Wedidthreesetsofanalysis:
one where both Fei and Feii lines were fitted, one where only rations can be used to estimate Teff. There are not many appli-
cationsofthismethodintheliterature,butKovtyukh&Gorlova
Feilineswerefitted,andonewhereonlyFeiilineswerefitted.
(2000)illustratedthattheline-depthratiosarepowerfulindica-
Ineachcasealllineswereallfittedsimultaneously.
tors of Teff at least for supergiants. We will not further explore
TheresultsareshowninFig.3. WefindthatwhenwefitFei thismethodhere.
andFeiilinessimultaneouslythedifferencebetweenourvalues
Finally,wecanusecalibrationofstellarphotometrytoderive
and the recommended values is 0.01dex with a σ of 0.10dex.
Teff from a colour index, such as (B−V)0 (see, e.g., González
Figure3showsthatitisthecooleststarsthatdrivesthesizeof
Hernández&Bonifacio2009). Thismethodhasitslimitations.
the scatter, whilst the warmer stars have a smaller difference.
Forexample,forstarsintheGalacticbulgeorintheplaneofthe
WhenwefitonlytheFeilinesthedifferenceis0.01dexwitha
Galaxythephotometricapproachishamperedbythepoorlyde-
σof0.07dex,andwhenweanalysetheFeiilinesonlywefind
termined reddening of individual stellar colours. Although this
adifferenceof0.03dexwithaσof0.07dex. Therearenodis-
methodisnotverydependableforbulgestars,thankstothelarge
cernibletrendswithTeff,althoughthereisaweakindicationthat reddeningalongtheline-of-sight,itneverthelessprovidesuseful
Feiilinesdoabetterjobinreproducingthereferencevaluesfor
startingvaluesforouranalysis.
the coolest stars (αCet, γSge, and αTau) while in the warmest
stars(βGem,(cid:15)Vir,andξHya)Feilinesappeartodoamuchbet-
terbetterjobthantheFeiilines. However,thetrendisweakand 4.2. Methodstoderivesurfacegravity
more data would be needed to draw a firm conclusion regard-
ingifcertainspeciesarebetteratacertaintemperaturerangefor It is common to measure logg by imposing ionization equilib-
thesetypesofstars. riumwhichmeansthatwerequireFeiandFeiilinestoproduce
Articlenumber,page5of25
thesameabundance4. Feiilinescanbeweakandtheyarenotas those in Jofré et al. (2014). Rotational velocities of red giants
numerousastheFeilines. Thismethodthusrequireshighqual- and horizontal branch stars are typically small (vsini < 5 km
ityspectrawithlargewavelengthcoverage. Asdiscussedabove s−1), therefore a good assumption is to set vsini to 1 km s−1.
(Sect.4.1)FeilinescanbesusceptibletodeparturesfromLTE. Which is what we do for the rest of this paper. We note that
ThisisnottrueforFeiilines.Whichmeansthationizationalbal- thereisoftenadegeneracybetweenvsiniandv whichishard
mac
ancecanbeinfluencedbydeparturesfromLTE.Determination tobreakintheanalysis. Forthetypeofstudypresentedhere–
oftheironabundanceisaby-productofthismethodanderrors where the aim is to get the best measure of [Fe/H] – the exact
inloggand[Fe/H]mustcorrelate. values of these two parameters is of less relevance to the final
Severallinesshowstronglypressure-broadenedwingsinthe outcome of the investigation and we can allow them to be de-
spectra of cooler stars. This means that the surface gravity of generate. Thisimpliesthatinthethisstudywecanregardthem
late-type stars can be determined from analysis of these lines. (together)asnuisancenecessarytofitbutnotnecessarilygiving
Lines that have pressure broadened wings include the Mgi b physicalinsightintothestar.
lines at 516.7, 517.2, 518.3nm, the Nai D lines at 588.9 and To test the three methods we adopted ten benchmark stars
589.5nm,andtheCailinesat612.2,616.2,and643.9nm(see, (seeHeiteretal.2015a;Jofréetal.2014,andSect.2.1.1).
e.g., Bonnell & Bell 1993; Edvardsson 1988; Fuhrmann et al.
1997). The analysis of the wings of these strong lines require
4.3.1. Method1: FeiandFeiilines
that the elemental abundance of the element the line is arising
from is also determined, from other lines than the one used to Inthismethodwefitallfreeparameterssimultaneouslybycom-
derivelogg. Thismeansthaterrorsinloggandtheabundance paring theobserved spectrum witha synthetic onefor short re-
ofthatelementcorrelate. gionsaroundtheFeiandFeiilines. Itshouldbementionedthat
Finally, when we have independent measurements of Teff themethodismorecommonlyperformedwithequivalentwidths
and metallicity, logg can be derived through isochrone fitting intheliteratures(e.g.,Bensbyetal.2003).Thismethodisspeed-
(see,e.g.,Sozzettietal.2007). Wewillnotfurtherexplorethis ier if we start with realistic initial values for stellar parameters
methodhere. (seealsoSect.3.2).Forthebenchmarkstars,theirrecommended
values are used as the initial input, however, experience shows
thattheexactvaluesareunimportanttoachiveconvergence. An
4.3. Determiningstellarparameters
initial value for v was obtained using the relation given in
mic
InSects.4.1and4.2wediscussedvariouswaystodetermineTeff Jofré et al. (2014). The initial vmac value was set to 5.0 km s−1
andlogg. Althoughthisisnotanexhaustivesummary,combin- forallstars.
ingthevariouswaystoderiveTeff andloggstillleadstoquitea All parameters are simultaneously fitted inside SME. As
fewpossiblecombinations. Herewewillexplorethefollowing SMEstrivestofitalllinesequallywellthisisineffectthesame
combinations: asrequiringionizationalandexcitationalequilibrium–hence,all
parameters are determined simultaneously. The method differs
Method1: InthismethodweonlyuseFeiandFeiilinestocon- slightlyfromitsmostcommonimplementationintheliterature
strain all stellar parameters (i.e., excitation and ionizational where an iterative scheme is employed and one parameters is
equilibriaareimposed). variedineachstep(see,e.g.,Drake1991;Drake&Smith1991,
Method2: In this method we use the Hα line to constrain Teff, anddiscussionstherein). Instead,theusageofSMEinfullyfree
thestrongCailinestoconstrainlogg,andFeilinestoderive mode is more akin to the method used in Feltzing et al. (2009)
theironabundance. wheretheparameterspaceissearched(byhand)forabestfitto
Method3: In this method we use the Hα line to constrain Teff, allcriteriasimultaneously.
thestrongCailinestoconstrainlogg,andFeiilinestoderive
theironabundance.
4.3.2. Method2: Hα,Ca,andFeilines
WhileinMethod1allparametersarecorrelated,Method2and To break the degeneracy between the different parameters we
3aimatbreakingthesedegeneraciesbyusingseparatemeasures use different spectral indicators for each of the main stellar pa-
foreachofthethreemainparameters. Wedidnotattempttouse
rameters. Thismethodrequiresasetofinitialparameterstoget
theMgibandNaiDlinesasthesearetooblendedbytheatomic started. These could be obtained in different ways (e.g., from
and molecular lines to determine logg from them in metal-rich
photometry). For this test we take the parameters obtained in
giant stars as we are interested in here. For cool giants with
Method1asinitialinput.
Teff < 4400 K, we further found that the wings of the Hα line
almost vanished (see also AppendixC). This lead us to modify Method2:Forwarmgiants(Teff >4400K),thefollowingsteps
areused:
Method2tobeabletoincludealsosuchstarsinourstudy(see
Sect.4.3.2).
1. Asetofparametersasinitialinput;
InadditiontoTeff,logg,and[Fe/H]aspectroscopicanalysis 2. FitthewingsofHαtoderiveTeff,whiletheotherparameters
normally calls for the determination of a few other parameters;
arekeptfixed;
microturbulance(vmic),marcotublence(vmac),androtationalve- 3. Fit the wings of the three strong Cai lines (λ 612.2, 616.2,
locity(vsini).
and 643.9nm) to determine logg. To break the degeneracy
Microturbulanceandmacroturbulencecaneitherbederived of logg and Ca abundance, several weak Cai lines are also
fromthespectrumitselforobtainedfromacalibration,suchas
fittedatthesametime;
4. Derive[Fe/H]fromtheFeilinesbysettingbothv andv
4 Inprincipleotherelementscanalsobeused(e.g.,Ti).However,there mic mac
free, whilethe otherparametersarekept fixedatthe values
areonlyafewelementsthathavelinesarisingfromboththeneutraland
singlyionisedvarietyoftheatomthatareobservableintheopticalpart derivedinthestepsabove;
ofthespectrum. Inthosecases,oftenoneoftheionshasveryfewor 5. Repeat steps 2 to 4 with updated parameters until all five
veryweaklines. parametersreachconvergence.
Articlenumber,page6of25
C.Liu etal.:Determinationofrobustmetallicitiesformetal-richredgiantbranchstars
1
0.95
0.9
0.85
x
u
Fl 0.8
0.75
0.7
0.65
0.04 6556 6558 6560 6562 6564 6566 6568
al 0.02
u
d
si 0
e
R-0.02
-0.04
6556 6558 6560 6562 6564 6566 6568
˚
Wavelength(A)
Fig.4. ComparisonofsyntheticspectrawiththewingsofHαlinein(cid:15)Vir. Themiddlesyntheticspectrum(inred)showsthebestfit. Theother
twosyntheticspectra(blueandgreen)indicatetheshapeofthewingswhenTeff ischangedaccordingtoourestimateduncertainty(here50K).
Thegrayareasmarktheregionsusedtoevaluatethegoodnessofthefit. Notethatthesearerelativelynarrowsincethespectrumhasverylittle
clean"linecontinuum"thankstothecooltemperatureofthestar,whichresultsinmanylinesbeingpresentinthespectrum.
Table3.StellarparametersfortheGaiabenchmarkstars. Columns2to4givethereferencevaluesforthestellarparameters. Columns5till11
listourresults,derivedusingMethod2andModifiedMethod2(Sect.4.3.2).
Referencevalues ResultsfromMethod2
Name Teff,r loggr [Fe/H]r Teff σTeff logg [Fe/H] σ[Fe/H] Vmic Vmac
(K) (dex) (K) (K) (dex) (dex) (kms−1) (kms−1)
µLeo 4474 2.51 0.25 4513 100 2.50 0.31 0.08 1.5 4.8
HD107328 4496 2.09 –0.33 4484 50 2.00 –0.48 0.09 1.8 4.4
— — — 4483 50 2.01 –0.45 0.06 1.8 5.4
βGem 4858 2.90 0.13 4846 50 2.89 0.11 0.08 1.2 4.2
(cid:15)Vir 4983 2.77 0.15 5056 50 2.84 0.16 0.08 1.5 5.5
— — — 5055 50 2.80 0.17 0.08 1.5 5.7
ξHya 5044 2.87 0.16 4991 50 2.96 0.10 0.08 1.4 6.1
ResultsfromModifiedMethod2
Arcturus 4286 1.64 –0.52 4305 100 1.69 –0.58 0.09 1.7 5.4
— — — 4321 100 1.63 –0.61 0.09 1.7 5.2
αCet 3796 0.68 –0.45 3888 100 0.72 –0.43 0.12 1.6 8.9
γSge 3807 1.05 –0.17 3988 100 0.96 –0.17 0.09 1.6 6.6
αTau 3927 1.11 –0.37 3910 100 1.12 –0.27 0.11 1.4 5.7
— — — 3930 100 1.10 –0.28 0.10 1.4 6.1
βAra 4197 1.05 –0.05 4250 100 1.03 –0.17 0.08 3.0 10.4
— — — 4277 100 1.26 –0.13 0.08 3.0 9.8
Notes.Thefirstcolumngivesthenameofthestar.Thesecondandthirdcolumnsgivetherecommendedeffectivetemperatureandsurfacegravity
obtained from Heiter et al. (2015a), while the recommended metallicity from Jofré et al. (2014) is listed in the column 4. For some stars we
havetwospectrafromdifferentinstruments(seedetailsinSect.2.1.1). Thesecondspectrumisindicatedbyadashinthesethreecolumns. The
followingsevencolumnsgiveourresults.
For step 2 a number of synthetic spectra are generated and Step 5 require us to decide when a given parameter has
theirfitisevaluatedusingthespectralregionsindicatedinFig.4. converged. For the current work the following convergence
Further examples can be found in the on-line material in Ap- criteria were applied: between two iterations the differences
pendixC. should be ∆Teff < 50K for most stars, but for stars with very
InStep3thethreestrongCailinesaresimultaneouslyfitted. high S/N-ratios we required < 20K, ∆logg < 0.05dex, and
It would be possible to fit them each individually instead. A ∆[Fe/H]<0.05dex.
discussionofthemeritsofthedifferentapproachescanbefound
intheon-linematerialinAppendixD.
Articlenumber,page7of25
Asmentioned,itisnotfeasibletomeasureTeff fromtheHα recommend Method 2 as providing a sound basis for an analy-
line for the cooler giants (Teff < 4400 K). Therefore, the only sis of a large sample of stars. It is reassuring that this method
optionistoderiveTeff usingFeilines(excitationalequilibrium) notonlygivesgoodmetallicityestimatesbutalsoreliablestellar
rather than the wings of the Hα line for these stars. However, parametersingeneral.
thisre-introducesadegeneracybetweenTeff and[Fe/H].Weare The uncertainty in Teff can be estimated by inspecting the
stillabletousethethreestrongCailinestodeterminelogg. comparison of synthetic spectra with the observed spectrum.
ThisisrelativelystraightforwardforthehighS/Nandhighres-
ModifiedMethod2: Forcoolgiants(Teff <4400K,thefollow-
olutionspectrawehavefortheGaiabenchmarkstars. Wefound
ingstepsareused:
thatthetypicaluncertaintyinTeff isabout50Kformostofthe
1. Asetofparametersasinitialinput; warmgiants. Oneexample, (cid:15)Vir, isshowninFig.4. Forlogg,
2. FitthewingsofthethreestrongCailines(λ612.22,616.22, we found that for most stars the typical uncertainty is around
and643.91nm)todeterminelogg. Tobreakthedegeneracy 0.10dex(seemoredetailsinAppendixD).
of logg and Ca abundance, several weak Cai lines are also For [Fe/H] we calculate the error in the mean by using the
fittedatthesametime; ironabundancefromeachironlineindiviudally(rememberthat
3. Settingbothv andv freewhilekeepingloggfixed,we the parameters are decoupled in this method). Calculating the
mic mac
only fit Fei lines to determine Teff and [Fe/H] at the same formal error in the mean we find errors typically around 0.02
time; dex,whilstσisjustbelow0.1dex(seeTable3).
4. Repeat steps 2 to 3 with updated parameters until all five Forthebenchmarkstars,thetypicaluncertaintiesintherec-
parametersconverge. ommended Teff and logg are about 60 K and 0.10 dex (Heiter
et al. 2015a), respectively. The scatter in Teff and logg around
the recommended values for the benchmark stars found in this
4.3.3. Method3: Hα,Ca,andFeiilines studyiscomparablewiththetypicaluncertaintiesoftherecom-
SincetheonlydifferencebetweenMethod3andMethod2isthat mendedstellarparameters. Thereisaverysmalloffsetbetween
weuseFeiiratherthanFeilines,theatmosphericparametersare therecommended[Fe/H]andourresultswhenusingMethod2.
Thetypicaluncertaintyintherecommended[Fe/H]iscompara-
measuredmakinguseofthesameiterativeprocessdescribedin
Sect.4.3.2bychangingfromFeilinetoFeiilines. bletowhatwefind(<0.02dex,Jofréetal.2014).
ForModifiedMethod2wedidmakeuseofexcitationequi-
librium using the Fei lines. However, the number of Feii lines 4.5. HowmuchdotheresultsdependontheS/Ninthe
available is much fewer than Fei lines and they do not cover a spectra?
largeenoughrangeinexcitationpotentialforustotrytodeter-
immipnleemTeeffntferdomforewxcairtmatigoinanetqsu(iTliebffri>um4.40M0Ket)h.od 3 is thus only OS/uNrtsepsetsctorfadoifffetrheentmmeetathl-oridcshh,acvoeorlelgiieadntosnitnheGaaniaalybseinscohfmhiagrhk
sample. Clearly, astudyofforexampletheGalacticbulgewill
havespectraofmuchlowerS/N.Howwillthisinfluencethere-
4.4. Discussionanderrorestimates sults? Weanalysethisintwosteps. Firstlywewilldegradethe
spectrafortheGaiabenchmarkstarstomimicthatofhighqual-
We now proceed to compare our results for the ten benchmark
itydataforstarsintheGalacticbulgeandsecondlywewillmake
stars derived using the three methods. A comparison is shown
useoftheextensivedatasetofstarsinNGC6528thatwehave
inFig.5andthestellarparametersobtainedusingMethod2and
ModifiedMethod2arelistedTable3. Inparticularewefind5: collected.
TotestthedependenceofourfinalresultsonS/Nandreso-
Method1∆Teff =56K(σ=79),∆logg=–0.04(σ=0.20),and lutionwehavedegradedthespectraforthetenbenchmarkstars
∆[Fe/H]=0.03dex(σ=0.11); andre-analysedthem. Wechose45000and20000forthereso-
lutionandatthreedifferentS/N(25,35,45). 20000isaresolu-
Method2∆Teff =35K(σ=54),∆logg=0.02(σ=0.07),and tionthatiscommonforFLAMES-GIRAFFE(usedintheGaia-
∆[Fe/H]=–0.03dex(σ=0.08); ESO Survey) and the future massively multiplex spectrographs
Me∆t[hFoed/H3]∆=T0eff.0=4d1e9xK(σ(σ==0.5034)),(∆wlaorgmg=gia–n0t.0s3on(σly=).0.08),and (2e0.1g4.,,WresEpAeVctEivealnyd).4MOST, Dalton et al. 2014; de Jong et al.
Comparingwiththeresultsderivedfromtheoriginalspectra
wefoundthat[Fe/H]isweaklyoverestimatedwhenthespectra
Of the three methods method 1 clearly performs the least
arenoisier, but[Fe/H]doesnotdependontheresolutionofthe
well.Itisnoticeablethatthescatterinallthreestellarparameters
spectrum. It should be noted that we did not investigate if the
arequiteabithigherforthismethodthanfortheothertwo. The
offsetsarealsosomewhatlarger. FromFig.5weseethatthere abundances of other elements were unaffected. The iron lines
isnoparticulartrendin∆Teff,∆logg,and∆[Fe/H]asafunction wanealuyssee,arfeorcaortehfeurlelylesmeleencttsedthtiosmbeaythneoctlebaentersutea.ndmosteasyto
ofTeff. Thisisreassuringasitindicatesthatourmethodsdonot
havehiddentrendsinthemandthattheestimatedscatterscanbe
trusted.
5. ApplyingouranalysistostarsinNGC6528
Method3suffersfromtheshortcomingthatitcannotbeap-
pliedtocoolergiants(Teff <4400K).Thisisaseverelimitation 5.1. StellarparametersforNGC6528stars
forthestudyofglobularclustersandfieldgiantsintheGalactic
bulge. Tostudythemetallicitydistributions,wewouldtherefore Initial Teff for the stars were calculated using the colour-Teff-
[Fe/H] relation from González Hernández & Bonifacio (2009).
5 FortheseestimatesweexcludedthestarHD107328asthe[Fe/H]for Aswecouldnotobtainphotometricdataintheopticalforallour
thatstarisverydifferent,andwedonothaveastraightforwardanswer stars,thedereddenedJ−Kscolourisusedtocalculatetheinitial
tothisdiscrepancy. estimateofTeff. Followingpreviousstudiesofthemetallicityof
Articlenumber,page8of25
C.Liu etal.:Determinationofrobustmetallicitiesformetal-richredgiantbranchstars
200 0.2
150
0
H]r
−Tffe,r 10500 −[Fe/-0.2
Tffe,x 0 /H]x-0.4
Fe
-50 [-0.6
-100 -0.8
3600 3800 4000 4200 4400 4600 4800 5000 5200 3600 3800 4000 4200 4400 4600 4800 5000 5200
Teff,r Teff,r
Method 1 Method 2 Method 3
0.2
0 αCet Teff,r=3796K
ggr-0.2 µγSLgeeo TTeeffff,,rr==34840774KK
−lo-0.4 HD107328 Teff,r=4496K
ggx-0.6 αβGTaeum TTeeffff,,rr==34982578KK
lo-0.8 βAra Teff,r=4197K
-1 ǫVir Teff,r=4983K
Arcturus Teff,r=4286K
-1.32600 3800 4000 4200 4400 4600 4800 5000 5200 ξHya Teff,r=5044K
Teff,r
Fig.5. ComparisonofthestellarparametersderivedusingthethreemethodsdiscussedinSects.4.3.1till4.3.3withthereferencevalues(Table3).
Oneachy−-axisisindicatedthedifferencebetweenthevalueswehaveobtainedandthereferencevalue(indicatedbyasubscript"r"). Method
1isindicatedbyredsymbols, Method2byblack, andMethod3isindicatedbycyansymbols. Differentsymbolsrepresentthedifferentstars
(asindicatedinthefigure, notethateachsymbolrepresenttwostars.TheyshouldbeeasytoidentifythankstotheirdifferentTeff ). Notethat
somestarshavemorethanonespectrumanalysed(seeSect.2.1.1). ThestarscanbeidentifiedbytheirrecommendedTeff whichisplottedonthe
x-axis.Thedashedlineindicatestheseparationof"cool"(left)and"warm"(right)giants(seeSect.4.3.2).
NGC6528(e.g.,Zoccalietal.2004),weset[Fe/H]=–0.10dex
0.25
astheinitialvaluefortheanalysisforallstars.Sincemostofour
starsareeitherhorizontalbranchorredclumpstars,wesimply 0.2 2σ
set the initial logg to 2.5dex for warm giants (Teff ≥ 4400 K)
and 2.0dex for the cooler. For the analysis we used Method 2 0.15
andModifiedMethod2,asdesribedinSect.4.3.2. H]r 0.1
Inspectingthespectrumofstar1-24,wefoundthatmostof /
e
the lines are asymmetric. Zoccali et al. (2004) found that this F 0.05 1σ
[
−
star likely is a binary. Our inspection of the spectrum supports
x 0
thisconclusion. Thestarwasremovedfromoursample. H]
/
For stars 61, 66, 68, and 84 we were unable to analyse the e-0.05
F
spectraastheyallhavelowS/Nandinadditionthespectraap- [
-0.1
pear to have several unexpected features. These stars were ex-
cludedfromtheanalysis. -0.15
This leaves us with 29 stars successfully analysed. The re-
-0.2
sultsarelistedinTable4. Eightofthesestarsarenotradialve- 10 20 30 40 50 60
locitymembersofNGC6528(seeSect.2.3). S/N
Fig.6. Thedifferencebetween[Fe/H]derivedfromspectraofvary-
5.2. AnalysisofasuiteoflowS/Nspectraforstarsin ingS/N(perpixel)forstarsinNGC6528. [Fe/H]x indicatesourvalue
NGC6528 measuredforeachspectrum,while[Fe/H]r indicatethevalueobtained
in Sect. 5.1 for each star. The full line indicated the average differ-
ForseveralofthestarsinNGC6528wehavemultipleexposures. enceevaluatedasarunningaverage. Theshadedregionindicatesthe
This allows us to analyse spectra of different S/N for the same 1σdifference,whilethedashed-dottedlineindicatesthe2σdifference.
star. Using Method 2 and Modified Method 2 we analysed the DetailsonindividualstarsaregiveninonlinematerialinAppendixE.
Notethatinthisfigurewedonotdistinguishbetweenstarsforwhich
actual observed spectra of five stars (star-05, -07, -62, -65 and
-67,IDsasinTable2). differentmethodstoderiveTeff havebeenused(compareFig.7).
Twooftheclusterstars(-62and-71)havealargenumberof
spectraallowingustostudytheresultsinamorestatisticalway.
For reference value we use the final parameters determined for We find that the scatter, for a given star and for the whole
eachstaraslistedinTable4. sample,increasesaswegotospectrawithlowerandlowerS/N.
Articlenumber,page9of25
Table4.StellarparametersforthesamplestarsderivedusingMethod2.
# Object Teff σTeff loggσlogg[Fe/H]σ[Fe/H] Vmic VmacMember
(K) (K) (kms−1)(kms−1)
(01) 01 4550 100 2.78 0.02 0.40 0.12 1.8 4.2 N
(02) 02 6042 50 4.51 0.05 0.03 0.04 1.1 8.2 N
(03) 03 4029 100 1.23 0.15 –0.15 0.12 1.5 5.3 Y
(04) 04 4304 100 1.52 0.15 0.04 0.11 1.4 5.3 Y
(05) 05 4277 100 1.95 0.11 0.01 0.10 1.5 4.5 Y
(06) 06 4623 100 1.98 0.08 –0.04 0.14 1.9 6.8 Y
(07) 07 4776 100 2.50 0.09 0.03 0.08 1.7 6.1 Y
(08) 1-02 4258 100 1.67 0.12 0.05 0.09 1.3 9.8 Y
(09) 1-16 4640 100 2.56 0.14 –0.02 0.09 1.5 7.1 Y
(11) 1-36 4337 100 2.14 0.08 –0.08 0.11 1.7 4.8 Y
(12) 1-42 4125 100 1.39 0.19 0.09 0.14 0.8 7.8 Y
(13) 60 4289 100 2.08 0.09 –0.07 0.08 1.7 6.2 Y
(15) 62 3967 100 1.89 0.10 –0.08 0.11 1.8 7.1 Y
(16) 63 3977 100 1.45 0.07 –0.15 0.09 1.8 7.0 Y
(17) 64 4079 100 1.94 0.15 –0.07 0.12 1.7 5.6 Y
(18) 65 4289 100 2.28 0.08 –0.09 0.12 1.9 6.5 Y
(21) 69 4044 100 1.65 0.08 –0.17 0.12 1.7 6.2 Y
(22) 70 4123 100 2.12 0.12 0.09 0.20 1.1 7.3 Y
(23) 71 4560 150 2.64 0.04 0.11 0.08 1.9 7.7 Y
(24) 72 4506 150 2.55 0.04 0.26 0.13 2.2 6.7 N
(25) 73 4702 100 2.62 0.20 –0.02 0.10 2.4 10.9 Y
(26) 75 4153 100 2.00 0.13 0.01 0.10 1.7 4.8 N
(27) 76 4569 150 2.74 0.22 0.43 0.13 2.1 5.4 N
(28) 80 4451 100 2.51 0.05 0.19 0.14 1.7 6.4 Y
(29) 82 4521 100 2.34 0.17 0.40 0.12 2.0 5.2 N
(30) 83 4883 100 2.48 0.21 –0.48 0.07 1.7 5.6 N
(32) 86 3650 150 1.15 0.38 0.03 0.34 1.7 10.0 N
(33) 3014 4797 100 2.21 0.10 0.21 0.11 1.4 6.7 Y
(34) 3025 4877 100 2.02 0.15 0.14 0.09 1.7 15.8 Y
Notes. Columnonegivesthe#fromTable2inAppendixA,whicharealsousedintheFindingChartinthesameappendix. Columntwothe
original IDs, Columns three to eight lists the derived parameters and their associated errors. Columns nine and ten list the micro and macro
turbulences,respectively."Y"and"N"inthelastcolumnindicateifthestarisaradialvelocitymemberofNGC6528ornot.
This is not a new finding, but it is here quantified in detail for, Table 5. Metallicity estimates for NGC6528 using different samples.
The two first lines in the table gibes the results using Method 2 and
what we believe, is the first time for evolved, metal-rich giant
stars. AlthoughthescatterincreasesaswegotolowerS/Nthe Modified Method 2 together to analyse the whole sample. The line
markedrecalibratedpresentsourfinalresult. Belowthis, wegivethe
meanvalueofthemeasurementsmoreorlessreproducestheref-
resultsifthesampleissplitaccordingtowhichmethodisusedtoanal-
erencevalue. AtthelowestS/Nwefindapositiveoffset(Fig.6).
ysethespectra.
Further details are available in the online material in Ap-
pendixE. S/N Nstars <[Fe/H]> σ Error
All 21 0.00 0.10 0.02
>35 13 –0.03 0.08 0.02
Recalibrated >35 13 0.04 0.07 0.02
5.3. Discussion: DoMethod2andModifiedMethod2
producecomparableresults? Method2 All 8 0.07 0.10 0.03
>35 3 0.04 0.06 0.03
Unfortunately, theanswertothequestionposedintheheadline ModifiedMethod2 All 13 –0.04 0.09 0.02
>35 10 –0.05 0.08 0.02
of this section is – no. This should perhaps not come as a sur-
prise, butgiventheresultsinSect.4.4wewouldhaveexpected
Notes.The first column indicates which methods are included in the
thattheresultswouldberelativelysimilarandno(obvious)sys- average,thesecondcolumnindicatesifallS/Nareincludedorifthere
tematicdifferencespresent. Thisis,however,notthecase. isacut-off, thethirdcolumngivesthenumberofstarsinthesample,
Figure7 shows the cumulative distributions of [Fe/H] for thefifthcolumnliststheaverage[Fe/H],while√columnssixandseven
liststheassociatedσanderror-in-the-mean(σ/ N ).
stars that are radial velocity members of NGC6528. We plot stars
the distribution for all stars, but also for stars analysed using
Method2andModifiedMethod2,respectively. Table5liststhe
numberofstarsineachsub-sampleandtheaverage[Fe/H].Stars analysedonlystarswithS/N>35.Althoughthisresultsinrather
analysedusingMethod2areabout0.1dexmoremetal-richthan smallsamplestheend-resultremains(Fig.7b).
starsanalysedwithModifiedMethod2. Themedianissimilarly We also note that when selecting only stars with S/N > 35
off-set. TocheckthatthisresultdoesnotdependonS/Nwealso the full sample as well as the two sub-samples all give a lower
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