On the relation between metallicity and RGB color in HST/ACS data

2.4 MB·

by  David Streich

Astronomy&Astrophysicsmanuscriptno.rgbpaper˙completed (cid:13)c ESO2014
January14,2014
On the relation between metallicity and RGB color in HST/ACS data
D.Streich1,R.S.deJong1,J.Bailin2,P.Goudfrooij3,D.Radburn-Smith4,andM.Vlajic1
1 Leibniz-Institutfu¨rAstrophysikPotsdam(AIP),AnderSternwarte16,14482Potsdam,Germany,e-mail:[email protected]
2 DepartmentofPhysics&Astronomy,UniversityofAlabama,Box870324,Tuscaloosa,AL35487,USA
3 SpaceTelescopeScienceInstitute,3700SanMartinDrive,Baltimore,MD21218,USA
4 DepartmentofAstronomy,UniversityofWashington,Box351580,Seattle,WA98195,USA
Received.../Accepted...
ABSTRACT
4 Context.Thedeterminationofstellarmetallicityanditsgradientinexternalgalaxiesisadifficulttask,butcrucialfortheunderstanding
1
ofgalaxyformationandevolution.
0
Aims.ThecoloroftheRedGiantBranch(RGB)canbeusedtodeterminemetallicitiesofstellarpopulationsthathaveonlyshallow
2
photometry.WewillquantifytherelationbetweenmetallicityandcolorinthewidelyusedHSTACSfiltersF606WandF814W.

n Methods.WeuseasampleofglobularclustersfromtheACSGlobularClusterSurveyandmeasuretheirRGBcoloratgivenabsolute
a magnitudestoderivethecolor-metallicityrelation.Weespeciallyinvestigatethescatterandtheuncertaintiesinthisrelationandshow
J itslimitations.
3 Results.ThereisaclearrelationbetweenmetallicityandRGBcolor.Acomparisonwithisochronesshowsreasonablygoodagreement
withBaSTImodels,asmalloffsettoDartmouthmodels,andalargeroffsettoPaduamodels.
1
Conclusions.Evenforthebestglobularclusterdataavailable,themetallicityofasimplestellarpopulationcanbedeterminedfrom
theRGBaloneonlywithanaccuracyof0.3dexfor[M/H](cid:46) −1,and0.15dexfor[M/H](cid:38) −1.Formixedpopulations,astheyare
]
A observedinexternalgalaxies,theuncertaintieswillbeevenlargerduetouncertaintiesinextinction,age,etc.Thereforecautionis
necessarywheninterpretingphotometricmetallicities.
G
. Keywords.Galaxy:globularclusters:general-Stars:RGB-Galaxies:stellarcontent
h
p
-
o 1. Introduction Furthermore,anobservationalrelationforthewidelyusedHST
r ACS filters F606W-F814W is still missing in the literature1.
t Measuring the metallicity and its gradients in galaxies is a key
s Hereweaimtoaddresstheseshortcomings.
a issueforunderstandinggalaxyformationandevolution.
Thispaperisorganizedasfollows:Afteranintroductionto
[ OutsidetheLocalGroup,spectroscopicmetallicitydetermi-
the data and isochrones we use in chapter 2, an observational
nation of (resolved) stars is not feasible at the moment, except
1 color metallicity relation is derived in chapter 3. A discussion
v forthefewverybrightsupergiants(Kudritzkietal.2012).Atthe andsummaryfollowinchapters4and5.
7 same time, the number of available color magnitude diagrams
4 (CMDs) of nearby galaxies is increasing rapidly, e.g. from the
8 GHOSTS(Radburn-Smithetal.2011)andANGST(Dalcanton
2. DataandIsochrones
2 etal.2009)surveys.TheseCMDscanbeusedtoderivemetal-
1. licities. Inthisworkweusethedataof71globularclustersobservedas
0 The color of the red giant branch (RGB) has long been partoftheACSGlobularClusterSurvey(ACSGCS;Sarajedini
4 known to depend on the metallicity (Hoyle & Schwarzschild etal.2007)anditsextension(Dotteretal.2011).Thesedatacon-
1 1955;Sandage&Smith1966;Demarqueetal.1982).Thishas tainphotometryintheF606WandF814Wfiltersandispublicly
v: been extensively used to measure metallicities of old popula- available at the homepage of the ACSGCS team2. For the de-
i tions. termination of photometric uncertainties and completeness, the
X There are many ways to convert the color to a metallicity: resultsfromartificialstartestsarealsoavailable.Adetailedde-
r someauthorsdefineindicesofanobservedpopulation,e.g.the scriptionofthedatareductionisgiveninAndersonetal.(2008).
a
coloroftheRGBatagivenmagnitudeortheslopeoftheRGB, Tocomparethedifferentclusters,itisnecessarytotransform
(as defined for example in Da Costa & Armandroff 1990; Lee the apparent magnitudes into absolute, reddening-free magni-
etal.1993;Savianeetal.2000;Valentietal.2004),whileothers tudes. For this purpose, we use the distance modulus and color
measured metallicities on a star by star basis by interpolating excess from the GC database of W. Harris (Harris 1996, 2010)
between either globular cluster fiducial lines (e.g. Tanaka et al. and the extinction ratios for the ACS filters given by Sirianni
2010; Tiede et al. 2004) or analytic RGB functions (calibrated et al. (2005, Table 14). Metallicities, metallicity uncertainties
withglobularclusterdata,e.g. Zoccalietal.2003;Gullieuszik and α-abundances are taken from Carretta et al. (2009, 2010),
et al. 2007; Held et al. 2010) or stellar evolution models (e.g. ifnotstatedotherwise.
Richardson et al. 2009; Babusiaux et al. 2005), and therefore
generatingmetallicitydistributionfunctionsforapopulation. 1 Momanyetal.(2005)actuallyhavefoundsucharelation,butthey
Uncertaintiesthatarisefromaspecificcalibrationoragiven usedonlythreeclustersanddidnotpublishthedetails.
isochrone or cluster template set are typically not well studied. 2 http://www.astro.ufl.edu/˜ata/public_hstgc/
1
D.Streichetal.:OntherelationbetweenmetallicityandRGBcolorinHST/ACSdata
InordertomeasurethecoloroftheclustersRGBstheymust 3.2. Metallicitydetermination
have a sufficient number of stars in the RGB region. We se-
The iron abundance [Fe/H] is often used synonymously with
lected therefore only those clusters for our study, which have
more than five stars brighter than M = −2 and least one metallicity.However,fromthetheoreticalpointofviewofstellar
star brighter than M = −3. A Fli8s1t4Wof the clusters used is evolution,allelementsareimportantindeterminingtheproper-
F814W ties of stellar atmospheres. Therefore the color of red giants is
giveninAppendixB(TableB.1).
expectedtodependontheoverallmetallicity[M/H]ratherthan
Forcomparisonwiththeoreticalmodels,weusefoursetsof on [Fe/H]. Unfortunately, there are very few measurements of
isochrones: the new PARSEC isochrones (Bressan et al. 2012)
theabundancesofotherelementsinglobularclusters.
andtheirpredecessors,the(old)Paduaisochrones3(Girardietal.
We use here the abundances given in Carretta et al. (2010),
2010; Marigo et al. 2008, and references therein), the BaSTI
who have measured [Fe/H] for all GCs in our sample and have
isochrones4 (Pietrinferni et al. 2006, 2004) and the Dartmouth
compiled[α/Fe]valuesformanyofthem.AccordingtoSalaris
isochrones5(Dotteretal.2007).
et al. (1993), these two measurements can be combined to get
theoverallmetallicitywiththeformula
3. Results [M/H]=[Fe/H]+log (0.638∗10[α/Fe]+0.362).
10
3.1. Colormeasurement For clusters that have no individual α measurement, we had to
estimateitsαabundance.Sincethespreadof[α/Fe]amongglob-
We use two indices to define the color of the RGB: C =
−3.0 ularclustersisrathersmall,suchanestimatewillonlyintroduce
(F606W−F814W)M=−3.0andC−3.5 =(F606W−F814W)M=−3.5, small errors. In Fig. 1, [α/Fe] is plotted against [Fe/H], where
i.e.thecoloroftheRGBatanabsoluteF814Wmagnitudeof-
wehaveassumedanuncertaintyof0.05intheαabundance.The
3.0and-3.5,respectively(seeFig.A.1forsometypicalCMDs).
straightlineisalinearregression,whichweusefortheestima-
EquivalentindicesfortheJohnson-Cousinsfiltersystemwereal-
tionof[α/Fe],whereitisnotavailable.Thescatteraroundthis
readyusedbyDaCosta&Armandroff(1990),Leeetal.(1993)
regressionlineis0.1dex,whichweadoptastheindividualun-
and also by Saviane et al. (2000). These indices have the ad-
certaintyintheestimated[α/Fe].
vantage of only depending on relatively bright stars and can
thereforebemeasuredindistantgalaxies,aswell.Weusealsoa
thirdindex,theS-index,whichistheslopeoftheRGB(Saviane
et al. 2000; Hartwick 1968). This slope is measured between
twopointsoftheRGB,oneatthelevelofthehorizontalbranch
and the other two magnitudes brighter. While this index needs
deeper data, and therefore its usage in extragalactic systems is
limited,ithastheadvantageofbeingindependentofextinction
anddistanceerrors.
In order to provide a robust measurement of the color at a
given magnitude we interpolated the RGB with a hyperbola of
theform:
M =a+b·color+c/(color+d)
Such a function was already used by Saviane et al. (2000) to
findaone-parameterrepresentationoftheRGB;theydefinedthe
parameters a, b, c, and d as a quadratic function of metallicity.
Here, we are only interested in a good interpolation in sparse
parts of the RGB and can therefore use a, b, c, and d as free
parametersforeachcluster.Inordertoreduceproblemsdueto
Fig.1.Alphaabundanceasafunction of[Fe/H]forallclusters
contamination,wedefinearegionofprobableRGBstars,which
alsoexcludesthehorizontalbranch/redclumppartoftheCMD. in Carretta et al. (2010). The text in the lower left corner gives
Notethatwefitthecurvedirectlytothecolor/magnitudepoints theformulaoftheregressionlineandthescatteraroundthisline.
We used these for estimating the [α/Fe] and its uncertainty for
of the stars and not to the ridge line of the RGB (in contrast
clusterswithoutindividualalphameasurement.
to Saviane et al. 2000). More details of the fitting process and
someexampleplotswiththeexclusionregionareshowninthe
Appendix.
To calculate the S-index, we first determined the horizon-
3.3. Uncertainties
talbranchmagnitudeofeachsystembyvisualinspectionofthe
associatedCMDs.ThiswastypicallyF606W≈0.40mag,witha
To determine the uncertainties of our color measurements, we
1-sigma variation of 0.10mag. We measured the color at this
performedabootstrapanalysis.Theuncertaintyinthefitisde-
magnitude (and at 2 magnitudes brighter) from the fitted RGB
rivedbyfittingtheRGBof500samplesthataredrawnrandomly
usedpreviously,andcalculatedtheS-indexastheslopebetween
fromtheoriginaldata.Eachre-samplehasthesamenumberof
thesepoints
starsastheoriginalsample,butmaycontainsomestarsmultiple
timeswhileothersareabsent.
3 http://stev.oapd.inaf.it/cgi-bin/cmd We also incorporated in the bootstraps a shift due to the
4 http://albione.oa-teramo.inaf.it/ uncertainties in extinction and distance. According to Harris
5 http://stellar.dartmouth.edu/˜models/index.html (2010),theuncertaintyinextinctionisoftheorder10%inE(B-
2
D.Streichetal.:OntherelationbetweenmetallicityandRGBcolorinHST/ACSdata
V), but is at least 0.01mag, while the uncertainty in distance
modulusis0.1mag.
Theuncertaintyindistanceisimportantbecausewemeasure
thecoloratagivenabsolutemagnitude.Thisisparticularlysig-
nificant for the metal-rich clusters where the color of the RGB
is strongly dependent on magnitude, as opposed to metal-poor
clusterswheretheRGBisnearlyverticalonaCMD.Theresult-
inguncertaintyinC rangesfromapproximately0.01magat
−3.5
[M/H]=-2toapproximately0.1magat[M/H]=-0.2.
The uncertainties in the metallicity are the sum of the un-
certainties in [Fe/H] Carretta et al. (as given by 2009), and in
[α/Fe], which we adopt as 0.05dex for clusters with individual
alpha-abundancemeasurementsand0.1dexforclusterswithes-
timatedvalues.
3.4. Colormetallicityrelation
Usingthecolorsandmetallicitiesdescribedabove,wecannow
lookatthecolor-metallicityrelations.
The results are shown in Fig. 2. There is a clear relation
between RGB color and spectroscopic metallicity. This rela-
tioncanbeparametrizedwiththefunctionF606W −F814W =
a exp([M/H]/a ) + a . Using the orthogonal distance regres-
0 1 2
sion (ODR) algorithm (Boggs et al. 1987, 1992)6, we deter- Fig.3. top panel: The RGB slope as a function of metallicity.
minedthethreeparameters,thatareshowninTable1.TheODR Thesolidblacklineisthebest-fitquadraticfunction,asgivenin
uses the uncertainties on both variables to determine the best the equation in the bottom left. Grey lines give the 1σ, 2σ and
fit.Hence,boththeuncertaintiesincolorandmetallicity,asde- 3σconfidencerangesofthethebestfitrelation.Bottompanel:
scribedabove,areconsideredduringthefitandtheireffectsare weighted orthogonal residuals, i.e. the orthogonal distances to
includedinthefinaluncertaintiesoftheresultingfitparameters. thebestfitlinedividedbytherespectiveuncertainties.
The residual varinaces for both relations are σ2 < 1, so the
res
adopteduncertaintiescanexplaintheobservedscatterinthere-
lations. intheresiduals.Moreover,thevarianceoftheresidualsisonly
σ2 = 1.17, i.e. the residuals are only slightly larger than ex-
res
pectedfromtheindividualmeasurementuncertainties.Themax-
Table 1. Fit parameters of the color–metallicity relations. imum of the parabola is at [M/H]=-2.14, which is beyond the
For C and C the relation is exponential: C =
−3.5 −3.0 i metallicityrangeoftheobservedclusters.
a exp([M/H]/a ) + a , for the S-index it is linear S = a +
0 1 2 0
a [M/H].
1
4. Discussion
a a a
0 1 2
C 0.95±0.11 0.602±0.069 0.920±0.015 4.1. Analyzingresiduals
−3.5
C−3.0 0.567±0.056 0.75±0.12 0.845±0.018 We examine the residuals to look for a possible second pa-
S-index 3.67±0.76 −9.3±1.2 −2.08±0.44 rameter that influences the color or slope of the RGB and
could produce some scatter in a simple color-metallicity rela-
tion. Figures 4 and 5 show the residuals of the fit of the color-
metallicityrelation,thatisshowninFig.2,andFigures6and7
the residuals of the fit to the slope metallicity relation, that is
3.5. TheS-index
showninFig.3.
The slope of the RGB as a function of metallicity can be seen Theresidualsasafunctionofmetallicity,[Fe/H]and[α/Fe],
inFig.3.ThereporteduncertaintiesoftheS-indexareacombi- areshowninFig.4andFig.6.Thereisnotrendwithanyofthese
nation of the uncertainties of the RGB fit (determined through parameters,neitherinthecolor-norslope-metallicityrelations.
a bootstrap analysis as described above) and the uncertainty Fromtheoreticalstudies,theageisknowntohaveaneffect
in the determination of the HB level, which we set here to on the color of the RGB. In fact, a weak trend of the residu-
σ =0.1mag. als with age can be seen in Figure 5 (upper panel), with older
HBmag
As expected, the slope of the RGB gets smaller with in- clusters being slightly redder than younger clusters. The slope
creasing metallicity, while at the low-metallicity end the RGB oftheregressionlinesshownthereis1.94±2.13forC and
−3.5
slope is insensitive to metallicity. We have fitted a quadratic 3.00±1.85forC ,whichmakesthetrendsignificantforthe
−3.0
functiontothedata,whichisshowninFig.3togetherwiththe C index.InordertoquantifytheeffectsofageontheCMD,
−3.0
associated best-fit parameters. The choice of a quadratic func- weanalysetheresidualsincolorspace7 inFigure8.Assuming
tion for the fit proves to be appropriate as no trends are seen atypicalageforglobularclustersof12.8Gyr(asMar´ın-Franch
etal.(2009)dousingtheisochronesofDotteretal.(2007))we
6 We used the Python implementation of this algorithm that is
part of the Scipy library: http://docs.scipy.org/doc/scipy/ 7 i.e.weignoreuncertaintiesinmetallicityandonlylookatthecolor
reference/odr.html offsetbetweenthedataandthebestfitrelation
3
D.Streichetal.:OntherelationbetweenmetallicityandRGBcolorinHST/ACSdata
Fig.2. Color of the RGB as function of metallicity, based on the fitted RGBs. Black circles are for the color at M = −3.5,
F814W
orangediamondsfor M = −3.0.Smallpointsareforclusterswithoutindividualalphameasurements.Thesolidlinesarethe
F814W
best-fittingfunctionsasgivenintheupperleftcornerandthelightercontoursshowthe1σ,2σand3σregionsofthefit.
can transform the slopes of the regression lines in Figure 8 to but this effect is relatively small. An age difference of 5Gyr
actual color changes. These are 0.0062 ± 0.0041mag/Gyr for causes the same color difference as a metallicity difference of
C and0.0078±0.0026mag/GyrforC .Whilethisisavery only 0.1dex (see Fig. 9, top row). At a given total metallicity
−3.5 −3.0
small effect for the age range observed in our globular clusters [M/H],theα-abundancehasalmostnoeffectontheRGBcolor
(10Gyrto14Gyr),itcanmakesignificantdifferenceswhenex- (Fig.9,middlerow).Thissupportstheassumptionthatthecolor
trapolated toyoungerpopulations; e.g.an 8Gyrold population oftheRGBismainlyinfluencedby[M/H]andnot[Fe/H].
wouldbebluerthanpredictedbyourrelationbyabout0.03mag. TheincreasingcurvatureoftheRGBwithincreasingmetal-
NotealsothattheSindexdoesnotshowanysystematictrends licitypreventstheRGBofsomemetalrichclustersfromreach-
withage. ingF814W=−3.5mag,butbenddownatfaintermagnitudes.In
To test for problems with the extinction values, we looked the Dartmouth models this applies for isochrones with [M/H]>
for trends with E(B-V) and galactic latitude (Fig. 5 and Fig. 7, −0.4,inPaduamodelsisochroneswith[M/H]> −0.3.However,
middleandlowerpanel).Wedonotfindanysystematicshere. the BaSTI RGB isochrones all reach F814W= −3.5mag, even
at super-solar metallicities. Among our clusters, NGC6838
([M/H]= −0.53; it also has very few stars in the RGB) and
4.2. Comparison NGC6441([M/H]=−0.29)areaffectedbythis.
Wecancompareourrelationstothosederivedfromstellarevo- Inordertoquantifytheagreementbetweenourrelationsand
lution models, and to relations from ground-based data trans- other relations, we have performed a Monte Carlo resampling
formedtotheHST/ACSfiltersystems. of our relations by drawing random parameter sets ai from a
For comparison with theoretical relations, we use the multivariateGaussiandistributionwiththemeanandcovariance
isochronesetfromthePadua,DartmouthandBaSTIgroups.For matrix as given by the best fit. The 68.3%, 95.5%, and 99.7%
allisochronesetsweusedagesof8Gyr,10Gyrand13Gyr.For confidenceintervalareshownascontoursinFigures2,3,9,and
Dartmouth, we use α-enhancements of [α/Fe] = {0.0,0.2,0.4} 10.
and for BaSTI models [α/Fe] = {0.0,0.4}. The PARSEC8 and AscanbeseeninFigures9and10,BaSTIisochronesshow
Padua isochrones are available only with solar scaled abun- goodagreementwithourobservationalresult.Atmostmetallici-
dances. tiestheα-enhancedBaSTIisochronefallswithinthethe1σcon-
Alltheseisochronesetsshowaqualitativelysimilarbehav- fidencerangeofourobservationalrelation;onlyfor[M/H]>-0.4
ior. The RGB gets redder (Fig. 9) and shallower (Fig. 10) with aretheisochronessignificantlyredder(>3σ)andshallowerthan
increasingmetallicity.AhigheragealsoleadstoaredderRGB, our relation. The Dartmouth isochrones agree well at very low
metallicities,buttendtopredictslightlyreddercolorsandshal-
8 Actually, Bressan et al. (2012) write about α-enhanced PARSEC lowerslopesatintermediateandhighermetallicities.Incontrast,
isochrones,butthesearenot(yet)publiclyavailable. resultsfromthePaduaisochronesarebluerbyalmost0.15mag
4
D.Streichetal.:OntherelationbetweenmetallicityandRGBcolorinHST/ACSdata
Fig.9.Comparisonofcolor-metallicityrelationswiththeoreticalisochronesofdifferentage(toprow)anddifferentα-enhancement
(middle row) and transformed (V-I) relations (bottom row). Left panels compare the relations at F814W = −3.5, right panels at
F814W =−3.0.The(V-I)relationsaretakenfromSavianeetal.(2000,S+00),Leeetal.(1993,L+93)andDaCosta&Armandroff
(1990,DA90).TheS+00relationsaregivenontwometallicityscales:theZWscale(Zinn&West1984)andtheCGscale(Carretta
& Gratton 1997). The gray contours show the 1σ, 2σ, and 3σ confidence levels of the fit. The two lines for the observational
relationsareduetodifferencesbetweentheobservationalandsynthetictransformationsfromSiriannietal.(2005).
and much steeper at lower metallicities, and redder and shal- beenknowntoleadtohighermetallicityestimates,whenPadua
lower at the high metallicity end. Determining the reason for isochronesareused(Lejeune&Buser1999).
thisoffsetisbeyondthescopeofthispaper,butthisproblemhas
5
D.Streichetal.:OntherelationbetweenmetallicityandRGBcolorinHST/ACSdata
Fig.4. Residuals of the fit of the color-metallicity relation as Fig.5. Residuals of the fit of the color-metallicity relation as
function of metallicity (upper panel), iron abundance (middle functionofage(upperpanel,Mar´ın-Franchetal.2009),extinc-
panel)andalphaenhancement(lowerpanel).Symbolsandcol- tion(middlepanel)andgalacticlatitude(lowerpanel).Symbols
orsareasinFig.2. andcolorsareasinFig.2.
Existing color-metallicity relations are given in the standard
Johnson-Cousin filters. Thus to compare these with our anal- Notethatthesetwotransformationshavearelativeoffsetof
ysis we use the transformations to the HST/ACS filter set de- ofabout0.05mag,whichcanbeseeninFig.9asthetwoalmost
scribed in Sirianni et al. (2005). Two such transformations are parallellinesinthelowerpanel.9
provided,oneobservationallybasedandtheothersynthetic.The From Fig. 9 it can be seen that these transformed relations
formerusesobservationsofhorizontalbranchandRGBstarsin are always bluer at the low metallicity end and have a steeper
themetal-poor([Fe/H]=−2.15)globularclusterNGC2419.This slopethanourrelations.10
clusterdoesnotcontainstarswith(V−I)>1.3,hencethetrans- Part of this discrepancy can be explained by the different
formationatthesereddercolorsareextrapolatedandshouldbe metallicity scales used for the various relations. While we use
usedwithcaution.Thetransformationis: themetallicityscaleofCarrettaetal.(2009,,C+09),earlierre-
lationsweredeterminedeitherintheZinn&Westscale(Zinn&
F606W−F814W =−0.055+0.762(V−I) West 1984, ZW84) or the Carretta & Gratton scale (Carretta &
Gratton1997,CG97).TheadoptedC+09scaleiscomparableto
For the synthetic transformation, stellar models with (V − the ZW84 scale; however, the CG97 scale yields higher metal-
I) < 1.8 were used. Hence, for redder colors, the extrapolation licities for [Fe/H](cid:46) −1 and lower metallicities for [Fe/H](cid:38) −1
shouldagainbetreatedwithcaution.Thetransformationisgiven (see11).
as:
9 TheoffsetcanalreadybeseeninSiriannietal.(2005,Fig.21)as
anoffsetinplotof(V-I)versusV-F606W.
F606W−F814W =0.062+0.646(V−I)+0.053(V−I)2 10 Strictly speaking, we compare slightly different things here: The
transformedrelationsmeasurethecoloratconstantI-bandmagnitude,
whileinthisworkwehavemeasuredthecoloratconstantF814Wmag-
We use both these transformations on the color-metallicity
nitude. We can ignore this difference here because the difference be-
relationsof Savianeet al.(2000),who determinedrelations for
tween I-band and F814W is small. According to the transformations
the indices (V − I)−3.0 and (V − I)−3.5, and for Da Costa & givenabove,thedifferencesbetweenF814WandIarealwayssmaller
Armandroff (1990, for (V − I) ) and Lee et al. (1993, for
−3.0 than0.05magandtheresultingerrorinthecolormeasurementofthe
(V − I)−3.5). To shift these transformations, which are defined RGBisalwayssmallerthan0.01mag(exceptforthetworeddestclus-
for[Fe/H],tothe[M/H]scale,weusedthesame[Fe/H]-[α/Fe] ters,forwhichitcanreach0.06mag).Thereforetheeffectonthetotal
relationasforthedata. color-metallicityrelationisnegligible.
6
D.Streichetal.:OntherelationbetweenmetallicityandRGBcolorinHST/ACSdata
Fig.6. Residuals of the fit of the slope-metallicity relation as Fig.7. Residuals of the fit of the slope-metallicity relation as
function of metallicity (upper panel), iron abundance (middle functionofage(upperpanel,Mar´ın-Franchetal.2009),extinc-
panel)andalphaenhancement(lowerpanel). tion(middlepanel)andgalacticlatitude(lowerpanel).
Hence, using the CG97 scale will lead to a steeper color-
metallicty relation than found from our measurements (see the
bottompanelofFig.9).
4.3. Invertingtherelation
Themainpurposeofthecolormetallicityrelationistoestimate
metallicities of old stellar population. The uncertainties arising
from the inverted relation are highly nonlinear. In Fig. 12 we
plot the difference between the spectroscopic metallicities and
themetallicitiesderivedwithourrelation.Itisapparentthatfor
bluer colors (i.e. lower metallicities) the difference can be very
large.Ifthecolorisnearthepoleofthemetallicity-colorfunc-
tion, the formal uncertainties can be infinite. Then only an up-
perlimitonthemetallicitycanbederived.Forallclusterswith
C < 1.2(orC < 1.0)thescatterinthemetallicitydiffer-
−3.5 −3.0
encesisabout0.3dex.Wesuggestusingthisasaminimumun-
certaintyformetallicitiesderivedfromourrelationinthatcolor
Fig.8.Colorresidualsofthefitofthecolor-metallicityrelation
range.Forreddercolors,theuncertaintydropsinhalf.
as function of age. The text gives the regression line formulas
forbothindices.
5. Conclusionsandsummary
In this paper, we derived relations between the colors and the
Therefore, inverting the relation in this regime introduces
slopeoftheRGBandmetallicityusingdatafromglobularclus-
largeuncertainties.Thismakesaphotometricmetallicityde-
ters. The details of the relations are summarized in Table 1.
terminationratherinaccurateinthismetallicityrange.
When using these relations for determining metallicities of old
– Our relation agrees well with the prediction from BaSTI
resolvedstellarpopulations,thefollowingpointsshouldbekept
isochrones.Dartmouthisochronesareslightlyredder,Padua
inmind:
isochronesbluerthanourdata.Thus,forthepurposeofde-
– The color changes very little with metallicity for [M/H] (cid:46) terminingmetallicitiesofoldpopulationswerecommendthe
−1.0, the slope changes little below [M/H] (cid:46) −1.5. useofBaSTIisochrones.
7
D.Streichetal.:OntherelationbetweenmetallicityandRGBcolorinHST/ACSdata
Fig.12.Errordistributionofthemetallicitydeterminationusing
theinvertedcolormetallicityrelations.Lineswitherrorbarsare
Fig.10.ComparisonoftheobservedS-indexmetallicityrelation
the running mean and standard deviation which are computed
withisochronesofvaryingage.Thegraycontoursshowthe1σ,
using a bin width of 0.3mag for C and 0.15mag for C .
2σ,and3σconfidencelevelsofthefit. SymbolsandcolorsareasinFig.2.−N3.5otethedifferentscales−3o.0n
thex-axisforthetwodistributions.
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AppendixA: DescriptionofthefitoftheRGB
WeparametrizedtheRGBwiththefunction
M =a+b·color+c/(color+d),
asgiveninSavianeetal.(2000).Sincethedatadonotonlycon-
tain RGB stars, but also the horizontal branch, blue stragglers
and foreground stars, we have defined a region to guarantee a
high fraction of RGB stars in our fit sample. The extent of this
region can be seen as the red frame in Fig. A.1. Note that this
regionexcludesalsotheredclump.
Insomeclusters,thereisadistinctasymptoticgiantbranch
(AGB) visible, which lies on the blue side of the RGB (it is
mostly seen at F814W magnitudes between -1 and -2). As in
Saviane et al. (2000), we have removed these AGB stars by
excluding all detections that lie blue wards of a reference line
with the same slope for all clusters (denoted in Figures A.1
throughA.9byadashedredline).Thehorizontalpositionofthe
reference line was set to be 0.05mag blue wards (at F814W=-
0.5)ofafirstfitofallstarsintheRGBregionandthenexcluding.
ThefitincludingallstarsisshownintheCMDsasblackdashed
line,whilethefinalfitaftertheAGBremovalisshownasblack
solidline.
Fortheactualfitweusedthepythonpackagescipy.odr.This
routine performs an orthogonal distance regression, i.e. it min-
imizes the orthogonal distance between the curve and the data
points.Thedistanceofeachdatapointisweightedwithitsmea-
surement uncertainty. This method is a variation of the typical
χ2 minimization,nowgeneralizedfordatawithuncertaintieson
bothvariables.
The ACSGCS team reports photometric uncertainties for
eachindividualstar,whicharetypicallyquitesmall;themedian
uncertainty in F814W is only 0.003mag. This is much smaller
thanboththeobservedscatterintheRGBandtheerrorsthatare
foundintheartificialstartestatalevelofF814W≈0.(Thereare
no artificial star tests at brighter magnitudes.) The mean mea-
surement error estimated from the difference of the input and
recovered magnitudes in the artificial star test are 0.06mag in
F814W and 0.03mag in color. These estimated are added in
quadraturetothereporteduncertaintiesofeachstar.Thesmaller
errorincolorisduetothefactthaterrorsinbothbandsarecor-
related. Thus the uncertainty of the difference of both bands is
smallerthantheuncertaintyineachband.
Finally,wevisuallyinspectedeachCMDwithitsfit,tocheck
for any residual problems of our clusters. After this inspection
we excluded four more clusters from the sample: NGC6838
and NGC6441, because their RGB fits do not reach the M =
I
−3.5level;NGC6388(andagainNGC6441),becausetheirred
clumpsseemtobetofaint(Bellinietal.2013,alsofoundprob-
lems with differential reddening and multiple populations in
these two clusters); and NGC6715, because it has a clear and
strongsecondRGB.
AppendixB: PropertiesoftheGlobularclusters
The properties of the globular clusters, from the literature and
determined in this work, are summarized in Table B.1 and
TableB.2respectively.
9
D.Streichetal.:OntherelationbetweenmetallicityandRGBcolorinHST/ACSdata
Fig.A.1.CMDsofthe53clustersinoursample,withfittedRGBcurves.Thetwohorizontalgraylinesindicatethemagnitudesat
whichthecolorsaremeasured.Theredframegivestheregionwherestarsareusedforthefit.ThereferencelinetoseparateAGB
fromRGBstarsisshownasreddashedline.Thesolidblacklineshowsthebest-fitRGBfunctionaftertherejectionoftheAGB.
Note,thatallstarsintheCMDareactuallydrawnwitherrorbars,butformanystarsthereportederrorsaretoosmalltobevisible
intheseplots.
10