The Optical Colors of Giant Elliptical Galaxies and their Metal-Rich Globular Clusters Indicate a Bottom-Heavy Initial Mass Function

1.1 MB·English

by  Paul Goudfrooij

PUBLISHEDASAPJ,762,107(2013)
PreprinttypesetusingLATEXstyleemulateapjv.08/22/09
THEOPTICALCOLORSOFGIANTELLIPTICALGALAXIESANDTHEIRMETAL-RICHGLOBULARCLUSTERS
INDICATEABOTTOM-HEAVYINITIALMASSFUNCTION
PAULGOUDFROOIJ1ANDJ.M.DIEDERIKKRUIJSSEN2
PublishedasApJ,762,107(2013)
ABSTRACT
We reporta systematic and statistically significantoffset betweenthe optical(g- zorB- I) colorsof seven
3 massiveellipticalgalaxiesandthemeancolorsoftheirassociatedmassivemetal-richglobularclusters(GCs)in
1 thesensethattheparentgalaxiesareredderby∼0.12–0.20magatagivengalactocentricdistance. However,
0 spectroscopicindicesintheblueindicatethattheluminosity-weightedagesandmetallicitiesofsuchgalaxies
2 areequalto thatoftheiraveragedmassivemetal-richGCsat a givengalactocentricdistance, to withinsmall
uncertainties. TheobservedcolordifferencesbetweentheredGCsystemsandtheirparentgalaxiescannotbe
n
explainedbythepresenceofmultiplestellargenerationsinmassivemetal-richGCs,astheimpactofthelatter
a
J tothepopulations’integratedg- zorB- Icolorsisfoundtobenegligible.However,weshowthatthisparadox
canbeexplainedifthestellarinitialmassfunction(IMF)inthesemassiveellipticalgalaxieswassignificantly
2
steeperat subsolarmasses thancanonicalIMFs derivedfrom starcountsin the solarneighborhood,with the

] GCcolorshavingbecomebluerduetodynamicalevolution,causingasignificantflatteningofthestellarMF
O oftheaveragesurvivingGC.
C Subjectheadings:galaxies: ellipticalandlenticular,cD—galaxies: stellarcontent—galaxies: formation—
. galaxies:starclusters:general—globularclusters: general
h
p
- 1. INTRODUCTION have shown that stars form in clusters or unbound associa-
o
tions with initial masses M in the range 102- 108 M
r Theshapeofthestellarinitialmassfunction(IMF)isafun- cl,0 ⊙
t (e.g.,Lada&Lada2003;PortegiesZwartetal.2010;Kruijs-
s damentalpropertyforstudiesofstarandgalaxyformation. It
sen 2012, and references therein). While most star clusters
a constitutes a crucial assumption when deriving physical pa-
[ rametersfromobservations.However,itsoriginremainsrela- with Mcl,0 .104 M⊙ are thought to disperse into the field
tivelypoorlyunderstood.Aparticularlyimportantquestionis populationof galaxies within a few Gyr, the survivingmas-
2 siveGCsconstituteluminouscompactsourcesthatcanbeob-
whetherornot the IMF is “universal”among differentenvi-
v
served out to distances of severaltens of megaparsecs. Fur-
1 ronments,sincegalacticmass-to-light(M/L)ratiosarevery
thermore,starclustersrepresentverygoodapproximationsof
3 sensitive to variations in the shape of the IMF at subsolar
a “simple stellar population” (hereafter SSP), i.e., a coeval
1 masses. Several observational studies find that the IMF in
populationofstarswithasinglemetallicity,whereasthedif-
5 variousenvironmentswithin ourGalaxy and the Magellanic
fuse light of galaxies is typically composed of a mixture of
. Clouds seems remarkably uniform down to detection limits
11 of∼0.1- 1M⊙ (Kroupa2001;Chabrier2003;Bastianetal. dpirfofbeeresnotfptohpeusltaatriofnosr.mTahtiuosn,srataterc(lSuFsRte)rsarnedprcehseemnticinalvaelnuraicbhle-
2010, and referencestherein). However, recentstudies indi-
2 mentoccurringduringthemainstarformationepochswithin
catethattheIMFmaybedifferentinmoreextremeenviron-
1 agalaxy’sassemblyhistory.
ments: stronggravity-sensitivefeaturesinnear-IRspectraof
v: luminousellipticalgalaxiesbyvanDokkum&Conroy(2010, Deep imaging studies with the Hubble Space Telescope
i 2011)favorabottom-heavyIMF(α≃- 3indN/dM∝Mα). (HST)revealedthatgiantellipticalgalaxiestypicallycontain
X richGCsystemswithbimodalcolordistributions(e.g.,Kundu
Ifconfirmed,thisresultwouldhavewidespreadimplications
r &Whitmore2001;Pengetal.2006).Follow-upspectroscopy
on studies of stellar populations and galaxy evolution. For
a showed that both “blue” and “red” GC subpopulations are
example,suchabottom-heavyIMFwouldincreasetheM/L
nearly universallyold, with ages &8 Gyr (e.g.,Cohen et al.
ratio in the K band by a factor ∼3 relative to a “standard”
2003;Puziaetal.2005;Brodieetal.2012).Thisimpliesthat
Kroupa(2001)IMF,andhenceinvalidatethewidespreadas-
the color bimodality is mainly due to differences in metal-
sumptionthatM/Lratiosinthenear-IRarehighlyindepen-
licity. The colors and spatial distributions of the blue GCs
dentofgalaxytypeormass.
are usually consistent with those of metal-poorhalo GCs in
Inthispaper,wedescribeanefforttofindindependentevi-
ourGalaxyand M31, while red GCs havecolorsandspatial
dencetoconfirmordenythepresenceofabottom-heavyIMF
distributions that are similar to those of the “bulge” light of
in nearby giant elliptical galaxies. We use observed optical
their host galaxies (e.g., Geisler et al. 1996; Rhode & Zepf
colorsandspectrallineindicesofmetal-richglobularclusters
2001;Bassinoetal.2006;Brodie&Strader2006;Pengetal.
(GCs)andtheirparentgalaxiesinconjunctionwithdynamical
2006;Goudfrooijetal.2007). Thus,the redmetal-richGCs
evolutionmodelingofGCs.
arecommonlyconsideredtobephysicallyassociatedwiththe
Infraredstudies of star formationwithin molecularclouds
stellarbodyofgiantellipticalgalaxies.Thisrepresentsanas-
1Space Telescope Science Institute, 3700SanMartin Drive, Baltimore, sumptionfortheremainderofthispaper.
MD21218,USA;[email protected] 2. GALAXYSAMPLEANDGCSELECTION
2Max-Planck Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-
85741Garching,Germany;[email protected] Ourmaingalaxyselectioncriterionisthepresenceofavery
clearbimodalopticalcolordistributionofitsGCsasderived
2 P.Goudfrooij&J.M.D.Kruijssen
fromhigh-quality,highspatial-resolution(i.e.,HST)imaging inNGC1407fromForbesetal.(2006)werealreadycorrected
thatallowsGCdetectionasclosetothegalaxycentersaspos- forGalactic foregroundreddening. For each galaxy we cal-
sible. With this in mind, most galaxies in our sample were culate a mean color of the red GC populationalong with its
drawn from the ACS Virgo Cluster Survey (ACSVCS; Côté radialgradientbymeansofaweightedlinearleast-squaresfit
etal. 2004),a homogeneoussurveyof 100early-typegalax- betweenthe GC’s colorscol(i.e., g- zor B- I)and the loga-
iesandtheirGCsintheVirgogalaxycluster,usingtheF475W rithmofR inarcsec:
gal
andF850LPfilters(hereafterg and z, respectively). Specifi-
cally,weusegalaxyphotometryfromFerrareseetal.(2006) col(Rgal)=col0+Gcollog(Rgal) (1)
supplementedbyGCdatafromJordánetal.(2009).Galaxies wherecol istheg- zorB- Icoloratlog(R )=0andG is
0 gal col
were selected based on the properties of GC color distribu- the colorgradientper dex in radius, ∆(col)/∆log(R ). For
gal
tionsasmodeledbyPengetal.(2006)usingtheKaye’sMix- eachGC,uncertaintiesassociatedwithitsmeasuredcolorand
tureModel(KMM;McLachlan& Basford1988;Ashmanet its membership of the red populationare taken into account
al.1994),fittingtwoGaussianstothedata. Twocriteriawere in the fit by adding the followingtwo parametersin quadra-
used for selection: (i) the p-value of the KMM fit needs to ture: (i)the photometricerrorof the GC’s color,and (ii)the
be ≤ 0.01, and (ii) the color distribution of the GCs needs inverseprobabilityoftheGCbeingamemberoftheredpopu-
toclearlyshowtwodistinctpeaksasjudgedbyeyeinFig.2 lation(p ),ascalculatedbytheKMMalgorithmmentioned
red
ofPengetal.(2006). Finally,we excludeNGC4365dueto above, expressed in magnitudes (i.e., log(1/p )/log(2.5)).
red
conflicting results on the presence of intermediate-age GCs Radialcolorprofilesforthediffuselightoftheparentgalax-
amongitsredGCsintheliterature3. Thisselectionyieldsthe iesweredeterminedusingthesamefunctionalformasEq.(1).
high-luminositygalaxiesNGC4472, NGC4486, NGC4649, ForNGC1407,B- Idataofthediffuselightweretakenfrom
NGC4552,NGC4621,andNGC4473(seeTable1). the surface photometryof Spolaoret al. (2008a), which was
Inthecontextofthecurrentstudy,itisimportanttoinclude derivedfrom the same HST/ACS data as the GC photometry
a comparisonbetween metallicity measurementsof red GCs ofForbeset al. (2006). ACSVCS galaxycolorgradientsare
from colors versus from spectral line indices (see Section 3 takenfromLiuetal.(2011),whousedthesurfacephotometry
below). As adequate line index data for several red GCs is ofFerrareseetal. (2006). ObservedACSVCS galaxycolors
currentlyonlyavailableforonegalaxyintheACSVCSsam- atR =1arcsecweretakenfromFerrareseetal.(2006)and
gal
ple,weaddNGC1407toourgalaxysamplegiventhathigh- listedinTable1.Panels(a)–(c)and(e)–(g)ofFigure1show
qualityHST/ACSimaging(infiltersF435W(hereafterB)and g- zversusR forthe6ACSVCSgalaxiesandtheirmassive
gal
F814W(I)) as well as opticalspectroscopyof both red GCs redGCs. Panel(a)ofFigure2showstheequivalentforNGC
andthediffuselightareavailable(Forbesetal.2006;Cenarro 1407 and its red GCs. Note that while the radial gradients
etal.2007;Spolaoretal.2008a,b). of the galaxies’ colors are similar to those of the “average”
TheselectionofredGCsinthesegalaxieswasdonebyse- colorsoftheirredGCsystems,thereisasystematicoffsetbe-
lectingGCsredderthanthecolorforwhichtheKMMproba- tweenthetwosetsofradialcolorprofilesinthesensethatthe
bilityofa GCbeingmemberoftheblueversustheredpeak averagecolorofredGCsis≃0.12–0.20magbluering- zor
is equal. In addition, we require GCs to be massive enough B- I than that of their parent galaxies. This colordifference
torendertheeffectofstochasticfluctuationsofthenumberof wasalreadynotedbyPengetal.(2006),buttheydidnotpur-
red giantbranch(RGB) and asymptotic giantbranch(AGB) sueaninvestigationofitspossiblecause(s). Thesignificance
stars on the integratedcolorssmaller than the typicalphoto- ofthiscolordifferenceis7σto22σdependingonthegalaxy,
metric error of σ(g- z) = 0.04 mag. Using the methodology whereσ isthemeanerrorofthefitofeq.(1)tothecolorsof
ofCerviño&Luridiana(2004)foranageof12Gyrandsolar redGCsinthesamplegalaxies(seeTable1).
metallicity4,thisrequirementtranslatesinaminimumcluster
massMcl≃2.5×105M⊙. ForgalaxiesintheVirgocluster,
thismasslimitisequivalenttoselectingGCswithz ≤21.91 TABLE1
AB
magundertheassumptionsof(i)Mcl/Lz =1.5M⊙/Lz,⊙ for COLORSOFSAMPLEGALAXIESANDTHEIRMASSIVEREDGCS.
eZt=alZ.⊙20(t0h7is)vaanldue(ivia)rmies- oMnly=s3li1g.h0t9lymwaigthfmorettahlelicVitiyrg;oJocrlduásn- N(G1)C M(2V)T0 (g- (z3))0,gal (g(-4z))0 G(5g-)z r(m6)s
ter (Jordán et al. 2009). The equivalentmagnitude limit for
4472 - 22.90 1.586±0.005 1.425 - 0.021 0.010
theGCsinNGC1407isI≤23.28mag,usingMcl/LI =2.1 4486 - 22.66 1.598±0.005 1.413 +0.000 0.007
M⊙/LI,⊙ forZ=Z⊙ (Maraston2005)andm- M=31.60mag 4649 - 22.41 1.592±0.005 1.449 - 0.022 0.010
(Forbesetal.2006). 4552 - 21.36 1.558±0.005 1.372 +0.000 0.014
4621 - 21.18 1.596±0.005 1.365 - 0.023 0.013
3. RADIALCOLORGRADIENTSOFGALAXIESANDTHEIRRED 4473 - 20.70 1.563±0.005 1.358 - 0.005 0.017
GCSYSTEMS NGC MV0 (B- I)0,gal (B- I)0 GB-I rms
T
In this section we compare the colors of the red GCs (se- 1407 - 21.86 2.313±0.005 2.103 - 0.004 0.007
lectedas mentionedabove)with thoseofthe diffuselightof
theirparentgalaxiesasafunctionofprojectedgalactocentric NOTE. —Column(1): NGCnumberofgalaxy. Column(2): absoluteV
radius(hereafterR ). AllobservedcolorsfortheACSVCS magnitudeofgalaxy. Column(3:) col0 ofgalaxy. Column(4): col0ofred
galaxieswerederedgadlenedusingtheGalacticforegroundred- GCs. Column(5): colorgradientGcolofredGCsinmag/dex. Column(6):
meanrmserroroffitofEq.(1)tocolorsofredGCs(inmag).
deningvalueslistedinJordánetal.(2009).ThecolorsofGCs
Under the assumption that surviving GCs represent the
3 SeePuziaetal.(2002), Larsenetal.(2003), andKunduetal.(2005) high-mass end of the star formation process that also popu-
versusBrodieetal.(2005)andChies-Santosetal.(2011).
lated the field (Elmegreen & Efremov 1997), this color dif-
4Fluctuationmagnitudesforthegandzpassbandsareestimatedbyinter-
ferenceisdifficulttounderstandintermsofametallicitydif-
polatingbetweenthoseofBandVandICandJ,respectively,usingthevalues
inTable5BofWorthey(1994). ference. While we deem it likely that the spread of colors
NewEvidenceforaBottom-HeavyIMFinGiantEllipticalGalaxies 3
FIG.1.—RadialcolorgradientsofgiantellipticalgalaxiesfromtheACSVCSsurveyandtheirsystemsofmassiveredGCs.Panels(a)–(c)and(e)–(g)show
dereddened(g- z)ABversusprojectedgalactocentricradiusfortheACSVCSgalaxiesmentionedatthetopleftofthepanelinquestion.Blacksolidlinesrepresent
linearleast-squarefitstothegalaxycolors,redcircleswithblackerrorbarsrepresentindividualredGCs,andthereddashedlinesdepictlinearleast-squarefits
totheredGCsystemsasawhole.Thedashedlinesinpanel(d)plotintegrated(g- z)ABversusmassfunction(MF)slopeαMFforMarigoetal.(2008)isochrones
foranageof12Gyrandthetwo[Z/H]valuesshowninthelegend.Thedottedlinesinpanel(d)indicatethecolorsforaKroupa(2001)MF.Panel(h)issimilar
topanel(d),butnowtheupper(black)linesaredrawnfor[Z/H]=- 0.2.Thegreyshadedregioncrossingpanels(a)through(d)and(e)through(h)illustratethe
rangeofMFslopesreproducingthegalaxycolorsfortheupperisochronelinesdrawninpanels(d)and(h),respectively.
dentofvariationsin[α/Fe]ratio. Thisisrelevantsincegiant
ellipticalgalaxiesandtheirmetal-richGCsareknowntoex-
hibitsupersolarα/Feratios(e.g.,Trageretal.2000;Puziaet
al. 2006). Figure 3 shows Hβ versus [MgFe]′ for the GCs
inNGC4472fromCohenetal.(2003),subdividedintoblue
and red GCs. As the uncertaintiesare significant forthe in-
dividualGCs, we also indicate weighted averageindices for
theblueandredGCs(seelargeblueandredsymbolsinFig-
ure 3). Note that [Z/H] ≃+0.30 for the average red GC in
Figure3,whichcorrespondsto[Z/H]=- 0.07ontheZinn&
West (1984) scale (Cohen et al. 2003). For comparison, we
overplotHβ and [MgFe]′ forthe diffuse lightof NGC 4472
PaFnIeGl.(a2).—shoSwimsi(lBar- Ito)0Fviegrusrues1p,robjuetctneodwgafloarctNocGeCntr1ic40r7adaiunsd.itTshreeddaGshCesd. (Daviesetal.1993;Fisheretal.1995)atRgal=50′′. Notethat
linesinpanel(b)plotintegrated(B- I)0versusMFslopeαMFforMarigoet themedianRgaloftheredGCstargetedbyCohenetal.(2003)
al.(2008)isochronesforanageof12Gyrandthetwo[Z/H]valuesshownin is59.′′1.Similarly,Figure4showsHβversus[MgFe]′forthe
thelegend.Symbols,lines,andshadingasinFigure1.
blueandredGCsinNGC1407fromCenarroetal.(2007)and
the diffuselightof NGC 1407at R = 50′′ fromSpolaoret
gal
exhibitedbytheredGCsystemsinFigure1isdue(atleastin al.(2008b). Forcomparison,themedianRgal oftheredGCs
part)toarangeofGCmetallicities(and/orages),onewould targetedby Cenarroet al. (2007)is 50.′′3. We concludethat
expect that the same range of metallicities (and/or ages) be theaverageredGCandthediffuselighthaveequalvaluesof
presentamongthefieldstarsandhencethattheaveragecol- Hβ and[MgFe]′ to within1σ forbothNGC 1407and NGC
orswouldbesimilar. 4472,thetwogalaxiesforwhichwecouldfindspectroscopic
This argument is corroborated by spectroscopic Lick in- agesandmetallicitiesforbothredGCsandthediffuselight,
dex data for red GCs and the diffuse light in the two gi- atcomparablegalactocentricdistances,intheliterature. This
ant elliptical galaxies in our sample (or in the literature at indicatesthatthemeanagesandmetallicitiesoftheredGCs
large) for which we found such data available in the litera- andtheunderlyingdiffuselightofgiantellipticalgalaxiesare
ture for both a significant number of red GCs and the dif- indeedthesamewithintheuncertainties.
fuse light within a range in R sampled by both compo- Wethusarriveatasituationwherethemeanspectroscopic
gal
nents. As to the GC spectra, Cohen et al. (2003) obtained ages and metallicities of the diffuse light of giant elliptical
Keck/LRIS spectra of 47 GCs in NGC 4472, while Cenarro galaxiesandtheirredGCsseemconsistentwithoneanother
etal.(2007)usedKeck/LRIStoobtainspectrafor20GCsin whiletheg- zorB- Icolorsofthediffuselightofthegalaxies
NGC1407. Inbothstudies, theresultingGCsweresplitap- aresystematicallyredderthanthoseoftheiraverageredGC.
proximately evenly between blue and red GCs. To evaluate Weevaluatethreepossiblesolutionstothisparadoxbelow.
spectroscopic ages and metallicities, we use the indices Hβ
4. POSSIBLECAUSESOFTHECOLOROFFSETBETWEENREDGC
and[MgFe]′=(Mgb×(0.72Fe5270+0.28Fe5335))1/2,respec- SYSTEMSANDTHEIRPARENTGALAXIES
tively, and compare them to predictions of the SSP models
4.1. AMismatchbetweenPhotometricandSpectroscopic
of Thomasetal. (2003). The [MgFe]′ metallicity indexwas
Samples?
chosenbecauseThomasetal.(2003)foundittobeindepen-
4 P.Goudfrooij&J.M.D.Kruijssen
4. Dotted black lines indicate the mean g- z or B- I colors
of the GCs with Lick index data, which are consistent with
themeancolorsofthefullredGCsystemstowithin1σ. Re-
callingthatthesignificanceoftheobservedcolordifferences
betweenthemetal-richGCsystemsandtheirhostgalaxiesis
intherange7–22σ,weconcludethattheredGCswithLick
indexdataarenotmisrepresentingthefullsystemsofredGCs
intermsoftheirg- zorB- Icolors.
FIG.3.—Hβversus[MgFe]′forGCsinNGC4472fromthedataofCohen
etal.(2003).SmallblueandredcirclesindicateGCsdesignatedbyGeisleret
al.(1996)as“blue”and“red”,respectively.Largefilledblueandredsquares
representweighted averagevalues ofHβ and[MgFe]′ oftheblueandred
GCs,respectively. LargeopenredcirclesindicateredGCswithHST/ACS
photometry (seeFigure5aandSect. 4.1). Errorbarsatthetoprightindi-
catetypicaluncertainties forindividualGCs. SSPmodelsofThomasetal.
(2003)areoverplottedfor[α/Fe]=+0.3.Dashedlinesindicate[Z/H]values
of- 2.25,- 1.35,- 0.33,0.00,0.35,and0.67dex.Solidlinesindicateagesof
1,2,3,5,10,and15Gyr. Forcomparison,theblacktrianglerepresentsHβ
and[MgFe]′forthediffuselightofNGC4472atRgal=50′′.SeeSect.3.
FIG.5.—Panels(a)and(b)arenear-copiesofFigures1aand2a,respec-
tively, exceptthaterrorbarsarenowshowningrey. Largeopencircles in
panels(a)and(b)identifytheredGCsintheHSTdataforwhichLickin-
dexdatawereshowninFigures3and4,respectively. Theblackdottedlines
indicatethemeancolorsofthetwosetsofredGCsshownwithlargeopen
circles. Notethattheblackdottedlinesalmostcoincidewiththereddashed
lines,whichdepictlinearfitstoEq.1forthefullredGCsystems.
4.2. AnEffectofthePresenceofMultipleStellarPopulations
inMassiveGCs?
Several detailed photometric and spectroscopic investiga-
tionsoverthelastdecadehaveestablishedthatmassiveGalac-
tic GCs typically host multiple, approximately coeval, stel-
larpopulations(seetherecentreviewbyGrattonetal.2012,
and references therein). The recognition of this fact came
mainlywiththecommonpresenceofanticorrelationsbetween
[Na/Fe] and [O/Fe] among individual stars (often dubbed
“Na-Oanticorrelations”;see,e.g.,Carrettaetal.2010),which
areseenwithinvirtuallyallGalacticGCsstudiedusingmulti-
object spectroscopy with 8-m-class telescopes to date. The
leadingtheory on the cause of these abundancevariationsis
the presence of a second generation of stars formed out of
FIG.4.—SimilartoFigure3,butnowforGCsinNGC1407fromthedata
ofCenarroetal.(2007)andforthediffuselightofNGC1407atRgal=50′′ enriched material lost (with low outflow velocity) by “pol-
fromthedataofSpolaoretal.(2008b).Largeopenredcirclesarenotshown luters” (massive stars and/or intermediate-mass AGB stars)
inthiscasesinceallGCsshownhaveHST/ACSphotometry(cf.Figure5b). of the first generation. High-temperatureproton-capturenu-
cleosynthesisintheatmospheresofthe“polluters”increased
Asafirstpossiblesolutiontotheparadoxdescribedin the theabundancesofHe,N,andNarelativetoFe(e.g.,Renzini
previousSection,weconsiderthehypothesisthattheredGCs 2008).
inNGC4472andNGC1407whosespectroscopicLickindex Note that this theory only predicts observable star-to-star
datawereshowninFigures3and4,respectively,happentobe abundance variations among light elements (up to 13Al),
redderandmoremetal-richonaveragethantherespectivefull whichisconsistentwithwhatisseenamongalmostallGalac-
photometricsamplesofredGCs. Thishypothesisisrejected tic GCs. Variations in heavy (e.g., Fe-peak) element abun-
by the data, as illustrated in Figure 5 in which open circles danceshaveonlybeenfoundwithintwoverymassivemetal-
highlighttheredGCsthathavecounterpartsinFigures3and poor GCs: ωCen (e.g. Lee et al. 2005; Johnson & Pila-
NewEvidenceforaBottom-HeavyIMFinGiantEllipticalGalaxies 5
chowski 2010) and M22 (Marino et al. 2009). It is thought metallicity, for which we showed spectroscopic evidence in
that such GCs represent surviving nuclei of accreted dwarf Figs.3and4.Inthisregarditisimportanttonotethatthede-
galaxieswhose escape velocitieswere highenoughto retain pendenceoftheblue-visualspectralindicesHβ and[MgFe]′
Fe-peakelementsfromSN explosions(e.g.,Lee et al. 2007; tochangesintheMFslopeintherangeindicatedbythecolor
Georgievetal.2009). However,wedeemthisaccretionsce- differencesbetweenredGCsandtheirparentgalaxiesisneg-
nario rather unlikely for the formation history of red GCs ligible. ThisisillustratedinFigure6wherewecomparethe
given their high metallicities. We therefore restrict the fol- valuesof Hβ and [MgFe]′ forNGC 4472 and NGC 1407at
lowingdiscussiontoGCswithoutaspreadinironabundance. R =50′′(cf.Figs.3and4)withpredictionsoftheVazdekis
gal
The effect of light-element abundance variations within etal.(2010)SSPmodelswhichwerecalculatedforavariety
GCs to photometry seems to be more subtle than that to ofIMFtypesandslopes5. Weplotmodelpredictionsfor(i)a
spectroscopic line indices. While photometric splitting of KroupaIMF,(ii)anIMFwithaSalpeterslope(α=- 2.3)for
RGB, main sequence (MS), and/or subgiant branch (SGB) stellarmasses M>0.6M⊙ andα=- 2.8forM≤0.6M⊙,
sequences have been observed in color-magnitude diagrams and(iii)anIMFwithα=- 2.8forallstellarmasses. AsFig-
(CMDs)ofseveralGalacticGCs,suchsplitsonlyshowupin ure6shows,thethreesetsofmodelpredictionsareconsistent
CMDsthatinvolvefiltersshortwardof∼4000Å,whilethey with one anotherto within the measurementuncertaintiesin
disappearwhenusingvisualpassbandssuchasB,V,and/orI therelevantregionofparameterspace.
(see,e.g.,Marinoetal.2008;Kravtsovetal.2011;Miloneet
al.2012).
To evaluate the effect of the presence of multiple stellar
populationsinmassiveGCstotheircolors,wedeterminecol-
orsofvariousstellartypesfromsyntheticspectrawithchemi-
calcompositionstypicaloffirst–andsecond-generationstars
foundin massiveGCs, andwe usetheresultingstellarspec-
tra to calculate integrated colors of the full stellar popula-
tion. This procedure is described in detail in Appendix A.
As shown there, the expectedimpact of the presence of two
stellar generations to the integrated B- I and g- z colors of
metal-richGCsisoffsetsof- 0.021and- 0.027mag,respec-
tively, relative to a true SSP. As this is only a small fraction
oftheobservedcoloroffsetsbetweenredGCsystemsandthe
diffuselightofgiantellipticalgalaxies,itseemsthatanaddi-
tionaleffectisneededtoproducethatcoloroffset.
4.3. ASteepStellarMassFunctionSlopeintheFieldStar
Component?
Ata givenageandchemicalcomposition,the onlyfunda-
mentalpropertyofasimplestellarpopulationthatcanaffect
itsintegratedcolor(orspectrallineindex)significantlyisthe
shapeofitsstellarMF.Figures1d,1h,and2billustratetheef-
FIG.6.—Hβversus[MgFe]′forSSPmodelpredictionsofVazdekisetal.
fectofchangingtheslopeαofthestellarMFtotheintegrated
(2010)usingdifferentIMFs(seelegendontheright). Blacklines: Kroupa
g- zor B- I colorof a stellar population. Thedashed curves (2001)IMF.Redlines: α=- 2.8forM≤0.6M⊙ and Salpeter IMFfor
in these panels were determined from Padova isochrones M>0.6M⊙. Blue lines: α=- 2.8 for all stellar masses. Dashed lines
(Marigoet al. 2008)of age 12 Gyr and forthe [Z/H] values indicate [Z/H]values of- 2.32, - 1.71, - 1.31,- 0.71, - 0.40, 0.00,and0.22
dex. Solidlinesindicateagesof1,2,3,5,10,and15Gyr. Forcomparison,
showninthefigure. Afterrebinningtheisochronetablestoa thegreyandopentrianglesrepresentHβand[MgFe]′atRgal=50′′forthe
uniformbinsizeinthestellarmassM⋆ usinglinearinterpo- diffuselightofNGC4472andNGC1407,respectively. Seethediscussion
lation, weightedluminositiesof the populationwere derived inSect.4.3.
fortherelevantpassbandsbyweightingindividualstellar lu-
minositiesbyafactor(M⋆/Mmax)αwhereMmaxisthemax- Similar conclusions can be drawn when comparing pan-
imumstellar mass reachedin the isochronetable. Forrefer- els (e)–(g) with panel (h) of Figure 1 and panel (a) with
ence, the dotted lines show the expected colors for a “stan- panel (b) of Figure 2, except that the average colors of the
dard”Kroupa(2001)IMF. redGC systemsof the less luminousgalaxiesdepictedthere
Acomparisonofpanels(a)–(c)withpanel(d)ofFigure1 (see Table 1) are better matched by a slightly lower metal-
revealsseveralitemsofinterest. First,the“average”colorsof licity ([Z/H] ≃ - 0.2). This is consistent with the color-
theredGCsystemsareconsistentwiththepredictionofaSSP magnituderelationamongelliptical galaxieswhen interpret-
modelwithage=12Gyr,[Z/H]=0.0,andaKroupaMF.This ingcolorchangesintermsofmetallicitychanges:theslopein
isalsoconsistentwiththespectroscopicageand[Z/H]found theV- Kvs.V relationamongEgalaxiesintheVirgogalaxy
fortheaverageredGCfoundaboveinSection3. Second,the clusteris- 0.079±0.007(Boweretal.1992),whichtranslates
reddercolorsoftheparentgalaxieswithrespecttotheaverage to a [Z/H] vs. galaxy magnitude relation of - 0.093 ± 0.008
colorsoftheredGCsystemscanbeexplainediftheMFofthe dex/magaccordingtotheMarigoetal.(2008)SSPmodelsat
fieldstarcomponentis“bottom-heavy”(- 3.0.α.- 2.4for anageof12Gyr.
[Z/H]=0.0)relativetothatoftheredGCsystem,especially
in the inner regions. This assumes that the field stars and 5 Notethat Vazdekis etal.(2010)defined IMFslopesµasdN/dM∝
themassive redGCs sharethe same distributionsof ageand M- (µ+1).Hence,ourα=- (µ+1).
6 P.Goudfrooij&J.M.D.Kruijssen
ApossiblemechanismforproducingthesteepMFsingiant IMF:α =- 3.00and- 2.35,respectively. Wealsoindicate
IMF
ellipticalgalaxies(relativetothoseoftheirmassiveredGCs) “weighted mean” values of α for a GC population with
MF
indicatedbyourresultsisdiscussedinthenextSection. Mcl ≥2.5×105 M⊙ at an age of 12 Gyr that was formed
with a Schechter (1976) initial cluster mass function and a
5. DYNAMICALEVOLUTIONEFFECTSONSTELLARMASS maximuminitialmassof107M⊙. Forreference,apower-law
FUNCTIONSOFGLOBULARCLUSTERS fit to the KroupaIMF in the mass range0.3–0.8M yields
⊙
Thegradualdisruptionofstarclustersovertimeaffectsthe α =- 1.7(cf.panels(d)and(h)ofFig.1).
MF
shape of their stellar MF, because the escape probability of
starsfromtheirparentclusterincreaseswithdecreasingstellar
-3.0
mass(e.g.,Baumgardt&Makino2003).Thiseffecthasbeen
used to explain the observedstellar MFs in ancientGalactic )⊙ -2.5
GCs, someofwhichareflatterthancanonicalIMFs(e.g.,de M
Marchietal.2007;Paustetal.2010). SuchflatMFsinGCs -2.0 aver.
8
canexplaintheirlowobservedmass-to-lightratioswhencom- 0.
paredwithpredictionsofSSPmodelsthatusecanonicalIMFs 3 - -1.5 Kroupa
(e.g.,Kruijssen&Mieske2009).TheflatteningoftheMFsin 0.( -1.0
GalacticGCsisgreatestforGCsthatareclosesttodissolution F
M (a)
(Baumgardtetal.2008;Kruijssen2009). -0.5
Here,weexplorethehypothesisthattheIMFinthe(high- a a IMF = -3.00
0.0
metallicity, and likely high-density) environments that pre-
-3.0
vailedduringthe main starformationeventsthatformedthe
stars in the bulge and the red GCs of giant elliptical galax- )⊙ -2.5
ies was relatively steep (- 3.0. α . - 2.4, as indicated by M

the analysis in the previous Section), i.e., steeper than the -2.0 aver.
8
canonical IMF seen in the solar neighborhood, and that dy- 0.
namical evolution of the star clusters formed during those 3 - -1.5 Kroupa
eventscausedthestellarMFofthe“average”survivingmas- 0.( -1.0
sivestarclustertobesimilartoacanonicalIMF.Tothisend, F
M (b)
weusetheGCevolutionmodelofKruijssen(2009,hereafter -0.5
K09)whichincorporatestheeffectsofstellarevolution,stel- a a IMF = -2.35
0.0
larremnantretention,dynamicalevolutioninatidalfield,and
mass segregation. For the purposesof the currentstudy, we 5 5.5 6 6.5 7
select K09 models that (i) feature solar metallicity and “de- Log (M /M ) at age = 12 Gyr
cl ⊙
fault” kickvelocitiesof stellarremnants(white dwarfs, neu-
tronstars,andblackholes),and(ii)produceGCswithmasses FIG.7.— Panel(a): MF slopeαMF inthe range0.3<M⋆/M⊙ <0.8
Mcl≥2.5×105M⊙ atanageof12Gyr,i.e.,theGCsshown vmeertsaulslicGitCy mmoasdselastoafnKa0g9e othfa1t2prGodyurcfeorsuαrvIMivFin=g-G3C.0s0waictchorMdincgl≥to2s.o5l×ar
inFigures1and2(cf.Section2). We furtherconsiderKing 105M⊙atanageof12Gyr. SolidlinesrepresentmodelswithKing(1966)
(1966) profiles with W0 values of 5 and 7 and environmen- parameterW0=7,whiledashedlinesdosoforW0=5. Fromtoptobottom,
1ta.l0l,yadnedp3e.n0dMenytrc.luFsotrerredfiesrseonlcueti,otn=tim1.e3sMcaylersyite06ldosfa0r.e3a,s0o.n6-, tohnelylifnoersWre0p=re7s)e.nCtimrcoledselisndwiciathtet0we=ig3h.t0e,d1m.0e,a0n.6va,launedsf0o.r3thMeyarbs(cthisesalaattnedr
0 ordinate for each model, assuming a Schechter (1976) initial cluster mass
ablefittotheglobularclustermassfunctionofall(surviving) functiontoassignweightsandclustermasses2.5×105≤Mcl/M⊙≤107
GalacticGCs(Kruijssen&PortegiesZwart2009). atanageof12Gyr. Themagentadash-dottedline(alongwithanerrorbar)
NotehoweverthatGCsystemsinanygivengalaxyareex- indicatestheweightedaverageαMFofallcircles(usinginversevariancesas
weights), whilethegreendottedlineindicates theKroupaIMF.Panel(b):
pected to exhibit a range of t values. For example, disrup-
tion rates of GCs in dense hi0gh-redshift environments were Similartopanel(a),butnowforaSalpeter(1955)IMF(αIMF=- 2.35).
likelyhigherthanin currentquiescentgalaxies(Kruijssenet
al. 2012) due to the enhanced strength and rate of tidal per- Focusing on the “weighted mean” values of αMF for the
turbations. Likewise, GCs on eccentric orbits with smaller K09modelsshownin Figure7, we findoverallmeanvalues
optehriegrwaliasceti(cindiitsitaalnlyc)essiRmpeilriarshGoCulsdwhaitvhelsamrgaelrlevratl0uveasluoefsRthpearin. fαoMrFα=IM-F1=.8-42±.305.,2i6ndfoicraαtiInMgFt=ha- t3G.0C0sawndithαMaFst=ee-p1e.r8I0M±F0e.1x1-
Finally, the rate of mass loss from GCs by evaporation, µ , perienceastrongerevolutionofthestellarMF.Notethatboth
ev
effectivelyscales with the mean GC half-massdensity ρ as of these values are consistent with a Kroupa MF and hence
h
µ ∝ρ0.5 for tidally limited GCs (e.g., McLaughlin & Fall consistentwith the observedmean colors of red GCs shown
ev h in Figure 1. It is important to realize that the stronger flat-
2008;Gielesetal.2011;Goudfrooij2012). AmongGCsfor
teningofα overtimeinmassiveGCswithsteeperIMFsis
which two-bodyrelaxationhas beenthe dominantmass loss MF
mainlycaused by the weaker effectofretained massive stel-
mechanism, high-ρ GCs thus feature smaller t values than
h 0
low-ρ GCsatagivenM . larremnantsontheescaperateofmassivestarsinGCswith
h cl
steeper IMFs relative to that in GCs with flatter IMFs. As
Figure7showsthepresent-dayMFslopesα inthestel-
MF
describedin detailin K09, retainedmassivestellarremnants
lar mass range 0.3–0.8 M according to the K09 models
⊙
forsurvivingGCs as a functionof M . The two panels(a) boosttheescaperateofmassivestarsrelativetothatoflow-
cl
mass stars. For a Kroupa IMF, this effect limits the flatten-
and(b)showtheresultsfortwodifferentslopesofthestellar
ing rate of α overtime relative to GCs with a lowerfrac-
MF
γs6etts0tihsedmefiansesddebpyetnddise=ncte0Mofcγclluwstheerrdeitsdriuspitsiothne.ScleuestKer09difsorurpdteiotaniltsi.meand twioitnhostfeempaesrsIivMeFsstefellaatrurreemansmanatlsle(rsemeaKss0f9ra).ctiHonowtaekveenr,uGpCbys
NewEvidenceforaBottom-HeavyIMFinGiantEllipticalGalaxies 7
massive remnants. This notably reduces the ‘dampeningef- largest values of (M/L) /(M/L) have the highest ve-
stars Salp
fect’ of retained massive remnants on the evolution of α . locity dispersions (see also Tortora et al. 2012). However,
MF
As a result, the present-day stellar MFs in GCs are consis- dynamical modeling such as that done by Cappellari et al.
tentwith anyIMF slopeα.- 1.7. Thisdegeneracyimplies (2012) cannot unambiguously constrain whether the highest
thattheIMFcannotbeuniquelyconstrainedinthisrangefor valuesof(M/L) /(M/L) areduetoalargepopulation
stars Salp
individualGCs. However, the large spread of observed MF oflow-massstars(i.e.,abottom-heavyIMF)orlargenumber
slopes amongGalactic GCs (de Marchiet al. 2007;Paust et ofmassivestellarremnants(i.e.,atop-heavyIMF).Thesame
al. 2010) seems to be more consistent with a bottom-heavy degeneracy is present for mass estimates from gravitational
IMF(comparebothpanelsinFigure7). lensing (e.g., Treu et al. 2010). In contrast, ourresults indi-
Weconcludethatthedifferenceing- zorB- Icolorbetween catethatthebottom-heavyIMFisthemorelikelysolution.
giantellipticalgalaxiesandtheir“average”massiveredGCs Finally, we review the dependence of our results on SSP
showninFigures1and2isconsistentwithlong-termdynam- model ingredients. At old ages (&10 Gyr) and high metal-
icalevolutionofstarclustersthatwereformedwithasteeper licities ([Z/H] &- 0.5), SSP models still suffer from several
IMFthanthosederivedfromstarcountsinthesolarneighbor- limitations. The likely most significant internal uncertainty
hood. Amongthethreemechanismswethinkcouldconceiv- is related to lifetimes of AGB stars (see, e.g., Melbourne et
ablycausethiscolordifference,thisistheonlyonethatseems al. 2012). In terms of external uncertainties, we note that
consistent with the data. Hence we suggest that this color integratedcolorsand spectralindices of severalSSP models
differenceconstitutesevidencefora “bottom-heavy”IMFin arecalibratedto observationsofthetwo Galactic bulgeGCs
luminousellipticalgalaxies. NGC6528andNGC6553thathaveZ≃Z⊙ (e.g.,Thomaset
al. 2003; Maraston 2005). However, there are no published
6. DISCUSSION MFsforthosetwoGCsavailabletoourknowledge,yielding
Ourresultsaddtoadevelopingconsensusthatluminousel- an uncertaintyin the absolute calibration7. Notwithstanding
lipticalgalaxieshave“heavy”IMFs,withagreatercontribu- suchlimitations,ourmainresultisbasedong- zorB- Icolor
tion from low-mass dwarf stars than IMFs determined from differencesbetweentheaverageredmassiveGCandtheirpar-
star count studies in the Milky Way. Cenarro et al. (2003) ent galaxies and the absence of such differences in Hβ and
[MgFe]′ indices. As the interpretation of relative colors or
studied the CaII triplet near 8600 Å, which is stronger in
line strengths should be largely model-independent, our re-
RGB stars than in MS stars, in a sample of elliptical galax-
sultstronglysuggestsabottom-heavyIMFinmassiveellipti-
ies. TheyfoundthatthestrengthoftheCaIItripletdecreases
calgalaxies.
with increasing velocity dispersion among elliptical galax-
ies. This is hard to explain in terms of an Ca abundance
trend since Ca is an α element, and [α/Fe] as derived from
Mg and Fe features near 5200 Å does not show this trend. The authors acknowledge useful discussions with Tom
Hence,theysuggestedthatthistrendmightreflectanincreas- Brown, Mike Fall, Harry Ferguson, Jessica Lee, Guido de
ing IMF slope with increasing galaxy mass, as indicated by Marchi,andThomasPuzia.WethankFiorellaCastelliforher
SSPmodelsofVazdekisetal.(2003).Similarly,vanDokkum helpincompilingsomeroutineswithintheSYNTHEproce-
& Conroy (2010, 2011) found strong equivalent widths of dure. Weappreciatedthereferee’sswiftreview,including in-
the NaIλλ8183,8195 doublet and the molecular FeH band sightfulcommentswhichimprovedthepresentationofsome
at 9916Å in near-IR spectra of giant elliptical galaxies. As results. TheSAO/NASAAstrophysicsDataSystemwasused
both of those indices are stronger in red dwarf stars than heavilywhilethispaperwaswritten. Thisresearchhasmade
in red giants, their strongly favored explanation is the pres- useoftheNASA/IPACExtragalacticDatabase(NED)which
ence of a significantly larger number of late M dwarf stars isoperatedbytheJetPropulsionLaboratory,CaliforniaInsti-
than that implied by a Kroupa IMF, even though there is a tuteofTechnology,undercontractwiththeNationalAeronau-
slightdegeneracywith[Na/Fe]ratio(seealso Conroy&van tics and Space Administration. PG was partially supported
Dokkum 2012;Smith et al. 2012). Finally, Cappellari et al. during this project by NASA through grant HST-GO-11691
(2012)studied stellar M/L ratios [(M/L) ] derivedfrom fromtheSpaceTelescopeScienceInstitute,whichisoperated
stars
integral-field spectroscopy of 260 early-type galaxies. They bytheAssociationofUniversitiesforResearchinAstronomy,
found that the ratio of (M/L) by the M/L predicted by Inc.,underNASAcontractNAS5–26555.
stars
SSP modelsthat use a SalpeterIMF[(M/L) ] variessys- Facilities: HST (ACS), Keck:I (LRIS), ESO:3.6m
Salp
tematicallywithgalaxyvelocitydispersion:galaxieswiththe (EFOSC2)
7Ifthepresent-dayMFofthoseGCsisflatterthantheKroupaorChabrier
and/or [Z/H] values of old metal-rich populations derived from integrated
IMFs,asmightbeexpectedgiventhestrongtidalfieldattheirlocationdeep
colorswouldcurrentlybeslightlyoverestimated.
intheGalaxy’spotentialwell,theiropticalcolorswouldbebluerthanifthey
had Kroupa or Chabrier MF’s (cf. Figures 1 and 2). Thus, absolute ages
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APPENDIX
BUILDINGSYNTHETICINTEGRATEDCOLORSOFMETAL-RICHGLOBULARCLUSTERSCONTAININGTWOSTELLAR
GENERATIONS
Inthisappendix,wedeterminecolorsofvariousstellartypesfromsyntheticspectrawithchemicalcompositionstypicaloffirst–
andsecond-generationstarsfoundinmassivemetal-richGCs. Weassume[Z/H]=0.0andexploretwochoicesfortheabundances
ofHe,C,N,O,andNa. Tosimulatefirst-generation(FG)stars,wechoosetheprimordialHeabundance(Y =0.235+1.5Z),we
followCannonetal.(1998)bychoosing[C/Fe]=0.06and[N/Fe]=0.20,andweadopt[O/Fe]=0.40and[Na/Fe]=0.00from
Carrettaetal.(2009). Tosimulatesecond-generation(SG) stars,wechoose[C/Fe]=- 0.15,[N/Fe]=1.05,[O/Fe]=- 0.10,and
[Na/Fe]=0.60(seeCarrettaetal.2009).FortheHeabundanceofSGstars,weconsiderthecaseofNGC6441,ametal-richGC
inthebulgeofourGalaxy([Fe/H]=- 0.59, Zinn&West1984).NGC6441(aswellasthesimilarclusterNGC6388)isunusual
amongmetal-richGCsinourGalaxyinthatitshowsahorizontalbranch(HB)thatextendsbluewardoftheRRLyraeinstability
stripintheCMDwhereasallothermetal-richGCshavepurelyredHBs(e.g.,Richetal.1997)8. Thebluewardextensionofthe
HBofNGC6441iswidelythoughttobeduetoenhancedHeinafractionofitsconstituentstars,andweadoptthevalueY =0.33
fromCaloi & D’Antona(2007). As blue HBs are very unusualamongmassive metal-richGCs in ourGalaxy, this value ofY
shouldprobablybeconsideredanupperlimitforSGstarsinthecontextofthecurrentpaper.
Toproducesyntheticintegratedcolorsofstellarpopulations,wefirstbuildtwosetsofsyntheticspectraforsixstellartypesthat
spanalmostthefullrangeofluminositiesLandtemperaturesT encompassedbytheisochrones(seeFigure8).Forthispurpose
eff
8NotehoweverthattheimpactoftheblueextensionoftheHBseeninNGC6388andNGC6441totheoverallopticalcoloroftheirHBisnegligible. In
termsof∆(V- I),definedbyDotteretal.(2010)asthemediancolordifferencebetweentheHBandtheRGBattheluminosityoftheHB,theaveragedHBof
NGC6388andNGC6441is0.003±0.010magredderthantheaverageHBofthe8otherGalacticGCswithAge>12Gyrand- 0.70<[Fe/H]<- 0.50inthat
study,i.e.,Lyngå7,NGC104,NGC5927,NGC6304,NGC6496,NGC6624,NGC6637,andNGC6838.
NewEvidenceforaBottom-HeavyIMFinGiantEllipticalGalaxies 9
TABLE2
STELLARPARAMETERSOFTHEMODELATMOSPHERES.
Teff(FG) Teff(SG) logg Vturb
(1) (2) (3) (4)
3602 3665 4.79 2.0
4526 4795 4.59 2.0
5630 5700 4.20 2.0
4835 4941 3.48 2.0
4237 4311 1.96 2.0
3537 3608 0.70 2.0
NOTE.—Column(1):Effectivetemperatureforfirst-generationstarsinK.Column(2);Effectivetemperatureforsecond-generationstarsinK.Column(3):
logarithmofsurfacegravityincms- 1.Column(4):Turbulentvelocityinkms- 1.
weselectDartmouthisochrones9(Dotteretal.2007)with[Z/H]=0.0,[α/Fe]=+0.4,andthetwovaluesofY mentionedinthe
previousparagraph.[Z/H]valuesforalpha-enhancedpopulationsareevaluatedusing[Z/H]=[Fe/H]+0.929[α/Fe](Trageretal.
2000). Theparametersofthemodelatmospheresarelistedin Table2. Thesetemperatures,gravities,andchemicalabundances
are then used to calculate model atmospheres and synthetic spectra using the codes ATLAS12 and SYNTHE (Kurucz 2005;
Castelli2005;Sbordoneetal.2007),respectively.ATLAS12allowsonetousearbitrarychemicalcompositions.Indoingso,we
usemodelatmospheresfromthe[Fe/H]=0.0,[α/Fe]=+0.4modelgridofCastelli&Kurucz(2004)10asreferenceandadjust
T ,g,[Fe/H],andtheindividualelementabundancesintheATLAS12runs. Theresultingsyntheticspectraarethenredshifted
eff
accordingto the heliocentric radial velocity of the Virgo galaxycluster (1035kms- 1, Mould et al. 2000) and integrated over
passbandsofJohnson/Cousins(U ,B ,V ,R ,I ; Bessell1990)andSloanugriz11toproducesyntheticmagnitudesandcolors.
J J J C C
FIG.8.—TheoreticalisochronesfromthelowerMStotheupperRGBforthetwodifferentchemicalcompositionsassociatedwithtwostellargenerations
withinmassiveGCs. Thesolidlinecorrespondstothefirst-generationpopulation(withprimordialHeabundance),whereasthedashedlinecorrespondstothe
second-generation population(withenhancedHeabundanceY =0.33). Thefilledandopensquaresindicatethestellartypesforwhichwecalculated model
atmospheresandsyntheticspectra(cf.Table2).Seetextformoredetails.
ThreeexamplesofthesyntheticspectraforFGandSGstarsareshowninFigs.9–11. Labelsineachplotindicateprominent
absorption features that change significantly in strength between the two chemicalcompositions. These spectra are described
brieflybelow.
Figure9comparesRGBspectraoftheFGandSGmixtures. Thehigher[N/Fe]oftheSGmixturecausesstrongermolecular
bandsofCN. Thisis especiallyclearat λ&7000Å.ThemainreasonwhythisisnotasobviousfortheCN bandsnear3590,
3883,and4150ÅandtheNHbandnear3360ÅisthattheenhancedabsorptionintheblueregionfortheSGmixtureispartially
compensatedbyitsenhancedHeabundancewhichelevatesthestellarcontinuumintheblue. Theincreasedopacityatλ.4500
ÅfortheSGmixturealsocausesasomewhatelevatedstellarcontinuumatlongerwavelengths,whichlikelycausestheslightly
higherfluxoftheSGmixtureinthe4500–6200Åregion. Finally,thelowerOabundanceoftheSG mixturecausesaweaker
OHabsorptionbandbetween3050and3200ÅwhichjustfallswithintheU andubandsfortheradialvelocitiesofthegalaxies
J
inoursample.
InthespectraofTOstars(Figure10),thehighertemperaturecausesgenerallyweakermolecularbands,renderinggenerally
9seehttp://stellar.dartmouth.edu/models/index.html
10seehttp://wwwuser.oat.ts.astro.it/castelli/grids.html
11seehttp://www.sdss.org/dr1/instruments/imager/index.html#filters
10 P.Goudfrooij&J.M.D.Kruijssen
FIG.9.—Toppanel: Synthetic spectraforRGBmodelswithlogg=1.96fortheFG(black)andSG(red)mixtures. Thespectrawereconvolvedwitha
Gaussianwithσ=12Åtoimprovereadability. Relevantmolecularbandsarelabelled. Bottompanel:TransmissioncurvesforJohnson/CousinsUJ,BJ,VJ,RC,
andICfilters(solidcurves,lefttoright)andSDSSugrizfilters(dashedcurves).Seetextfordetails.
FIG.10.—LikeFigure9,butnowforTOmodelswithlogg=4.20.
smalldifferencesbetweentheFGandSGspectra. OnlytheNHandCNbandsremainslightlystrongerintheSGmixture.
ThedifferencesbetweentheFGandSGspectraofcoolMSstars(Figure11)aregenerallysimilartothoseseenfortheRGB
spectra,exceptthattheMSstarsshowweakerredCNbandsandaslightlystrongerOHbandinthe3000–3200Åregion.
Differencesin stellar absolutemagnitude∆M≡M - M are thenevaluatedasa functionof log g forall filterpassbands
SG FG
consideredhere. TheresultsareillustratedinFigure12whichshows∆M asafunctionoflogg. Thelargestdifferencesshow
up in the U and u passbands, due to their sensitivity to relevant parameters: (i) T and henceY; (ii) N abundance through
J eff
the NH band near3360Å as well as the CN bandsnear3590 and 3883 Å; and (iii) O abundancethroughthe OH bandat the
short-wavelengthedgeoftheU andufilters. TheweakerOHabsorptionfortheSGpopulationisthemainreasonwhy∆Mfor
J
theU andupassbandsisnegativeatthetopoftheRGB(i.e.,lowestlogg). ∆Mthenincreasessignificantlywithincreasinglog
J
gtobecomepositiveattheTO(duemainlytostrongerNHandCNabsorptionintheSGpopulation),andthendecreasesagain
tothebottomoftheMS(i.e.,highestlogg).Theotherpassbands(longwardof∼4000Å)showasimilardependenceof∆Mon
logg,althoughtheabsolute∆Mvaluesatλ&4000ÅaremuchsmallerthanforU anduatagivenlogg.
J
Thedependenceof ∆M betweenFG and SG populationsasa functionof wavelengthfoundhereare qualitativelysimilarto
thoseofSbordoneetal.(2011)whodidasimilarstudyatlowmetallicity([Fe/H]=- 1.62). However,wefindthat∆M values
aredifferentformetal-richpopulationsinaquantitativesense,sometimesbyasignificantamount.
IsochronetablesfortheSGpopulationarethencalculatedbyadding∆M totheabsolutemagnitudesforeachfilterpassband