Biases in the inferred mass-to-light ratio of globular clusters: no need for variations in the stellar mass function

0.24 MB·English

by  Rosemary L. Shanahan

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed18February2015 (MNLaTEXstylefilev2.2)
Biases in the inferred mass-to-light ratio of globular clusters: no
need for variations in the stellar mass function
5 Rosemary L. Shanahan1 & Mark Gieles2
1
0 1InstituteforAstronomy,UniversityofEdinburgh,RoyalObservatory,BlackfordHill,EdinburghEH93HJ,UK.
2 2DepartmentofPhysics,UniversityofSurrey,Guildford,GU27XH,UK.

b
e
F
Accepted2014December22.Received2014December20;inoriginalform2014November19

7
1

ABSTRACT
]
Fromastudyoftheintegratedlightpropertiesof200globularclusters(GCs)inM31,Strader
A
et al. found that the mass-to-light ratios are lower than what is expected from simple stel-
G
lar population(SSP) modelswith a ‘canonical’stellar initial mass function(IMF), with the
. discrepancybeinglargerathighmetallicities.Weusedynamicalmulti-massmodels,thatin-
h
clude a prescription for equipartition, to quantify the bias in the inferred dynamical mass
p
- astheresultoftheassumptionthatlightfollowsmass.ForauniversalIMFandametallicity
o dependentpresentdaymassfunctionwefindthattheinferredmassfromintegratedlightprop-
r ertiessystematicallyunderestimatesthetruemass,andthatthebiasismoreimportantathigh
t
s metallicities,aswasfoundfortheM31GCs. Weshowthatmasssegregationandaflattening
a
of the mass function have opposingeffects of similar magnitudeon the mass inferred from
[
integratedproperties.Thismakesthemass-to-lightratioasderivedfromintegratedproperties

2 aninadequateprobeofthelow-massendofthestellarmassfunction.Thereis,therefore,no
v needforvariationsintheIMF,northeneedtoinvokedepletionoflow-massstars,toexplain
1
theobservations.Finally,wefindthattheretentionfractionofstellar-massblackholes(BHs)
7
is an equally important parameter in understandingthe mass segregation bias. We specula-
9
tively put forward to idea that kinematicaldata of GCs can in fact be used to constrain the
4
totalmassinstellar-massBHsinGCs.
0
. Keywords: globularclusters:general–openclustersandassociations:general.
1
0
5
1
:
v 1 INTRODUCTION and Pryor&Meylan (1993). A more significant correlation was
i found from a larger sample of GCs by Kimmigetal. (2014).
X Thestellarinitialmassfunction(IMF) playsavitalroleinastro-
McLaughlin&vanderMarel (2005) found an average hΥ i ≃
V
r physicsanditisanongoingdebatewhethertheIMFisuniversalfor 1.45forMilkyWayGCs,whichisslightlylowerthantheSSPpre-
a
allmetallicities(Bastianetal.2010;vanDokkum&Conroy2010;
diction of Υ ≃ 2, appropriate for low metallicities. Thissmall
V
Gehaetal.2013).Globularclusters(GCs)areimportanttest-beds
difference andthetrendwithM hasbeen attributedtothepref-
forstudiesoftheIMFandthepresentdaymassfunction(MF)be-
erentialescapeoflow-massstarsoverthetidalboundary,reducing
causetheyare,inmostcases,singleagedstellarpopulationswith
M,buthardlyaffectingL (e.g.Kruijssen2008).
V
asingle[Fe/H],andthekinematicsofthestarswithinthemisdue
tothegravityof thestarsonly. Becausemost of theGC massis Straderetal. (2011, hereafter S11) published the ΥV values
inlow-massstars,whereastheluminosityisduetothehigh-mass of 200 GCs in M31, spanning a range of metallicity of −2 .
stars,theGCmass-to-light ratioΥ ≡ M/L isconsider tobe [Fe/H] . 0.TheyfoundthatatlowmetallicitiestheaverageΥV
V V
agrees well with the values from simple stellar population (SSP)
a good probe of the shape of the stellar MF. Here L is the V-
V
models, assuming aKroupa IMF, albeit witha scatter of a factor
band luminosity and M is independently found from a measure-
oftwo.Forincreasingmetallicities,agrowingdifferencebetween
mentofthecluster’sradiusandvelocitydispersion.Recentobser-
vational advances have allowed us to measure the structural pa- thedynamicalΥV andtheSSPmodelswasfound,withΥV falling
rameters and kinematical properties of GCs in external galaxies belowtheSSPvalues,byuptoafactorof3at[Fe/H]≃0. Similar
resultswererecentlyobtainedforMilkyWayGCs(Kimmigetal.
up to distances of several tens of Mpc (Smith&Gallagher 2001;
2014).Theseresultsarehardtoexplainbythepreferentialescape
Bastianetal.2006;Brodie&Strader2006),spanningalargerange
oflow-massstars,becauseitimpliesthatalmostallmetal-richclus-
ofenvironments,thereby potentiallyincreasingtheapplicabilityof
Υ asaprobeoftheIMF. tershavelostasignificantfraction(∼60%−70%)oftheirinitial
V
mass.
For Galactic GCs, a slight positive correlation between Υ
V
and M was found by early work by Mandushevetal. (1991) An alternative interpretation is that the IMF gets more bot-
(cid:13)c 0000RAS
2 RosemaryL. Shanahan& MarkGieles
tom light (fewer low-mass stars) with increasing [Fe/H]. Before issimilartothevalueformorerealisticIMFsthatrolloveratlow
accepting the possibility of a varying IMF, we need to establish masses toflatter slopes and are truncated at mlo = 0.1M⊙. For
that thereareno metallicitydependent biasesasthe result of dy- ourpurposethissuffices,becausethebehaviourofthemulti-mass
namical evolution of GCs in the Υ measurements. A possible modelsissensitiveonlytothetotalmassinlow-massstars,andin-
V
biasistheeffectofmasssegregationonthemeasurementsofthe sensitivetothemeanmassofthelow-massstars(seeSection5of
GCradiusandvelocitydispersion. MostGCsareolderthantheir GG79).Testsconfirmthatourresultsareinsensitivetothischoice.
half-massrelaxationtime-scaleτrh(e.g.He´non1961;Gielesetal. Tostudytheeffectofmasssegregationinasystemwithabottom
2011).Thismeansthattheyhadtimetoevolvetowardsequiparti- lightIMF,oraclusterthatisdepletedinlow-massstarsbecauseof
tionand,asaresult,themostmassiveobjects(stellarremnantsand dynamicalevolution,wealsoconsideradoublepower-law(‘flat’)
turn-offstars)aremorecentrallyconcentratedandmovewithlower IMF
velocities.ForresolvedGCsthiseffectcanbetakenintoaccount
byfittingmulti-massmodels(e.g.Paustetal.2010;Sollimaetal. dN = B, mlo<mi61M⊙, (2)
2012),whicharedistributionfunctionbasedmodelsthatincludean dmi (Am−i α, 1M⊙ <mi<mup,
approximate prescription for equipartition (DaCosta&Freeman
whereB = Atomakethefunctioncontinuous.Wenormalisethe
1976; Gunn&Griffin 1979, hereafter GG79). However, in extra-
high-massendinthesamewayasforthe‘canonical’IMF(i.e.the
galactic samples where the individual stars are not resolved, this
sameA),sothereduction inmassduetoflatteningcanbefound
ishardertodo(althoughnotimpossible),anditisthereforeoften
straightforwardly.
assumedthatlightfollowsmass.
Weevolveeverystar particletoanageof 12Gyrusing SSE
For a universal IMF, the stellar mass function at an age of
(Hurleyetal. 2000) for 11metallicities,linearlyspaced in−2 6
12Gyrdoesdependonthemetallicityofthestarsbecauseofdif-
[Fe/H] 6 0.Wesplitthedataintobinscorrespondingtothestel-
ferences in stellar evolution, and as a result we may expect that
lartypesat12Gyr:mainsequencestars(MS),evolvedstars(EV),
clusterswithdifferentmetallicities,havedifferentobservableprop-
whitedwarfs(WD),neutronstars(NS)andblackholes(BH).The
erties.Theideathatametallicitydependentbiasintheobservation-
allyderivedclusterpropertiesmayexistisnotnew.Jorda´n(2004) logarithmicspacing1 inmi andthefastSSEcodeallowustoeffi-
cientlymodelMFsofoldstellarpopulationsthatarewellsampled
consideredmulti-massKingmodels,withmassbinsappropriatefor
atallevolutionarystagesandhencepresentdaymassesm.
differentmetallicities.Heshowedthatasaresultofmasssegrega-
The resulting MFs for a metal-richand a metal-poor cluster
tion,clusterswiththesamehalf-massradiusrhandthesameage,
witha‘canonical’IMFareshowninFig.1.Fromthisfigurewesee
havesmallerhalf-lightradiiinprojection, rhp,L,athigher metal-
licities.Thisisbecauseathigh[Fe/H]theturn-offmassishigher thatat[Fe/H] = −2theturn-offmassisslightlylower(0.8M⊙)
andasaresultthesestarsandthebrightevolvedstars,whichhave thanat[Fe/H] = 0(1M⊙)andthattheaveragemassofWDsis
similarmasses,aremorecentrallyconcentratedthaninmetal-poor higher at low [Fe/H] (0.77M⊙) than at high [Fe/H] (0.65M⊙).
Also,thecontributionofremnantstothetotalmassishigheratlow
clusters.Jorda´nproposedthatthiseffectisresponsiblefortheob-
[Fe/H]. Although these differences are small, they are important
servedsizedifferencebetweenmetal-richandmetal-poorGCs(e.g.
forthedistributionofthevisiblestars,aswewillshowinthenext
Larsenetal. 2001). An apparent size difference between metal-
section.
rich and metal-poor GCs was also found in N-body simulations
Forourdynamicalmodelswecreate13masscomponents:we
(Sippeletal.2012)andMonteCarlosimulations(Downing2012)
splittheMSstarsinto5binsthatareequallyspacedinlog(m),the
ofclusterswithdifferentmetallicities.
WDsinto5binsthat areequallyspaced inm,theEV stars,NSs
InthisLetterweusemulti-massKingmodelstoquantifythe
and,finally,theBHs.Withthe[Fe/H]dependentmassfunctionsin
masssegregationbiasinΥ asafunctionof[Fe/H]andfordif-
V
place,wecannowdescribethedynamicalmulti-massmodels.
ferentassumptionsfortheretentionofremnants.In§2wemodel
stellarmassfunctionsfordifferent[Fe/H]anddescribethedynam-
icalmodels.In§3wepresenttheresultsofacomparisontothedata
byS11andourconclusionsanddiscussionarepresentedin§4. 2.2 Multi-massmodels
In this section we describe the dynamical models that we use to
quantify the effect of mass segregation on the inferred dynami-
2 DESCRIPTIONOFTHEMODELS calmassfromobservations.Foraself-gravitatingsysteminvirial
equilibrium,themassM canbewrittenasafunctionofthemass-
2.1 Stellarmassfunctionsatanageof12Gyr
weightedmean-squarevelocityofthestars,hv2i,andthevirialra-
Here we describe how we compute the stellar mass components diusofthecluster,rv,asM = 2hv2irv/G.Hererv isdefinedas
forclusterswithdifferentmetallicities.WecreateNp = 104 star rv ≡ −GM2/(2U),whereGisthegravitationalconstantandU
particleswithinitialmassesmi equallyspacedinlogmi between is the total potential energy of the cluster. Our focus ison extra-
a lower mass of mlo = 0.2M⊙ and an upper mass of mup = galacticclustersamplesforwhichindividualstarsarenotresolved,
100M⊙.Weconsiderapower-law(‘canonical’)IMF sowewritethevirialrelationsintermsoftheluminosity-weighted
mean-squarevelocityinprojectionhv2i andtheradiuscontaining
dN p L
dmi =Am−i α, (1) halfthetotalluminosityinprojectionrhp,L(or,‘effectiveradius’)
where α = 2.35 and A is a constant that normalises the to-
tal number of stars in the cluster: A = (1 − α)/(m1−α −
m1−α), for α 6= 1. Every star particle is given a weighutpw = 1 Approximatingthemeanmassinabinbythecentrallogarithmicvalue
Amlo1i−α(lnmup − lnmlo)/Np, such that Nj=p1wj = 1 and ifisnodntlhyaetxfaocrt1fo0r4astpaorwseoru-rlamwowdeitlhpirnodpeexrt−ies1.s5u.cFhroasmthaecotontvaelrMgenocfettheestMwFe
Nj=p1wjmi,j ≃ 0.68M⊙ is the mean masPs of the IMF, which areaccuratetoabout10−5.
P
(cid:13)c 0000RAS,MNRAS000,000–000
The mass-to-lightratioofglobularclusters 3
100 1.6
m [Fe/H] = −2 MEVS 10-1 1.4 [[FFee//HH]]==0−2
d10-1
N/ WNSD 10-2 1.2
d
2m10-2 BH 10-3 01fi.0
1100-03 0.67 0.01 0.23 0.02 0.07 ρ/ρj010-4 2/v 0fi›.8
[Fe/H] = 0 2vj0.6
/dm10-1 10-5 MS 0›.4
N EV
2md10-2 10-6 WNSD 0.2
10-31.0 0.707.5 0.01 0.00.16 l0o.g002(.5m) 0.041.0 1.5 2.0 10-170-1 1r00/r0 101 0.00 2 4 r6/r08 10 12 14
Figure2.DensityandvelocitydispersionprofilesfortwoofourGCmodels
Figure1.Massfunctions fortwoofourevolvedstellar populations: one
withW0=7.Althoughourmulti-massmodelshave13bins,forclaritywe
metal poor (top panel), one metal rich (bottom panel). Each distribution
haveonlyplottedthemiddlemassbinvaluesforMSandWD.Solidlines:
issplitintothefivestellartypes:mainsequencestars(MS),evolvedstars
[Fe/H]=−2.Dashedlines:[Fe/H]=0.
(EV),whitedwarfs(WD),neutronstars(NS),andblackholes(BH).The
numbersarethefractionofthetotalmassineachcomponent.
stars.Foratypicalmass-luminosityrelationforMSstarsweesti-
matethatabout70%oftheMSluminosityisemittedbystarsinthe
massrangeofEVstars(&0.65M⊙).Wethereforeassumethatthe
M =2 η hvp2iLrhp,L. (3) dynamicalpropertiesofEVstarsaretheonesthatoneinfersfrom
η η G integratedlightstudies.
r v
InFig.2weshow theresultingdensityandvelocityprofiles
Here we introduce three factors η, η and η to convert 3-
r v for a metal-rich and a metal-poor cluster without BHs. For both
dimensionalpropertiestoobservablequantities,namely
clusterstheEVstarsaremorecentrallyconcentratedandmovewith
η= hv2i rh rv, η = rhp,L, η = hvp2iL. (4) lowervelocitiesthantheMSstarswhichimpliesthatbothηr < 1
hvp2irhprh r rhp v hvp2i and ηv < 1. The underestimation of M is more severe for the
metal-richclusterthanforthemetal-poorcluster.Thisisbecauseat
Herehvp2iisthemass-weightedmean-squarevelocityinprojection high[Fe/H],theturn-offmassishigher,andtheremnantsareless
and rhp is the radius containing half the mass in projection. The massive(seeFig.1),allowingthebrightstarstosegregatefurtherto
valueofηdependsonthemodel,andforaPlummer(1911)model thecentreofthecluster(seealsoJorda´n2004;Sippeletal.2012).
withanisotropicvelocitydistributionη≃3×(4/3)×(5/4)=5, Wenowneedtomakeachoiceforthedimensionlesscentral
and this value is relatively insensitive to the choice of the model potential W0. We choose W0 such that the EV stars have a ra-
(Spitzer 1987; PortegiesZwartetal. 2010). From now on we as- tioof thecore radius r0 (or King radius) over rh that isequal to
sumethatuncertaintiesinηaresmallandcanbeignored. what is found for the M31 GCs by S11. We obtained the values
The factors ηr and ηv equal unity if light follows mass, i.e. forr0/rhp,L oftheGCsinM31fromS11andfoundthatthereis
ifΥV isthesameeverywhereinthecluster.Ifthisassumptionis nocorrelationbetweenr0/rhp,L and[Fe/H].Wethereforeadopt
made for clusters for which this does not hold, then the product 3values:themeanobservedvalueandthevaluescorrespondingto
ηrηv istheerrorthatismadeinthemassestimate.Hurley(2007) themeanand theplusandminus1σ standarddeviation. Because
finds from N-body simulations that ηr ≃ 0.5 which implies an r0fortheindividualcomponentshasadifferentmeaningthenr0in
errorinM ofafactoroftwo,confirmingthatmasssegregationis singlemassmodelsbecause,wedecidetodefiner0asthedistance
animportanteffecttoconsider. tothecentrewherethedensityofEVstarshasdroppedto1/3ofthe
Wederivethebiasfactorηrηvfromisotropicmulti-massKing centraldensity,asisthecaseinsinglemassmodelswithW0 &5.
modelsasdescribedindetailinGG79.Thedistributionfunctionof Finally,weuserhp,L=0.75rhEV,whererhEVisthe(3D)half-mass
eachcomponentmj (section2.1)is radiusoftheEVstars.
E Using these three r0/rhp,L values, we produce ten models
fj(E)=Aj exp −σ2 −1 . (5) with W0 ranging from 6 to 24, for each [Fe/H]. We then inter-
(cid:20) (cid:18) j(cid:19) (cid:21) polate to obtain the values of W0 to obtain the desired r0/rhp,L
HereE = 12v2+φ,andφisthe(lowered)specificpotentialandσj value.AsampleoftheW0valuesusedcanbefoundinTable1.
isascalevelocity2thatischosentodependonm asσ ∝m−1/2.
j j j
FromtheMaraston(2005)SSPmodelswefindthatabout65%
of the V-band light comes from EV starsand 35% from theMS 3 RESULTS
Foreach[Fe/H],r0/rhp,Landdifferentremnantfractions,wecal-
culatetheratioofthemassasitwouldbederivedfromtheevolved
2traWl1eDnvoetelotchiatytodnislypeinrstihoenlvimrmitsooffinbfiinnijt.eFcoornrceeanltirsatitciocnoσncjeenqtruaatilosnthveaclueens- stars,Mobs,over thetruemassM,i.e.ηrηv (equation 4).Inthis
tthheererafotiroevnjrom0tsin/σejqu<ipa1rtiatinodnj.i0sInmfaosrsthdceopmenindgenstt.uMdieuslti(-Smoolldimelasemtoadl.e2ls01ar5e; cstaalrcsutloatdioenri,vweeMuosbesd,ienxoclrudseirvteolybethceocnosinsttreinbtuwtioitnhftrhoemobthseervevaotilovnesd.
Peutenetal.,inprep)weshowthatmulti-massmodelsdescribethephase Forthemodelswitha‘canonical’IMFMobs/M = Mobs/MSSP,
spacedistributionofstarsinN-bodysystemsverywell. and for the models with a ‘flat’ IMF we multiplied Mobs/M
(cid:13)c 0000RAS,MNRAS000,000–000
4 RosemaryL. Shanahan& MarkGieles
4 CONCLUSIONSANDDISCUSSION
Table 1. A sample of the W0 values used for different [Fe/H] and the
differentassumptionsforretentionofNSsandBHsfora‘canonical’IMF.
Inthisstudy weshow that thediscrepancy between the observed
mass-to-light ratio Υ and simple stellar population (SSP) mod-
V
[Fe/H] r0/rhp,L AllBH&NS NoBH NoBH&NS els as found in a sample of 200 globular clusters (GCs) in M31
byS11,canbeexplainedbymasssegregation.WemodelledGCs
0.45 15.9 8.86 8.41
witharange of metallicitiesand withdifferent remnant retention
−2 0.29 17.5 11.1 10.3
0.13 19.8 14.2 12.9 fractions.Ourkeyresultsare:
0.45 23.0 10.8 10.5 • Forclusterswithoutstellar-massblackholes(BHs)andneu-
0 0.29 24.4 13.4 12.4 tronstars,thedynamicalmassderivedfromevolvedstars(Mobs)of
0.13 25.8 16.6 15.1 amasssegregatedclusterunderestimatesthetruemassM,andthis
biasisstrongerathigh[Fe/H](factorof∼ 4)thanatlow[Fe/H]
(factorof∼2).Thisisduetothehigherturn-offmassandthelower
whitedwarfmassesathigh[Fe/H]whichcausetheevolvedstars
tobemorecentrallyconcentratedandmovewithlowervelocities,
compared to turn-off stars in low [Fe/H] clusters with the same
by M/MSSP ≃ 0.41, slightly dependent on [Fe/H], to obtain massdensityprofile(seealsoJorda´n2004;Sippeletal.2012).
Mobs/MSSP. The results are shown in Fig. 3. The three panels • ThepresenceofBHshasalargeeffectonthederivedMobs,
show the results of three assumptions for the remnant retention
in that its value iscloser to the real M for higher retention frac-
fraction, fromleft toright: allBHsand allNSsretained, no BHs
tions. Despite the fact that a large fraction of BHs probably gets
retained and all NSs retained, no BHs and no NSs retained. The
ejectedfromGCsastheresultofsupernovakicks,itisimportant
resultsforamodel inwhichallBHsareretainedandnoNSsare
toconsidertheBHsindynamicalmassmodellingofGCs.Asmall
retainedwerefound tobe almostidentical tothemodel inwhich
remainingBHpopulationcansurviveforaslongas10half-mass
allNSsandallBHswereretained.
relaxationtimes(τrh, Breen&Heggie2013).Therecentdiscov-
We divided the inferred Υ of each GC in M31 by its cor-
V eryoftwoBHcandidatesinM22(Straderetal.2012)confirmsthe
responding value of the SSP model (Fig. 1 of S11), based on a
needtoconsiderBHswhenderivingΥ .
V
KroupaIMF,toobtainMobs/MSSPforM31GCs,whereMSSPis • Forclusterswitha‘flat’massfunction,wefindthattheeffect
thepresentdaymassofastellarpopulationwitha‘canonical’IMF.
ofmasssegregationonMobs/Mislessimportant,suchthatthera-
Wenotethatthereisaslightinconsistencyinthecomparisonbe-
tioMobs/MSSP,withMSSPisthepresentdaymassforacanonical
tweenourmodelsandthedatabecausetheΥ valuesoftheSSP
V IMF,issimilartoM/MSSP modelswitha‘canonical’ IMF.This
modelsarebasedonasinglevaluefortheretentionfractionofNSs
makesΥ insensitivetothelow-massendoftheMF.
V
andBHs.However,asweshowinFig.1thetotalmassinNSsand
BHsneverexceeds9%ofthepresentdayM,sothiseffectissmall. S11findthatthediscrepancybetweenΥ andtheSSPmod-
V
If all NSs and BHs are retained (left panel), there is hardly els is more important for clusters with lower mass and for clus-
any bias because of mass segregation and the correct M is in- terswithshorter τrh,whichwasalsofoundforGCsintheMilky
ferred from the EV stars. Without NSs and BHs (right panel), Way(Mandushevetal.1991;Kimmigetal.2014)andCentaurusA
0.25 . Mobs/MSSP . 0.5 for both MFs. The mass segrega- (NGC5128,Rejkubaetal.2007).Thisisconsistentwiththesce-
tionterm(ηrηv)ishigherwhenthemassfunctionisflatter,while narioputforwardinthisLetter,becausemasssegregationismore
M/MSSPissmaller.Thetwoeffectsappeartoroughlycancel,such importantforclusterswithshorterτrh,i.e.thosewithlowermass.
that the resulting ratio Mobs/MSSP is similar. This means that a Zaritskyetal. (2014) report a bi-modality in ΥV, after all
lowMobs/MSSP cannotbeinterpretedasaflatteningoftheMF, clustershavebeenagedtoacommonageof10Gyr(ΥV,10).They
northeIMF,becauseamasssegregatedmodelwitha‘canonical’ determinedynamical massesfromintegratedlight propertiesof a
IMFgivessimilarresults. sampleofstarclusterswithdifferentagesandmetallicitiesandin
Thetwoextremesoftheretentionfractionmodels(i.e.allthe differentgalaxies.Theauthorsinterprettheirresultasevidencefor
BHandNSretained,andnoneoftheBHandNSretained)encom- twodistinctIMFs.Althoughwedonotdiscussthemasssegrega-
pass themajorityof theGC values, and it ispossible tointerpret tion bias in their sample in detail here, we caution to invoke the
thespreadinthedataasaspreadinBHretention. need of a varying IMF in a study based on integrated light mea-
The [Fe/H] dependence in the middle and right panels can surement,beforebiasesasaresultofmasssegregationhavebeen
beexplained withsomesimplestellarevolutionarguments. From fullyquantified.
Fig.1weseethatatlowermetallicitiestheturn-offmassislower ThereducedΥ ofMWGCs(McLaughlin&vanderMarel
V
andthereismoremassinremnants,andtheaveragemassofwhite 2005) and other galaxies has been explained by the depletion
dwarf mass and black holes is higher (see also the discussion in of low-mass stars as the result of dynamical ejections (Kruijssen
Sippeletal.2012).Asaresult,inalow-metallicitycluster,therem- 2008).Thiseffectisalsomoreimportantforclusterswithshorter
nantsaremoreefficientinpushingtheevolvedstarsout,whichin- τrh/lower mass, therefore degenerate with the mass segregation
creasestheirvelocitiesandtheirhalf-lightradius,suchthatη and biasreportedhere.Wenotethatpreferentialdepletionoflow-mass
v
η areclosertounity. starsrequiresmasssegregation,butnotviceversaanditistherefore
r
These results suggest that the discrepancy between the ob- necessarytoconsider thebiasesduetomasssegregationtogether
served GC masses of S11 and the SSPmodels, can be explained withtheeffectofthedepletionoflow-massstars.Hereweshowed
bymetallicitydependent masssegregationeffectsandaspreadin that the two effects have opposing effects on Mobs/MSSP, such
theretentionfractionofNSsandBHs.Ourresultssuggestthatthe thatΥ isinsensitivetotheslopeoftheMF.
V
low-mass end of the MF can not be constrained from integrated TheΥV valuesofyoung(few100Myrs)massive(&106M⊙)
lightproperties. clustersinmergerremnantsareconsistent withthepredictionsof
(cid:13)c 0000RAS,MNRAS000,000–000
The mass-to-lightratioofglobularclusters 5
All BH and NS No BH No BH and NS
2.0
) NormalIMF S11data
P
SS FlatIMF r0,L/rhp,L =0.13
M
/ 1.5 r0,L/rhp,L =0.29
M r /r =0.46
0,L hp,L
(
)
v
η
ηr1.0
(
=
P
S
S
M 0.5
/
bs
o
M
0.0
2.5 2.0 1.5 1.0 0.5 0.0 0.5 2.5 2.0 1.5 1.0 0.5 0.0 0.5 2.5 2.0 1.5 1.0 0.5 0.0 0.5
[Fe/H] [Fe/H] [Fe/H]
Figure3.RatioofinferredmassMobsoverSSPmassMSSPversus[Fe/H]fora‘canonical’IMF(solidlines)andflatIMF(dashedlines).Thebluepoints
arethecorrespondingvaluesfortheM31GCstakenfromS11.Thethreelinesineachoftheplotsshowtheresultsformodelsdesignedto‘look’assimilarto
theS11GCsaspossible,usingthemeanr0/rhp,Lvalueandtwoσvalues.Forthe‘canonical’IMFM/MSSP=1,andforthe‘flat’IMFM/MSSP≃0.41
.
SSPmodelswitha‘canonical’IMF(Bastianetal.2006).Although GehaM.,BrownT.M.,TumlinsonJ.,KaliraiJ.S.,SimonJ.D.,
these values were derived from integrated light properties, these Kirby E. N., VandenBerg D. A., Mun˜oz R. R., Avila R. J.,
clusters are significantly younger than their two-body relaxation GuhathakurtaP.,FergusonH.C.,2013,ApJ,771,29
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C.J.,2001,AJ,121,2974
This work was carried out as part of the ISIMA programme on MandushevG.,StanevaA.,SpasovaN.,1991,A&A,252,94
Gravitational Dynamics held in July 2014 at CITA, Toronto. We MarastonC.,2005,MNRAS,362,799
acknowledgePascaleGaraudfortheorganisation,thefinancialsup- McLaughlinD.E.,vanderMarelR.P.,2005,ApJS,161,304
port andforproviding astimulatingenvironment. MG thanksthe Paust N. E. Q., Reid I. N., PiottoG., Aparicio A., Anderson J.,
Royal Society for financial support in the form of a University SarajediniA.,BedinL.R.,ChaboyerB.,DotterA.,HempelM.,
Research Fellowship (URF) and the European Research Council MajewskiS.,Mar´ın-FranchA.,MiloneA.,RosenbergA.,Siegel
(ERC-StG-335936,CLUSTERS).RLSacknowledges thesupport M.,2010,AJ,139,476
of the Scienceand Technology FacilitiesCouncil (STFC)viathe PlummerH.C.,1911,MNRAS,71,460
award of an STFC Studentship. RLS thanks Anna Lisa Varri for Portegies Zwart S. F., McMillan S. L. W., Gieles M., 2010,
her support and guidance throughout this work. We thank Mik- ARA&A,48,431
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fordiscussionsduringthe‘GaiaChallenge’meetingandDiederik StructureandDynamicsofGlobularClustersVol.50ofAstro-
Kruijssen,Vincent He´nault-Brunet, Jay Strader and Nate Bastian nomicalSocietyofthePacificConferenceSeries,VelocityDis-
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