APreprinttypesetusingLTEXstyleemulateapjv.04/03/99
MASSIVEFIELDSTARSANDTHESTELLARCLUSTERINGLAW
M.S.OeyandN.L.King
LowellObservatory,1400W.MarsHillRd.,Flagstaff,AZ86001;Sally.Oey@lowell.edu
DepartmentofSpaceStudies,SouthwestResearchInstitute,Suite426,1050WalnutSt.,Boulder,CO
and
J.Wm.Parker
80302
AcceptedtotheASTRONOMICALJOURNAL26November2003
arXiv:astro-ph/0312051v1 2 Dec 2003ABSTRACT
ThedistributionofN∗,thenumberofOBstarsperassociationorcluster,appearstofollowauniversal
−2
power-lawformN∗inthelocalUniverse.WeevaluatethedistributionofN∗intheSmallMagellanicCloudusingrecentbroadbandopticalandspace-ultravioletdata,withspecialattentiontothelowestvaluesofN∗.Wefindthatthepower-lawdistributioninN∗continuessmoothlydowntoN∗=1.Thisstronglysuggeststhattheformationoffieldmassivestarsisacontinuousprocesswiththoseinassociations,andthatthefieldstarsdonotoriginatefromadifferentstarformationmode.Ourresultsareconsistentwiththemodelthatfieldmassivestarsrepresentthemostmassivemembersingroupsofsmallerstars,asexpectediftheclusteringlawappliestomuchlowermassesasisexpectedfromthestellarinitialmassfunction(IMF).TheseresultsareconsistentwiththesimultaneousexistenceofauniversalIMFandauniversalclusteringlaw.Jointly,theselawsimplythatthefractionoffieldOBstarstypicallyrangesfromabout35%to7%formostastrophysicalsituations,withaninverselogarithmicdependenceonthemostpopulouscluster,andhence,ongalaxysizeand/orstarformationrate.Thereareimportantconsequencesforglobalfeedbackeffectsingalaxies:fieldstarsshouldthereforecontributeproportionatelytothevolumeofthewarmionizedmedium,andequalrelativecontributionsbysuperbubblesofallsizestotheinterstellarporosityareexpected.
Subjectheadings:stars:early-type—stars:formation—stars:statistics—galaxies:starclusters—
galaxies:stellarcontent—galaxies:individual(SMC)
1.INTRODUCTION
Itiscommonlyheldthatmostmassive,OBstarsarefoundinstellarclusters,orassociations,sincetheirshort(∼10Myr)lifetimesarenotlongenoughtopermitspa-tialdispersionfromtheirnatalcompanions.However,apparently-isolated,massivefieldstarsarewell-knowntoexist,includingaclassofrunawayOBstarswithunusually
−1
large(>∼30kms)velocities.WhilerunawayOBstarsaregenerallybelievedtobekinematicallyejectedfromaparentOBassociation,theordinarynon-runawayfieldOBstarshavebeensuggestedtooriginateinadifferentmodeofstarformationfromtheircounterpartsinassocia-tions.Suggesteddifferencesbetweenclustersandthefieldinthestellarinitialmassfunction(IMF)forhigh-massstars(Massey2002;Kroupa&Weidner2003)supportthispossibility.Thiscontributionexplorestherelationshipbe-tweenOBassociationsandmassivefieldstars.
Inrecentyears,ithasemergedthatthenumberofstarsN∗perclusterappearstofollowauniversalpowerlawdistribution:
Thishasbeenfoundempiricallyforyoung,massiveclus-ters(e.g.,Hunteretal.2003;Zhang&Fall1999),superstarclusters(Meureretal.1995),globularclusters(e.g.,Harris&Pudritz1994)andHIIregions(Oey&Clarke1998).Theapparentuniversalityofthisrelationisemerg-ingasfundamental(e.g.,Oey&Mu˜noz-Tu˜non2003;Oey&Clarke1998;Elmegreen&Efremov1997),similartotheconstantpower-lawrelationfortheIMF.Ifindividual,
−2
N(N∗)dN∗∝N∗dN∗
fieldOBstarshaveafundamentallydifferentoriginfrom
clusteredOBstars,thenthisislikelytobemanifestinthedistributionofN∗,nearN∗=1,whereN∗specificallycountsmassivestarsonly(here,m>∼10M⊙).Inwhatfollows,weexaminetheformofN(N∗),forsmallN∗,aregimethathasnotbeeninvestigatedtodate,toillumi-natetherelationshipbetweenmassivestarclusteringandmassivefieldstars.
2.THESMCSAMPLEOFOBSTARS
.(1)
1
AstudyofOBstarclusteringpropertiesandfieldstarsrequireshighspatialresolutionandessentiallycompletedetectionoftheOBstarsoveralargeareaofagivengalaxy.TheMagellanicCloudsareoptimaltargetgalax-iesbyvirtueoftheirproximityandhighGalacticlatitude.Indeed,someoftheearliestworkonOBassociationsandmassivestarcensuseswascarriedoutfortheMagellanicCloudsbyFeastetal.(1960),Sanduleak(1969),Lucke&Hodge(1970),Azzopardi&Vigneau(1982),andHodge(1985).Morerecently,theUBVRsurveydataofMassey(2002)fortheSmallMagellanicCloud(SMC),togetherwithUVphotometry(Parkeretal.1998)fromtheUl-travioletImagingTelescope(UIT),provideunprecedenteddepth,resolution,completeness,andbroadbandcoverageforthemassivestarpopulationoveralargefractionoftheSMC.TheareaobservedbyUITissmallerthantheopticalsurvey,butcoverstheSMCbar,whichincludesmostoftheactivestarformationinthatgalaxy.Figure1showstheregionscoveredbythetwosurveys.SMCOBassociationshavepreviouslybeenidentifiedandcataloguedbyHodge
2FieldandclusterOBstars
Fig.1.—GrayscaleR-bandimageoftheSMC(Bothun&Thompson1988)showingtheareacoveragefortheUBVRsurvey(Masseyetal.2002;rectangularregions)andtheUITsurvey(Parkeretal.1998;circularregions).Theopticalfieldsare79′square,andtheUITfieldsare37′indiameter.Northisup,easttotheleft.
(1985)andBattinelli(1991),thelatterfromthephoto-graphicOBcensusofAzzopardi&Vigneau(1982).Here,were-examinetheclusteringpropertiesofthesemassivestarsintheSMC,usingthemoderndatasetstofirstsys-tematicallyidentifyOBstars,andthentosystematicallyidentifygroupsorassociationsofthem.Wewillespeciallyfocusonthestatisticalpropertiesofthelow-N∗regime.Parkeretal.(1998)provideUITphotometryintheB5filter(λeff=1615˚A,∆λ=225˚A),whichrecentlyhasbeenrecalibratedbyParker,Cornett,&Stecher(2004,inpreparation).TheUBVRphotometryofMassey(2002)wasobservedthroughaHarrisfiltersetandtransformedtotheJohnson-Cousinssystem(Landolt1992).Reddening-freeQindiceswerecomputedusingtheextinctionlawofCardelli,Clayton,&Mathis(1989)withatotaltoselec-tiveextinctionratioRV=3.1.Differentcombinationsoffilterswereusedtobestselecttwodifferentstellarsam-ples:Starswithinitialmasses>∼10M⊙,correspondingtospectraltypesofB0V,B0.5Iandearlier,wereselectedonthebasisoftheiropticalphotometryonly;andstarswithinitialmasses>∼20M⊙,correspondingtospectraltypesofO9V,B0IandearlierwereselectedonthebasisofboththeirUBVRandUITphotometry.WerefertotheformerastheOBsample,andthelatterastheO-starsample,al-thoughweemphasizethatneithersampleconsistsofspec-troscopicallyconfirmedstars.Ourcriteriaareasfollows,usinganSMCdistancemodulusDM=18.88(Dolphinetal.2001)andglobalaverageextinctionAB=0.53:
mB≤−4.2+DM+AB
QU−R,B−RQB5−U,B−RQB5−V,U−V
where
≤15.21≤−0.84,≤−1.45,≤0.03,
AU−AR
(2)(3)(4)(5)
QU−R,B−R=(mU−mR)−
QB5−V,U−V
(mB−mR)
AB−AR
=(mB5−mU)−1.668(mB−mR),(7)
AB5−AV
=(mB5−mV)−
Oey,King,andParker
3
selected,onehadnebularemissionaffectingthephotome-tryandtwoothershadweakmetallines(designationWinspectraltype).Thefalsepositiveswere8out26stars;themajorityofthefalsepositiveswereweaklinedstars(W),emissionlinestars,andpeculiarstars.
3.IDENTIFICATIONOFOBASSOCIATIONS
Havingidentifiedtwosamplesof1360OBand382Ostars,wethenusedthefriends-of-friendsalgorithmde-scribedbyBattinelli(1991)toidentifytheassociationsofthesestars.OurparameterN∗refersspecificallytocountsofOBstarsfromthesesamples,identifiedasdescribedabove.Battinelli’salgorithmadoptsastheclusteringdis-tancedsbetweenassociatedmembersthevalueofdthenumberofclustersforNsthatmaximizes∗withindsofanothermemberstararedefined≥3.tobeAllwithinstarsthesamegroup.(Wedonotdistinguishbetween“group,”“association,”and“cluster”inthiswork.)Figure2showsthenumberofclustersNasafunctiondfortheOBsample(Figure2a)andO-starsnearthepeakinNsample(Fig-ure2b).′′FortheOBsample,thecharacteristicd)isstraightforwardtodetermine,butfors=28pc(97theO-starsample,itisapparentthatNislesssensitivetodWeadoptd=34pc(117′′)fortheO-starsample,cor-s.respondingstothemeanvalueovertheconsideredrange;thelargervalueofdthelowersascomparedtotheOBsampleisconsistentwithstellardensityforOstars.Al-thoughtheclusteringpropertiesarerelativelyinsensitivetothechoiceofdswithinafewpc,wecautionthatlargervaluesofdN(Nswillresultinflatterslopesfortheclusteringlaw∗)(e.g.,equation1),asdiscussedbelowin§4.OurvaluesofdthisissaremuchsmallerthanBattinelli’svalueof60pc;consistentwithamuchgreatercomplete-nessinourdata,yieldingahigherdensityofOBstars,andthereforesmallerclusteringdistance.
Table2presentsthegroupshavingatleast3starsthatareidentifiedfromourOBsample.Column1showsthegroupIDnumber,columns2and3givethegroupcentroidpositionindecimaldegrees(J2000.0),columns4and5givethegroupdiameterDinarcminandpc,respectively,andcolumn6liststhenumberofstarsinthegroup.Ta-ble3presentsthegroupsidentifiedfromtheOstarsam-pleinthesameway.ThegroupdiametersaredefinedasD=1
N(logN∗):thesolid
lineshowsthefitfortheentiredistribution,yielding−samples,2.51±0respectively;.29and−2.33and±the0.42dottedforthelineOBshowsandO-starthefitomittingthefirstbin,whichcorrespondstosinglestars,resultinginfitsof−2.27±0.38and−2.11±0.55fortheOBandO-starsamples,respectively.Thefitsomittingthesin-glestarsagreewiththepower-lawslopeof–2(equation1),foundfortheN∗distributioninavarietyofsystems,asdiscussedin§1.Weagainemphasize,asmentionedabove,thatthefittedslopehasadependenceontheclusteringdistanceds:forlargeds,morestarsaredrawnintotheas-sociations,causingtheresultantslopeoftheclusteringlawtobeflatterrelativetoclusteringdefinedbyasmalldweseekacharacteristicvaluefortheslopeofN(Ns.Since∗),itisimportanttoensurethatdofthesample.Forthedsisinturncharacteristic40pc(seeFigure2b),thesintheextremerangeof20–O-starsampleshowsavariationinfittedslope,omittingthefieldstars,of−2.79±0.84to−1It.85is±apparent0.52,respectively.
thatthesinglestarsareslightlygreaterinnumberthanthepowerlawfortheremainderoftheN∗distribution,particularlyintheOBsample.Howsignifi-cantisthisexcessintheisolated,“field”stars?Wenotethatthemagnitudeoftheexcessmaybealowerlimit,sincetheslopeoftheN∗distributionisexpectedtoflattenslightlyatthesmallestvaluesofN∗,owingtostatisticaleffects,asfollows.Weassume,assuggestedabove,thattheOBstarscountedinthevalueofN∗representonlythemostmassivestarsforapopulationofstarclustersthatareinrealitypopulatedbyamassdistributiondescribedbyaconventionalIMF.SinceweidentifiedonlyOBstars,ourclustersareselectedwiththecriterionthateachclus-tercontainsastarofatleastmassmclustershavealowerprobabilitycut.Thesmallest,“unsaturated”ofhavingtheirmaximumstellarmassmmax≥mcut,sotheywillbe
4FieldandclusterOBstars
Table1
ComparisonofO-starcriteria
CatIDa168285869168851792722837437244603527731437345082564064061047540130751550318614237024368651575
aCatalog
SpTypebO5III(f)O7VO7IIIO7.5Iaf+O7.5VO7VO7IIIO8.5VO8VO8VnO9+NEBO9VO9IIIB0.5IIIB0.5VB0IIWB0IWB0.5VB0III
Identifiedc
yyyyyyyynynyyynnyny
54456907918700427404478445438506095322532907548184384447028457225308421801408514321552992
B0IWB1.5VB1IbB1IIIB1IIIB1VeB1IIIB1VB2IIB2IB3IB3IB8VeB8-A0IBpecBextrA0IA1I
ynynnnnnnnnnynyynn
numberfromMassey(2002)
typecompiledbyMassey(2002)byO-starcriteriaequations2–5
bSpectroscopiccIdentified
Oey,King,andParker5
Fig.2.—NumberofgroupswithN∗≥3asafunctionofclusteringdistancedsfortheOBsample(panela)andO-starsample(panelb).
Fig.3.—CentroidsandsizesofassociationsidentifiedbyHodge(1985;solidblack),Battinelli(1991;dottedblack),ourOBsample(blue)andourO-starsample(red).Notethatallbluecircleshaveadotatthecenter,thusoverplottedidenticalcirclescanbeidentifiedbysmalldotsinthecenterofredcircles.(RAandDecgivenindegreesofarc.)
6FieldandclusterOBstars
Table2
GroupsfromthecandidateOBsample
OBgrp
RA
Dec
D(min)
D(pc)
N∗
Oey,King,andParker7
Table2(continued)
OBgrp
RA
Dec
D(min)
D(pc)
N∗
8FieldandclusterOBstars
Table3
GroupsfromthecandidateO-starsample
Ogrp
RA
Dec
D(min)
D(pc)
N∗
Table4
GroupmembershipforthecandidateOBsamplea
RA
Dec
U
Uerr
B
Berr
V
Verr
R
Rerr
ID
OBgrp
completeversionofthistableisintheelectroniceditionoftheJournal.Theprintededitioncontains
onlyasample.
aThe
Table5
GroupmembershipforthecandidateO-starsamplea
RA
Dec
U
Uerr
B
Berr
V
Verr
R
Rerr
B5
B5err
ID
Ogrp
aThe
completeversionofthistableisintheelectroniceditionoftheJournal.Theprintededitioncontainsonlyasample.
Oey,King,andParker9
Fig.4.—LogarithmicsizedistributionforgroupsidentifiedfromthecandidateOBandO-starsamplesareshowninthetoprow(panelsaandb,respectively).ThelineardistributionsfortheOBandandO-starsamplesareshowninthebottomrow(panelscandd,respectively).ThefirstbininFigure4chasamaximumof391.
Fig.5.—ThedistributioninN∗forgroupsdefinedfromthecandidateOBsample(panela)andO-starsample(panelb).Fitstothepower-lawexponent(−β)areshownfortheentiredistributions(uppervalues)andomittingthefirstbinofsinglestars(lowervalues).Notethattheslopefittedinlogarithmicspaceis−β+1.
10FieldandclusterOBstars
Fig.6.—MonteCarlomodelsfordistributionsoflogN∗,selectedbythecriterionthatthemaximumstellarmassineachclusterbeatleastmmax≥mcut,showingmcut=20M⊙and40M⊙inpanelsaandb,respectively.
progressivelymissingfromasampleofclustersselectedinthisway(seeOey&Clarke2003foradetaileddiscussionofthiseffect).
Figure6showsMonteCarlomodelsthatdemonstratethiseffect.N∗isdrawnfromapower-lawdistributionofslope–2(equation1),withtheindividualstellarmassesdrawnfromaSalpeter(1955)IMFhaving10≤m≤100M⊙.Figure6ashowsthedistributioninN∗for10,000clustershavingatleastonestarwithmassmmax≥20M⊙,andFigure6bisthesame,butselectedformmax≥40M⊙.WeseeaflatteninginthedistributionsforsmallN∗,andtheflatteningisstrongerinFigure6b,sincetheprobabilityofdrawinga40M⊙starislessthanfora20M⊙star.Figure7showsthestellardensityofallcataloguedstarsintheUBVRsurveyasafunctionofradiusaroundtheiso-lated,fieldmassivestarsfoundintheOB(solidline)andO-star(dashedline)samples.Theerrorsarecomputedas√
Oey,King,andParker11
Fig.7.—Meanstellardensity(arcsec−2)withinradiusr(arcsec)fromisolatedmassivestarsinthecandidateOB(solidline)andO-star(dashedline)samples(10′′=2.9pc).TheO-starsampleshowsahigherbackgrounddensitysincethatsampleislimitedtotheSMCbarregion(Figure1).
formationdensityoccursintheSMCbar,where,asseeninFigure3,mostoftheassociationsarelocated.Individualmassivefieldstars,ontheotherhand,haveamuchmoreuniformdistribution,asseeninFigure9.Theunevenstarformationdensitydistributioninthisgalaxythereforefa-vorsthefieldstarsandenhancestheN∗=1binfortheOBsampleinFigure5.TheeffectismuchlesspronouncedintheO-starsample,whichislimitedtotheSMCbarregion.Consideringtheseeffects,itisapparentthatthereisnostrongvariationorchangeincharacterofthepower-lawdistributionseeninFigure5forthesmallestvaluesofN∗.Theempiricalsamples(Figure5)aremuchsmallerthanthoseinthemodelsandthereforehavesignificantlypoorerstatisticsinlogN(logN∗).Thus,themodeledef-fectswillbemoredifficulttodiscerninthedata.Sinceourresultsarelargelyconsistentwithasingleintrinsicpower-lawformfortheclusteringlaw,thissuggeststhatthemassivefieldstarpopulationsimplyrepresentsanex-tensionofthemassiveclusterpopulationextendingdowntoN∗=1.Thereisnoevidencethatthemajorityofmassivefieldstarsoriginatefromamodeofstarforma-tionthatisdifferentfromthoseinassociations.However,furtherstudiesofmassivefieldandclusterpopulationsinotherenvironmentsarenecessarytoconfirmthegeneralityoftheseresults.
tion1,thetotalnumberofOBstarsis,
N∗,up
N∗,tot∝
N∗=1
−2
N∗·N∗
,(9)
whereN∗,upreferstotheupper-limit,maximumclusterofstars.Equation9correspondstoadivergentharmonicserieswhichcanbeapproximatedforlargeN∗,upas:
N∗,tot∝∼lnN∗,up+γ
,
(10)
5.DISCUSSION
ForauniversalIMF,theconstantslopeoftheN∗dis-tributionextendingtothefieldstarshasprofoundconse-quencesfortheirglobalfeedbackinfluenceingalaxies.We
cannowquantifytheassertionthatmostmassivestarsforminassociations:foranN∗distributiongivenbyequa-
whereγ≃0.5772istheEuler-Mascheroniconstant.ThusthefractionofN∗=1fieldstarsis(lnN∗,up+γ)−1ofthetotalN∗,tot.ForourOBandOstarsamples,respectively,logN∗,up≃2.0and1.8,yielding19%and21%fractionsforthefieldstars.
CountingtheactualstarsinourOBandOstarsam-ples,wefindthat374and91candidates,respectively,hadnomassivecompanionswithintheclusteringradius.Thesecorrespondto28%and24%,reflectingtheexcessfoundabove.ThesefractionsareaboutafactortwolowerthanthefindingbyParkeretal.(2001)thatoverhalfoftheirUIT-selectedcandidateOstarsareoutsidecat-aloguedassociationboundariesintheLargeMagellanicCloud(LMC).TheresultsforboththeSMCandLMCmaybeoddswiththeresultsofMasseyetal.(2002),whofoundamuchsteeperIMFslopeforfieldvsclustermassivestars:asteeperIMFslopeinthefieldwouldbemanifestedasasmallernumberoffieldOBstars,yettheslopeoftheN∗distributiontendstobesteeperthanex-pected,ratherthanflatter.IfthefieldstarIMFisindeedsteeperthaninclusters,thentheclusteringlawmustalsosteepensubstantiallyforthesmallestclusters,insuchawayastocompensateforasteepIMFinourdata.Fur-therinvestigationisnecessarytoresolvethisissue.
12FieldandclusterOBstars
Fig.8.—MonteCarlomodelsforevolutioninthelogN∗distribution,assumingthatallobjectswerecreatedsimultaneously.Modelsforagesof0,15,and25Myrareshown,withfittedpower-lawslopes.AsinFigure5,thelinearpower-lawexponentsareshown,whilethefittedslopeis−β+1inlogarithmicspace.
Oey,King,andParker13
Fig.9.—SpatialdistributionofisolatedfieldstarsfortheOBsample(plussymbols),andO-starsample(crosssymbols).ScaleandaxesareasinFigure3.
Inthemeantime,thedataappeartobebroadlyconsis-tentwiththesimplerscenarioof,simultaneously,auniver-salIMFanduniversalclusteringlawgivenbyequation1.AsemphasizedbyMcKee&Williams(1997),thetotalOBstarpopulation,andthusthefractionofisolatedfieldmas-sivestars,isdrivenbyN∗,upwithaninverselogarithmicdependence.FormaximumN∗,uprangingbetween10and106,equation10yieldsafractionoffieldOBstarsrangingfrom35%to7%,respectively.
Theclusteringlawinequation1hasimportantconse-quencesforfeedback,implyingthattheinterstellarporos-itycausedbytheformationofsuperbubblesandsupernovaremnantshasequalrelativecontributionsfromobjectsofallsizes(Oey&Clarke1997).And,sincetheStr¨omgrenvolumeVs∝N∗,italsoimpliesthatastrongmajorityofthefieldmassivestarslikelycontributetoionizingthediffuse,warmionizedmedium,whichconstitutesabout40%ofthetotalHαluminosityinstar-forminggalaxies(e.g.,Walterbos1998).Ourresultisquantitativelycon-sistentwiththeresultofHoopes&Walterbos(2000)thatfieldOBstarscanpower40%±12%ofthewarmionizedmediuminM33,wherethefractionoffieldOBstarsislikelyaround15%.
6.CONCLUSION
process.Rather,wefindthatthecontinuouspower-lawdistributioninN∗downtoN∗=1stronglysuggeststhatthestar-formingprocessiscontinuousfromrichclusterstopoorgroups,apparentlyforallensemblesthatformOBstars.Thedataareconsistentwiththemodelthatsingle,fieldOBstarsareusuallythemostmassivememberofagroupofsmallerstars,asexpectedfromtheuniversalN∗distribution(equation1).TheseresultsareconsistentwiththesimultaneousexistenceofauniversalIMFanduniver-−2
salN∗clusteringlaw.ThesejointuniversalpowerlawsimplythatfieldOBstarsconstituteroughly35%to7%ofthetotalmassivestarpopulation,withaninverselogarith-micdependenceonN∗,upofthethemostpopulouscluster.Thus,thefractionisdependentongalaxysizeand/orstarformationrate.Thecontributionofthesefieldstarstotheionizedvolumeinthewarmionizedmediumislikelytoscaleaccordingtotheirrelativefraction.Theuniversalclusteringlawalsoimpliesequalrelativecontributionsbysuperbubblesofallsizestotheinterstellarporosity.WearepleasedtoacknowledgediscussionswithRen´eWalterbos,CristianoPorciani,ToddSmall,andespecially,ChrisMcKeeandtheanonymousreferee.WealsothankPhilMasseyforgenerouslyprovidingtheUBVRdatainadvanceofpublication.ThisworkwassupportedbytheNASAAstrophysicsDataProgram,grantNAG5-10768.
WefindnoevidencethatthefieldmassivestarsintheSMCareformedbyafundamentallydifferentstar-forming
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