PAGE 2 2 PAGE 3 3 PAGE 4 page LISTOFTABLES ...................................... 6 LISTOFFIGURES ..................................... 7 ABSTRACT ......................................... 9 CHAPTER 1BLUESTRAGGLERS:THECURRENTSCENARIOANDMOTIVATION .... 11 1.1BlueStragglerFormation ........................... 11 1.2Motivation .................................... 15 1.3Methodology .................................. 16 1.3.1Ground-BasedSurvey ......................... 16 1.3.2ACSLuminosityFunctions ....................... 18 1.4SummaryofGoals ............................... 20 2GROUND-BASEDSURVEY ............................ 22 2.1TargetSelection ................................ 22 2.2Observations .................................. 23 2.3DataReduction ................................. 24 2.4BlueStragglerSelection ............................ 26 2.5VariableDetection ............................... 29 2.6Completeness ................................. 32 2.6.1ArticialStarTests ........................... 32 2.6.2PeriodDetection ............................ 36 2.6.2.1VariabilityCriteria ...................... 36 2.6.2.2TestingOurCriteria ..................... 37 3SXPHEANDTHEIRHOSTCLUSTERS:RESULTSOFTHEGROUND-BASEDSURVEY ....................................... 40 3.1WhyNoBinaries? ............................... 40 3.1.1BinaryDetectionProbability:Simulations .............. 40 3.1.2BSSBinaryFraction:ComparisonWithOtherStudies ....... 43 3.2NewVariables ................................. 46 3.3PlacingOurResultsInContext:PropertiesofSXPheinGGCs ...... 47 3.3.1TheUpdatedSXPheCatalog ..................... 47 3.3.2PeriodandAmplitudeDistribution ................... 48 3.3.3SXPheLuminosityFunction ...................... 51 3.3.4SXPheandClusterProperties .................... 52 3.4SXPhePeriod-LuminosityRelation ...................... 55 3.5Results:IndividualSXPhe .......................... 63 3.5.1NGC6101 ................................ 64 4 PAGE 5 ................................ 69 3.5.3NGC5986 ................................ 71 3.6TheSXPhe-BlueStragglerConnection ................... 71 4THEBLUESTRAGGLERLUMINOSITYFUNCTION ............... 76 4.1TheACSGalacticGlobularClusterTreasurySurvey ............ 76 4.2BSSSelection ................................. 77 4.3CompletenessFunctions ........................... 78 4.4CalculationoftheBSSLuminosityFunction ................. 79 4.5BSSLuminosityFunctions:Results ...................... 82 4.6SXPheandtheACSSurvey ......................... 88 5CONCLUSIONSANDFUTUREPROSPECTS .................. 91 5.1GroundBasedSurvey ............................. 91 5.1.1SXPheandHostClusterProperties ................. 91 5.1.2SXPhePeriod-LuminosityRelation .................. 91 5.1.3TheFutureofSXPhe ......................... 93 5.2BSSLuminosityFunctionsFromtheACSSurvey .............. 94 REFERENCES ....................................... 98 BIOGRAPHICALSKETCH ................................ 103 5 PAGE 6 Table page 2-1TargetClusterPositionalProperties ........................ 22 2-2TargetClusterObservationalProperties ...................... 23 2-3Observations ..................................... 24 3-1NewSXPheVariables ................................ 46 6 PAGE 7 Figure page 2-1CMDofM55illustratingourBSSselectionprocess ................ 28 2-2LSandANOVAperiodogramsfor8oftheNGC6101variables ......... 31 2-3CMDofNGC6101showingresultsofarticialstartests ............. 34 2-4ThecompletenessofBSSinNGC6101 ...................... 35 2-5CompletenessofNGC6101BSSdividedinradialbins .............. 36 3-1Binarydetectionprobabilityasafunctionofperiod ................ 41 3-2TheprobabilityPversusbinaryfraction ...................... 43 3-3Amplitudevs.PeriodforSXPhe .......................... 48 3-4PeriodandAmplitudedistributionsofSXPhe ................... 49 3-5LuminosityfunctionofallobservedSXPheinGGCs ............... 52 3-6ThenumberofBSSvs.thenumberofSXPhe .................. 54 3-7HistogramsofallGGCsfromH96vs.6differentclusterproperties ....... 55 3-8MVvs.LogPeriodforallfundamental-modeSXPheinGGCs .......... 59 3-9Period-luminosityrelationsforavarietyofinstabilitystrippulsators ....... 62 3-10Periodogramsandlightcurvesfor5variableBSSinNGC6101 ......... 65 3-11Periodogramsandlightcurvesfortheother5variableBSSinNGC6101 ... 66 3-12CMDofNGC6101(top)withdetectedvariables ................. 67 3-13Periodogramandlightcurveforthe2ndfrequencyofbss205 .......... 68 3-14SameasforFig. 3-10 ,butforvariablesinNGC6352. .............. 69 3-15SameasFig. 3-12 ,butforNGC6352. ....................... 70 3-16SameasFig. 3-12 ,butforNGC5986. ....................... 72 3-17SameasforFig. 3-10 ,butforvariablesinNGC5986. .............. 73 3-18CMDofallGGCSXPhe ............................... 73 3-19Asabove,butshownrelativetothehostclusterturnoff .............. 74 4-1CompletenessfromACSarticialstartestsvs.longexposures ......... 81 7 PAGE 8 .. 82 4-3BSSluminosityfunctions .............................. 85 4-4BSSandSXPheluminosityfunctions ....................... 89 8 PAGE 9 9 PAGE 10 10 PAGE 11 11 PAGE 12 12 PAGE 13 13 PAGE 14 14 PAGE 15 15 PAGE 16 16 PAGE 17 17 PAGE 18 18 PAGE 19 19 PAGE 20 1. UseSXPhepulsationperiodsandamplitudestodeterminetheirformationmechanism,andcorrelatethiswithclusterproperties.Forexample,doesthepresenceandlocationofabinaryorcollisionallyformedBSSmakesenseinlightofthepropertiesofitshostcluster? 2. IfbinaryBSSarediscovered,investigatethesequestionsaswell. 3. UseSXPheperiodsandmagnitudestoinvestigatetheSXPheperiod-luminosityrelation.Theoryindicatesthatitcouldbeausefuldistanceindicator,butpracticaltestsofthisconceptaresparse,especiallyatthehigh-metallicityend. 20 PAGE 21 AugmenttheexistingSXPhecatalogwithSXPhediscoveredsinceitspublicationaswellasournewdiscoveries,andexplorecorrelationsbetweenvariabilityproperties(period,amplitude,magnitude)andhostclusterproperties(metallicity,HBmorphology,concentration,integratedmagnitude).ComparetheSXPheluminosityfunctiontopredictedcollisionalandbinaryBSSluminosityfunctions. 5. UsetheACSdatatocorrelateobservedBSSluminosityfunctionswithclusterproperties.Usingalessdeepandprecisedataset,Piottoetal.(2004)foundthattheluminosityfunctionsoftheBSSinthemostluminous,massiveclustershaveabrighterpeakandmoreextendedtail-doesourdatasupportorrefutethisclaim? 6. AswiththeSXPhe,compareobservedBSSluminosityfunctionstopredictedonesforbinaryvs.collisionalBSS.Arethereanytrendswithobservableclusterproperties?WeareespeciallyinterestedintheintegratedclustermagnitudesinceMiloneetal.(2008)foundafairlytightcorrelationbetweenthisquantityandclusterbinaryfractioninthesensethattheleastluminousclustershavethehighestbinaryfraction.Whatdotheobservedluminosityfunctionstellusaboutobservedbinaryfractionvs.BSSoriginatingasbinaries? 7. ComparetheobservedSXPheluminosityfunctiontotheobservedBSSluminosityfunctionsfromtheACSdata.IsitlikelythatmostBSSareSXPheandtheyhaveremainedundetectedbecausetheirpulsationalamplitudesareextremelysmall? 21 PAGE 22 1. Theyallhavesignicant(N>10)BSSpopulationsobservablewitha1m-classtelescope.ThiscriterionisbasedonthephotometryofRosenberg(1999),whoseeldsofviewweresignicantlysmallerthanours,andBrocatoetal.(1996),bothofwhomused0.9mtelescopestoconstructtheirCMDs.WithoutknowledgeofasizeableBSSpopulation,notonlyisthelikelihoodofdetectingvariablesamongthemsmaller,butconclusionsbasedonthefractionofvariablesaresuretobehamperedbysmallnumberstatistics. 2. TheyhavenotpreviouslybeensearchedforvariablesdowntothemagnituderangeoftheirBSS(belowtheHB).WehaveintentionallyincludedtwoclusterswhichhavesizeableknownvariableBSSpopulations,M53(Jeonetal.2003)andM55(Pychetal.2001).Theseclusterswillserveasgaugesofourdetectioncapability,andwillbediscussedfurtherinthecontextofcompleteness. 3. Theycoverabroadrangeofparameters,includingmetallicity,concentration,HBmorphology,locationinthegalaxy,andintegratedmagnitude.ThepositionalpropertiesofourtargetclustersfromtheHarris(1996,2003revision,hereafterH96)catalogarelistedinTable2-1,includingtheirrightascensionanddeclination(J2000.0)andheliocentricandgalactocentricdistancesinkpc.InTable2-2,welisttheirobservationalproperties,namelyreddening,distancemodulus,integratedabsoluteVmagnitude,horizontalbranchtype,metallicity,andcentralconcentration. Table2-1. TargetClusterPositionalProperties NGCRADecRSunRGC 22 PAGE 23 TargetClusterObservationalProperties NGCE(B-V)(m-M)VMV(tot)HBType[Fe/H]c 48330.315.07-8.160.93-1.801.250240.016.31-8.700.81-1.991.859860.315.96-8.440.97-1.581.261010.116.07-6.910.84-1.820.861710.315.06-7.13-0.73-1.041.563520.214.44-6.48-1.00-0.701.165840.115.95-7.68-0.15-1.491.268090.113.87-7.550.87-1.810.8 23 PAGE 24 Table2-3. Observations ClusterSiteTimespan(days)N(obs) NGC4833CTIO7.0831NGC5024(M53)KPNO7.0853NGC5986CTIO3.0820NGC6101CTIO5.0643NGC6171KPNO33.0541NGC6352CTIO7.0741NGC6584KPNO5.1333NGC6809(M55)KPNO1.1851 24 PAGE 25 25 PAGE 26 26 PAGE 27 2-1 : 1. ItmustberedderthantheZAMS,whichisindicatedbytheblacklinebluewwardoftheclusterducialsequenceinFig. 2-1 2. Itmustbebluerthanthe3linetotheblueofthemainsequence,indicated(alongwiththe3lineredwardofthemainsequence)asaredlineinFig. 2-1 3. Itmustbefainterthanabrightmagnitudecutoff,settoexcludehorizontalbranchstars,shownastheupperhorizontallineinFig. 2-1 4. ItmustbebrighterthantheintersectionoftheZAMSandtheline3bluerthantheclusterducialsequence(theisochrone).ThismagnitudeisindicatedbythelowerhorizontallineinFig. 2-1 5. Itmustbebluerthanalinewhichparallelsthemainsequenceextensionandlies0.2magredderthantheextensionin(B-V).ThislineisshownasadiagonalstraightblacklineinFig. 2-1 .ThisisasimilarcuttothatmadeintheACSdata,andthevalueof0.2isbasedonthefactthataparallelline0.2magbluerthanthemainsequenceextensioncoincidesapproximatelywiththeZAMS,andinourcase,theparallellineontheredsideoftheMSextensionservesprimarilytoexcludeeldstarswhichhavesimilarcolorstothemainsequenceturnoffandsubgiantbranchbutareseveralmagnitudesbrighter.ThesecriteriahaveintentionallybeendevisedtobesomewhatconservativeinthesensethatsomestarswhicharenottrueBSSmaybeincluded.However,forthesakeofavariabilitysearch,thisstrategyisbetterthanmakingoverlyrigorousCMDcutsto 27 PAGE 28 CMDofM55illustratingourBSSselectionprocess.ThelinesshownherewhichdemarcatetheBSSregionaredescribedinthetext.AllBSSmeetingourselectioncriteriaareplottedingreen,andallknownvariableBSS(fromPychetal.2001)areoverplottedasbluediamonds. 28 PAGE 29 29 PAGE 30 2-2 theANOVApowerspectraofseveralvariableswiththeLSpowerspectraoverplottedinred.Itisclearthat,inadditiontoitssuperiorabilitytodetectatrueperiod,ANOVAyieldsmuchbetterfrequencyresolutionforagivennumberofdatapoints,aswellashighersignicancevaluesforthetrueperiod.HavingdescribedourtechniquesforselectingBSSandsearchingthemforvariability,wewillnowdescribethetestsofthesetechniqueswhichwehaveconductedtoquantifyourabilitytodetectvariableBSS. 30 PAGE 31 ANOVAperiodogramsfor8ofthevariableswhichwedetectedinNGC6101.Foreachperiodogram,theLomb-Scarglepowerspectrum(asformulatedforunevenlysampleddatabyHorne&Baliunas1986)isshowninredforcomparison.TheperiodsandperioderrorsresultingfromANOVAaswellasthosefromLomb-Scarglearegivenatthetopofeachplotforcomparison. 31 PAGE 32 2-3 .Next,theimageswerereducedidenticallytoourscienceimages:PSFsweret,aperturecorrectionswereapplied,andeach 32 PAGE 33 2-3 .WeplottheCMDofNGC6101inFig. 2-3 ,withtheinputandoutputmagnitudesandcolorsofthearticialstarsoverplotted.Wecanseefromtheinputandoutputmagnitudesofthesubgiantsthatthewidthoftheobservedclustersequencesisduesolelytophotometricerror,reinforcingouruseofthephotometricerrorasacolorcriterion(albeitaconservativeone)toseparatetrueBSSfromthemainsequenceandsubgiantbranch.Ourgoalwastoquantifythecompletenessallthewaydowntotheturnoff,toensurethatstarsfainterthantheBSSregionintheCMDweren'tbeingrecoveredwithmagnitudeswhichcausedthemtomasqueradeasBSS.Tothisend,wehaveincludedinputstarsfainterthanouractualfaintBSSmagnitudecutoff.However,oftheinputstarswhichdomeetourBSSselectioncriteria,over95%ofthemwererecoveredwithoutputcolorsandmagnitudesalsomeetingourBSSselectioncriteria.Wenowwishtoexaminethecompletenessasafunctionofmagnitudeaswellascrowding,sowedividedthearticialstarsinto4concentricradialannulifromthecenterofthecluster,similartothemethodemployedwiththearticialstartestsintheACSdata.InFig. 2-4 ,weplotcompletenessasafunctionofmagnitudefortheBSS,thesubgiants,andbothtypesofstarstogether.Wecanseethat,towithintheerrors,thecompletenessdoesnotdependstronglyontheB-Vcolorsofthestars.ThismeansthatwecanapplyourcompletenessforthisclustertootherclustersinwhichtheBSSregionoftheCMDfallsatdifferentobservedcolors,dueprimarilytodifferencesinmetallicityandreddeningbetweenourvarioustargetclusters(althoughtheyallhaveE(B-V)<0.4).Withthisresultinhand,inFig. 2-5 33 PAGE 34 CMDofNGC6101showingallrealstarsinsidetheclustertidalradius(blackpoints),inputarticialstars(red),andtheirrecoveredcolorsandmagnitudes(blue). 34 PAGE 35 ThecompletenessofstarsinNGC6101overthemagnituderangeoccupiedbyBSS,determinedbyaveragingtheresultsof10completenesstests,eachofwhichcontains2500articialstars.Tocheckforacorrelationbetweencolorandcompleteness,wehaveplottedtheBSSinblue,thesubgiantsinred,andbothtogetherinblack. weshowcompletenessasafunctionofmagnitudefortheBSSonly,dividedintoradialbinsfromtheclustercentertoexaminetheeffectsofcrowding.Basedonourradialcutsforthearticialstars,onecanseeinFig. 2-5 that,althoughthestarsfarfromthecoretendtobemoresuccessfullyrecoveredingeneral,thefaintendoftheBSSmagnitudedistributionisnotpreferentiallyaffectedbycrowdingatsmallradiifromthecore.Towithintheerrors,ourphotometryovertheentiremagnituderangeoftheBSSisatleast80%complete,andthisvalueissignicantlyhigherforstarswhichliebeyondafewcoreradii.Also,thesenumbersshouldbeviewedaslowerlimitsontheactualcompletenessinourtargetclusterssinceNGC6101wasintentionallychosenbecauseithasthefaintestBSSandthereforeisthemostsusceptibletoscattercausedbyphotometricerrors. 35 PAGE 36 CompletenessofthearticialBSS,witheachoffourradialbinschosenbasedonthecoreradiusrCplottedinadifferentcolor.Forclarity,errorbarsareonlyshownfortheinnermost(r<1.5rC)andoutermost(r>4.5rC)radialbins. 2.6.2.1VariabilityCriteriaOncewecanidentifyastarasabluestraggler,wemustthendeterminehowtoassesswhetheritisarealvariableornot.Thetime-domainlightcurves(fromISISandfromDAOPHOT)weresearchedforperiodicityusingANOVA,overtheperiodrange0.017-0.5d.ObservedSXPheperiodsrangefrom0.017to0.4days,andthisperiodrangeisingoodagreementwithwhatisastrophysicallyexpectedbasedonthetworecentsetsofpulsationalSXPhemodelsofSantolamazzaetal.(2001,hereafterS01)andTempletonetal.(2002,hereafterT02).ArmedwithourANOVApowerspectra,wecalculatedthesignal-to-noiseofthehighestpeakinthepowerspectrumforeachBSS,andonlythosestarsforwhichthehighestpeakhadS/N>5wereconsideredfurtheras 36 PAGE 37 37 PAGE 38 38 PAGE 39 39 PAGE 40 3.1.1BinaryDetectionProbability:SimulationsHavingfailedtodetectanyeclipsingbinariesinoursample,wecanusethisinformationtoconstrainthefrequencyofclosebinaryBSSinourtargetclusters.Therststepinthisprocessistocalculated,theprobabilityofdetectinganeclipsingbinarysystemasafunctionofitsperiod.Tothisend,wehaveusedthebinarylightcurvemodelingandttingprogramNightfall1togeneratesyntheticlightcurvesofbinarysystemswithvaryinginclinationsandperiods(orseparations,foraxedmass).Becausethetotaltimespanoftheobservationsforagiventargetclusterisgenerallyseveraldays,werestrictouranalysistosystemswithperiodsof10daysorless,andwewilldiscusstheobservedperioddistributionofbinaryBSSbelowinthecontextofoursimulationresults.Wealsoassumedmassesof0.8MSunforthecomponents,correspondingapproximatelytotheturnoffmassinourtargetclusters.Weperformedthesimulationsseparatelyforeachtargetclustersincetheexacttimesamplingoftheobservationsisuniquetoeachcluster.Syntheticlightcurvesweregeneratedforagridofinclinationanglesfrom0to90andperiodsfrom0.1to10days.Foreachperiod,lightcurvesforeachinclinationwereshiftedinphaseinstepsof0.05throughonefullphase,resultingin100modelsperinclinationperperiodvalue(ourperiodsweresampledinintervalsof0.05days).Thesyntheticlightcurvewasthensampledwiththeobservingcadenceoftheactualdatafortheclusterinquestion.Toaccountforphotometricerror,thesedatapointsonthesyntheticlightcurvewerethenoffsetbyarandomamountdrawnfromaGaussiandistributioncenteredonthemean 40 PAGE 41 3-1 ,wheretheresultforeachindividualclusterisplottedasthinlines,andthemeanoftheseindividualfunctionsacrossallclustersisplottedasathickline.Asaconsequenceoftheobservingcadencesusedformostoftheclusters,featurescorrespondingtointegernumbersofdays(mostnotably2days)arevisibleinthisplot. Figure3-1. Thedetectionprobabilitydasafunctionofperiod,shownasathinlineforeachofourtargetclusters,andthethicklinerepresentsthemeanacrossalltargetclusters. 41 PAGE 42 3-2 .Clearly,itwillhaveamaximumatf=0,andwhiletheexactshapeofthisfunctiondependsontheassumedperioddistribution,theresultregardingthefractionofbinaryBSSinourtargetclustersisnotparticularlysensitivetothetypeofperioddistribution(at,truncatedGaussian,etc.)whichweassumesincetheweightedmeandisnotverysensitivetotheassumedperioddistribution.BasedonthebinaryfractionwhichcorrespondstotheprobabilityP=0.05,wehavefoundthatthe95%condencelevelupperlimitonthebinaryfractionis15%orlessforallofourtargetclustersexceptone.ThisisconsistentwiththestudyofMiloneetal.(2008),whofoundananticorrelationbetweenbinaryfractionandtotalclusterluminositysuchthatallbutthefaintest,mostsparseGGCshavebinaryfractionsofunder20%,albeitwithsomedegreeofscatter.Theoneclusterforwhichthe95%condencelevelupperlimitonthebinaryfractionismuchhigher,at56%,isNGC4833.Thisislikelytobeanartifactproducedbyacombinationofthefollowingtwoeffects:Firstly,NGC4833hasasmallnumberofobservationsandashorttimebaselinecomparedtoourothertargetclusters.Secondly,ithasamuchsmallernumberofBSSaccordingtoourCMD-basedselectioncriteria,whichistheprimaryfactoraffectingtheextenttowhichwecanconstrainthebinaryfractionusingEq.3.1. 42 PAGE 43 TheprobabilityPofdetectingzerobinariesasafunctionofbinaryfraction.TheresultingPforeachclusterisshownasaseparateline.AscanbeseenbythebinaryfractioncorrespondingtoP=0.05,alloftheclustersexceptonehavea95%condenceupperlimitontheirbinaryfractionsof15%orless,ingoodagreementwithpreviousestimatesofGGCbinaryfractions. 43 PAGE 44 44 PAGE 45 45 PAGE 46 Table3-1. NewSXPheVariables ClusterStarPeriodAVhBi-hVihViFAPComments NGC5986bss10.05860.040.65419.2380.000Fmode?NGC6101bss690.05310.60.26319.0470.000FmodeNGC6101bss1200.04560.100.37618.8060.0001OTmodeNGC6101bss1760.04690.30.35419.0620.010FmodeNGC6101bss2010.05470.20.46819.1400.036FmodeNGC6101bss1280.0422N/A0.28519.3520.001FmodeNGC6101bss1400.0783N/A0.47519.0090.020g-mode?NGC6101bss1680.0251N/A0.20717.9940.014p-mode?NGC6101bss1920.0335N/A0.23518.0750.000p-mode?NGC6101bss2050.0456N/A0.32919.2430.003FmodeNGC6101bss2200.0382N/A0.31319.0650.0021OTmodeNGC6352bss1440.17220.020.80018.4420.001prob.eldstarNGC6352bss1830.17970.150.71817.3750.000prob.eldstar Ascanbeseen,wehavefailedtodetectanyvariablesin3ofourpreviouslyunsearchedtargetclusters.Basedontheaforementionedcompletenesstests,the 46 PAGE 47 3.3.1TheUpdatedSXPheCatalogThedetectionandcharacterizationofSXPhehasbecomevastlymorefeasibleinrecentyearsduetotheadventofhigh-resolutiondigitaldetectorsaswellasmoreadvanceddatareductionandvariablesearchtechniquessuchasPSFttingandimagesubtraction.Infact,25additionalSXPhein4clustershavebeendiscoveredbyotherauthorsjustsincewebeganthisprojectseveralyearsago.Forthisreason,ourrststepininvestigatingthecurrentlyknownGGCSXPhepopulationwastoupdatethemostrecentcatalogofSXPheinGGCs,publishedbyRodriguez&Lopez-Gonzalez(2000),withalloftheSXPheinGGCsdiscoveredsinceitspublication.TheupdatedtotalnumberofknownSXPheinGGCsisnow215,sothatwehaveupdatedtheoriginalcatalogof122starswith93additionalSXPhewithknownperiodsandamplitudesdiscoveredinthelastnineyears.Next,armedwithacomplete-to-datetableofpropertiesofSXPheinGGCs,wehavesearchedforcorrelationswithintheirvariabilityproperties,includingnumber,fraction(percentageofBSSwhichareSXPhe),period,amplitude,andmeanmagnitude(relativetotheclusterturnoff),andimportantly,wehavesearchedforcorrelationsbetweenthesepropertiesandpropertiesoftheirhostclusters,includingmetallicity,HBmorphology,numberofBSS,centralconcentration,andGalactocentricdistance,andwenowdiscussourndings. 47 PAGE 48 Amplitudevs.PeriodforallSXPheinGGCswithknownV-bandperiodsandamplitudes.Forthe4clusterswiththelargestnumberofSXPhe,theirSXPhehavebeenplottedinadifferentcolorforeachclustertoillustratetheuniformityoftheSXPheperiod-amplitudedistributionamongGGCs.Theperiodsusedherehavebeenfundamentalizedsothatknownrst-andsecond-overtoneradialpulsatorshavehadtheirperiodscorrectedtothefundamental-modeperiodusingwell-constrainedperiodratiosfromrecentmodels. 3-3 fortheentirecatalogofallSXPheinGGCs.Inaddition,wehave 48 PAGE 49 PeriodandAmplitudedistributionsofSXPheinGGCsnormalizedtotheirtotalnumber.ThefourclusterswiththemostSXPheareshownindividuallyindifferentcolors. plottedtheSXPheofdifferenthostclustersindifferentcolorsforthe4GGCswiththelargestSXPhepopulations.Fig. 3-3 illustratesthatSXPheindifferentclustersdistributethemselvesinaremarkablysimilarwayintheperiod-amplitudediagram.Tofurtherillustratethispoint,weshowinFig. 3-4 thenormalizedperiodandamplitudedistributionsforthe4mostpopulous(inSXPhe)clustersindividuallyaswellasthemeanforalloftheSXPheinGGCs.WecanseefromFig. 3-4 that,forallGGCsharboringSXPhe,eventhosewithasmalltotalnumberofSXPhe,averysmallfractionofSXPhehavelarge(AV>0.2)amplitudesandlong(P>0.07d)periods,andthemajorityofSXPheareconcentrated 49 PAGE 50 50 PAGE 51 3-5 ,whereweusemagnitudefromthemain-seqenceturnoffasourluminosityindicatortoavoidsystematicerrorscausedbyuncertaintiesindistanceestimates.BasedontheobservedSXPheLF,SXPhewhichliemorethan1.6magabovetheturnoffarerare.Infact,inthisrespect,Fig. 3-5 bearsadistinctsimilaritytotheBSSLFinFig.4ofSarajedini(1993)intworespects:Firstly,thedropoffatthefaintendofbothLFsisrenderedlesssharpbyaselectioneffect.Intheircase,itwasduetothesimilarityincolorbetweenBSSandmainsequencestarsattheturnoff.Inourcase,itisduetothebroadmetallicityrangeofclusterswithSXPhecausingsomespreadinestimatesof 51 PAGE 52 LuminosityfunctionofallobservedSXPheinGGCs,normalizedtotheirtotalnumberandexpressedinunitsofVmagnitudefromtheturnoffoftheirhostcluster. V(SX)-V(TO)betweenclusters.Specically,clustersoverabroadmetallicityrangehavevaryingCMDmorphologiesaroundtheturnoffandthesubgiantbranch,someofwhichallowamorepreciseestimateofV(TO)thanothers.ThesecondsimilarityisthedropoffonthebrightsideoftheLFpeak,whichinbothcasesoccurs1.6magbrighterthantheturnoff.Sarajedini(1993)pointsoutthatthismagnitudecorrespondstoamasstwicethetypicalGGCturnoffmass,fairlyindependentlyofchemicalcomposition.Inourcase,theSXPheLFimpliesthatSXPhepulsatingwithobservableamplitudes(AV>0.01)haverelativelylowmassesandluminosities,andthebrighttailseenontheSXPheLFcouldlikelybeexplainedby3-bodyinteractionsbetweenbinariesandsinglestarsandsubsequentevolution.WewillrevisittheSXPheLFinthecontextoftheBSSLFsfromtheACSsurveyinChapter3. 52 PAGE 53 3-6 representsafractionofN(SX)/N(BSS)=0.5,andthefactthatfourclusterslieexactlyonthislineisanartifactoftheestimationofN(BSS)tobeapproximatelytwiceN(SX).ItisclearthatinallGGCs,SXPhepulsationsareobservedinunderhalfoftheBSS,andwerevisitthispointinthecontextoftheSXPheluminosityfunctionlater.WithregardtocorrelationsbetweenthenumberofSXPheandhostclusterproperties,wefoundthatneitherthefractionnorthetotalnumberofobservedSXPhecorrelateswithanyoftheaforementionedclusterproperties.Next,weinvestigatedwhetherthemerepresenceofSXPhecorrelateswithanyclusterproperties.Todoso,weplottednormalizedhistogramsofallGGCsfromtheH96catalogwithrespecttoeach 53 PAGE 54 ThenumberofBSSvs.thenumberofSXPheinallGGCswhichhaveknownSXPhe.Asdiscussedinthetext,thenumberofBSSwasestimatedfromthestudyreportingthedetectionoftheSXPhe.ThedottedlinerepresentsafractionofN(SX)/N(BSS)=0.5. property,andcomparedthemwithnormalizedhistogramsofonlytheclusterscontainingSXPhe.ThiscomparisonisshowninFig. 3-7 WiththecaveatthatthenumberofclusterswithknownSXPheisstillfairlysmallsothatthePoissonianerrorbarsarerelativelylarge,weseeaninterestingresult,whichisthatthedistributionofclustersharboringSXPheisverysimilartothedistributionofalltheclusterswithrespecttoagivenproperty,suchasmetallicityorHBmorphology.Thisimpliesthat,indeed,whetherornotaclusterhasSXPheisrandomratherthanbeinginuencedbyanyspecicpropertiesofthecluster.TheonlypropertiesforwhichthisisnotthecaseareheliocentricandGalactocentricdistance,duetoselectioneffects:BecauseSXPhearelow-amplitudepulsators,theyaremosteasilydetectedintheclosestclusters,thosewiththesameGalactocentricdistanceastheMilkyWay.ClusterswithverysmallGalactocentricdistancesaredifculttosurveyforSXPhesincetheylieinthedirectionofthebulge,whereeldstarcontaminationandreddeningcanhinderselectionofBSS(orclustermembersingeneral)andphotometricprecisionrespectively. 54 PAGE 55 NormalizedhistogramsofallGGCsfromH96vs.6differentclusterproperties.NormalizedhistogramsofonlytheclusterscontainingSXPheareoverplottedinred,alongwiththecorrespondingerrorbars. Predictably,thiswasthecasetosomeextentwithourtargetclustersNGC5986andNGC6352,andisoneoftheprimaryreasonsformakingourCMD-basedBSSselectionprocessoverlyinclusiveratherthanoverlyexclusive. 55 PAGE 56 56 PAGE 57 57 PAGE 58 3-8 ,alongwiththePLRweobtainedfromalinearleast-squarest,andweoverplotthePLRofJeonetal.(2004)forcomparison.Inaddition,weshowthefundamentalblueedge(FBE)fromT02aswellasOlechetal.(2005).TheFBEisthebrightmagnitudelimitasafunctionofperiodforagivenradialpulsationmode 58 PAGE 59 MVvs.LogPeriodforallfundamental-modeSXPheinGGCs.OurPLR,whichisalinearttothesedata,isshownasasolidline.Forcomparison,theuniversalempiricalPLRofJeonetal.(2004)isshownasadashedline,thetheoreticalPLRofT02asareddottedline,theFBEofT02asabluedottedline,andtheFBEofOlechetal.(2005)asabluedot-dashedline.TypicaluncertaintiesonindividualMVvaluesare0.1mag. (inthiscasefundamental)orinthecolor-magnitudeplane,thebluelimitatagivenmagnitude.TheFBEservesastheprincipaldiscriminantbetweenmodes,so,forexample,ifastarhasaperiodshorterthantheFBE(oracolorbluerthantheFBE,equivalenttoatemperaturehotterthantheFBE)foritsmagnitude,itcannotbeafundamentalmodepulsator.WehavealreadymentionedthezeropointoffsetinthePLRofT02,anditisevidentthattheT02FBE(andthatofS01sincetheyarenearlyidentical)isalsosystematicallyabout0.2magfainterthanthatofOlechetal.(2005),althoughforhigher-orderradial 59 PAGE 60 3-8 ,is: 60 PAGE 61 3-9 .TheclassicalCepheidsareGalacticeldCepheidsfromFouqueetal.(2007),theTypeIICepheidsarefromPritzletal.(2003),theRRLyraearemeanvaluesfor30GGCsfromBonoetal.(2007),andtheScutisarefundamentalmodeeldstarsfromMcNamara(1997).TheresultwithrespecttotheSXPheisquiteinteresting,whichisthat,whilethemetal-poorandmetal-richrelationsintersectintheregionofthediagramoccupiedbytheSXPhe,thePLRwhichwederivefromtheSXPheagreesremarkablywellwiththatoftheGalacticCepheids,whicharemetalrich.Furthermore, 61 PAGE 62 Period-LuminosityrelationsforourfundamentalmodeSXPhe(Blackpoints,solidline)comparedtotheJeon(2004)SXPhePLR(dottedline),classicalCepheids(red),eldScuti(green),TypeIICepheids(blue)andGGCRRLyrae(blackcrosses). nometallicitycutinourSXPhepopulationwouldproduceaslopeconsistentwiththemetal-poorTypeIICepheidrelation,duetotheaforementionedlackofarelationshipbetweenthemetallicityandtheindividual(orclustermean)residualsfromourPLR.OneinterestingpossibilityisthatthemetallicitiesofatleastsomeofourSXPhe,becauseofevolutionaryprocessesresultinginthecreationofBSS,arenotidenticaltotheirhostclustermetallicitiesaswehaveassumed.However,suchasystematicenrichmentofallofthefundamentalmodeSXPheseemsunlikely,althoughfurtherstudyofindividualpulsatorsaswellasBSSformationandevolutionisclearlyrequired.HavingdiscussedtheSXPhePLRandFBEinlightofrecentmodelsaswellasobservations,wewillnowapplyourPLRasadiagnostictoolinordertocharacterizethenewvariableswhichwehavediscovered. 62 PAGE 63 63 PAGE 64 3-10 and 3-11 ,weshowtheANOVApowerspectraandphasedlightcurvesofallofthedetectedSXPheinNGC6101.Foreachvariable,theleftplotshowsthepowerspectrumandgivestheperiod,itserror,andthesignal-to-noiseofthepeakinthepowerspectrumcorrespondingtothedetectedperiod.Therightplotshowsthelightcurve,phasedwiththatperiod,andgivesthenumberofthestar(assignedarbitrarilybasedonverticalpositiononthedetector),theperiod(again),andthefalsealarmprobability(FAP)correspondingtothatperiod.InFig. 3-12 ,weshowourCMDoftheeldcontainingNGC6101,withthelocationsoftheSXPheindicatedbydiamonds.Belowthat,weshowtheperiod-magnitudediagram,withourvariablesagainplottedasdiamonds.NGC6101istheonlyoneofourtargetclusterswhichwasfoundtoharbormultiplevariablespulsatinginthefundamentalmodeandtherstovertonemode.Thevefundamentalmodevariablesarebss69,128,176,201,and205.BasedontheirpositionsontheCMD,theyallhavemassesintherange0.85-0.95MSun,andthesemassesareconsistentwiththeirpositiononthePLDaccordingtoFig.5ofOlechetal.(2005).Itisunlikelythatbss140isalsoafundamentalmodepulsatoraswell:ItslocationontheCMDandthePLDarebothconsistentwithamassof0.9MSunanditsperiodiswelldetermined.Thisstarmaybeexhibitingag-mode,whichwouldbe 64 PAGE 65 Periodograms(left)andphasedlightcurves(right)forveofthedetectedvariableBSSinNGC6101. 65 PAGE 66 Periodograms(left)andphasedlightcurves(right)fortheremainingvevariableBSSinNGC6101. 66 PAGE 67 CMDofNGC6101(top)withdetectedvariablesoverplottedasdiamonds.EvolutionarytracksfromDotteretal.(2008)areshownforthetwometallicities(redandblue)whichbrackettheclustervalue,andthethreeparallellinesshowtheF,1OTand2OTblueedgesfromOlechetal.(2005).InthePLD(bottom),ourvariablesareagainplottedasdiamondsandcomparedwithSXPhePLRsandtherstthreemodeblueedges(BE). 67 PAGE 68 Powerspectrumandphasedlightcurveforasecondmodedetectedinbss205inNGC6101,shownafterprewhitening. especiallylikelysinceitstemperatureisnotespeciallyhigh-wendTe7000-7200Kbasedonthesingle-starevolutionarytracks.Ofthefourremainingvariables,bss120andbss220areprobablyradialrstovertonepulsatorsastheycanbeseendeningasecondsequenceparalleltothefundamentalmodeandoffsetbyanamountcorrespondingtothecorrectperiodratiooftherstovertonetothefundamentalmode.Inthiscase,theybothhavemassesof0.95MSun,inexcellentagreementwithFig.5ofOlechetal.(2005).Oneofthefundamentalmodepulsators,bss205,istheonlystarinoursamplefoundtobeexhibitinganysignicantadditionalperiodsafterprewhitening.Thisstarwasfoundtohaveasecondperiod,andthecorrespondingperiodogramandphasedlightcurve(shownafterprewhiteningoftheprimaryperiod)areshowninFig. 3-13 .AlthoughthepositionofthesecondperiodonthePLDappearsapproximatelyconsistentwiththe1OTsequence,theperiodratiois0.700.01,toolowfortheshorterpulsationtoberadialsinceallrecentmodels(S01,T02,Olechetal.2005)ndthattheperiodratioof1OT/Fisatleast0.76,andhighermodeshaveperiodratioscloserto1.Thisperiodisprobablyindicativeofanon-radialmode,extremelycommoninSXPhe,especiallyincloseproximitytoradialovertonemodesinfrequencyspace(Olechetal.2005),inthiscasethe1OTradialmode.Thetworemainingstarshaveveryshortperiodsandveryhighluminosities,andtheirlocationsontheCMDimplymassesof1.1-1.2MSun.Theyarenotpulsatinginhigh 68 PAGE 69 SameasforFig. 3-10 ,butforvariablesinNGC6352. orderradialmodesbecausethesemodeshaveperiodratiostothefundamentalmodeofclosetoone,sotheirperiodswouldbelonger.Theprobableexplanationisthattheyareexhibitinghigh-orderp-modes.Thisisnotuncommoninluminous,short-periodSXPheandhasbeenseeninseveralotherGGCs,includingtheSXPheV221andothersin!CenfromOlechetal.(2005)aswellastwoSXPheinNGC3201seeninthePLDofMazuretal.(2003). 3-14 ,andtheirlocationsontheCMDandperiod-magnitudediagramareshowninFig. 3-15 .Bothofthesevariablesarelikelytooredtolieinsidetheinstabilitystripatthedistanceofthiscluster.Thepositionsofthestarsdon'tprovidemuchofaclue-theyarebothoutsidetheclusterhalf-massradiusbutwellinsidethetidalradius.MostlikelytheyareeldScuti,whichmakessensegiventhestellardensityofthebulgeeldsuperimposedonourimagesofNGC6352,andtheymadeitintotheBSSsampleasaconsequenceofourrelativelyrelaxedCMD-basedBSSselectioncriteria. 69 PAGE 70 SameasFig. 3-12 ,butforNGC6352. 70 PAGE 71 3-17 and 3-16 .AlthoughitisonthefaintborderofthefundamentalmodePLRsandclosetotheredborderoftheinstabilitystrip,theCMD,thePLD,andthemodelsofOlechetal.(2005)allconsistentlypredictamassof0.85-0.9MSun.This,incombinationwiththelargeuncertaintyinthedistancemodulusofNGC5986,suggeststhatthisstarislikelyafundamentalradialmodeSXPhe. 3-18 .acolor-magnitudediagramshowingallSXPheinGGCswithknownB-VcolorsandVmagnitudes,correctedfordistanceandreddeningusingtheclusterdistancemoduliandreddeningvaluesfromtheH96catalog.Inaddition,wehaveoverplottedisochronesandzero-agemainsequences(ZAMS)fromtheDartmouthstellarevolutiondatabase(Dotteretal.2008)for2setsofages(8and14Gyr)andmetallicities([Fe/H]=-0.5and-2.5)whichbrackettheageandmetallicityrangeofGGCs.Todemarcatethelocationoftheinstabilitystrip,wehavealsooverplottedtheblueedgesfortherstthreepulsationmodesasintheprevioussectiontoindicatetheapproximatelocationoftheblueedgeoftheinstabilitystrip.MultiplestudiesofSXPheandScutipulsatorshaveconrmedthat,aswithRRLyraes,thewidthoftheinstabilitystripis0.3magin(B-V),correspondingto200-300Kintemperature(e.g.McNamaraetal.1997,Porettietal.2008).Basedonthisgurealone,itappearstobethecasethatSXPhearenotalwaysBSSandviceversadepending 71 PAGE 72 SameasFig. 3-12 ,butforNGC5986. 72 PAGE 73 SameasforFig. 3-10 ,butforvariablesinNGC5986. Figure3-18. CMDshowingallGGCSXPhewithknownVmagnitudesandB-Vcolors.Theblueandredlinesrepresentisochroneswith[Fe/H]=-2.5and[Fe/H]=-0.5respectivelyandeachpairofisochronescorrespondstoagesof8and14Gyr.TheZAMScorrespondingtothetwo[Fe/H]valuesisshownalso.ThethreeparallellinesaretherstthreeradialmodeFBEsasintheprevioussection,showntodemarcatetheblueedgeoftheinstabilitystrip. 73 PAGE 74 Asabove,butshowingcolorandmagnituderelativetothehostclusterturnoff.TheZAMSareshownasintheupperplot,andthedottedlinesareusedtoindicatethelocationofthebluestragglerregion. ontheageandmetallicityofthepopulationinquestion.Forexample,ifapopulationismetal-poorandyoung,asignicantportionoftheuppermainsequencepassesthroughtheinstabilitystripintheluminosityrangeofSXPhe.Why,then,haveallSXPheinGGCsbeenfoundtobeBSSratherthanmainsequencestarsneartheturnoff?Togainsomeinsightintothisquestion,wereplottedthecolorsandmagnitudesofalloftheGGCSXPhe,butthistimerelativetotheturnoffcolorandmagnitudeintheirhostclusters.ThisdiagramisshowninFig. 3-19 .Bearinginmindthatbothofthesevaluestypicallyhavesystematicerrorsofatleast0.1mag,asomewhatdifferentpictureemerges.Wendthat,intheclustersinwhichtheyarefound,allSXPheareprobablyBSS,meaningthattheyareallbluerandbrighterthantheturnoffoftheirhostclustersothatnonearesubgiantsormainsequencestars.Theprimaryreasonforthisisthat,intheMilkyWay,allofthemostmetal-poorclustersareold,andonlyatintermediatemetallicitiesdosome(butnotall)GGCshaveyoungerages(Marin-Franchetal.2009,Dotteretal.2010).Ifitisthecaseinotherstellarsystemsthatyounger 74 PAGE 75 3-19 alsoshedssomelightonwhytherearesofewSXPhefoundinmetal-richGGCs:TheBSSintheseclusters,eveniftheylieveryclosetotheZAMS,mustbeatleast0.5magbrighterthantheturnofftoliewithintherededgeoftheinstabilitystrip.WehaveseenthattheSXPheluminosityfunctionpeaksatabout0.6-0.8magabovetheturnoffdependingontheclusterintegratedmagnitude.Hence,formetal-richGGCs,themajorityofSXPhewouldneedtobesignicantlyredderthantheZAMSinordertofallwithintheredboundaryoftheinstabilitystrip.Inotherwords,althoughaphotometricselectionbiaswoulddictatethatthesebrighterBSS,whichlieintheinstabilitystrip,wouldbemoreeasilyfound,theyarealsointrinsicallymorerare,aswewillseeinChapter4.InChapter4,wewilldiscusstheluminosityfunctionsforallBSSinGGCsasdetectedusingtheACSGalacticGlobularClusterTreasurySurvey,andtheirimplicationsforBSSformationandevolutionaswellasSXPhe. 75 PAGE 76 76 PAGE 77 2-1 canbeusedasaschematicguidetoourselectionprocesshereaswell.Thetwoaforementionedminordifferencesbetweentheground-basedselectionprocessandthatusedhereareduerespectivelytotheincreasedphotometricprecisionoftheACSdataandtheuseofadifferentltercombination.Theselectioncriteriaare: 1. Theyarebrighterthantheintersectionofthemainsequenceextensionandthe5-sigmalineonthebluesideoftheducialsequence.Thismeansthatinsomecases,itispossibleforaBSStobeslightlyfainterthantheclusterturnoff,whichispredictedincertaincasesforprimordialbinaries(Chen&Han2008),andalsoallowsforphotometricerror. 2. BSSmustliewithin0.1magincolorfromthemainsequenceextension. 3. BSSmustbebluerthanthe5-sigmalineonthebluesideoftheducialsequence.ThepoweroftheACSdatasetisharnessedbyapplyingthismethodinasystematic,unbiased,andhomogenouswaytoalloftheACSclusters.However,as 77 PAGE 78 78 PAGE 79 79 PAGE 80 4-1 ,wehaveplottedtheactualtotalnumberofBSSineachcluster,selectedfromtheCMDmadefromlongandshortexposures,versusthenumberofBSSthatwecalculatebasedontheshortexposuresandourcompletenesscorrections.Wecanseethatformostoftheclusters,thecompletenessfunctionaccountsforthemissingBSStowithin10%.However,foronecluster,Terzan8,thearticialstartestsresultinacompletenesscorrectionwhichonlyaccountsforabouthalfofthemissingBSS,andwesuspectthatthisisacoincidenceoftheselectionoflongandshortexposuretimesinthiscluster:ThemagnituderangeoccupiedbytheBSSismorethantwomagnitudesbrighterthanthemagnitudewherethecompletenessfunctionbeginstodeclinesteadilybelow80%,evenfortheleastpopulatedouterradialbin.WehavechosentoexpressourluminosityfunctionsintermsofmagnitudesfromtheturnoffintheF606Wlter.ThischoiceisadvantageousnotonlybecauseitminimizessystematiceffectsfromclusterpropertiesduetodifferencesinCMDmorphology,buttheACSclustersallhaveturnoffmagnitudes,reddenings,anddistance 80 PAGE 81 Completenessfromthearticialstartestsvs.theactualfractionofBSSinthelongexposureswhicharemissingfromtheshortexposures. moduliwhichweredeterminedusingthesamemethodologyfromMarin-Franchetal.(2009).WenowanalyzetheresultingBSSluminosityfunctionsintheGGCstargetedbytheACSsurvey,andbeforeweconductedthisanalysis,severalclusterswererejected.ThreeclusterswererejectedbecausetheirCMDmorphologiesarecomplicatedenough(generallyduetothepresenceofmultiplestellarpopulations)thatselectionofaBSSregionisimpossible.TheseclustersareLynga7,M54,!CenandNGC2808.Inadditiontotheseclusters,wewereforcedtorejectveadditionalclustersduetoissueswiththeoriginalarticialstartestsfromwhichcompletenesscorrectionsarecalculated.TheseclustersareNGC6121,NGC6388,NGC6397,NGC6441,andNGC6624. 81 PAGE 82 CombinednormalizedluminosityfunctionforallofourACStargetclusters. 4-2 .ThemostnotablefeatureoftheBSSLFisthedownturnnearthemainsequenceturnoff.Inpreviousinvestigations,thiscouldbeconsideredaselectioneffectcausedbythedifcultyinseparatingBSSfromturnoffstarsatfaintermagnitudes,sincefainterBSSareredderincoloraswell.However,thephotometricprecisionoftheACSdatacombinedwiththehomogenityofourBSSselectionmethodhasallowedustoidentifyBSSreliablyevendowntotheturnoff,sointhecaseoftheACSdata,thedownturnintheBSSLFisunlikelytobeaselectioneffect.Therearetwopossibleexplanationsforthistheory,anditislikelythatbothplayarole.TherstexplanationisthatatleastsomeoftheBSSinGGCshaveenhancedamountsofhelium.Increasingtheamountofheliuminastarwithaxedmasswillcauseittobehotter(bluer)andmoreluminous 82 PAGE 83 83 PAGE 84 4-3 ,alongwithpredictedLFsfromthesimulationsofBailyn&Pinsonneault(1995).ThedifferencebetweentheLFsofthemoreandlessluminousclustersappearstobesignicantatthe2-3level,andthisissupportedbytheresultsofa2-sidedKolmogorov-Smirnovtest,whichndsthataDstatisticof0.296atan85%probabilitythatthecumulativeLFsofthemoreandlessmassiveclustersarefromdifferent 84 PAGE 85 Normalized(top)andcumulative(bottom)BSSluminosityfunctions,dividedintoclusterswithVt<8.8(black)andVt>-8.8(red).ThemodelsofBP95areshownforcomparisoninblueandbrownforhigh(Z=0.005)andlow(Z=0.0006)metallicitiesrespectively.Theircollisionalmodelsareplottedassolidlinesandprimordialbinarymodelsareplottedasdottedlines. 85 PAGE 86 86 PAGE 87 87 PAGE 88 4-4 .SincethetotalnumberofknownSXPheisnotlarge,theerrorbarsontheSXPheLFarecorrespondinglylargerthanthosefortheACSBSS.However,a2-sidedK-StestshowsthattheprobabilitythatthecumulativeSXPheLFandthecumulativeLFforalltheBSSintheACSdataarefromdifferentparentdistributionsisunder2%,althoughtheDstatisticof0.13reinforcesthelimitedstatisticalsignicanceofthisgurewhencomparedtotheerrorsontheSXPheLF.ThissupportsourhypothesisinSect.3.3.4that,atleastamongclusterGGCs,therearenoclusterpropertieswhichdictatewhetherSXPhearepresent,andtheirpresence,number,andfraction(ofBSS)isessentiallyrandom.GiventheageandmetallicityrangeofGGCs,itisplausiblethatSXPhecanexistintheBSSregionofallGGCs.Thenextlogicalquestionisalongstandingone,namely,whyisitthatnotallstarsintheinstabilitystrippulsate.WhilethepulsationmodesandperiodsofSXPhearefairlywellunderstood,theirpulsationamplitudesare 88 PAGE 89 Normalized(top)andcumulative(bottom)SXPheluminosityfunction(black)comparedtotheluminosityfunctionfromallACSBSS(red). 89 PAGE 90 90 PAGE 91 5.1.1SXPheandHostClusterPropertiesWehaveconductedtheonlyanalysisofthevariabilitypropertiesofSXPheinGGCsandtheirrelationshiptothepropertiesoftheirhostclustersandtheclusterBSSpopulations.AlthoughtheheterogeneityofthevariabilitystudiesresultingintheSXPhediscoveriespreventsusfrommakinganyquantitativestatementsaboutthecompletenessofthisdatabase,wemaystilldrawsomeconclusions.Firstly,thepresenceofSXPhedoesnotshowanycorrelationwithanyclusterproperties.Indeed,theirpresence(atleastregardingthosewithdetectableamplitudes)seemstobecompletelyrandom.Thisissupportedbytwomainpiecesofevidence:Firstly,thedistributionofclusterswithSXPhemirrors,towithinstatisticalerrors,thedistributionofallGGCsintheH96catalogwithregardtoallnon-distance-dependentclusterproperties,suchasmetallicity,centralconcentration,horizontalbranchmorphology,andintegratedmagnitude.Secondly,atwo-sidedK-StesthasshownthatthemeanluminosityfunctionofalloftheBSSdetectedintheACSsurveyhasadifferentparentdistributionfromtheluminosityfunctionoftheSXPheatonlya2%condencelevel,althoughtheerrorsduetosmallnumberstatisticsareadmittedlylarge.ThismakessensesincethelocationoftheSXPhe(i.e.lower-luminosity)instabilitystripiscoincidentwiththeBSSregionovertheentireageandmetallicityrangeoccupiedbyGGCs,althoughforothercombinationsofageandmetallicity,thismaynotbethecase. 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RogerE.CohenwasborninBoston,Massachusettsin1981andspenttherst18yearsofhislifeinthesuburbofAndover.There,heattendedpublichighschoolwhileworkingavarietyofrestaurantandclericaljobsanddevelopinghisafnityformusicofalltypes.Whenhewas17,asummercourseatTuftsUniversityrekindledhischildhoodpassionforastronomy.HeattendedcollegeatWesleyanUniversityinMiddletown,CTfrom1999-2003,wherehemajoredinastronomyandphysics.Duringthesummershetraveledtocontinuetofeedhisappetiteforresearchandexplorationintheeld,participatinginREUswithKarenKwitteratWilliamsCollege,wherehestudiedspectraofplanetarynebulae,andthefollowingsummeratFloridaInternationalUniversity,observingandmodellingclosebinarystarswithWalterVanHamme.BackinMiddletown,RogerdecidedtoworkwithBillHerbstwritingaseniorthesisonTTauristarvariability,andintheprocess,heaccidentallydiscoveredthelongeststellareclipsecurrentlyknown.Afterfailingtogetacceptedatanyofthegradschoolsheinitiallyappliedto,hecontactedhisrstundergradadvisor,AtaSarajedini,whoinvitedhimtocometotheUniversityofFloridaandworkonglobularclusterphotometryandsimulationsforthethen-proposedSIMmission.AfterworkingwithDr.Sarajediniforayear,RogerwasacceptedintograduateschoolatUF.FollowingachancemeetingwhileonanobservingrunatKittPeak,RogerdecidedtoworkwithJianGefortwoyearsgettinghisM.S.,usingGe'sExoplanetTrackerinstrumenttodeterminestellarparametersofplanetsearchcandidates.Afterwards,RogerdecidedtoreturntoDr.Sarajedini'ssupervisionforhisPh.D.Whennotobserving,reducing,oranalyzingobservationaldata,Rogerenjoysplayingdrums,andwhileingraduateschool,hisbandshavereleasedCDs,records,andtapesandtouredtheeastcoastnumeroustimes. 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