<%BANNER%>

Blue Straggler Variability and Luminosity Functions in Galactic Globular Clusters

Permanent Link: http://ufdc.ufl.edu/UFE0042387/00001

Material Information

Title: Blue Straggler Variability and Luminosity Functions in Galactic Globular Clusters
Physical Description: 1 online resource (103 p.)
Language: english
Creator: Cohen, Roger
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: Astronomy -- Dissertations, Academic -- UF
Genre: Astronomy thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: We have conducted a study of the photometric variability and magnitude distribution of blue straggler stars in Galactic globular clusters. We have conducted a ground-based photometric variability survey of blue stragglers in a carefully selected set of eight globular clusters. All of these clusters, except for two which serve as gauges of our detection capability, have remained unsearched for variability below their horizontal branches until now. This ground-based survey has resulted in the detection of zero binaries, which we use to constrain the blue straggler binary fraction, as well as a total of thirteen new SX Phoenicis pulsators, including a significant population of 10 variables in NGC 6101 comprised largely of fundamental and first overtone radial pulsators. To place these results in context, we have updated a previously existing catalog of SX Phoenicis pulsators in globular clusters, nearly doubling its size, and for the first time analyzed the pulsation properties of the composite variables. We find that these pulsators have a remarkably similar distribution in period-amplitude space, and that neither their frequency nor their pulsational properties correlate with any known properties of their host clusters. We have used our updated catalog to refine a period-luminosity relation which can be usefully applied to populations without known reddening or metallicity values. The other facet of our study makes use of the unprecedented photometric database of Galactic globular clusters acquired using ACS on HST. The precision of this photometry has resulted in the creation of a homogenous, internally consistent database of blue stragglers in Galactic globular clusters which is five times larger than any previous such databases. We find that, in accord with these earlier investigations, the luminosity functions of these blue stragglers do not correlate strongly with any cluster properties. We also use these luminosity functions to show that, due to the age and metallicity range occupied by these clusters in the Milky Way, there is a 98% chance that the SX Phoenicis pulsators have the same parent distribution as cluster blue stragglers in general.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Roger Cohen.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Sarajedini, Ata.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-06-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042387:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042387/00001

Material Information

Title: Blue Straggler Variability and Luminosity Functions in Galactic Globular Clusters
Physical Description: 1 online resource (103 p.)
Language: english
Creator: Cohen, Roger
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: Astronomy -- Dissertations, Academic -- UF
Genre: Astronomy thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: We have conducted a study of the photometric variability and magnitude distribution of blue straggler stars in Galactic globular clusters. We have conducted a ground-based photometric variability survey of blue stragglers in a carefully selected set of eight globular clusters. All of these clusters, except for two which serve as gauges of our detection capability, have remained unsearched for variability below their horizontal branches until now. This ground-based survey has resulted in the detection of zero binaries, which we use to constrain the blue straggler binary fraction, as well as a total of thirteen new SX Phoenicis pulsators, including a significant population of 10 variables in NGC 6101 comprised largely of fundamental and first overtone radial pulsators. To place these results in context, we have updated a previously existing catalog of SX Phoenicis pulsators in globular clusters, nearly doubling its size, and for the first time analyzed the pulsation properties of the composite variables. We find that these pulsators have a remarkably similar distribution in period-amplitude space, and that neither their frequency nor their pulsational properties correlate with any known properties of their host clusters. We have used our updated catalog to refine a period-luminosity relation which can be usefully applied to populations without known reddening or metallicity values. The other facet of our study makes use of the unprecedented photometric database of Galactic globular clusters acquired using ACS on HST. The precision of this photometry has resulted in the creation of a homogenous, internally consistent database of blue stragglers in Galactic globular clusters which is five times larger than any previous such databases. We find that, in accord with these earlier investigations, the luminosity functions of these blue stragglers do not correlate strongly with any cluster properties. We also use these luminosity functions to show that, due to the age and metallicity range occupied by these clusters in the Milky Way, there is a 98% chance that the SX Phoenicis pulsators have the same parent distribution as cluster blue stragglers in general.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Roger Cohen.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Sarajedini, Ata.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-06-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042387:00001


This item has the following downloads:


Full Text

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. 91

PAGE 92

92

PAGE 93

93

PAGE 94

94

PAGE 95

95

PAGE 96

96

PAGE 97

97

PAGE 98

Ahumada,J.A.&Lapasset,E.,2007,A&A,463,789 Alard,C.,2000,ASPC,203,50 Anderson,J.etal.,2008,AJ,135,2055 ArellanoFerra,A.,Giridhar,S.&Bramich,D.D.,2010,MNRAS,402,226 Beccari,G.etal.,2008,ApJ,679,712 Bramich,D.M.,2008,MNRAS,386,77 Bono,G.,Caputo,F.,Castellani,V.&Marconi,M.,1997,A&AS,121,327 Bono,G.,Caputo,F.&DiCriscienzo,M.,2007,A&A,476,779 Brocato,E.,Buonanno,R.,Malakhova,Y.&Piersimoni,A.M.,1996,A&A,311,778 Bruntt,H.,Fradsen,S.,Gilliland,R.L.,Christensen-Dalsgard,J.,Petersen,J.O.,Guhathakurta,P.,Edmonds,P.D.&Bono,G.,2001,A&A,371,614 Carney,B.W.,Latham,D.W.&Laird,J.B.,2005,AJ,129,466 Cenarro,A.J.,Cervantes,J.L.,Beasley,M.A.,Marin-French,A.&Vazdekis,A.,2008,ApJ,689,29 Chen,X.&Han,Z.,2008,MNRAS,384,1263 Chen,X.&Han,Z.,2009,MNRAS,395,1822 Dalessandro,E.,Lanzoni,B.,Ferraro,F.R.,Vespe,F.,Ballazzini,M.&Rood,R.T.,2008,ApJ,681,311 D'alessandro,E.,Lanzoni,B.,Ferraro,F.R.,Rood,R.T.,Milone,A.,Piotto,G.&Valenti,E.,2008,ApJ,677,1069 Davies,M.B.,Piotto,G.&deAngeli,F.,2004,MNRAS,349,129 Dieball,A.,Long,K.S.,Knigge,C.,Thompson,G.S.&Zurek,D.R.,2010,ApJ,710,332 Dotter,A.,Chaboyer,B.,Ferguson,J.W.,Lee,H.-C.,Worthey,G.,Jevremovic,D.&Baron,E.,2007,ApJ,666,403 Dotter,A.,Chaboyer,B,Jevremovic,D.,Kostov,V.,Baron,E.&Ferguson,J.W.,2008,ApJS,178,89 Dotter,A.etal.,2010,ApJ,708,698 Ferraro,F.R.,Clementini,G.,FusiPecci,F.&Buonanno,R.,1991,MNRAS,252,357 98

PAGE 99

Ferraro,F.R.,Paltrinieri,B.,FusiPecci,F.,Cacciari,C.,Dorman,B.,Rood,R.T.,Buonanno,R.,Corsi,C.E.,Burgarella,D.&Laget,M.,1997,A&A,324,915 Ferraro,F.R.,Beccari,G.,Rood,R.T.,Bellazzini,M.,Sills,A.&Sabbi,E.,2004,ApJ,603,127 Ferraro,F.R.etal.,2006,ApJ,647,53 Ferraro,F.R.,Beccari,G.,Dallesandro,E.,Lanzoni,B.,Sills,A.,Rood,R.T.,FusiPecci,F.,Karakas,A.I.,Miocchi,P.&Bovinelli,S.,2010,arXiv1001,1096 Ferraro,F.R.,D'Amico,N.,Possenti,A.,Mignani,R.P.&Paltrinieri,B.,2001,ApJ,561,337 Fouque,P.etal.,2007,A&A,476,73 Gerashchenko,A.N.,Kadla,Z.I.&Malakhova,Y.N.,1999,ARep,43,20 Gilliland,R.L.,Bono,G.,Edmonds,P.D.,Caputo,F.,Cassisi,S.,Petro,L.D.,Saha,A.&Shara,M.M.,1998,ApJ,507,818 Glebbeek,E.,Sills,A.&Leigh,N.,2010,MNRAS,1129 Iben,I.,1986,ApJ,304,201 Jeon,Y.-B.,Kim,S.-L.,Lee,H.,Lee,M.G.,2001,AJ,121,2769 Jeon,Y.-B.,Lee,M.G.,Kim,S.-L.,Lee,H.,2003,AJ,125,3165 Jeon,Y.-B.,Lee,M.G.,Kim,S.-L.&Lee,H.,2004,AJ,128,287 Jeon,Y.-B.,Kim,S.-L.,Lee,M.G.,Lee,H.&Lee,J.W.,2006,ApJ,636,129 Kaluzny,J.,Rozyczka,M.,Thompson,I.B.&Zloczewski,K.,2009,AcA,59,371 Kaluzny,J.,Thompson,I.B.,Rucinski,S.M.,Pych,W.,Stachowski,G.,Krzeminski,W.&Burley,G.S.,2007,AJ,134,541 Knigge,C.,Leigh,N.&Sills,A.,2009,Nature,457,288 Kopacki,G.,2005,AcA,55,85 Kopacki,G.,2007,AcA,57,49 Kovacs,G.,Bakos,G.&Noyes,R.W.,2005,MNRAS,356,557 Kravtsov,V.V.&Zheleznyak,A.P.,2003,IBVS,5452,1 99

PAGE 100

Lanzoni,B.,Sanna,N.,Ferraro,F.R.,Velanti,E.,Beccari,G.,Schiavon,R.P.,Rood,R.T.,Mapelli,M.&Sigurdsson,S.,2007,ApJ,663,1040 Latham,D.W.&Milone,A.A.E.,1996,ASPC,90,358 Leigh,N.,Sills,A.&Knigge,C.,2007,ApJ,661,210 Lombardi,J.C.,Warren,J.S.,Rasio,F.A.,Sills,A.&Warren,A.R.,2002,ApJ,568,939 Majaess,D.J.,Turner,D.G.,Lane,D.J.,Henden,A.&Karjci,T.,2010,astro-ph1007.2300 Mapelli,M.,Ripamonti,E.,Battaglia,G.,Tolstoy,E.,Irwin,M.J.,Moore,B.&Sigurdsson,S.,2009,MNRAS,396,1771 Mapelli,M.,Sigursson,S.,Ferraro,F.R.,Colpi,M.,Possenti,A.&Lanzoni,B.,2006,MNRAS,373,361 Mapelli,M.,Sigurdsson,S.,Colpi,M.,Ferraro,F.R.,Possenti,A.,Rood,R.T.,Sills,A.&Beccari,G.,2004,ApJ,605,29 Marin-Franch,A.etal.,2009,ApJ,694,1498 Mateo,M.,Hurley-Keller,D.&Nemec,J.,1998,AJ,115,1840 Mathieu,R.D.&Geller,A.M,Nature,462,1032 Mazur,B.,Krzeminski,W.&Thompson,I.B.,2003,MNRAS,340,1205 McNamara,D.,1995,AJ,109,1751 McNamara,D.,1997,PASP,109,1221 Milone,A.P.,Piotto,G.,Bedin,L.R.&Sarajedini,A.,2008,MmSAI,79,623 Milone,A.P.etal.,2010,inpreparation Momany,Y.,Held,E.V.,Saviane,I.,Zaggia,S.,Rizzi,L.&Gullieuszik,M.,2007,A&A,468,973 Monkman,E.,Sills,A.,Howell,J.,Guhathakurta,P.,deAngeli,F.&Beccari,G.,2006,ApJ,650,195 MoniBidin,C.,Moehler,S.,Piotto,G.,Recio-Blanco,A.,Momany,Y.&Mendez,R.A.,2006,A&A,451,499 Moretti,A.,deAngeli,F.&Piotto,G.,2008,A&A,482,777 100

PAGE 101

Nemec,J.M.,Nemec,A.F.&Lutz,T.E.,1994,AJ,108,222 Olech,A.,Dziembowski,W.A.,Pamyatnykh,A.A.,Kaluzny,J.,Schwarzen-Czerny,A.&Thompson,I.B.,2005,MNRAS,363,40 Paust,N.etal.,2010,AJ,139,476 Petersen,J.O.&Freyhammer,L.M.,2002,ASPC,259,142 Piersimoni,A.M.,Bono,G.&Ripepi,V.,2002,AJ,124,1528 Piotto,G.etal.,2002,A&A,391,954 Piotto,G.,DeAngeli,F.,King,I.R.,Djorgovski,S.G.,Bono,G.,Cassisi,S.,Meylan,G.,Recio-Blanco,A.,Rich,R.M.&Davies,M.B.,2004,ApJ,604,109 Pribulla,T.etal.,2008,MNRAS,391,343 Pritzl,B.J.,Smith,H.A.,Stetson,P.B.,Catelan,M.,Sweigart,A.,Layden,A.C.&Rich,M.R.,2003,AJ,126,1381 Poretti,E.,1999,A&A,343,385 Poretti,E.,Clementini,G.,Greco,C.,Mateo,M.,Dell'Arciprete,L.,Rizzi,L.,Gullieuszik,M.&Maio,M.,2008,ApJ,685,947 Pych,W.,Kaluzny,J.,Krzeminski,W.,Schwarzenberg-Czerny,A.&Thompson,I.B.,2001,A&A,367,148 Rodriguez,E.&Lopez-Gonzalez,M.J.,2000,A&A,359,597 Rodriguez,E.,Lopez-Gonzalez,M.J.&LopezdeCoca,P.,2002,ESASP,485,317 Rosenberg,A.,Piotto,G.,Saviane,I.&Aparicio,A.,2000,A&AS,145,451 Rucinski,S.M.,2000,AJ,120,319 Santolamazza,P.,Marconi,M.,Bono,G.,Caputo,F.,Cassisi,S.&Gilliland,R.L.,2001,ApJ,554,1124 Sarajedini,A.etal.,2007,AJ,133,1658 Sarna,M.J.&DeGreve,J.-P.,1996,QJRAS,37,11 Schiavon,R.P.,Faber,S.M.,Rose,J.A.&Castilho,B.V.,2002,ApJ,580,873 Sigurdsson,S.,Davies,M.B.&Bolte,M.,1994,ApJL,431,115 Sills,A.&Bailyn,C.D.,1999,ApJ,513,428 101

PAGE 102

Sills,A.,Adams,T.,Davies,M.B.&Bate,M.R.,2002,MNRAS,332,49 Sills,A.,Adams,T.&Davies,M.B.,2005,MNRAS,358,716 Sills,A.,Karakas,A.&Lattanzio,J.,2009,ApJ,692,1411 Sollima,A.,Lanzoni,B.,Beccari,G.,Ferraro,F.R.&Fusi,Pecci,F.,2008,A&A,481,701 Templeton,M.,Basu,S.&Demarque,P.,2002,ApJ,576,963 Xin,Y.,Deng,L.,&Han,Z.W.,2007,ApJ,660,319 Xin,Y.,deGrijs,R.,Deng,L.&Kroupa,P.,2010,IAUS,226,556 102

PAGE 103

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. 103