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Rr Lyrae Variables in the Andromeda Group Galalxies

Permanent Link: http://ufdc.ufl.edu/UFE0042832/00001

Material Information

Title: Rr Lyrae Variables in the Andromeda Group Galalxies
Physical Description: 1 online resource (137 p.)
Language: english
Creator: YANG,SOUNG-CHUL
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: ANDROMEDA -- RRLS
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 present the results of an extensive survey of RR Lyrae stars in the companion galaxies (M33, NGC 147, And XI and And XIII) around the Andromeda galaxy (M31). From images taken with the Advanced Camera for Surveys (ACS) Wide Field Channel (WFC) on-board the Hubble Space Telescope (HST) through two passbands (F606W and F814W), we have identified and characterized a total of 119 RR Lyrae variables (96 RRab (RR0) and 23 RRc(RR1)) in M33. Using the properties of 83 RR Lyrae stars (65 RRab and 18 RRc) in the innermost ACS field (hereafter DISK2), we find mean periods of <Pab> = 0.553 +/- 0.008 (error1) +/- 0.05 (error2) and <Pc> = 0.325 +/- 0.008 (error1) +/- 0.05 (error2), where the `error1' value represents the standard error of the mean and the `error2' value is based on the error of an individual RRL period calculated from our synthetic light curve simulations. The distribution of RRab periods and the frequency of RRc stars (Nc=n(c)/n(abc)=0.22) strongly suggest that these RR Lyraes follow the general characteristics of those in Oosterhoff type I Galactic globular clusters. The metallicities of 65 individual RRab stars are calculated from the period-amplitude-metallicity relationship, yielding a mean metallicity of <Fe/H> = -1.48 +/- 0.05 dex, where the uncertainty is the standard error of the mean. The VI minimum-light colors of the RRab stars are used to calculate a mean line-of-sight reddening toward the DISK2 field of <E(V-I)>=0.175. By adopting this line-of-sight reddening and using a relation between RR Lyrae luminosity and metallicity (M(V)=0.23Fe/H+0.93), we estimate a mean distance modulus of <(m-M)0>=24.52 +/- 0.11 for M33, where the error is the quadratic sum of the uncertainties in the absolute and dereddened V magnitudes of the RRLs. We used both Thuan-Gunn g-band ground-based photometry from the literature and HST Wide Field Planetary Camera 2 (WFPC2) archival data in the F555W and F814W passbands to investigate the pulsation properties of RR Lyrae variable candidates in NGC 147. These datasets represent the two extreme cases often found in RR Lyrae studies with respect to the phase coverage of the observations and the quality of the photometric measurements. Extensive artificial variable star tests for both cases were performed. We conclude that neither dataset is sufficient to confidently determine the pulsation properties of the NGC 147 RR Lyraes. Thus, while we can assert that NGC 147 contains RR Lyrae variables, and therefore a population older than $\sim$10 Gyr, it is not possible at this time to use the pulsation properties of these RR Lyraes to study other aspects of this old population. Our results provide a good reference for gauging the completeness of RR Lyrae variable detection in future studies. We present a comprehensive study of the stellar populations in two faint M31 dwarf satellites, And XI and And XIII. Using deep archival images from the WFPC2 onboard HST, we characterize the horizontal branch (HB) morphologies and the RR Lyrae populations of these two faint dwarf satellites. Our new template light curve fitting routine (RRFIT) detected RR Lyrae populations from both galaxies. The mean periods of RRab (RR0) stars in And XI and And XIII are <Pab>=0.621 +/- 0.026 (error1) +/- 0.022 (error2), and <Pab>=0.648 +/- 0.026 (error1) +/0- 0.022 (error2) respectively. The ``error1'' represents the standard error of the mean, while ``error2'' is the error subject to the individual RRab periods estimated from our synthetic light curve simulation. Even though the RRL populations show a lack of RRab stars with high amplitudes (Amp(V) > 1.0 mag) and relatively short periods (Pab ~ 0.5 days), their period -- V band amplitude (P-Amp(V)) relations track the lower part of the general P-Amp(V) trend in the M31 outer halo RRL populations. The metallicities of RRab stars were calculated via the Fe/H-logPab-Amp(V) relationship of Alcock et al. The metallicities thus obtained (Fe/H(And XI)=-1.75$; Fe/H(And XIII)=-1.74$) are consistent with the values calculated from the RGB slope indicating that our measurements are not significantly affected by the evolutionary effects of RRL stars. The distance to each galaxy was calculated using the absolute V magnitudes of the RRab stars. We obtained (m-M)0,V=24.54 for And XI and this value becomes (m-M)0,V=24.71 for And XIII. We discuss the origins of And XI and And XIII based on a comparative analysis of the luminosity-metallicity (L-M) relation of Local Group dwarf galaxies.
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 SOUNG-CHUL YANG.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Sarajedini, Ata.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0042832:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042832/00001

Material Information

Title: Rr Lyrae Variables in the Andromeda Group Galalxies
Physical Description: 1 online resource (137 p.)
Language: english
Creator: YANG,SOUNG-CHUL
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: ANDROMEDA -- RRLS
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 present the results of an extensive survey of RR Lyrae stars in the companion galaxies (M33, NGC 147, And XI and And XIII) around the Andromeda galaxy (M31). From images taken with the Advanced Camera for Surveys (ACS) Wide Field Channel (WFC) on-board the Hubble Space Telescope (HST) through two passbands (F606W and F814W), we have identified and characterized a total of 119 RR Lyrae variables (96 RRab (RR0) and 23 RRc(RR1)) in M33. Using the properties of 83 RR Lyrae stars (65 RRab and 18 RRc) in the innermost ACS field (hereafter DISK2), we find mean periods of <Pab> = 0.553 +/- 0.008 (error1) +/- 0.05 (error2) and <Pc> = 0.325 +/- 0.008 (error1) +/- 0.05 (error2), where the `error1' value represents the standard error of the mean and the `error2' value is based on the error of an individual RRL period calculated from our synthetic light curve simulations. The distribution of RRab periods and the frequency of RRc stars (Nc=n(c)/n(abc)=0.22) strongly suggest that these RR Lyraes follow the general characteristics of those in Oosterhoff type I Galactic globular clusters. The metallicities of 65 individual RRab stars are calculated from the period-amplitude-metallicity relationship, yielding a mean metallicity of <Fe/H> = -1.48 +/- 0.05 dex, where the uncertainty is the standard error of the mean. The VI minimum-light colors of the RRab stars are used to calculate a mean line-of-sight reddening toward the DISK2 field of <E(V-I)>=0.175. By adopting this line-of-sight reddening and using a relation between RR Lyrae luminosity and metallicity (M(V)=0.23Fe/H+0.93), we estimate a mean distance modulus of <(m-M)0>=24.52 +/- 0.11 for M33, where the error is the quadratic sum of the uncertainties in the absolute and dereddened V magnitudes of the RRLs. We used both Thuan-Gunn g-band ground-based photometry from the literature and HST Wide Field Planetary Camera 2 (WFPC2) archival data in the F555W and F814W passbands to investigate the pulsation properties of RR Lyrae variable candidates in NGC 147. These datasets represent the two extreme cases often found in RR Lyrae studies with respect to the phase coverage of the observations and the quality of the photometric measurements. Extensive artificial variable star tests for both cases were performed. We conclude that neither dataset is sufficient to confidently determine the pulsation properties of the NGC 147 RR Lyraes. Thus, while we can assert that NGC 147 contains RR Lyrae variables, and therefore a population older than $\sim$10 Gyr, it is not possible at this time to use the pulsation properties of these RR Lyraes to study other aspects of this old population. Our results provide a good reference for gauging the completeness of RR Lyrae variable detection in future studies. We present a comprehensive study of the stellar populations in two faint M31 dwarf satellites, And XI and And XIII. Using deep archival images from the WFPC2 onboard HST, we characterize the horizontal branch (HB) morphologies and the RR Lyrae populations of these two faint dwarf satellites. Our new template light curve fitting routine (RRFIT) detected RR Lyrae populations from both galaxies. The mean periods of RRab (RR0) stars in And XI and And XIII are <Pab>=0.621 +/- 0.026 (error1) +/- 0.022 (error2), and <Pab>=0.648 +/- 0.026 (error1) +/0- 0.022 (error2) respectively. The ``error1'' represents the standard error of the mean, while ``error2'' is the error subject to the individual RRab periods estimated from our synthetic light curve simulation. Even though the RRL populations show a lack of RRab stars with high amplitudes (Amp(V) > 1.0 mag) and relatively short periods (Pab ~ 0.5 days), their period -- V band amplitude (P-Amp(V)) relations track the lower part of the general P-Amp(V) trend in the M31 outer halo RRL populations. The metallicities of RRab stars were calculated via the Fe/H-logPab-Amp(V) relationship of Alcock et al. The metallicities thus obtained (Fe/H(And XI)=-1.75$; Fe/H(And XIII)=-1.74$) are consistent with the values calculated from the RGB slope indicating that our measurements are not significantly affected by the evolutionary effects of RRL stars. The distance to each galaxy was calculated using the absolute V magnitudes of the RRab stars. We obtained (m-M)0,V=24.54 for And XI and this value becomes (m-M)0,V=24.71 for And XIII. We discuss the origins of And XI and And XIII based on a comparative analysis of the luminosity-metallicity (L-M) relation of Local Group dwarf galaxies.
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 SOUNG-CHUL YANG.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Sarajedini, Ata.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0042832:00001


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RRLYRAEVARIABLESINTHEANDROMEDAGROUPGALAXIES By SOUNG-CHULYANG ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2011

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c 2011Soung-ChulYang 2

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IdedicatethisdissertationtomyMomandDad. 3

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ACKNOWLEDGMENTS ThisPhDdissertationwouldnothavebeenpossiblewithoutthesupportof manypeople.Theauthorwishestoexpresshisgratitudetohissupervisor,Prof. Dr.AtaSarajediniwhohasalwaysbeenalifelongmentorandofferedinvaluable assistance,supportandguidance.Deepestgratitudearealsoduetothemembers ofthesupervisorycommittee,Prof.Dr.RafaelGuzman,AssociateProf.Dr.Anthony Gonzalez,AssociateProf.Dr.EricFord,andProf.Dr.AdegbolaT.Adesoganwithout whoseknowledgeandassistancethisstudywouldnothavebeensuccessful.Special thanksalsotoallhisgraduatefriends,especiallyhisresearchgroupmembers;Roger CohenandIzaskunSanRomanforsharingtheliteratureandinvaluableassistance.Not forgettingtohisbestfriends;JiWangandMarkKeremedjievwhoalwaysbeenthere. Theauthorwishestoexpresshisloveandgratitudetoherbelovedfamilies;fortheir understandingandendlesslove,throughthedurationofhisstudies. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 10 CHAPTER 1INTRODUCTION ................................... 13 2RRLYRAEVARIABLESINM33.OOSTERHOFFPROPERTIESANDRADIAL TRENDS ....................................... 16 2.1BackgroundStudy ............................... 16 2.2ObservationsandDataReduction ...................... 17 2.3DetectionofRRLyraeVariableCandidates ................. 18 2.4Results ..................................... 21 2.4.1SyntheticLightCurveSimulations ................... 34 2.4.2Period-AmplitudeDiagrams ...................... 41 2.4.3Reddening ................................ 48 2.4.4Metallicities ............................... 52 2.4.5DistanceofM33 ............................ 54 2.5Discussion ................................... 58 2.6Summary .................................... 62 3RRLYRAEVARIABLESINTHELOCALGROUPDWARFGALAXYNGC147 63 3.1BackgroundStudy ............................... 63 3.2ObservationsandDataReduction ...................... 65 3.2.1GroundBasedData .......................... 65 3.2.2HubbleSpaceTelescopeData .................... 66 3.3RRLyraePeriodDetermination ........................ 67 3.3.1ReanalysisoftheSahaetal.Data .................. 70 3.3.2Analysisof /WFPC2ArchivalData ................ 82 3.4Summary .................................... 88 4HST/WFPC2IMAGINGOFTHEDWARFSATELLITESANDXIANDAND XIII:HBMORPHOLOGYANDRRLYRAES .................... 93 4.1BackgroundStudy ............................... 93 4.2ObservationandDataReduction ....................... 95 4.3Color-MagnitudeDiagrams(CMDs) ..................... 95 4.3.1GeneralDescriptionoftheCMDs ................... 95 5

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4.3.2HorizontalBranchMorphologies ................... 97 4.4RRLyraeVariables(RRLs) .......................... 105 4.4.1DetectingRRLsandLightCurves ................... 105 4.4.2SyntheticLightCurveSimulation ................... 109 4.4.3Period-Amplitude(P-A)Diagrams .................. 116 4.5Metallicity .................................... 119 4.6Distance ..................................... 121 4.7Discussion ................................... 123 4.8Summary .................................... 126 REFERENCES ....................................... 129 BIOGRAPHICALSKETCH ................................ 135 6

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LISTOFTABLES Table page 2-1ObservingLog. .................................... 19 2-2PropertiesofAnomalousCepheidCandidates. .................. 22 2-3PropertiesofRRLyraestars. ............................ 43 3-1PhysicalpropertiesofNGC147. .......................... 65 3-2WFPC2ObservingLog ............................... 67 3-3Characteristicsofthevariablestars ......................... 72 3-4CharacteristicsofRRLyraeCandidates ...................... 87 4-1ObservingLog. ................................... 96 4-2HBparameters .................................... 100 4-3HBindexandotherphysicalparametersofsampledSphgalaxies. ....... 100 4-4PropertiesofRRLyraestars. ............................ 107 7

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LISTOFFIGURES Figure page 2-1ThelocationoftheRRLyrae(RRL)candidatesinthe color-magnitude diagramsofthethreeACSelds(DISK2,DISK3,DISK4). ............ 23 2-2ThebestttinglightcurvesoftwoAnomalousCepheid(AC)candidatesfound intheDISK2eld. .................................. 23 2-3ExamplesofthebestttinglightcurvesforDISK2RRLcandidatesobtained fromourtemplatelightcurvettingroutine(FITLC;Layden1998,Mancone& Sarajedini2008) ................................... 24 2-4TheresultofoursyntheticlightcurvesimulationsfortheDISK2RRLs. ..... 37 2-5ThedistributionoftheperioddeviationforsyntheticRRabandRRcstars. ... 40 2-6ThisgureillustratestheP-AdiagramsandtheperioddistributionsforRRL candidatesinthethreeACSelds. ......................... 46 2-7ThebestttinglightcurvesfortheRRdcandidatesfoundintheDISK2eld. .. 47 2-8Theupperpanel(zoomed-inVICMD)illustratesthecolor-magnitudetrendof DISK2RRLs;itappearstobewellmatchedwiththereddeningvectorinthis eld. .......................................... 50 2-9ThereddeningdistributionforDISK2RRabstars. ................. 51 2-10TheP-AdiagramoftheDISK2RRLs. ....................... 52 2-11Themetallicitydistributions(binnedandgeneralized)oftheM33DISK2RRab stars(solidred-thisstudy)andtheM31RRLs(dottedblue-Brownetal.2004 (B2004);dashdot-Sarajedinietal2009(S2009)). ................ 54 2-12ThelocationoftheM33TRGBintheVICMD.Starsbelowthedashedblue linewereusedfortheconstructionoftheI-bandluminosityfunction. ...... 57 2-13TheI-bandluminosityfunction(upperpanel)ofM33RGBstarsintheDISK2 eld. .......................................... 58 2-14ThemetallicityoftheM33stellarpopulationsasafunctionofdeprojecteddistance fromthegalacticcenter. ............................... 61 3-1VIcolor-magnitudediagramforthedwarfellipticalgalaxy,NGC147. ...... 68 3-2AcompletenesstestfortheWFPC2VIphotometry. ................ 69 3-3TheleftpanelsshowtheRRLyraelightcurvesphasedusingtheperiodderived bySahaetal.(1990)viatheL-Kperioddeterminationmethod. ......... 73 8

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3-4AcomparisonbetweenperiodsdeterminedfromtheL-KandFITLCmethods usingthe -bandphotometryofRRLyraecandidatesinNGC147. ....... 83 3-5TheresultsofRRLyraevariablesimulationsbasedonthe -bandphotometry ofSahaetal.(1990)withtheL-Kmethodareshown. .............. 84 3-6SameasFig 3-5 exceptthattheFITLCtemplate-ttingalgorithmisemployed todeterminetheperiodsoftheRRLyraecandidates. .............. 85 3-7ThebestttingtemplatelightcurvesforpossibleRRLyraecandidatesinNGC 147basedonarchivalWFPC2imaging. ...................... 88 3-8ThepositionsofthemostprobableRRLyraecandidatesfromtheFITLCanalysis ofWFPC2archivaldataintheVICMD. ...................... 91 3-9TheresultofarticialRRLyraevariabletestforWFPC2archivaldatawith FITLCroutine. .................................... 92 4-1TheVIcolor-magnitudediagramofAndXI. .................... 101 4-2SameasFigure4-1,butforAndXIII. ........................ 102 4-3Theillustrationsofthe (V-I)indexmeasurementsareshown. ......... 103 4-4Themetallicity-HBmorphologydiagramfor65GalacticGlobularClusters(D10) ispresented. ..................................... 104 4-5Thecorrelationbetween (V-I)and(B-R)/(B+V+R)indices. ........... 105 4-6Thebest-tlightcurvesofRRLcandidatesinAndXI. .............. 108 4-7Thebest-tlightcurvesofRRLcandidatesinAndXIII. .............. 109 4-8TheresultsfromoursyntheticlightcurvesimulationfortheAndXIdata. .... 112 4-9TheresultsfromoursyntheticlightcurvesimulationforAndXIII. ........ 113 4-10Thecomparisonsbetweenthebest-tlightcurvesandtheRRctemplatets fortheunclassiedRRLcandidates. ........................ 114 4-11ThedistributionsoftheoutputperioddeviationforsyntheticRRabandRRc stars. ......................................... 115 4-12TheP-ArelationsofRRLcandidates(opencircles)ofAndXIandAndXIII. .. 118 4-13ThecomparisonsofP-AdiagramsfortheM31dSphgalaxies. .......... 120 4-14TheillustrationofSindexmethodforthemetallicitymeasurement(Savianeet al.2000). ....................................... 122 4-15Luminosity-metallicity(L-M)relationsoftheLocalGroupdwarfgalaxies. .... 127 9

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy RRLYRAEVARIABLESINTHEANDROMEDAGROUPGALAXIES By Soung-ChulYang May2011 Chair:AtaSarajedini Major:Astronomy WepresenttheresultsofanextensivesurveyofRRLyraestarsinthecompanion galaxies(M33,NGC147,AndXIandAndXIII)aroundtheAndromedagalaxy(M31). FromimagestakenwiththeAdvancedCameraforSurveys(ACS)WideField Channel(WFC)on-boardtheHubbleSpaceTelescope(HST)throughtwopassbands (F606WandF814W),wehaveidentiedandcharacterizedatotalof119RRLyrae variables(96RRab(RR0)and23RRc(RR1))inM33.Usingthepropertiesof83RR Lyraestars(65RRaband18RRc)intheinnermostACSeld(hereafterDISK2),we ndmeanperiodsof < > =0.553 0.008(error1) 0.05(error2)and < > =0.325 0.008(error1) 0.05(error2),wheretheerror1'valuerepresentsthe standarderrorofthemeanandtheerror2'valueisbasedontheerrorofanindividual RRLperiodcalculatedfromoursyntheticlightcurvesimulations.Thedistributionof RRabperiodsandthefrequencyofRRcstars( = / =0.22)stronglysuggest thattheseRRLyraesfollowthegeneralcharacteristicsofthoseinOosterhofftypeI Galacticglobularclusters.Themetallicitiesof65individualRRabstarsarecalculated fromtheperiod-amplitude-metallicityrelationship,yieldingameanmetallicityof < / > =-1.48 0.05dex,wheretheuncertaintyisthestandarderrorofthe mean.TheVIminimum-lightcolorsoftheRRabstarsareusedtocalculateamean line-of-sightreddeningtowardtheDISK2eldof < > =0.175.Byadoptingthis line-of-sightreddeningandusingarelationbetweenRRLyraeluminosityandmetallicity 10

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( =0.23 / +0.93),weestimateameandistancemodulusof < > =24.52 0.11forM33,wheretheerroristhequadraticsumoftheuncertaintiesintheabsolute anddereddenedVmagnitudesoftheRRLs. WeusedbothThuan-Gunn -bandground-basedphotometryfromtheliterature andHSTWideFieldPlanetaryCamera2(WFPC2)archivaldataintheF555W andF814WpassbandstoinvestigatethepulsationpropertiesofRRLyraevariable candidatesinNGC147.Thesedatasetsrepresentthetwoextremecasesoftenfoundin RRLyraestudieswithrespecttothephasecoverageoftheobservationsandthequality ofthephotometricmeasurements.Extensivearticialvariablestartestsforbothcases wereperformed.Weconcludethatneitherdatasetissufcienttocondentlydetermine thepulsationpropertiesoftheNGC147RRLyraes.Thus,whilewecanassertthat NGC147containsRRLyraevariables,andthereforeapopulationolderthan # 10Gyr, itisnotpossibleatthistimetousethepulsationpropertiesoftheseRRLyraestostudy otheraspectsofthisoldpopulation.Ourresultsprovideagoodreferenceforgauging thecompletenessofRRLyraevariabledetectioninfuturestudies. WepresentacomprehensivestudyofthestellarpopulationsintwofaintM31 dwarfsatellites,AndXIandAndXIII.UsingdeeparchivalimagesfromtheWFPC2 onboardHST,wecharacterizethehorizontalbranch(HB)morphologiesandtheRR Lyraepopulationsofthesetwofaintdwarfsatellites.Ournewtemplatelightcurvetting routine(RRFIT)detectedRRLyraepopulationsfrombothgalaxies.Themeanperiods ofRRab(RR0)starsinAndXIandAndXIIIare < > =0.621 0.026(error1) 0.022(error2),and < > =0.648 0.026(error1) 0.022(error2)respectively.The "error1"representsthestandarderrorofthemean,while"error2"istheerrorsubject totheindividualRRabperiodsestimatedfromoursyntheticlightcurvesimulation. EventhoughtheRRLpopulationsshowalackofRRabstarswithhighamplitudes ( > )andrelativelyshortperiods( # 0.5days),theirperiodVband amplitude(P-Amp(V))relationstrackthelowerpartofthegeneralP-Amp(V)trendinthe 11

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M31outerhaloRRLpopulations.ThemetallicitiesofRRabstarswerecalculatedviathe / relationshipofAlcocketal.Themetallicitiesthusobtained ( / ; / )areconsistentwiththevaluescalculated fromtheRGBslopeindicatingthatourmeasurementsarenotsignicantlyaffectedby theevolutionaryeffectsofRRLstars.Thedistancetoeachgalaxywascalculatedusing theabsoluteVmagnitudesoftheRRabstars.Weobtained =24.54forAndXI andthisvaluebecomes =24.71forAndXIII.WediscusstheoriginsofAndXI andAndXIIIbasedonacomparativeanalysisoftheluminosity-metallicity(L-M)relation ofLocalGroupdwarfgalaxies. 12

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CHAPTER1 INTRODUCTION ThecharacteristicsofoldstellarpopulationsintheMilkyWay(MW)andM31 havebeenextensivelystudiedandhaveyieldedawealthofinformationaboutthestar formationandchemicalenrichmenthistoriesofthesegalaxies.TheRRLpopulation oftheMWbothinthehaloeldandtheglobularclustersystemshowstwodistinct sub-groupsintheperiod-amplitudediagram(i.e.Baileydiagram),leadingtothe Oosterhoffdichotomy(Oosterhoff1938).Thisdichotomyislikelyexplainedbythe metallicitydifferencebetweenthosegroups(Lee&Carney1999;Clement&Rowe 2000).OosterhoffI(OoI)systemshaveintermediatemetallicities( / # 1.5dex) andab-typeRRL(RRab)meanpulsationperiodsof # 0.55dayswithalowfrequencyof c-typeRRL(RRc),whileOosterhoffII(OoII)systemsaregenerallymetal-poor( / $ 1.7dex)andhaveRRabmeanpulsationperiodsof # 0.65dayswithahighercontentof RRc(Castellani&Quarta1987).Theab-typeRRLstarsarefundamentalmodepulsator, whichexhibitsawtooth-likelightcurves,whereasRRcstarsarerstovertonepulsators withlightcurvesthataresinusoidal.Itisalsoimportanttokeepinmindthatthebimodal metallicitydistributionoftheMWglobularcluster(GC)systemhasbeenwellestablished andprovidesimportantinformationabouttheformationprocessoftheMWhaloby indicatingdistinctorigins(probablyages)ofthosetwogroupsofGCsatanearlystage ofgalaxyformation(Harris2001). ManycharacteristicsoftheM31haloaresimilartothoseoftheMW.Forexample, themetallicitydistributionofredgiantbranchstars(RGBs)inthehaloofM31is systematicallymoremetal-poorwithincreasinggalactocentricdistance(Kalirai,et al.2006).Inaddition,liketheMW,thedistributionofM31globularclustermetallicities showsabimodaldistributionwithpeaksat / #" and .Signicantnumbers ofRRLsarefoundintheM31halo(Brownetal.2004(B04);Sarajedinietal.2009 (SA09)).UnlikeRRLpopulationsintheMWhalo,therehavebeennosignicant 13

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signsoftheOosterhoffdichotomydetectedamongRRLsintheM31haloandits companiongalaxies.However,asmoreandmoreinvestigationsofRRLstarsinthe M31accumulate,itbecomesevidentthattheMWisnotthelonegalaxywhichexhibits theOosterhoffdichotomy.TheRRLpopulationsofM31alsoappearstodisplaya similardichotomyinaquiteuniqueway,suchthattheentirepatternsofthecanonical OosterhoffdichotomyfortheMWRRLsappearstobeshiftedtowardtheshortperiod directionandthegapbetweentwodistinctRRLpopulationsbecomesnarrower. WhydothesetwodominantbodiesintheLocalGroupshowsthisdifferenceinRRL populations?Whatistheimplicationofthisdifferencetotheearlystageofthestar formationhistoriesofthesegiantspirals? Inordertoanswerthesequestions,wehaveundertakenanextensivecomparison studyofRRLpopulationsintheAndromedaGroupgalaxies.M33,alatetypespiralin theLocalGroupisthestartingpointofourinvestigation(Chapter2).M33,isthethird mostmassivegalaxyandistheonlyotherspiralbesidesitsgiantcousins(theMilkyWay andM31).TheexistenceoftheeldhaloRRLyrae(RRL)populationwasconrmedby thepioneeringworkofSarajedinietal.(2006;PaperI).Theyfoundthemeanperiodof ab-typeRRL(RRab)starstobe < > days,whichisconsistentwiththemean periodofM31haloRRLsandRRLsinOosterhofftypeIMWglobularclusters.Aidedby highlyaccuratephotometryfromtheHubbleSpaceTelescope(HST)/ACS,weconducta systematicsurveyofRRLpopulationsinM33.Ourstudyprovidesampleinformationon theoldandmetal-poorstellarpopulationsinthisgalaxy. ThenexttargetofourinvestigationisNGC147,oneofdwarfsatellitesofM31 (Chapter3).Intermsofitsmorphology,NGC147isatypicaldwarfellipticalor spheroidalgalaxy.However,itisdistinctfromotherdwarfgalaxiesintheLocal GroupbecauseNGC147isdominatedbyanoldstellarpopulation(Hodge1989).The presenceofanRRLpopulationinNGC147wasreportedbySahaetal.(1990,(S90)). AndthisstudyappearstobetheonlypreviousstudyoftheRRLpopulationinNGC147. 14

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ArchivalimagingdatafromtheHST/WideFieldPlanetaryCamera2(WFPC2)forNGC 147thatmayallowustoupdatethelistofRRLyraespublishedbyS90. FinallyinChapter4,webringourattentiontowardtwofaintM31dwarfsatellites, AndXIandAndXIII.Therecentdiscoveryofultra-faintdwarf(uFd)systemsaround theMilkyWay(MW)andM31hasdramaticallychangedourunderstandingofthelower limitofthegalaxyluminosities(Willmanetal.2005a,b;Zuckeretal.2006a,b;Belokurov etal.2006,2007;Sakamoto&Hasegawa2006;Iwinetal.2007;Walsh,Jerjen,& Willman2007).ThesenewlydiscovereduFdgalaxiesaregenerallyfainterthan =8.0,signicantlydarkmatterdominated(atleast / > / ),andsome ofthemostmetal-poorstellarsystems( / < )everfoundintheLocalGroup (Simon&Geha2007).ThepresenceoftheseuFdgalaxieswaspredictedbymany cosmologicalsimulationsoftheformationoftherstgalaxies(Ricotti&Gnedin2005), whichsuggestedthatsomeofthesefaintgalaxiesmaybe"fossils"oftherstgalaxies inwhichthebulkofstarsformedbeforethereionizationoftheUniverseatz # 710 (Bovill&Ricotti2009).AndXIandAndXIIIareparticularlyinterestingobjectsbecause theyappeartollthegapbetweenthecanonicaldSphandthenewlydiscovereduFd populationsintheluminosity-metallicityrelationsoftheLocalGroupdwarfgalaxies. However,thereisstillinsufcientinformationaboutthegeneralproperitesofthesenewly discoveredgalaxies.ThedetailedinvestigationonthepropertiesoftheRRLpopulations inAndXIandAndXIIIusingdeepHST/WFPC2archivalimagescanshedlightonthe originofthesefaintsatellitesystemsandtheformationmechanismoftheirgianthost galaxy,M31. Basedonthecollectiveinformationfromouranalysis,wewillattemptndcluesto whytheMWandM31exhibitdifferentdichotomiesintheRRLpopulationsandwhatare thefundamentaldifferencesintheformationbetweentheMWandAndromedaGroup galaxies. 15

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CHAPTER2 RRLYRAEVARIABLESINM33.OOSTERHOFFPROPERTIESANDRADIALTRENDS 2.1BackgroundStudy IntheLocalGroup,theTriangulumgalaxy,M33,isthethirdmostmassivegalaxy andistheonlyotherspiralbesidesitsgiantcousins(theMilkyWayandM31).Unlike itsmoremassivecounterparts,M33hasalatetypemorphology(Scd)withoutabulge (oraveryweakbulge);thegalaxyhasarelativelylowdarkhalovirialmassof # 10 M (Corbelli2003)andahightotalgasmassfractionof to ,whichisatleast twotimeshigherthanthatinM31(Garnett2002;Corbelli2003).Thelatetypespiral galaxyM33hasnotbeenstudiedasextensivelyastheMilkyWay(MW)andM31.The measureddistancetoM33showsalargedispersion( # kpc)intheliterature andisstillcontroversial,mainlyduetotheuncertaintyinthereddeningvalues.The starformationhistorythroughoutseveraldifferentpartsofM33(innerdiskandouter disk/halo)wasrecentlystudiedbyBarkeretal.(2007)andWilliamsetal.(2009).The resultsintheliteraturearequiteintriguing.Whiletheinnerpart(r < kpc)ofthe galaxyshowsthesignatureofinside-outgrowth(Williamsetal.2009),theouterpart (r > kpc)showsanincreaseintheageofthestellarpopulationwithgalactocentric distance(Barkeretal.2007).LargenumbersofGlobularcluster(GC)-likeobjectshave beenfoundinM33.TheGCsysteminM33appearstohaveaverybroadrangeof agesexhibitingastrongerresemblancetotheclusterpopulationsofthelower-mass MagellanicCloudsthantheMWorM31(Sarajedinietal.2000;Chandaretal.2002; Sarajedini&Mancone2007;SanRomanetal.2009).Recently,Huxoretal.(2009) discoveredfourremotestarclustersintheouterhaloofM33.Bycomparingthe(VI) colorsofthenewclusterstotheMWandM31outerhaloGCs,theyconcludedthatthe M33haloclustersarearchetypicalGCsaswell.TheexistenceoftheeldhaloRRLyrae (RRL)populationwasconrmedbythepioneeringworkofSarajedinietal.(2006;Paper I).Theyfoundthemeanperiodofab-typeRRL(RRab)starstobe < > days, 16

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whichisconsistentwiththemeanperiodofM31haloRRLsandRRLsinOosterhofftype IMWglobulars.Theab-typeRRLstarsarefundamentalmodepulsator,whichexhibit sawtooth-likelightcurves,whereasc-typeRRL(RRc)starsarerstovertonepulsators withlightcurvesthataresinusoidal.ThepresenceandcharacteristicsofthoseRRLs providedirectevidencesupportingthenotionthattheM33halocontainsasignicantold population( > Gyr). InthisChapter2,wefocusontheRRLpopulationinM33usingnewspace-based observations.Thispopulationisaversatiletool;awiderangeofastrophysicalquestions canbenetfromthestudyofthesestars.RRLstarsareawellknownpopulationII standardcandleusedtoprovideanaccuratedistancetoM33.Inaddition,the(VI) minimumlightcoloriswellestablishedsothatitcanbeusedtoaccuratelydeterminethe lineofsightreddeningtowardeachRRLinM33.Thepulsationperiodsandamplitudes ofRRabexhibitarelationshipwithmetallicity.Bycombiningknowledgeoftheiroldages ( > Gyr),wecanconstrainageandmetallicityinformationintheearlystagesof M33'sformation. TheChapter2isorganizedasfollows.In ¤ 2.2wedescribetheobservationsand datareductionprocedure.In ¤ 2.3wepresentthedetailedprocedureusedtoselectand characterizetheRRLcandidates.Wepresentthesyntheticlightcurvesimulationsand theresultsin ¤ 2.4.TheradialtrendsinthemetallicityofourRRLcandidatesandtheir implicationsfortheformationoftheM33haloarediscussedin ¤ 2.5.Finally,in ¤ 2.6,we summarizeourresults,andpresenttheconclusionsofthisstudy. 2.2ObservationsandDataReduction ThescienceimagesusedinthisstudyweretakenalongthemajoraxisofM33with theAdvancedCameraforSurveysWideFieldChannel(ACS/WFC)on-boardHSTas apartoftheGO-10190program(P.I.:D.Garnett).Theobservationswereoriginally intendedtostudythestarformationhistoryoftheM33disk.Weusedthreeprimary ACS/WFCeldsinthesouthwestdirectionreferredtoas"DISK2"( =9.3'),"DISK3" 17

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( =15.9')and"DISK4"( =22.6')forthepresentsurveyofRRLstars,where represents thegalactocentricdistanceofeachtargeteldinarcmin.Foreachtargeteld,20 exposuresthroughtheF606Wand24exposuresthroughtheF814Wweretaken.The observinglogissummarizedinTable2-1. TherawimagesofthesethreetargeteldswereprocessedbythestandardSTScI pipeline(biasanddarksubtracted,andatelded);thesecalibrated"FLT"images weredownloadedfromtheHSTarchive.InordertopreparetheprogramFLTimages, whichwereusedforthepoint-spreadfunction(PSF)photometry,werstmultiplied thembythecorrespondinggeometriccorrectionframes;thebad-pixelsweremaskedby applyingthedata-qualitylesandthePSFphotometrywasperformedontheresulting framesofeachACSchip(WFC1andWFC2)usingtheDAOPHOT/ALLSTARand ALLFRAMEroutines(Stetson1994).AdetaileddescriptionofthePSFconstruction andthetime-seriesphotometryispresentedinSarajedinietal.(2006).Theeffectof adecreasingchargetransferefciency(CTE)forWFCwascorrectedontheresulting photometrybyusingtheACS/CTEcharacterizationdevisedbyRiess&Mack(2004). Then,thephotometriccalibrationoftheinstrumentalmagnitudestothestandard Johnson-CousinssystemwasperformedviathetheoreticaltransformationofSirianniet al.(2005).WeadoptedthelatestACSzero-pointvalues,whichwererevisedonMay19, 2009(ACSISR07-02). TheresultingphotometryreachesV # 29.5mag(Figure2-1).Theaverage photometricaccuracyatthelevelofthehorizontalbranchandtheredclumpofM33 is # 0.05mag.Therefore,wedonotexpectphotometricaccuracytoadversely affecttheremaininganalysisoftheRRLs. 2.3DetectionofRRLyraeVariableCandidates Weattempttodetectallpossiblevariablestarcandidateswithinarangeof magnitude( < < )bycalculatingthereduced valueformeasuringvariability ofeachstarwhichisdenedbythefollowingformula: 18

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Table2-1. ObservingLog. FieldR.A.(J2000)Dec(J2000)FiltersExpTimeDataSetsHJDRange(+2450000) DISK2013339.69+302859.98F606W16 % 1240s,j90o21,j90o233257.10472to3260.25101 2 % 650s,2 % 60s F814W20 % 1240s,j90o24,j90o263258.10428to3258.85153 2 % 750s,2 % 60s DISK3013320.49+302214.99F606W16 % 1240s,j90o31,j90o333416.70446to3416.85083 2 % 650s,2 % 60s3418.70294to3418.84935 3421.63415to3421.78837 F814W20 % 1240s,j90o34,j90o363386.71436to3386.93625 2 % 750s,2 % 60s3414.70627to3414.85230 3421.10114to3421.31423 DISK4013307.89+301506.98F606W16 % 1240s,j90o41,j90o433314.61986to3320.16401 2 % 650s,2 % 60s F814W20 % 1240s,j90o44,j90o463313.96950to3319.43119 2 % 750s,2 % 60 19

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" % " # Inordertoavoidfalsevariabilityduetooddphotometricmeasurements,any datapointthatdeviatesfromthemeanmagnitudeby3 wasexcludedfromthe calculation.Starswitha valuegreaterthan2.5wereconsideredtobevariable starcandidates.Forreference,thereduced valueforatypicalnon-variablestarat themagnitudeoftheRRLsinM33( < > fromPaperI)is # 2.5.This variabilitycriterionproducedalistofabout2000variablestarcandidatesfromthethree ACS/WFCeldsanalyzedherein. Weappliedourownlightcurvetemplate-ttingroutinedubbed,FITLC'(Layden 1998;Mancone&Sarajedini2008)tothe and passbandmagnitudes ofthesevariablestarcandidatesinordertondthebestcombinationofperiodand amplitude.ThelatestversionofFITLCimplementstheLomb-Scargleperiodogram (Lomb1976;Scargle1982)modulefortheinitialguessofthebestpossibleperiods. ThenthenaloutputperiodsandamplitudesarerenedbyrunningthePikaia' algorithm(Charbonneau1995),whichisarobustoptimizationroutinethatsearches forthebestcombinationofperiodandamplitudethroughagivenrangeoftestperiods thatminimizesthe valuesbetweentheobserveddatapointsand10differentlight curvetemplates(Layden1998).Inthiscase, representsthegoodnessoftemplate ttingatthetestperiodsforeachRRLcandidates.Starswithminimum lessthan3.0 atthebestttingperiodareconsideredprobableRRLcandidates.Fromourexperience, thisthresholdisgenerousenoughtoincludepracticallyallpotentialRRLcandidates. Finally,weexaminedthelightcurvesoftheprobableRRLcandidatestoconstructour nalRRLlist.Wend86RRLstarsfromtheDISK2eld(65RRab,18RRc,and3 RRd),and22(20RRaband2RRc)and14(11RRaband3RRc)RRLstarsinthe DISK3andtheDISK4elds,respectively. 20

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2.4Results Figure2-1showsthelocationofourRRLcandidatesinthe(V,VI)color-magnitude diagrams(CMDs)ofthethreeACSelds.Withfewexceptions,mostRRLsforma distinctgroupbetweentheblueedgeoftheinstabilitystrip( ,Mackey &Gilmore2003)andtheredclumpstars.Thereisacleartrendinthelocationsofthese RRLstarsandtheredclumpstarsintheCMDsduetoreddeningandextinction.In addition,thedistributionofDISK3RRLcandidatesintheCMDlooksmoredispersed thanthoseintheothertwoelds.ThisisprobablybecausethequalityoftheDISK3RRL lightcurvesisnotashighasthoseoftheothereldRRLcandidates.Furthermore,the numberofRRLcandidatesdecreasesdramaticallywithgalactocentricdistance.This ismainlyduetothedecreasingstellardensitytowardtheoutskirtsofthegalaxybutis alsoinuencedbytheincompletenessinthedetectionofRRLstarsineacheld.Wewill addresstheseissuesinmoredetailinthefollowingsection.Thebestttinglightcurves forournalRRLcandidatesfromourFITLCanalysisarepresentedinFigure2-2. AcoupleofbrightstarswellabovethemaingroupofRRLcandidatesintheDISK2 eldCMDarepossibleanomalousCepheids(ACs).TheseareunusualCepheid variablestarswithperiodsbetween0.4and2days.Hence,theyshareasignicant portionoftheirperiodrangewiththeRRLstars( < < ).However,ACs areeasilydistinguishedfromagroupofRRLstarsduetotheirbrightness,being0.5-2 magnitudesbrighterin thantheRRLs;thisindicatesthatACshavemassesof1-2M (Norris&Zinn1975;Zinn&Searle1976;Hirshfeld1980;Zinn&King1982;Wallerstein &Cox1984;Smith&Stryker1986;Bonoetal.1997).Stellarevolutionarymodelshave demonstratedthatstarsinthismassrangearerequiredtobequitemetal-poor(e.g. / < ,Demarque&Hirshfeld1975)inordertoevolveintotheinstabilitystrip. Theirrangeinmassandmetallicitysuggesttwopossiblescenariosfortheirorigin: ACsareeither1)relativelyyoungstarswithagesof1-3Gyr,or2)oldstarsbutwith increasedmassfrommasstransferinbinarysystems(Renzini,Mengel,&Sweigart 21

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Table2-2. PropertiesofAnomalousCepheidCandidates. IDR.A.(J2000)Dec(J2000) < >< > Period(days)A(V)(mag) 63275013344.38+303014.3124.950.82530.6010.535 165840013349.15+302835.0224.400.75610.9970.497 1977).WehaveuncoveredtwocandidateACs(ID63275,&ID165840)intheDISK2 eld.TheirphotometricandpulsationpropertiesaresummarizedinTable2-2.TheseAC candidatesarebrighterthantheRRLgroupby # 0.5and # 1.0mag,respectively,and theirVIcolorsplacethemneartherededgeoftheinstabilitystripintheCMD.Thus, theircolor-magnitudepositionsareconsistentwiththoseoftypicalACs. Figure2-3illustratesthebestttinglightcurvesforthetwoACs.Botharepulsating inthefundamentalmodewithperiodsandamplitudesintheexpectedrange.Since theseACsweredetectedintheDISK2eld,whichistheinnermostoftheelds consideredherein,theyaremorelikelytobelongtotheyoungtointermediate-age diskpopulationofM33thanitshalo. 22

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Figure2-1. ThelocationoftheRRLyrae(RRL)candidatesinthe color-magnitudediagramsofthethreeACSelds(DISK2,DISK3,DISK4). MostRRLcandidatesarelocatedintheinstabilitystripbetweentheblue edgeofthisstrip(dottedblueline, 0.28;Mackey&Gilmore 2003)andtheredclumpstars(RCs)ofM33.Theslopesshowninthe distributionofRRLsandRCsreecttheamountofreddeningandextinction towardthetargeteldsasshownbythevectorsineachpanel. Figure2-2. ThebestttinglightcurvesoftwoAnomalousCepheid(AC)candidates foundintheDISK2eld. 23

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Figure2-3. ExamplesofthebestttinglightcurvesforDISK2RRLcandidatesobtained fromourtemplatelightcurvettingroutine(FITLC;Layden1998,Mancone &Sarajedini2008) 24

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Figure 2-3 .Continued. 25

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Figure 2-3 .Continued. 26

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Figure 2-3 .Continued. 27

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Figure 2-3 .Continued. 28

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Figure 2-3 .Continued. 29

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Figure 2-3 .Continued. 30

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Figure 2-3 .Continued. 31

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Figure 2-3 .Continued. 32

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Figure 2-3 .Continued. 33

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Figure 2-3 .Continued. 2.4.1SyntheticLightCurveSimulations InordertoproperlyinterpretthepulsationpropertiesoftheRRLstars,itisimportant tocharacterizeanyobservationalbiasesinthesample.Propertiesoftheobserving windowsuchasthetimebaseline,numberofepochs,anddatasamplingintervalsare importantforthedetectionofRRLsbecausethephasecoveragedependsonthese parameters.Inaddition,theaccuracyoftheRRLbrightnessmeasurementsandthe techniqueusedtodeterminetheperiodscanalsoinuencethecompletenessofagiven RRLsample. InordertogaugethecompletenessofourRRLsamplesandincorporatethe parametersmentionedabove,weperformedthefollowingsetofsyntheticlightcurve simulations(Sarajedinietal.2009;Yang&Sarajedini2010).First,wecalculated analyticalformsof8representativeRRLlightcurves,6fundamentalmode(RRab) and2rst-overtonemode(RRc),byrunningFourierdecompositionsonthelightcurve templatesofLayden(1998).Wegenerated1000syntheticlightcurvesforbothpulsation modesusingthesefunctionalformsapplyingthesameobservingwindow(observing timebaseline,samplinginterval,numberofepochs,andphotometricerrors)aseach targeteld.PeriodsandamplitudeswererandomlyassignedtoeacharticialRRL fromreasonableperiod-amplituderangesfortypicalRRLstars( < < days; 34

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< < mag).Thephotometricerrorswerealsoassignedtoeachdatapoint byapplyinggaussiandeviateswiththemeanphotometricerroratthehorizontalbranch (HB)levelofM33( # 0.05mag).Then,weappliedourtemplatelightcurvetting techniquetothearticialRRLsinexactlythesamemannerasouroriginalperiodnding analysisandcomparedtheoutputpulsationpropertieswiththeinputones. Figure2-4illustratestheresultsofoursimulations.AmongthethreeACSelds, DISK2exhibitsthebestrecoveryefciencywithnosignicantaliasingintheoutput periods.Intheothertwoelds(DISK3andDISK4),weseesignicantbiasesinthe outputperiodsoftheRRLs.Further,wealsoconductedthesamesetofsimulations separatelyforRRabandRRcstarsinordertoinvestigatehowtherecoveryefciency varieswiththepulsationmode.Thistime,weconstrainedtheinputperiodsand amplitudesofthearticialRRLsusingtypicalrangesfromtheperiod-amplitudediagram (RRab: < < days, < < mag;RRc: < < days, < < mag).Oursimulationsrevealthat # 91 ofDISK2RRabperiodswere welldeterminedwithaperioderrorof 0.07days,and # 97 ofRRcstarsinDISK2 eldwereaccuratelyrecoveredwithin 0.05days. Oursyntheticlightcurvesimulationsalsomakeitpossibletoexaminethedegree towhichRRLyraestarsaremisidentiedbetweenRRabandRRcstarsinourperiod ndinganalysisbasedonthetypeofthebesttlightcurvetemplate.FortheDISK2 eld,only # 5 ofthefundamentalmodearticialRRLsendedupbeingidentied asrst-overtoneRRLsand # 9 oftherst-overtoneRRLsweremisidentiedas fundamentalmodeRRLs.Therefore,theeffectofcross-contaminationduetothe combinationoftheobservationalwindowsandperiodndingroutineisverysmallinthe DISK2RRLs. FortheDISK3andDISK4RRLcandidates,wewouldliketoinvestigatethepossible causesoftheperiodaliasingproblem.Thephotometricaccuraciesandthenumberof epochsarealmostthesameinourthreeACSelds.However,thesamplingintervals 35

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arequitedifferent(Table2-1).TheDISK2datapointsarealmostevenlyspacedand shownosignicantgapsduringa # 3dayobservingwindow.TheDISK3dataare composedofvedifferentsetsofobservations,andonedatasetisseparatedfromthe otherfourby # 1month.DISK4datahavetwosetsofobservationsseparatedby # 5 days.ThislikelyexplainswhythelocationoftheDISK3RRLcandidatesinthe(V,VI) CMDappearsmoredispersedthanthatoftheRRLsintheothertwoACSelds. Wenowre-plotthe P(thedifferencebetweentheoutputperiodsandtheinput periods)distributionsforthearticialRRLstarsalongwiththebestgaussiants.As seeninFigure2-5,the PdistributionsfortheDISK2,DISK3andDISK4articialRRL starsarerelativelywellapproximatedbysymmetricgaussianfunctionswithmeanvalues closetozero,suggestingthatthepositiveandnegativealiasedperiodslargelycancel eachother.Hence,thesystematicperiodshiftinthemeanoutputperiodsofourRRLs samplesislikelytobenegligible.Furthermore,inordertogaugetheeffectofaliasing onthecalculatedvalueofthemeanperiod,weperformedthefollowingstatisticaltest. Assumingthatthe1000articialRRLsrepresenttheparentRRLpopulationforeach targeteld,werandomlysampledeachparentpopulation,eachtimedrawingthesame numberofarticialRRabandRRcstarsasourobservedRRLsineacheld(DISK2 :65(RRab)and18(RRc);DISK3:20(RRab)and2(RRc);DISK4:11(RRab)and 3(RRc)).Then,wecalculatethemeanvalueof P.Afteriteratingthisprocess100times andcalculatingtheaverageofthemean Pvaluesforeachtrial,wend < > = +0.006and-0.0002daysfortheDISK2RRabandRRc,and+0.030and-0.042daysfor theDISK3RRabandRRc,respectively.FortheDISK4RRLs,thesevaluesare0.006 and0.019days.Thistestsuggeststhattheeffectofthealiasedperiodsonthemean periodsofourRRLsamplesinthreeACSeldsisinsignicantascomparedwiththe measuredperioderrors.Asaresult,themeanperiodsoftheRRLsintheDISK3and DISK4eldsarestillmeaningful,andcanserveasausefuldiagnosticintheremainder ofouranalysis. 36

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Figure2-4. TheresultofoursyntheticlightcurvesimulationsfortheDISK2RRLs.The upperpanelshowsthedifferencebetweentheinputandoutputperiodsasa functionoftheinputperiods.Thelowerpanelsexhibitthedistributionsofthe deviationoftheoutputperiodandVbandamplitudefromtheinputvalues. Oursimulationresultsshowthatthemeasuredperiodsandamplitudesof theDISK2RRLsarenotsignicantlyaffectedbyaliasingandyieldreliable results. 37

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Figure 2-4 .Continued. 38

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Figure 2-4 .Continued. 39

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Figure2-5. ThedistributionoftheperioddeviationforsyntheticRRabandRRcstars. Dashedlinesillustratethebestgaussiantsforeachdistribution. < > and representthepeakandstandarddeviationofthegaussians, respectively. 40

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2.4.2Period-AmplitudeDiagrams TheRRabstarsshowalinearrelationshipbetweentheirperiodsandamplitudes (P-A)-thelongertheperiods,thesmallertheamplitudes.TheRRcstarsformadistinct groupatthelower-left(shortperiodsandsmallamplitudes)corneroftheP-A(orBailey) diagram.Metallicityisthoughttobetheprimaryparameterdeterminingthelocationof theRRabsequenceintheBaileydiagram.Ingeneral,thesequenceofmetal-poorRRab starsislocatedatlongerperiodsascomparedwithmetal-richRRabvariables.This metallicitydependanceoftheP-ArelationsofRRabstarsisthoughttoberelatedtothe OosterhoffeffectthatispresentamongRRLsintheGalacticGlobularClusters(GGCs) andtheGalacticHalo.OosterhofftypeI(OoI)systemstendtohaveintermediate metallicitiesandameanpulsationperiodof # 0.55dayswithalowRRcfrequency(( = / =0.2),whileOosterhofftypeII(OoII)systemsaregenerallymetal-poorandhave meanpulsationperiodsof # 0.65daysinthefundamentalmodewithahigherfractionof RRcstars( =0.45;Castellani&Quarta1987).Similartothesecondparametereffect intheHBmorphologiesofGGCs,metallicityisprobablynotthelonephysicalparameter governingtheOosterhofftypes,butratherageandheliumabundancecouldbetheother parametersresponsiblefortheOosterhoffdichotomy(Lee&Carney1999). Figure2-6illustratestheP-AdiagramsandtheperioddistributionsforRRL candidatesinourthreeACSelds.TheopencirclesrepresenttheRRabstarsand theopentrianglesrepresenttheRRcstars.TheamplitudesintheF606Wpassband havebeenconvertedtoJohnsonV-bandamplitudesbyapplyingan adjustment asdiscussedbySarajedinietal.(2009).Forcomparison,weincludethelociforOoI (left)andOoII(right)globularclusterRRLsfromClement(2000)alongwiththeM31 haloeldRRLs(bluesymbols)identiedbyBrownetal.(2004).InFigure2-6,wesee thattheDISK2eldRRLsresemblethoseinOoIGalacticglobularclusters.Themean periodsofRRabandRRcstarsintheDISK2eldare < > =0.553 0.008(error1) 0.05(error2)and < > =0.325 0.008(error1) 0.05(error2),respectively, 41

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wherethequotederror1valuerepresentsthestandarderrorofthemeanandtheerror2 valueistheuncertaintyofanindividualRRLperiodcalculatedfromoursyntheticlight curvesimulations.ThefractionofRRcstarsintheDISK2eldis =0.22,whichis alsoconsistentwiththatofOoIclusters.OurresultsagreewellwiththoseinPaperI (Sarajedinietal2006). Threepossibledouble-modepulsators(RRd;lledsquares)havealsobeen uncoveredintheDISK2eld.Figure2-7illustratesthebesttlightcurvesforthese stars.Atagivenperiod,boththefundamentalandrst-overtonepulsationmodes appeartorepresenttheobservationswithalmostequalttingquality(i.e.comparable valuesoftheminimum ).Inordertodeterminewhetherthesestarsaregenuine doublemodepulsators,weneedtobeabletoisolateasecondaryperiodandpulsation modeagainstadominantprimaryperiodandmode.However,therelativelysmall numberofepochsinourdatasethindersourabilitytoperformthistypeofanalysis. TheDISK3eldRRLsseemtohaveaslightlylongerRRabmeanperiod[ < > =0.588 0.02(error1) 0.08(error2)]andsmallerRRcfraction( =0.1) thanthoseinDISK2,buttheyareindistinguishablewithintheerrors.TheDISK4RRLs appeartohavesimilarpulsationproperties[ < > =0.554 0.02(error1) 0.07 (error2)and =0.21]asthoseintheDISK2eld.ThephysicalpropertiesoftheRRL candidatesshowninFigure2-18aresummarizedinTable2-3. 42

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Table2-3. PropertiesofRRLyraestars. R.A.Decl.Period ID(J2000)(J2000) < >< > (days)A(V)Type DISK2 33705013343.58+303033.6025.50010.64080.55540.9500ab 37108013340.32+302725.0225.10800.67460.68450.4390ab 39703013334.53+302745.6925.34120.58410.60101.0300ab 44059013337.80+302704.9525.23770.64180.55980.7530ab 48640013336.50+302928.0525.27020.51720.51100.8750ab 48732013332.78+302947.6425.28410.56630.54240.7880ab 52467013342.76+302724.9925.47410.68960.60100.7430ab 52574013339.14+302811.5625.21910.46300.38890.3370c 54436013341.04+302759.2625.36560.59080.48460.8340ab 54552013339.34+302822.7825.17020.55930.47080.8430ab 58238013338.65+302831.0825.40560.58620.52250.9450ab 58887013333.54+302951.0025.41680.72560.54080.9950ab 64158013338.44+302658.9125.35150.45880.28890.3550c 64222013336.74+302745.5825.35540.53840.54020.9210ab 64530013337.85+302659.5425.48720.62600.57970.7100ab 66232013331.65+302933.9725.47020.54640.56290.5850ab 66373013334.44+302855.1825.45150.52600.48461.2070ab 67135013330.79+302909.1125.37980.63250.62621.0700ab 67613013341.60+302743.7925.54420.67290.52020.8920ab 68118013342.66+303041.2525.36340.63800.55310.8050ab 68304013339.12+302656.9425.45190.56790.51891.2140ab 69095013335.18+303007.3425.43390.66430.59520.6480ab 69523013338.39+302727.5825.32370.58250.57871.1120ab 69616013331.97+302944.2725.49480.49860.32660.5390c 69877013334.17+303005.4725.45700.58300.45480.5370ab 70274013332.20+302826.3325.49770.50850.32660.4090c 70413013333.97+302927.6725.50110.56820.51400.9550ab 70437013335.24+302956.0725.69140.63910.56291.0060ab 70883013332.12+302904.9825.31890.55360.59490.7580ab 71080013333.95+302807.8325.57800.71140.56290.4000ab 72183013333.50+302802.3425.50250.57440.51400.6410ab 72255013337.14+302724.1825.46450.51880.35450.4630c 72395013339.81+302718.0625.48000.47480.31520.5180c 72591013333.48+302927.6125.58020.65160.34800.2770c 72791013336.52+302850.6025.68790.62490.60760.5630ab 73530013333.73+302819.3525.55860.71260.57970.6410ab 73775013331.65+302844.4925.56210.60600.55330.8130ab 73857013335.62+302834.0925.51680.53240.30640.4920d? 73861013333.07+302848.7125.56880.58310.48461.0570ab 43

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Table 2-3 .Continued 74391013335.89+302758.7125.62370.54070.42071.2230ab 74866013337.16+302722.2325.40000.38640.30840.5250c 75980013332.65+302904.3125.53830.61370.54770.8050ab 76411013334.05+302927.3325.50960.45810.33160.3920c 76702013341.08+302730.7025.69230.83350.65080.4050ab 77327013332.74+302823.0725.38410.60840.63341.0380ab 78061013335.64+302816.9625.58050.40840.29710.4650c 78276013332.68+302815.0325.83770.78760.60880.6840ab 78711013336.91+302710.8625.51780.44900.27530.4020c 78837013332.23+302910.4825.63480.66400.36650.3830c 78978013336.74+302941.4625.48940.54120.65550.8130ab 78989013333.94+302802.5925.54050.55410.53140.9430ab 79908013334.58+302944.2625.79230.80980.65600.5960ab 81570013339.13+302754.4325.73330.70070.53220.6790ab 82761013333.09+302824.6925.61220.62910.49100.8010ab 83030013335.17+302913.1825.61360.65510.49911.1120ab 84269013339.20+302644.3425.84370.80990.53140.7550ab 84294013339.34+302859.0525.75030.78630.55750.7970ab 85891013338.79+302841.6125.68570.57530.53250.9150ab 86364013337.13+302711.5225.92620.92520.66370.7580ab 87852013337.53+302907.8025.65570.41840.25890.4170c 88070013339.21+302850.8625.88460.71700.45110.7930ab 88156013337.30+302833.3125.88400.69480.35760.5820c 88944013341.99+302804.3925.82440.76380.49530.6730ab 89028013335.18+302859.0726.06000.96850.70590.5080ab 92098013339.64+302736.1925.84940.72420.51870.7600ab 95220013341.45+302820.8325.99150.86190.51400.8860ab 99497013338.79+302851.7726.09900.84510.51400.9510ab 114604013349.15+302846.2625.47430.61810.52560.9470ab 114727013343.69+303014.5025.49280.50700.31060.4920d? 132832013347.58+302907.7425.58350.51290.33670.6390d? 136354013349.25+302839.8525.37520.62480.54760.8430ab 243724013340.29+303042.3225.91460.87540.62640.5080ab 345532013340.49+303016.8325.33640.54500.54090.4420ab 363388013339.36+303031.4625.39790.53510.51401.4250ab 366971013341.38+302957.4125.42420.65280.57970.4570ab 460914013337.78+303035.7425.40920.57260.53151.3020ab 485358013338.02+303026.1225.68570.55440.35760.3260c 498017013338.60+303013.6025.63000.55470.34210.3940c 499480013339.65+302955.7225.43270.68290.62660.5870ab 524355013338.91+303002.2925.44250.62580.57970.4980ab 575741013339.79+302935.6725.37050.71650.65600.6320ab 587244013337.46+303011.6425.80960.53090.42390.9550ab 647112013342.72+302830.3825.09540.40560.32460.2830c 44

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Table 2-3 .Continued 664395013340.70+302859.4226.12150.90000.50511.0310ab 718692013343.69+302757.3225.36640.39680.28190.4630c 720258013344.34+302746.3625.42360.61480.53740.9860ab DISK3 74810013320.54+302255.6225.54770.53260.49471.1250ab 83951013321.25+302241.9125.67370.53670.60340.8050ab 146812013313.79+302230.4725.42190.58780.53991.0880ab 184411013314.57+302229.1925.23310.64330.61190.9150ab 186337013322.60+302255.0125.72930.57790.51891.0270ab 186744013321.77+302316.6125.71410.67370.56000.6390ab 196320013316.18+302154.9225.49380.67060.61520.4900ab 213526013321.07+302346.8925.91020.84540.55000.9210ab 238563013326.70+302131.3125.37150.55910.56280.9240ab 253410013322.72+302323.2825.61890.71290.61690.8970ab 254214013318.35+302128.0825.37860.47710.35930.3480c 261564013320.54+302036.0125.52360.64200.61300.5200ab 271863013321.22+302023.4225.56420.70830.64400.8490ab 295746013322.10+302358.0025.77120.62670.51030.6960ab 302086013323.24+302331.7325.80410.52540.52871.2590ab 316752013317.47+302219.8725.38810.64920.58000.8500ab 366209013318.18+302225.8925.39270.46490.48441.1690ab 388301013327.50+302218.7025.59310.58180.76920.8080ab 393798013329.14+302137.1825.30590.41730.68000.8520ab 454675013325.28+302345.4125.54040.90720.73181.0980ab 471587013330.06+302145.8225.88860.57050.54090.6090ab 486862013328.60+302232.1925.04210.42930.34830.2430c DISK4 28911013303.16+301616.8625.43350.55500.55070.8100ab 37201013307.52+301658.6325.63210.61420.50341.1230ab 44542013313.33+301539.7225.32990.57420.54801.1420ab 75940013306.19+301414.9025.37040.63240.64980.4880ab 159071013313.76+301455.9325.18700.60140.37100.4240c 161615013311.25+301645.9825.33050.86080.57981.2350ab 170838013309.02+301619.1225.41950.44910.33270.4340c 177007013306.51+301550.9125.54750.70930.62080.7960ab 181971013311.23+301637.3525.33430.68990.62060.4800ab 189423013316.41+301509.8525.90280.54210.39011.0850ab 208128013306.91+301542.2225.47730.50390.48431.0320ab 222740013307.97+301546.9525.18870.49700.40930.2650c 277120013313.43+301403.1925.44550.59550.56480.6600ab 290021013306.88+301507.7625.51770.63810.57970.8260ab 45

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Figure2-6. ThisgureillustratestheP-AdiagramsandtheperioddistributionsforRRL candidatesinthethreeACSelds.FromtheP-ArelationofDISK2RRLs (leftpanel),inparticular,weseethatRRLsinthiseldexhibitOosterhoffI characteristics( < > =0.553 0.008(random) 0.05(systematic)days; < > =0.325 0.008(random) 0.05(systematic)days).Thefrequency ofRRcstarsintheDISK2eldRRLs( 0.22)alsoagreeswellwiththe valuesforOosterhoffIglobularclusters.Intermsoftheaveragebehaviorin theP-Adiagramandtheperioddistribution,DISK3andDISK4RRLslook similartothoseoftheDISK2RRLs. 46

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Figure2-7. ThebestttinglightcurvesfortheRRdcandidatesfoundintheDISK2eld. TheirperiodsandVbandamplitudesbelongtotheregimeofRRcstars. Bothfundamentalandrst-overtonepulsationmodescouldbepresentinthe lightcurveofeachcandidate. 47

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2.4.3Reddening TheupperpanelofFigure2-8showsazoomed-inviewoftheDISK2RRabstars intheVICMD,illustratingthattheircolor-magnitudedistributioniswellmatchedwith thereddeningvectorintheDISK2eld.ThelowerpanelofFigure2-8presentsthe (VI)colorhistogramoftheDISK2RRabstars,revealingthepresenceoftwopeaks -aprimarypeakat(VI) # 0.5andasecondaryoneat(VI) # 0.8.Wesuspectthat theRRabstarscomprisingthesecondarypeak-thosewith(VI) > 0.74inthe(VI) histogram-sufferfromhigherreddeningduetodustinternaltoM33.Inorderto investigatethishypothesis,wecancalculatetheline-of-sightreddeningofindividual DISK2RRabstarsusingtheir(VI)colorsatminimumlight.ItisknownthatRRab starsexhibitaverysmallrangeofintrinsic(VI)colorsatthefaintestpointontheirlight curvesindependentofperiodandmetallicity(Sturch1966;Mateoetal.1995).Weadopt =0.58 0.02fromthelatestworkbyGuldenschuhetal.(2005). Figure2-9illustratesthereddeningdistributionofDISK2RRabstars,revealing asharppeakat < > =0.175 0.014(random) 0.04(systematic)where therandomerrorrepresentsthestandarderrorofthemeanandthesystematicerror istheuncertaintypropagatedfromtheobserved(VI)minimumlightcolorscalculated byoursyntheticlightcurvesimulation.Thehistogramsinsolidblacklines(binnedand generalized)representthereddeningdistributionofall65RRabstars,whilethered dottedhistogramsincludeonlythosestarswith(VI) > 0.74.Ourhypothesisseemsto becorrectthatthefainter/redderRRabstarsarebeingaffectedbyextinctioninternalto M33.OnepossibilitytoexplainthisscenarioisthattheRRabstarsnear(VI) # 0.5are onthenearsideofM33whilethosewith # 0.8areonthefarsideofthegalaxy. Wenowre-plottheP-AdiagramofDISK2RRLstarstolookfordifferencesin thepulsationpropertiesofthelowandhighreddeningRRLs.Figure2-10showsthis comparison(opencircles-RRab,opentriangles-RRc,lledsquares-RRd;lled circles-highreddeningRRabstars).Thisgureshowsthatthehigherreddening 48

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RRLsexhibitthesamepulsationpropertiesasthosewithlowerreddening.Aswe seeinthenextsection,thissuggeststhatthemeanmetallicitiesofthelowreddening andhighreddeningRRabstarsareindistinguishablefromeachother;thesimplest scenariotoexplainthisistoassumethatthetwosetsofRRLyraesrepresentthesame stellarpopulation,oneinfrontoftheM33diskandtheotherbehindit.Asaresult,itis reasonabletoassertthatthemajorityoftheRRabstarsdetectedintheDISK2eldare likelytobeinthehaloofM33. 49

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Figure2-8. Theupperpanel(zoomed-inVICMD)illustratesthecolor-magnitudetrendof DISK2RRLs;itappearstobewellmatchedwiththereddeningvectorinthis eld.Thelowerpanelpresentsthe colordistributionofDISK2RRab stars,revealingthepresenceoftwopeaks-aprimarypeakat # 0.5 andasecondarypeakat # 0.8.TheRRLscomprisingthesecondary peakmightresideonthefarsideofM33,hencetheysufferfromhigher reddeningduetotheinternalreddeningoftheM33disk. 50

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Figure2-9. ThereddeningdistributionforDISK2RRabstars.Thelineofsightreddening ofindividualRRabstarswascalculatedusingthe(VI)minimumlightcolors fromtheirlightcurvesandtheintrinsicVIminimumlightcolor, =0.58,fromGuldenschuhetal.(2005).Thereddottedhistogram illustratesonlyRRabstarscomprisingthesecondarypeakofthe(VI)color distribution. 51

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Figure2-10. TheP-AdiagramoftheDISK2RRLs.HighreddeningRRabstarsare markedbylledcircles.ThelowreddeningandhighreddeningRRabstars shownosignicantdifferenceinboththeirP-Arelationandtheirmean period. 2.4.4Metallicities DuetothedistanceofM33( # 870kpc),itisdifculttodirectlymeasurethe metallicitiesoftheeldRRLsinthisgalaxy.Theyaretoofaint( < > =25.55) forspectroscopyandourdatasetdoesnothavesufcientphasecoveragetoemploy thefourierdecompositionmethod(Jurcsik&Kovacs1996).Instead,themetallicitiesof RRabstarsintheDISK2eldcanbeestimatedusingtheperiod-amplitude-metallicity relationshipdeterminedbyAlcocketal.(2000)fromtheMACHOproject.Therelationis giveninthefollowingform: / 52

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Therehasbeenconcernraisedabouttheuseofthisrelationtoestimate[Fe/H] values(Cacciarietal.2005)becauseRRLperiodshavesomedependenceon luminosity(i.e.evolutionarystate).InpaperI(Sarajedinietal2006,S06),weestablished anewperiod-metallicityrelationshipusingthedataofA.C.Layden(2005,private communication)for132GalacticRRLsinthesolarneighborhood.Usingtheordinary least-squaresbisectormethod(Isobeetal.1990),wefound / ThisrelationhasrecentlybeencorroboratedbyFeastetal.(2010).Inorderto checkthevalidityoftheMACHOequationfordetermining[Fe/H]valuesofeldRRab starsinourstudy,were-calculatedthemetallicitiesofthesestarsusingthe[Fe/H]vs relationfromPaperI(S06).WefoundthattheMACHOrelationyieldsslightly moremetalpoorvalues,however,thepeakmetallicityofthetwodistributionsdiffersby only # 0.1dex.ThereforeweconcludethattheresultsfromtheMACHOrelationarenot signicantlyaffectedbytheevolutionarystatesoftheRRLinthesample. Figure2-11showsthemetallicitydistributionfunction(MDF)oftheRRabstars thatresultsfromtheapplicationoftheMACHOequation.Forcomparison,wehave alsoplottedtheMDFofM31RRabstarsinthesamplesofB2004(dottedbinned andgeneralizedhistograms)andSarajedinietal.(2009,hereafterS2009;dashdot binnedandgeneralizedhistograms)bothcalculatedusingtheaboveequation.The histogramsarescaledtohavethesamenumberofstarsastheDISK2RRabsample. ThemetallicitydistributionsoftheDISK2RRabstarsandthoseintheM31spheroid locatedat4 6kpcfromthegalacticcenter(S2009)showacloseresemblancewith adominentpeakat < / > =-1.48 0.05,whiletheM31haloRRabstarsin thesampleofB2004at # 11kpcfromthecenterofM31yieldapeakmetallicityof < / > =-1.77 0.06.Theuncertaintieshererepresentthestandarderrorsof 53

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Figure2-11. Themetallicitydistributions(binnedandgeneralized)oftheM33DISK2 RRabstars(solidred-thisstudy)andtheM31RRLs(dottedblue-Brown etal.2004(B2004);dashdot-Sarajedinietal2009(S2009)). themeanvalues.Thesystematicerrorfromtheperiod-metallicityrelationshipisclose to # 0.3dex.ThemeanmetallicityoftheM33DISK2eldRRabstarscalculatedhere agreeswellwiththoseofthehaloglobularclusters( / =-1.27 0.11;Sarajediniet al2000)andtheeldhalostars( / =-1.24 0.04;Brooksetal2004)inM33.This isfurtherevidenceinsupportoftheassertionthattheseDISK2RRLsbelongtothehalo ofM33. 2.4.5DistanceofM33 Intheprevioustwosections,wepreparedtheframeworkforthecalculationofan accuratedistancetoM33.ThemeanVmagnitudeof65RRabstarsfromtheDISK2 eldis < > =25.55 0.03,wheretheerroristhestandarderrorofthemean. IndividualdereddenedVmagnitudesofDISK2RRabstarsareobtainedbycorrecting theapparentVmagnitudeofthosestarsfortheextinctionintheF606Wpassband. Byemployinganextinctionlaw[PaperI;A606W=2.1E(V-I)]andindividualreddening 54

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valuesfromSection2.4.2,wecalculateameanintrinsicVmagnitudeof < > =25.13 0.02(random) 0.08(systematic),wheretherandomerroristhestandard errorofthemeanandthesystematicerrorincludestheuncertaintyintheextinction propagatedfromthemeasurementsofthe(VI)minimumlightcolors. TheabsoluteVmagnitudeofeachDISK2RRabstariscomputedusingthe followingrelationship,Mv(RR)=0.23[Fe/H]+0.93,fromChaboyer(1999).Asshown inSection2.4.4,themetallicitiesofindividualRRabstarscanbeestimatedusing the / relation(Alcocketal2000).ThisgivesameanabsoluteV magnitudeof < > =0.61 0.01(random) 0.07(systematic),wherethe randomerroristhestandarderrorofthemeanandthesystematicerrorrepresentthe uncertaintypropagatedfromthecalculationofthemetallicity.Thus,themeanabsolute distancemodulusfortheDISK2RRabstarsis < > =24.52 0.11where theerroristhequadraticsumoftheuncertaintiesintheabsoluteanddereddenedV magnitudesoftheRRLs.Thisvalueofthedistanceshowsreasonableagreementwith ourpreviousresultinpaperI( < > =24.67)aswellaswiththeresultsofGalleti etal.(2004)( =24.69 0.15). WehavealsocalculatedthedistancetoM33usingtheI-bandmagnitudeofred giantbranchtip(TRGB)intheVICMDoftheDISK2eldasameansofcheckingthe validityofourRRLdistanceestimate.InordertodetecttheTRGB,aweightedSobel kerneledgedetector,[-1,-2,0,2,1](Madore&Freedman1995)wasappliedtothe generalizedIbandluminosityfunctionoftheM33RGB,whichisindependentofbin size.OneadvantageofusingthisweightedSobelkernelisthatitreducestheimpact ofnoisespikesbysmoothingthedataovertwobinsoneithersideofthecentralbin. FortheconstructionoftheIbandluminosityfunction,weexcludedstarsaboveandto theleftofthedashedline(Figure2-12)inordertominimizetheinuenceofforeground starcontamination.TheconvolutionoftheedgedetectorwiththeI-bandluminosity functionofM33RGBstarsproducesalterresponsethatpeakswhenasudden 55

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increaseintheluminosityfunctionisencountered.Figure2-13illustratestheIband luminosityfunction(top)andthelterresponsediagram(bottom).Wemeasuredthe apparentIbandmagnitudeattheTRGBtobeI=20.92 0.05mag.Thecorresponding errorreferstotheFWHMofthepeakofthelterresponse.TheTRGBlocationinthe VICMD(Figure2-12)conrmsthattheTRGBmagnitudeisreasonablydetermined fromouranalysis.WeuseareddeningvalueofE(VI)=0.175towardtheDISK2eld fromsection2.4.2andtheextinctionlawfortheHSTACSltersfromSiriannietal. (2005)( )tocalculatetheintrinsicI bandmagnitudeoftheTRGB.Doingsoyields =20.73.ByadoptingtheabsoluteI bandmagnitudeoftheTRGB, =-4.04 0.12fromtheliterature(Bellazzinietal 2001,2004),wend =24.77 0.13.Theerrorisaquadraturesumofthe errorsintheapparentandtheabsoluteIbandTRGBmagnitudes.Wenoteinpassing thatmeasurementsoftheTRGBdistanceusingtheCMDsofDISK3andDISK4are statisticallyindistinguishablefromthatofDISK2. ThemeasureddistancestoM33bythesetwoindependentmethods(RRLsand TRGB)onthesamedatasetstillshowadiscrepancy( =0.25mag) somewhatbeyondthemarginallowedbytheerrors.Theresultsfrombothmethods dependonthereddeningandthecalibrationoftheabsolutemagnitudescalesofthe RRLandTRGBstars.Sinceweadoptedthesamereddeningvalueindependently determinedbyourminimumlightcoloranalysisforourdistancemeasurements,the discrepancybetweenthesetwomethodsislikelycausedbytheuncertaintyinthe calibrationoftheabsolutemagnitudescales. 56

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Figure2-12. ThelocationoftheM33TRGBintheVICMD.Starsbelowthedashedblue linewereusedfortheconstructionoftheI-bandluminosityfunction. 57

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Figure2-13. TheI-bandluminosityfunction(upperpanel)ofM33RGBstarsinthe DISK2eld.Thelowerpanelillustratesthescaledresponseofaweighted Sobelkernel,[-1,-2,0,2,1](Madore&Freedman1995)ontheI-band luminosityfunctionofM33RGBstars. 2.5Discussion ItisinstructivetoinvestigatetheradialmetallicitytrendsinM33usingthemean metallicityofRRabstarsfoundinourthreeACSelds.Figure2-14showstheinner diskeldsofKimetal.(2002,K02,solidcircles)andtheouterdiskeldsofBarkeret al.(2007,B07,opencircles)bothofwhicharebasedonRGBsamples.Thedotted lineistheleastsquaresttotheinnerdiskpointsfromKimetal.(2002),whichalso 58

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reproducesthelocationoftheouterdiskpointsfromBarkeretal.(2007).Thesolidline inFigure2-14correspondstotheM33planetarynebulae(PNe,Magrinietal.2010), whicharebelievedtobedisktracerswithagesasoldas10Gyr(Maraston2005). Theirabundanceshavebeenconvertedfrom12+log(O/H)to[Fe/H]usingtherelation between[ # /Fe]and[Fe/H]fromBarker&Sarajedini(2008)forM33andassuming that[ # /Fe] & [O/Fe].AlsoplottedinFigure2-14arerepresentativesoftheM33halo population-ninehaloGCs(opentriangles)fromSarajedinietal(2000,S00)andthe RRLvariablesfromSarajedinietal.(2006,S06)andthepresentstudy.Thefurthest M33globularcluster(EC-1)isalsoplotted(Stonkuteetal.2008).Wenotethatthisisa modiedversionofFigure20intheworkofB07. Figure2-14suggeststhatthemetalabundanceoftheM33diskdecreaseswith increasinggalactocentricdistance( ). 1 Incontrast,thehalopopulationsshowno trendofmetalabundancewithradialpositionreminiscentofthehaloglobularcluster populationintheMilkyWaybeyond8kpcfromtheGalacticcenter.Recentworkby Marin-Franchetal.(2009),Dotteretal.(2010),andGrattonetal.(2010)hasshown thattheseGalacticglobularclusters(withR > 8kpc)exhibitpropertiesconsistent withhavingbeenaccretedinarelativelyslowandchaoticfashionfromdwarfsatellite galaxiesoftheMilkyWay.Similarly,thisarguesthatalloftheglobularclustersinM33, eventhoseascloseas2kpcfromitscenter,originatedelsewhereinitsenvirons.By extension,thisisalsolikelytobetrueoftheeldhalostarssuchastheRRLvariables. Infact,McConnachieetal.(2009)haveconductedawide-eldimagingsurveyof theM31-M33super-halo(Sarajedini2007)andconcludedthatM33haslikelybeen perturbedbyarecentdynamicalencounterwithM31.Suchanencountercouldbe 1 Itisworthnotingthat,inarecentpaper,Holtzmanetal(2010,submitted)present resultsonthestarformationandchemicalenrichmenthistoryofM33.Basedona syntheticCMDanalysis,theysuggestthatthediskmetallicitygradientintheM33disk isweakornonexistent. 59

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responsibleforthestellardebrisobservedneartheouterdiskofM33asdescribedby McConnachieetal.(2009).Inaddition,thedeciencyinthenumberofstarclusters relativetoelddiskstarsatradiigreaterthan # 3kpcfromthecenterofM33(Sarajedini &Mancone2007;SanRomanetal.2010)isconsistentwiththeideathatasignicant numberofstarclustersandeldhalostarsthatoriginatedinM33arenowlocatedinthe M31-M33super-halo(i.e.outsideofthemainbodyofM33). Theattenedmetallicitygradientandbroadrangeinmetallicityindicatethatthe M33halohasbeenbuiltupthrougharelativelyslowandchaoticfashion.Thisis incontrasttoitsmoremassivecousins(MW&M31),inwhichtheinnerhalo/bulge areconsideredtohaveformedviaarapidprocessofhierarchicalinfall.Infact,this slowandchoaticstarformationprocessinlessmassivegalaxies,suchasM33,is predictedinmanytheoreticalsimulationsofgalaxyformation(Tremontietal.2004; Brooksetal.2007;Finlator&Dave2008).Mostrecently,fromtheirhighresolution N-Body SPHsimulationsforstellarhalos,Zolotovetal.(2010)suggestthatthestellar halosoflessmassivegalaxiesareprimarilyformedfromtheaccretionoftheirdwarf companionsratherthaninsitustarformation.Theseaccretedstarsfromthemergersof dwarfcompaniongalaxiesareexpectedtohavelower # -element(suchasOandMg) abundances.Thisisbecausemassivestars,whichendtheirlivesastypeIIsupernova andareresponsiblefortheproductionof # -elementsintheearlyuniverse,formless effectivelyintheshallowerpotentialwellsofthesedwarfsatellites.Thesetheoretical predictionsareapowerfulimpetusforasystematicsurveyofthechemicalpropertiesof halostarsinM33. 60

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Figure2-14. ThemetallicityoftheM33stellarpopulationsasafunctionofdeprojected distancefromthegalacticcenter.Thedottedlineisaleastsquarestto theradialtrendoftheM33diskRGBs(Kimetal2002(K02);Barkeretal 2007(B07)).ThsolidlineshowsthemetallicitytrendoftheM33planetary nebulae(PNe)fromMagrinietal.(2010).Theshort-dashedlinerepresents themeanmetallicity( < / > =-1.36)oftheM33halostellarpopulations onthisplot.EC-1(openstar)isthefurthestM33starclusterwithknown metallicity(Stonkuteetal2008). 61

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2.6Summary WepresentananalysisofRRLstarsintheLocalGroupspiralgalaxyM33.From thepropertiesof86RRLstarsinthreeradialelds,weobtainthefollowingresults: OurtemplatelightcurveanalysisrevealsthattheM33RRLstarsexhibitproperties similartotheRRLsinGalacticglobularclustersofOosterhofftypeI. Theminimum-lightcolorsof65DISK2RRabstarsprovidereliableline-of-sight reddeningvaluesforeachindividualRRL.Fromthereddeningand(VI)colordistributions, weseeRRLstarsnotonlyonthenearside(lowreddening)ofthegalaxybutalsoonthe farside(highreddening).Furtheranalysissuggeststhattheselowreddeningandhigh reddeningRRLstarshavefundametallythesamepropertiesandlikelybelongtothe halooftheM33. ThemetallicitiesofRRabstarswerecalculatedviatheperiod-metallicityrelationship (Alcocketal.2000).Themeanvaluesandtheradialtrendofthesemetallicitiesagree wellwiththatofhaloglobularclustersinM33suggestingthattheseRRLstarsbelongto thehalopopulationofthisgalaxy. ThedistancetoM33wascalculatedwithtwodifferentmethods(RRLstarsandthe tipoftheRGB).Wend < > =24.52fromtheRRLsand24.77 0.13using theTRGB.Ourresultsareveryclosetothemeanvalue( < > =24.69)ofthe M33distancemodulusmeasurementsfromtheliterature. TheM33haloRRLsexhibitpulsationpropertiessimilartothoseofRRLinthe haloofM31.Thatistosay,theybothresembletheRRLvariablesinOosterhofftypeI Galacticglobularclusters.ThissimilaritybetweenM33andM31isnotsurprisinggiven thepastinteractionhistorybetweenthesetwogalaxies. 62

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CHAPTER3 RRLYRAEVARIABLESINTHELOCALGROUPDWARFGALAXYNGC147 3.1BackgroundStudy LocalGroupdwarfgalaxiesexhibitdiversityintheirstarformationhistories(Da Costa1998;Grebel1999).Mostofthesegalaxiesshowsomeevidenceforintermediate agestarsandsomehaveevenyoungerpopulationsalongwithasignicantamount ofgasanddust.Thebroadredgiantbranch(RGB)morphologyshownintheir color-magnitudediagrams(CMDs)reectsawiderangeofmetallicitiesand/orages, implyingthatthesegalaxieshaveexperiencedcomplexstarformationhistories.Despite theirdifferentandcomplexstarformationhistories,RRLyrae(RRL)variablesare believedtoexistinmost,ifnotall,dwarfgalaxiesintheLocalGroup.Theexistenceof RRLpopulationsinagivenstellarsystemindicatesthatthesystemisolderthat # 10 Gyr.Furthermore,theirpulsationpropertiesandabsolutemagnitudesarecorrelated withtheirmetallicities(Bonoetal.2003;Cacciari&Clementini2003).Therefore, detailedinvestigationsofthephysicalpropertiesofRRLvariablestarsarecrucialto improveourunderstandingoftheearlystagesofstarformationinLocalGroupdwarf galaxies. NGC147isoneofthedwarfspheroidal(dSph)satellitesoftheAndromedagalaxy (M31).Intermsofitsmorphology(seeTable3-1),NGC147isatypicaldwarfelliptical orspheroidalgalaxy.However,itisdistinctfromotherdwarfgalaxiesintheLocal Group,withthepossibleexceptionofTucana(Fraternalietal.2009),becauseNGC147 isdominatedbyanoldstellarpopulation(Hodge1989).Thereisaslightindicationof intermediateagestars(e.g.extendedasymptoticgiantbranchstars)concentratedinthe centralregions(Hanetal.1997),buttheirsignatureisweakerthantheintermediateage stellarpopulationsfoundinotherLocalGroupdwarfgalaxies.Furthermore,NGC147 appearstoshowsacompletedecitofgasanddust. 63

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ThepresenceofanRRLpopulationinNGC147wasreportedbySahaetal.(1990, hereafterS90).TheyusedThuan-Gunn -bandgroundbasedphotometryobtained fromtheHale5mtelescopeequippedwiththe4-shooterCCDsystemtoidentifyRRL variablesinthisgalaxy.Theyfound32RRLcandidatesanddeterminedthedistance modulusofNGC147tobe =23.92basedontheirmeanapparent -band magnitudes.Theirperiodsandamplitudeswereestimatedbyusingaprototypeof thephasedispersionminimizationmethoddevelopedbyLaer&Kinman(1965),the so-calledL-Kmethod.Sahaetal.(1990)didnotpresentacomparisonofthepulsation propertiesoftheseRRLcandidateswiththoseinotherLocalGroupgalaxies.One reasonforthismaybethatthelargephotometricerrors( > 0.15mag)atthelevel ofthehorizontalbranch(HB)ofNGC147producedsignicanterrorsintheperiod determinations-especiallyfortheshorterperiodRRLs(P < 0.4d).However,theeffect ofthephotometricerrorsontheperioddeterminationwasnotaddressedbecausethe L-Kmethodignoresthephotometricerrorsintheprocessofidentifyingtheoptimal period. Sahaetal.(1990)paperappearstobetheonlypreviousstudyoftheRRL populationinNGC147.Wearemotivatedtorevisitthepropertiesofthesestarsfor tworeasons.First,wehavehadgoodsuccessinusingalightcurvetemplate-tting algorithm(Layden&Sarajedini2000)todeterminethepropertiesofRRLssuchas periods,amplitudes,andmeanmagnitudes.Thismethodincludesthephotometric errorsintheanalysisandhasbeenstreamlinedandredesignedtobemoreuser-friendly byMancone&Sarajedini(2008).Thiswillallowustorenethedeterminationofthe RRLperiodsandplacebetterconstraintsonthetotalnumberofsuchvariablesinNGC 147.Second,therearearchivalimagingdatafromthe WideFieldPlanetaryCamera2(WFPC2)forNGC147thatmayallowustoupdatethe listofRRLspublishedbyS90.AlthoughtheWFPC2dataprovideaccuratephotometry attheleveloftheHBinNGC147,theyexhibitpoorphasecoveragewithatimebaseline 64

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Table3-1. PhysicalpropertiesofNGC147. PropertyValueReference RA00 33 11.9 Dec+48 30'24.8" ( )119.82 ,-14.25 V -193 3 / Benderetal1991 (m-M) 23.95Sharinaetal2006 M -15.1" E(B-V)0.18 0.03Schlegeletal1998 A 0.580" < / > -1.11 0.01Nowotnyelal2003 < / > -2.2 0.42DaCosta&Mould1988 of # 0.4day.However,itisstillusefulbecauseitcouldhelptoidentifytheshorterperiod, loweramplitudeRRLsthatmaynothavebeendetectedbyS90. Thenextsectiondescribestheobservationaldatasetsthatwewillanalyze. Sections3-2and3-3makeitclearthatneithertheS90datanortheWFPC2data areidealforthepurposeofstudyingtheRRLsinNGC147,buttheydocomplement eachothernicely.AsdiscussedinSection3-4,itisimportanttocarryoutsimulationsto fullyunderstandthebiasesandcaveatsinherentintheresultsobtainedfromeachofthe datasets.TheconclusionsarepresentedinSection3-5aswellasthecaseforfuture worktobettercharacterizethevariablestarsinNGC147anditsM31dwarfsatellite cousinNGC185. 3.2ObservationsandDataReduction 3.2.1GroundBasedData The -band(Thuan&Gunn1976)photometryofNGC147isavailableindata tablesprovidedbyS90.Thetargeteld,located6'northwestofthegalaxy'scenter alongwithsemi-majoraxis,wasobserved15timeswith20minexposuresin1986, and8timeswith30minexposuresin1987,duringfourconsecutivenights.Thelimiting magnitudeoftheirphotometryis ,whichisabout1.25magnitudefainter thantheHBmagnitudeofNGC147.ThephotometriccompletenessoftheHBstars (at # 25.5)is62%inthecrowdedregionsand72%inthosethatarelesscrowded. 65

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ThephotometricerrorsfortheHBstarsare > mag,whichiscomparable totheamplitudeofc-typeorlowamplitudeab-typeRRLs.Baileyab-typestarsare fundamentalmodepulsatorswhichhaveasawtooth-like,asymmetricallightcurve shape,whilerst-overtonec-typepulsatorshavesinusoidallightcurves.RRLwith ab-type(RRab)havelongerperiods(0.5 < P < 1.2days)thanthec-types(RRc)stars (0.2 < P < 0.5days;Smith2004). 3.2.2HubbleSpaceTelescopeData Observationstakenwith /WFPC2oftheouterregionsofNGC147are availableinthe archive(Hanetal,1997,programID:GO-6233).Thetarget eld,locatedat4'southofthegalaxy'scenter,wasimaged7timesinF555W( # V)and 6timesinF814W( # I),withexposuretimesfrom1300sto2800sasdetailedinTable 3-2.Thetimebaselineofthedatasetspans0.4days.Theobservationswereprimarily intendedtostudythecharacteristicsofthe(nonvariable)stellarpopulationsofNGC147. AlloftheWFPC2imageswerephotometeredbyusingtheHSTphotpackage (Dolphin2000),whichisdesignedforuseonWFPC2data.First,anyimagedefects, suchasbadpixels,cosmicrays,andhotpixelswereremovedbyusingtheutility softwareincludedwithinHSTphot.Then,thephotometricmeasurementsweremade oneachimagebyrunningHSTphotin"PSFtting"mode.HSTphotusesalibraryof pointspreadfunctions(PSFs)forWFPC2images.Theaperturecorrections,dened bytheaveragedifferencebetweenaperturephotometrywitha0.5"radiusandthePSF photometry,werealsoappliedbyHSTphot.Aminimumthresholdforobjectdetection wasset3 abovethebackgroundsignal.Weselectedstarswithhigh-qualityphotometry (i.e.stellarproleswith < mag)fromtheoutputofHSTphotforfurtheranalysis. Figure3-1showstheVICMDofNGC147fromthe /WFPC2data.The photometriclimitreachesV # 28.2mag.Thebroadredgiantbranch(RGB)ofNGC 147primarilyindicatesawiderangeofmetallicityamongthestellarpopulationsinthis galaxy.Thisgurealsoshowsabluehorizontalbranch(BHB)andadistinctinstability 66

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Table3-2. WFPC2ObservingLog DatasetFilterExptime2450000HJD u2ob0101tF555W2400s9890.01465 u2ob0102tF555W1300s9890.06934 u2ob0103tF555W1300s9890.08594 u2ob0104tF555W1300s9890.13672 u2ob0105tF555W1300s9890.15332 u2ob0106tF555W2800s9890.21289 u2ob0107tF555W2800s9890.27930 u2ob0108tF814W1300s9890.33789 u2ob0109tF814W1300s9890.35449 u2ob010atF814W1300s9890.40527 u2ob010btF814W1300s9890.42188 u2ob010ctF814W1300s9890.47168 u2ob010dtF814W1300s9890.48828 stripgapwhichisthewellknownlocationofRRLs.Weperformedcompleteness testsofourphotometryusingHSTphot'sarticialstarfeature.Thismodulecreatesa comparablenumberofarticialstarsforeachcolor-magnitudebinfromtheobserved CMDandrandomlydistributestheseineachoftheoriginalWFPC2image.Thearticial starsarephotometeredinexactlythesamemannerastheactualstars.Figure3-2 illustratestheresultofthesecompletenesstests.AtthemagnitudeoftheHB(V # 25.5 mag),thecompletenesslevelisabout95%.Therefore,wedonotexpectphotometric incompletnesstoadverselyaffectthedetectionofRRLcandidatesidentiedinthe WFPC2data. 67

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Figure3-1. VIcolor-magnitudediagramforthedwarfellipticalgalaxy,NGC147.A color-magnituderange( < < ,and < < )shownasa boxisusedtosearchforRRLyraecandidates. 68

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Figure3-2. AcompletenesstestfortheWFPC2VIphotometry.Averticallineindicates thehorizontalbranch(HB)magnitudeofNGC147.Thephotometric completenessofHBstarsreachesalmost93 3.3RRLyraePeriodDetermination Thepreviousstudy(Sahaetal1990)usedtheLaer-Kinman(L-K)algorithm (Laer&Kinman1965),aprototypeofthephasedispersionminimizationmethod (PDM)forperioddetermination.TheL-Kalgorithmdenesatestparameter, ,the sumofthesquaresofthedifferencesbetweentwoadjacentmagnitudesrearranged intheascendingorderofphasesforeachtrialperiod.Thealgorithmthensearches fortheperiodthatminimizethetestparameter.SincetheL-Kmethodusesonlyone freeparameter(period)fortheperiodoptimization,thecalculationisrelativelysimple, straightforward,andfasterthanotherperiodndingroutines.However,itdoesn'ttake intoaccountsomeimportantfactors,suchastheamountofphotometricerror.Large photometricerrorscaneffectivelymaskintrinsicvariabilitypresentinthedatamaking subsequentperiodsolutionshighlysuspect.Asaresult,asLaer&Kinmanstressedin theiroriginalpaper,theL-Kalgorithmmayhavedifcultyinobtainingreliableperiodsfor 69

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variableswithrelativelysmallamplitudes( $ 0.75mag)whenthedatasethasalimited numberofobservationsandmoderatephotometricaccuracy.Becausethemajority ofRRLvariableshaveamplitudesthatfallbelowthisthreshold,itisimportanttobe cautiousininterpretingperiodsandamplitudesderivedfromtheL-Kmethodespecially whenthephotometricerrorsaresignicant. Wehaveanalyzedboththe /WFPC2andthe -bandphotometricdatasets (Sahaetal.1990)usingourownlightcurvetemplate-ttingsoftwaredubbedFITLC' (Layden1998;Mancone&Sarajedini2008).ItusesanalgorithmknownasPikaia' (Charbonneau1995),whichisarobustoptimizationroutinethatcomputesthebest combinationofperiodandamplitudeinordertominimizethe valuesbetweenthe observeddatapointsand10differentlightcurvetemplatestakenfromtheworkof Layden(1998). TheadvantagesofusingtemplatettingforthedeterminationofRRLperiodsare twofold.First,basedonextensivetestswehaveperformed,thetemplate-ttingroutine generallyworksbetterforsmallnumbers(N $ 30)ofobservationsthantheL-Kmethod. Thepowerofthetemplate-ttingmethodforthedeterminationoflightcurveproperties fromrelativelysmallnumbersofpointsiswellpresentedintheliterature(Mackey& Gilmore2003;Sarajedinietal2006;Mancone&Sarajedini2008). Secondly,thetemplatettingmethodprovidesanassessmentofthevariable starclassicationbasedontheshapeofthephasedlightcurve.WhethertheRRLis anab-typeorc-typenaturallyfollowsfromtheresultsofthemethodbasedonwhich templateprovidesthebestttotheobservationaldata. 3.3.1ReanalysisoftheSahaetal.Data GiventheadvantagesoftemplatelightcurvettingovertheL-Kalgorithmforcases wherethenumberofobservationsissmall,wehavereanalyzedthe -bandphotometry of32RRLcandidatesinNGC147fromS90usingtheFITLCroutine.Figure3-3show thebestttinglightcurvesfortheRRLcandidatesfromFITLCascomparedwiththe 70

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resultsfromS90.Theactualperiodsdeterminedbythetwomethodsarecomparedin Figure3-4andlistedinTable3-3,whichalsoshowstheclassicationofeachvariable starandthemeanmagnitude.. Overall,theresultingperiodsfromtheL-KandFITLCmethodsappliedtotheS90 -banddatabearlittleresemblancetoeachother.Wefoundonly6cases(C1-V9, C1-V10,C1-V11,C3-V8,C3-V12,andC4-V9)outof32RRLswhereL-KandFITLC agreereasonablywellinbothperiodandclassication.However,wefoundthatL-K periodstendtobelongerthanFITLCperiods,especiallyintheshortperiodranges(P < 0.6days). InordertofurtherinvestigatethedifferencesweseebetweentheL-Kmethodand FITLC,wehaveperformedthefollowingofsetsimulations.Wegeneratedeighth-order FourierdecompositionsofthetemplatelightcurvesofLayden(1998),6ab-typesand 2c-types,andcalculatedtheirFourierparameters.Withthefunctionalformsofthese8 lightcurves,wecreatedsyntheticRRLlightcurveswithknownperiodsandamplitudes thatmimicthe -bandobservationsofS90.Wesampledeachlightcurveat23different epochs(themaximumnumberintheS90analysis)withmeasurementerrorsgiven bythemeanvaluetakenfromtheactual -banddata.Periodsandamplitudeswere randomlyassignedtoeachsyntheticRRLfromreasonableperiod-amplituderanges fortypicalRRLvariables(0.2 < P < 1.5days,0.2 < Amp < 1.5mag).Inthisway,the articialRRLvariablesproperlyrepresentimportantobservationalconditionsthatcan affecttheperioddeterminationsuchasthetimebaseline,thenumberofobservations, andthephotometricerrors.WethenappliedL-KandFITLCmethodstothesynthetic lightcurvesinexactlythesamemannerasouroriginalperiodndingroutinesand comparedthederivedperiodswiththeinputones. Figures3-5(L-Kmethod)and3-6(FITLC)showtheresultsofoursimulations forthe -bandobservationsofS90.TheyshowthatFITLCworksbetterthantheLK methodinndingperiodsusingtheS90photometry;however,somesystematicerrors 71

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stillremainintheFITLCresults.TheFITLCroutinerecovered # 59%oftheinput periodsfromthesyntheticRRLswithaperioderrorof 0.1days,whiletheLKmethod onlyrecovered # 15%oftheinputperiodswiththesameperioderror.Indeed,even thoughthe -bandphotometryofNGC147fromS90coveredasignicantobservational baseline( # 4to5days)andprovidedareasonablenumberofobservations( $ 23 epochs),theperiodndingresultsarelargelyunreliablebecauseoftherelativelyhigh errorsinthemeasuredphotometry.Ifwereducetheerrorsbyafactorof2,thenthe recoveryefciencyoftheinputperiodsfromtheFITLCroutineisenhancedupto # 72% butremainsunchangedfortheLKmethod.Weshouldnotethattheaveragephotometric erroroftheg-bandphotometryattheleveloftheHBis # 0.2mag.Evenifwereduce themagnitudeerrorbyafactorof2,mostofthephotometricdatastillexhibiterrors of # 0.1mag,whichisstilltoolargetofacilitateaccurateperioddetermination.Thus, thepropertiesoftheRRLcandidatesderivedfromtheg-bandphotometrymustbe interpretedwithextremecaution. 72

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Table3-3. Characteristicsofthevariablestars ObjectP(LK) < > (LK)Type(LK)P(FITLC) < > (FITLC)Type(FITLC) C1-V10.5854324.65ab0.2199024.60EB C1-V20.4948024.71ab0.9831824.69EB C1-V30.4297825.05ab0.2872324.95EB C1-V40.7225925.06ab0.3027424.86c C1-V50.3886124.62c?0.3788825.20ab C1-V60.2826024.46c?0.6453824.20c C1-V70.3483524.55c?0.4199824.58c C1-V80.8166024.95ab0.8491024.88c C1-V90.5365525.04ab0.5375325.08ab C1-V100.8605324.68ab0.8504424.86ab C1-V110.4310424.80ab0.4335224.79ab C1-V120.2789524.81c0.5579024.91EB C1-V130.7172424.99ab0.4103724.95ab C1-V140.2735525.11c0.2188825.04EB C3-V10.5293325.44ab0.5187925.21c C3-V20.8672925.25ab0.8573825.18c C3-V30.7450824.54ab0.6876624.56ab C3-V40.6087524.77?0.3054624.80c C3-V50.5464925.18ab0.3687025.37ab C3-V61.2229724.84AC0.7678824.88ab C3-V71.2353324.53AC0.5528424.57ab C3-V80.5419424.54ab0.5380624.53ab C3-V90.6996725.01ab0.3499124.88c C3-V100.6713225.17ab0.3358725.36ab C3-V110.5734624.69ab0.4551524.70ab C3-V120.7166625.00ab0.7581924.96ab C3-V130.7581624.70EB?0.7052924.65c C4-V10.7786524.76ab0.5733324.68ab C4-V20.7530425.58ab0.5989025.38c C4-V30.7636625.38ab0.4026725.59ab C4-V40.4634824.96ab0.8253925.02c C4-V50.7797925.28ab0.6095425.02c C4-V60.6437325.21ab0.6799425.30c C4-V70.5713725.43ab0.3456025.52ab C4-V80.2973125.22c0.3637525.08EB C4-V90.6045925.35ab0.5569625.31ab 73

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Figure3-3. TheleftpanelsshowtheRRLyraelightcurvesphasedusingtheperiod derivedbySahaetal.(1990)viatheL-Kperioddeterminationmethod.The rightpanelsshowthesamevariablesbutphasedusingperiodsderivedfrom thetemplated-ttingFITLCmethod.Inthisandsubsequentgures,itis apparentthatanumberofstarsthoughttobeRRLyraevariablescouldin factbeeclipsingorcontactbinaries. 74

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Figure 3-3 .Continued. 75

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Figure 3-3 .Continued. 76

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Figure 3-3 .Continued. 77

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Figure 3-3 .Continued. 78

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Figure 3-3 .Continued. 79

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Figure 3-3 .Continued. 80

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Figure 3-3 .Continued. 81

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Figure 3-3 .Continued. 82

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Figure3-4. AcomparisonbetweenperiodsdeterminedfromtheL-KandFITLCmethods usingthe -bandphotometryofRRLyraecandidatesinNGC147.TheL-K periodsarefromSahaetal(1990)whilethosefromFITLCcomefromthe presentstudy.Thereappearstobelittlecorrelationbetweenthetwosetsof values. 83

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Figure3-5. TheresultsofRRLyraevariablesimulationsbasedonthe -band photometryofSahaetal.(1990)withtheL-Kmethodareshown.Theupper panelcomparestheinputandoutput(recovered)periodswhilethelower panelshowsthedifferenceasafunctionofinputperiod. 84

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Figure3-6. SameasFigure 3-5 exceptthattheFITLCtemplate-ttingalgorithmis employedtodeterminetheperiodsoftheRRLyraecandidates. 85

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3.3.2Analysisof /WFPC2ArchivalData Asshowninsection3.2,the /WFPC2dataofNGC147aredeepenoughto provideaccurateVmagnitudesforRRLcandidates.Theaveragephotometricerrorin theVbandattheHBmagnitudelevel(V # 25.5)is < 0.05mag.Therefore,unlikethe -bandphotometryofS90,perioddeterminationfromtheWFPC2datashouldnot beadverselyaffectedbythephotometricerrors.However,theWFPC2archivaldata forNGC147haveashortobservationalbaseline( # 0.4days)withasmallnumberof availableepochs.Thec-typeRRLs,whichhaveperiodsof # 0.2-0.4dayswithrelatively smallamplitudes( $ 0.3mag),mightbelessaffectedbythisshortobservational baseline.Giventheselimitationsofthedata,weproceededwithcautionindening oursetofcandidateRRLs.First,weselectedstarswithacolor-magnituderange ( < < ,and < < ),shownasarectangularboxinFigure3-1. Then,wecalculatedthereduced oftheobservedVandImagnitudesofeachstaras avariabilityindexdenedbythefollowingformula. % " # ThisdiagnosticisdistinctfromthevariabilityindexofWelch&Stetson(1993) becausethelatterusescorrelationsinvariabilitybetweendifferentlterpassbands. Starswith valuegreaterthan2.0wereconsideredasvariablecandidates.Based onthiscriterion,931starswereselected.WeappliedtheFITLCtemplatelight-curve ttingroutinetotheV-andI-bandobservationsofthesevariablecandidatesinorder tondthebestcombinationofperiodandamplitude.Ofthese,36RRLs(32ab-type andfourc-type)havecolorsandmagnitudesthatplacethemalongtheHB,wherewe wouldexpectRRLstobelocated.Figure3-7showsthebest-ttinglightcurvesforthese RRLcandidatesandFigure3-8illustratestheirlocationsintheNGC147CMD.Table 3-4givestheirpositionsasmeasuredfromtheworldcoordinatesysteminformation intheimageheadersaswellastheirindividualmeanmagnitudesandcolors.The 86

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meanVmagnitudeoftheRRLcandidatesis < > .Giventhemean metallicityderivedbyNowotnyetal(2003)andtheRRLluminosity-metallicityrelation fromChaboyer(1999), / ,wendadistancemodulusof byapplyingareddeningofE(BV)=0.18fromSchlegeletal (1998).ThisvalueisinreasonableagreementwiththedistancequotedinTable1from Sharinaetal.(2006)andthevalueof fromHanetal.(1997); ourdistanceplacesNGC147approximately100kpcinfrontofM31. InordertoassesstheeffectsoftheobservingwindowontheFITLCperiods derivedfromtheWFPC2photometry,wecarriedoutsyntheticlightcurvesimulations aswedidontheground-baseddataofSahaetal.(1990).HundredsofarticialRRLs werecreatedusingtemplatelightcurveswithknownperiodsandamplitudes.The numberofepochs,magnitudesandphotometricerrorswerecarefullyassigned tomimictheWFPC2data.Then,weappliedtheFITLCalgorithmtothissimulated dataset.ThesimulationresultsarepresentedinFigure3-9.TheyshowthattheWFPC2 time-seriesdataofNGC147arebettersuitedfortheinvestigationofRRLperiodsthan theground-based -bandphotometryfromSahaetal.(1990).However,thatbeingsaid, fortheentirerangeoftestperiods(0.2d < P < 1.5d),only # 39%oftheoutputperiods areinagreementwiththeinputperiodsofthearticialRRLswithin 0.1days.The situationismarkedlyimprovedfortheshortperiodvariables(P < 0.40d),whichtendto bethec-typeRRLs.Theyexhibitgenerallybetterperiodrecovery( # 84%)withinthe givenperioderrors. 87

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Table3-4. CharacteristicsofRRLyraeCandidates ObjectRA(J2000.0)Dec(J2000.0) < >< > V1812003313.41482850.2225.1370.537 V1571903311.18482806.0525.0720.753 V1680303312.61482751.4925.0790.740 V1760003313.28482823.1025.2240.529 V1830403309.60482810.8625.1690.331 V2032503309.83482811.6825.2930.278 V2073103309.20482821.5525.4590.435 V2083403311.69482850.5525.3090.588 V2204603314.32482827.6825.3890.447 V2225103313.13482745.5825.4310.204 V2230803313.43482744.4725.4840.099 V2266003313.26482837.3225.3920.155 V2310403311.66482847.1925.6320.682 V2350503314.28482822.0325.5880.519 V2408003312.82482856.9625.6570.219 V3753703314.89482732.2325.1610.636 V3817003316.90482708.7525.2340.684 V3830203319.96482753.6525.3000.727 V3875703322.22482743.1525.3170.170 V3894403315.98482720.2425.3030.538 V3945103323.75482740.4325.3380.508 V3959103317.03482801.6525.3680.596 V3966803319.29482746.5425.4400.792 V3990603321.73482735.5625.4350.420 V4026403320.47482752.4625.4710.600 V4031503320.74482736.2325.5100.596 V4037803318.59482736.3125.5130.418 V4109403318.34482710.2125.5680.412 V4123203318.79482721.5125.6000.434 V5653503314.15482639.4525.3950.516 V5664103311.18482617.7725.4060.409 V5686803314.99482542.1925.3990.329 V5718503313.88482636.2825.5190.714 V5723103314.95482551.1525.4980.650 V5783103316.45482556.1125.6840.721 V5811703314.23482614.7625.6390.310 88

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Figure3-7. ThebestttingtemplatelightcurvesforpossibleRRLyraecandidatesin NGC147basedonarchivalWFPC2imaging.Thelledcirclesrepresentthe V-bandphotometrywhiletheopencirclesshowtheI-band.Thesolidcurve isthebest-ttemplatelightcurve.Thestarnumberandtheperiodisgivenin eachpanel. 89

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Figure 3-7 .Continued. 90

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Figure 3-7 .Continued. 91

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Figure3-8. ThepositionsofthemostprobableRRLyraecandidatesfromtheFITLC analysisofWFPC2archivaldataintheVICMD. 92

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Figure3-9. TheresultofarticialRRLyraevariabletestforWFPC2archivaldatawith FITLCroutine. Generallyspeakinghowever,ourinvestigationofboththe bandground-based photometryandtheVI /WFPC2archivaldataleadsustotheconclusionthatour currentknowledgeoftheperiodsandamplitudesofRRLstarsinNGC147ishighly uncertain.Weneedbetterobservationaldatawithhighaccuracyphotometry,sufcient 93

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coverageoftheobservationalbaseline,andmanyavailableepochs,inordertofully understandthecharacteristicsoftheRRLpopulationofNGC147. 3.4Summary Inthisstudy,wepresentaninvestigationoftheRRLpopulationinthelocalgroup dwarfgalaxy,NGC147usingavailabletime-seriesphotometryfromboththegroundand HST.Basedonourperiodndinganalysisandarticialvariablestartests,wedrawthe followingconclusions: The -bandphotometryfromtheworkofSahaetal.(1990)likelypossessesan adequateobservationalbaselineandavailableepochs.However,oursimulations showedthatthephotometricerrorsatthelevelofthehorizontalbranchsignicantly hindertheaccuratedeterminationofthepulsationperiodsoftheRRLcandidatesin NGC147. Ourtemplatelightcurvettingtechnique(FITLC)detected36probableRRL candidatesfrom /WFPC2archivaldata.However,oursimulationsrevealthatthe shortobservationalbaselineandsmallnumberofobservationsseverelyaffectthe accuratecharacterizationofRRLperiodslongerthan # 0.4days,whichareessentially theab-typeRRLyraes. The -bandphotometryandtheWFPC2archivaldataanalyzedhereinpresent twoextremecasesoftenfoundinperiodndingstudies-goodphasecoveragebut withlargephotometricerrors,andhighqualityphotometrywithpoorphasecoverage. Ourinvestigationofthesetwoextremecasesnotonlyprovidesagoodreferencefor interpretingthepulsationpropertiesofRRLvariablesinothersimilarsituations,but alsocallsattentiontoastrongneedfornewhighqualitytime-seriesobservationsof NGC147.Thus,whilewecancondentlyassertthatNGC147containsRRLvariables, andthereforeapopulationolderthan # 10Gyr,itisnotpossibleatthistimetousethe pulsationpropertiesoftheseRRLstostudyotheraspectsofthisoldpopulation. 94

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CHAPTER4 HST/WFPC2IMAGINGOFTHEDWARFSATELLITESANDXIANDANDXIII:HB MORPHOLOGYANDRRLYRAES 4.1BackgroundStudy SincetheSculptorandFornaxdwarfspheriodal(dSph)galaxieswererst discoveredbyShapley(1938),suchdSphsystemshavedrawnsignicantattention duetotheirpotentialrolesintheprocessofgalaxyformationandevolutionasthe basicbuildingblocksofgiantgalaxiesinthe CDMhierarchicalmodel(White&Rees 1978;Hernquist&Quinn1988,1989;White&Frenk1991).Accordingtothecollective informationsofar,dSphgalaxiesaretheleastluminousandtheleastmassivegalaxies. Thesegalaxiesarethemostcommontypeofdwarfgalaxies.Itisalsoconrmedthatall dSphsystemsintheLocalGroupharborancientstellarpopulationsasoldastheoldest GalacticGlobularClusters(GGCs)indicatingthatLocalGroupgalaxiesmaysharea commonepochofearlystarformation(Grebel&Gallagher2004).Thetotalmasses oftheLocalGroupdSphsystemsaregenerallyontheorderof # ,whichare comparabletothemassesofthemostmassiveGalacticGCs(i.e.themostmassive GGC, $ Cenhasthetotalmassof # ).Despiteofthisrelativelynarrowrangeof totalmasses,thesedSphgalaxiesexhibitawidevarietyintheirstarformationhistories, whichwasdescribedbyMateo(1998)inhisreviewas"notwoLocalGroupdwarfshave thesamestarformationhistory". Therecentdiscoveryofultra-faintdwarf(uFd)satellitesaroundtheMilkyWay(MW) andM31hasdramaticallychangedourunderstandingofthelowerlimitofthegalaxy luminosities(Willmanetal.2005a,b;Zuckeretal.2006a,b;Belokurovetal.2006,2007; Sakamoto&Hasegawa2006;Iwinetal2007;Walsh,Jerjen,&Willman2007).These newlydiscovereduFdsystemsaregenerallyfainterthan =8.0,signicantlydark matterdominated(atleast / > / ),andsomeofthemostmetal-poorstellar systems( / < )everfoundintheLocalGroup(Simon&Geha2007).The presenceoftheseuFdgalaxieswaspredictedbymanycosmologicalsimulationsofthe 95

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formationoftherstgalaxies(Ricotti&Gnedin2005),whichsuggestedthatsomeof thesefaintgalaxiesmaybe"fossils"oftherstgalaxiesinwhichthebulkofstarsformed beforethereionizationoftheUniverseatz # 710(Bovill&Ricotti2009). AndXIandAndXIIIwererstdiscoveredbyMartinetal.(2006,hereafterM06) alongwithAndXIIviaaMegaCamsurveywiththeCanada-France-HawaiiTelescope (CFHT).Bysumminguptheuxofbrightmembersintheupperpartofredgiantbranch (RGB),theycalculatedalowerlimitoftheabsolutemagnitudeofthesegalaxies.The obtainedabsolutemagnitudesareintherange,7.3 < < 6.4.Afollow-up investigationbasedonaKeck/DEIMOSspectroscopicsurveyandSubaru/Suprime-Cam imagingwascarriedoutforthesethreefaintsatellitesbyCollinsetal.(2010,hereafter C10).Basedontheirspectroscopicandphotometricdata,C10obtainedaverylow metallicity([Fe/H] # 2)forbothAndXIandAndXIII.C10alsoattemptedtomeasurethe distancetothesefaintsatellitesbyusingboththetipofRGBandthehorizontalbranch (HB)magnitudes.TheirresultslocateAndXIatadistanceof # 760kpc.ForAndXIII, theyobtainedadistanceintherangeof760940kpc. AndXIandAndXIIIareparticularlyinterestingobjectsbecausetheyappeartoll thegapbetweenthecanonicaldSphandthenewlydiscovereduFdpopulationsinthe L-MrelationsoftheLocalGroupdwarfgalaxies.However,thereisstillinsufcient informationaboutthegeneralproperitesofthesenewlydiscoveredgalaxies.In thischapter,wepresentacomprehensivestudyofthestellarpopulationsinthese twofaintM31satellitesbyusingdeeparchivalimagestakenwiththeWideField PlanetaryCamera2onboardtheHubbleSpaceTelescope(WFPC2/HST).This chapterisorganizedasfollows.Section4.2providesashortdescriptionofthedata setandphotometry;Section4.3describesgeneraltrendsinthecolor-magnitude diagrams(CMDs)andadetailedHBmorphologyanalysis;Section4.4illustratesour RRLyrae(RRL)detectionmethodandthepulsationpropertiesofRRLpopulations foundineachgalaxy;Section4.5describesthemetallicitymeasurementsbyusing 96

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twoindependentmethods(RGBslopeandRRLperiods);Section4.6describesthe distancemeasurement;Section4.7presentstheL-Mrelationsofourtargetgalaxiesand adiscussionoftheimplicationsoftheirL-Mrelationsonthepossibleorigins.;Section 4.8presentsasummaryofourresults. 4.2ObservationandDataReduction TheHST/WFPC2imagesofAndXIandAndXIIIareavailableintheHSTarchive (programID:GO-11084).Thecentralregionsofeachgalaxywereimaged16times inF606W( # V)and22 # 26timesinF814W( # I)withexposuretimeof1200s.The detailedobservinglogissummarizedinTable4-1.Wephotometeredthepointsources intheWFPC2imagesusingtheHSTphotpackage(Dolphin2000).Pre-constructed "pointspreadfunctions(PSFs)"foreachWFPC2passbandintheTinyTimPSFlibrary wereusedtofacilitatethePSFphotometry.Badpixels,cosmicrays,andhotpixelswere removedbyusingtheutilitysoftwareincludedintheHSTphotpackagebeforerunning HSTphotontheimages.ApertureandCTEcorrectionswerecalculatedusingthe defaultsettingsofHSTphot.Apperturecorrectionisdenedbytheaveragedifference betweenthePSFphotometryandtheaperturephotometrywitha0.5arcsecradius.The nallistofstarsfromtheresultantphotometryonlyincludesthepointsourcesaggedas a"goodstar"(Objecttype1)bytheHSTphotclassication. 4.3Color-MagnitudeDiagrams(CMDs) 4.3.1GeneralDescriptionoftheCMDs Color-magnitudediagramsofAndXIandAndXIIIintheVIpassbandsare presentedinFigures4-1and4-2.Therightpanelsofeachgureillustratethe photometriccompletenessderivedfromarticialstartest,indicatingthatthepoint sourcesinbothgalaxiesarewellphotometeredto # 1magnitudebelowtheHBlevelwith approximately # 90%photometriccompleteness.Thusweassumethatthephotometric incompletenessdoesnotsignicantlyaffecttherestofouranalysis,whichisfocusedon thehorizontalbranchstarsandbrighter. 97

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Table4-1. ObservingLog. ObjectR.A.(J2000)Dec(J2000)FiltersExpTimeDataSetsHJDRange(+2454000) AndXI004620.0+334730.0F606W16 % 1200su9x701-u9x702352.78677-353.26802 F814W22 % 1200su9x703-u9x705350.12355-364.38978 AndXIII005150.87+330018.20F606W16 % 1200su9x711-u9x712304.23383-305.44764 F814W26 % 1200su9x713-u9x715303.76789-314.70330 HJD=HeliocentricJulianDay 98

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Bothgalaxiesexhibitrelativelysteepandnarrowredgiantbranches(RGBs) comparedtomoreluminous( < )dwarfsatellitesintheLocalGroup.TheHBsare welldenedwithseveralRRLyraecandidates(section4)andspanalargerangeof(V-I) colors(0.1 < (V-I) < 1.0).RelativelyweakredHBandalmostnon-existingredclump (RC)aredistinctfeaturesofbothgalaxiesfrommoreluminouscounterpartsintheLocal Group.TheVICMDsalsoexhibitnosignicantsignsofyoung( < 1Gyr)mainsequence starsorintermediateage(1 # 10Gyr)asymptoticgiantbranchpopulationsinboth galaxies.TheoverallfeaturesoftheCMDsforAndXIandAndXIIIarereminiscentof metal-poorGGCs,indicatingthatthesegalaxiesseemtobepurelyoldandmetal-poor stellarsystemsandhaveexperiencedrelativelysimplestarformationhistories(SFHs). 4.3.2HorizontalBranchMorphologies WeusedanewHBindex, (V-I)(Dotteretal.2010,hereafterD10)inorderto characterizetheHBmorphologyofAndXIandAndXIII.Theadvantageofusingthis newmetricinthemeasurementofHBmorphologyistwofold:1)The (V-I)indexhas lessdegeneracyatboth(red&blue)extremeendsoftheHBmorphology(Figure. 2ofD10)thantheconventionalHBindex,(B-R)/(B+V+R)(Leeetal.1994),2)the calculationof (V-I)isquitestraightforwardsothatonecanavoidbiasoriginatingfrom theuncertaintyinthecensusofRRLyraevariablesandthecontaminationoftheredHB byintermediate-ageRCstars. Figure4-3illustratesthemeasurementofthe (V-I)indicesforAndXIandAnd XIII.ThemeanVmagnitudeoftheHB, < > wasobtainedfromthemeanV magnitudeofRRabstars, < > calculatedfromthebestttinglightcurves ( < > =25.31; < > =25.49,seesection4.1).Starsinside theblue-boxedregionswereconsideredasHBstars,whileRGBstarsatthelevelofHB wereselectedwithintheredrectanglesintheVICMDsofeachgalaxy.Thedifference betweenthemediancolorsofHBandRGBwascalculatedtoyield (V-I)indicesfor eachgalaxy.Theuncertaintiesinthe (V-I)indiceswerecalculatedbythequadratic 99

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sumof1 errorsinthemediancolorsofHBandRGB.Weusedabootstrappingmethod forestimatingerrorsinthemediancolors.Tenthousandre-samplesoftheHBandRGB starswereconstructedbyusingrandomsamplingwithreplacementsfromtheobserved HBandRGBdata.Thestandarddeviationofthebootstrappedmediansrepresentsthe 1! errorsinthemediancolorsoftheHBandRGB.TheHBparametersforeachgalaxy arelistedinTable4-2. The[M/H]vs (V-I)diagramfor65GGCs(D10)isshowninFigure4-4.Solid circlesandopensquaresrepresentinner( < 8kpc)andouter( > 8kpc)halo GCsrespectively.AndXIandAndXIIIaremarkedasblueopenstarsalongwitheight otherLocalGroupdSphgalaxies(Harbecketal.2001).Thesolidlineisanempirical ttotheinnerhaloGCs.Weadoptedthe[Fe/H]valuesofAndXIandAndXIIIfrom section4.5.2ofthepresentstudyinwhichthe / relationship (Alcocketal2000)wasusedforthemetallicityderivation.Then,these[Fe/H]values weretranslatedinto[M/H]byapplyingthefollowingrelation, / / % / (Salarisetal.1993)byassuming # / =0.15(Tolstoy etal.2003)forbothgalaxies.Fortheother8dSphgalaxies,theironabundancevalues weretakenfromthecompilationofGrebel,Gallagher&Harbeck(2003),thenthe corresponding[M/H]valueswerecalculatedbythesameprocedureabove.Sincethe HBindicesoftheadditional8dSphgalaxiesareinthecanonicalformof(B-R)/(B+V+R), thesevaluesneedtobeconvertedintothenewmetric,the (V-I)index.Figure4-5 illustratesthecorrelationbetween(B-R)/(B+V+R)and (V-I)derivedbyalinearleast squarestofacubicpolynomialtothedatasetobtainedfromtheFigure2ofD10.We usedthisrelationtocalculatethe (V-I)valuesforthe8dSphgalaxies. FromFigure4-4,weseethattheLocalGroupdSphgalaxiesandtheGGCs showquitedifferentbehaviorinthemetallicity-HBmorphologydiagraminthesense thatthedSphgalaxiesappeartobesystematicallymoremetal-poorthantheGGCs andtheHBsofthedSph'saregenerallyredderthanthoseoftheGGCsatthesame 100

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metallicity.IfinterpretedinthesamewayastheGGCHBmorphology,wemightreach theconclusionthattheLocalGroupdSphgalaxiesaresystematicallyyoungerthan theMWGCs,andmostoftheLocalGroupdSphgalaxiesthereforeexhibitthe2nd parameterphenomenonintheirHBmorphologies,whichislikelycausedbytheeffect ofage.However,wehaveanumberofpiecesofevidencethattheoldestpopulationsin theLocalGroupdSphsatelliteshavecomparableagestotheoldMWGCs(Monkiewicz etal.1999;Mighell1997;Pritzletal.2002(P02),2004(P04),2005(P05)).Inaddition, unlikesingle-agedGGCs,dSphgalaxiesareverycomplicatedmulti-populationsystems formedthroughanextendedstarformationhistoryandacomplexchemicalenrichment process.Thereforewelikelyneedamorecomprehensiveapproachtotheinterpretation oftheHBmorphologiesofdSph's.Forinstance,thismetallicity-HBmorphologyrelation fortheLocalGroupdSphsatellitesmightdescribedifferencesinthestarformation historyofeachgalaxyinthesensethatbluerHBsreectalackofrecentstarformation eventsanddSph'swithextendedandrecentstarformationexhibitgenerallyredder HBs.AndXIandAndXIIIexhibitrelativelybluerHBmorphologiescomparedtothe otherdSph's.Indeed,bothgalaxiesdonothaveanyindicationofintermediateoryoung stellarpopulationsintheirCMDs.TheirCMDsarereminiscentofthoseofpurelyold, metal-poorGGCs.ThestrangecaseoftheblueHBoftheSculptordSphshownin Figure4-4isalsointeresting.AccordingtothestarformationhistoryofSculptor(Dolphin etal2005),over90%ofthestarsformedolderthan10Gyragoandthesubsequentstar formationhassomehowceasedsothatthereisnosignofrecentstarformationevents untilnow.Asaresult,theHBmorphologyoftheSculptordSphremainsblueandhas notbeensignicantlycontaminatedbyintermediatedageRCstarscomparedtoother dSph's.WesummarizetheHBindicesandotherphysicalparametersofoursample dSphgalaxiesinTable4-3. 101

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Table4-2. HBparameters Object < > medianmedian AndXI25.31 0.020.559 0.0701.108 0.0200.549 0.074 AndXIII25.49 0.020.572 0.1091.061 0.0130.489 0.110 Table4-3. HBindexandotherphysicalparametersofsampledSphgalaxies. Object(B-R)/(B+V+R) [Fe/H][M/H] Sculptor0.060.674-1.5 0.5-1.40-9.8 Sextans-0.370.264-1.9 0.4-1.80-9.5 Tucana-0.200.313-1.7 0.2-1.60-9.6 AndI-0.800.186-1.4 0.2-1.30-11.8 AndII-0.700.201-1.5 0.3-1.40-11.8 AndIII-0.670.206-1.7 0.2-1.60-10.2 AndV-0.620.214-1.9 0.1-1.80-9.1 AndVI-0.700.214-1.7 0.2-1.60-11.3 AndXI-0.549-1.75 0.12-1.65-7.3 AndXIII-0.489-1.74 0.12-1.64-6.9 102

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Figure4-1. TheVIcolor-magnitudediagramofAndXI.RRabcandiatesdetectedfrom ourtemplatelightcurvettingroutine(section4.4)aremarkedasredopen circles.Therightpanelillustratesthephotometriccompletenessindicating thatourphotometryis # 90%completeatthelevelofthehorizontalbranch. 103

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Figure4-2. SameasFigure4-1,butforAndXIII. 104

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Figure4-3. Theillustrationsofthe (V-I)indexmeasurementsareshown.Theblueand redboxedregionsdescribetheselectionofHBandRGBstarsrespectively. Thehorizontallinepresentsthelevelofhorizontalbranchobtainedfromthe meanVmagnitudeofRRabstars.Theverticallinesindicatethemedian colorsofHBandRGBs.ThedottedlinesareRGBducialsforeachgalaxy obtainedbytheleastsquaretofaquadraticpolynomial. 105

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Figure4-4. Themetallicity-HBmorphologydiagramfor65GalacticGlobularClusters (D10)ispresented.Solidcirclesandopensquaresrepresentinner( < 8 kpc)andouter( > 8kpc)haloGGCsrespectively.Thesolidlineisthe ducialtfortheinnerGGCs.AndXIandAndXIIIaremarkedasblueopen starsalongwith8otherLocalGroupdSphgalaxies(Harbecketal.2001). TheLocalGroupdSphgalaxiesexhibitgenerallyredHBswiththree expectionsofAndXI,AndXIII,andSculptordSphsandappeartobe systematicallymoremetal-poorthantheGGCsatagivenHBmorphology. 106

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Figure4-5. Thecorrelationbetween (V-I)and(B-R)/(B+V+R)indices(Figure2.of D10).Dashedlineilluststratestheleastsquaretofacubicpolynomialfor thedata.Weusedthisrelationtoconvertthe(B-R)/(B+V+R)valuesof8 otherLocalGroupdSphgalaxiesobtainedfromHarbecketal.(2001). 4.4RRLyraeVariables(RRLs) 4.4.1DetectingRRLsandLightCurves WesearchRRLstarsinAndXIandAndXIIIbyemployinganewlydeveloped templatelightcurvettingmethoddubbed"RRFIT(RobustRRLyraelightcurveFITing)" writteninFORTRAN.Thisnewperiodsearchingroutineworksinasimilarfashionas FITLC(Mancone&Sarajedini2008),whichisourprevioustemplatelightcurvetting method,butitisespeciallydesignedforlargeRRLssurveyprograms.Unlikeother optimizingmethodsusingagradientsearchorabruteforcettingroutinefornding thebest-tmodelparameters,RRFITimplementsarobustgeneticalgorithm,"PIKAIA", 107

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whichefcientlyndsthebest-tmodelparametersviaanAI(articialintelligence) randommeshsearchingtechnique.RRFITtakesfulladvantageofthePIKAIAalgorithm andasaresult,signicantlyenhancescomputingspeed(e.g.RRFITisatleast10 timesfasterthanFITLC)withoutsacricingttingaccuracy.Anotheradvantageofusing RRFITisthevarietyofstandardtemplatesthatitcanemploy.Weadoptedanadditional 17uniqueRRabtemplatesfromtheworkofKovacs&Kupi(2007)intoourtemplatelight curvelibrarytoachieveabetterdescriptionofvarioustypesofRRLs. InordertodetectRRLpopulationsinthesefaintdwarfsatellites,rstweattempt tocatalogallofthevariablestarcandidateswithinarangeofVmagnitude(24.5 < < 26.0)bycalculatingthereduced valueofeachstarformeasuringvariability denedbythefollowingformula: % " # Anypeculiardatapointsthatstrayfromthemeanmagnitudeby 3 were excludedfromthe calculation.Wecompiledthelistofpotentialvariablesbyselecting starswitha valuegreaterthan3.0.Forreference,thereduced valuesofatypical non-variablestarattheHBlevels(V(HB) # 25.4)ofAndXIandAndXIIIarelessthan 3.0.Thisvariabilitythresholdgeneratedalistof69variablestarcandidates(46forAnd XI;23forAndXIIIrespectively)fromtheWFPC2imagesofbothgalaxies.Then,weran theRRFITroutineontheVItimeseriesphotometryofthesevariablestarcandidatesin ordertondbest-tlightcurveparameterssuchasPeriod,Amplitude,Maximumepoch, andMeanmagnitude.Aftercarefuleye-examinationoftheresultantlightcurves,we found17RRLs(10RRab,1RRcand6unclassied)inAndXIand9RRLs(8RRaband 1unclassied)inAndXIII.ThebestttinglightcurvesfortheseRRLcandidatesfrom ourRRFITanalysisarepresentedinFigure4-6and4-7.Thepulsationpropertiesof theRRLcandiatesineachgalaxyarelistedinTable4-4.ThemeanVbandmagnitudes ofRRabcandidatesfromthebestttinglightcurvesare < > =25.31 108

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Table4-4. PropertiesofRRLyraestars. R.A.Decl.Period ID(J2000)(J2000) < >< > < > (days)A(V)Type AndXI V0040904616.47+334659.8625.25000.70320.63470.8044ab V0041404616.13+334719.4725.16600.51680.46550.4905c V0042404615.75+334703.6625.35830.72560.56100.7979ab V0042504615.94+334716.7525.29510.53690.53130.9079ab V0044704617.30+334709.1225.26360.56150.42900.6292c? V0212004614.97+334706.5525.13770.71620.72300.6420ab V0215704615.81+334650.7425.26000.61070.80000.5667ab V0217204615.16+334712.9525.21490.60100.38520.3750c? V0219304616.75+334655.5825.31690.68850.55390.7725ab V0219504615.63+334657.8825.28080.63570.50800.4515alias? V0220004616.72+334654.4825.33530.63310.57640.7936ab V0220404616.48+334721.3725.38390.73410.63270.5899ab V0221904616.87+334709.7825.36400.58010.42750.6388c? V0222104616.86+334708.5325.35880.60540.37930.5809alias? V0222404617.24+334713.0625.39260.60890.57570.9582ab V0223704617.56+334654.7025.41840.70880.62570.7728ab V0433804617.04+334649.2625.36530.61230.40700.5766c? AndXIII V0002605146.00+33004.3825.56490.72990.59490.5677ab V0062005146.18+33011.1225.41530.78940.67590.6772ab V0062905144.58+33008.3225.40710.74640.61340.4953ab V0063605146.99+33008.7125.46050.76750.81160.2972ab V0065105146.81+33007.1125.57330.74600.59800.8240ab V0065205146.55+33016.7425.54190.64500.60460.8455ab V0212905146.35+33013.6025.48720.72520.67250.7452ab V0345105146.88+33009.6325.49990.71730.61580.5103ab V0214705146.48+33012.9625.37800.54910.42870.4970c? 0.02,and25.49 0.02forAndXIandAndXIIIrespectively.Thegivenuncertainties illustratethestandarderrorofthemean.Weconsider < > valuesasthebest estimateofthe < > valueforeachgalaxy.SeveralRRLcandidatesnotedas "unclassied"arepossiblyeithermisidentiedRRcoraliases.Detailedinvestigationsof these"unclassied"RRLcandidatesarepresentedinthefollowingsection. 109

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Figure4-6. Thebest-tlightcurvesofRRLcandidatesinAndXI. 110

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Figure4-7. Thebest-tlightcurvesofRRLcandidatesinAndXIII. 4.4.2SyntheticLightCurveSimulation Inordertoquantitativelygaugethedegreeoffalseperiods(aliases),weperformed thefollowingsetofsyntheticlightcurvesimulations(Sarajedinietal2009(S09);Yang& Sarajedini2010;Yangetal2010,hereafterY10).Applyingthesameobservingwindows oftheAndXIandAndXIIIWFPC2images, # 1000syntheticlightcurvesofRRab andRRcstarsweregenerated.Periodsandamplitudeswererandomlyassignedto eacharticialRRLwithinappropriaterangesofeachtype(RRab: < < < < ;RRc: < < < < ).Photometricerrorsfor eachdatapointwereassignedusinggaussiandeviatescenteredat0.06mag,whichis atypicalphotometricerroratthelevelofHBforbothgalaxiesintheWFPC2photometry. Then,werantheRRFITroutineonthesearticialRRLstars. TheplotsshowninthetoppanelsofFigure4-8andFigure4-9illustratethe differencebetweeninputandoutputperiodsasafunctionofinputperiod.ForAnd 111

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XI(Figure4-8),RRcstarsappeartoexperiencemoresignicantaliasingcompared toRRabstars.Quantitatively, # 84%ofinputperiodsforRRabstarswereaccurately recoveredwithin 0.05days,whileonly # 61%ofRRcperiodswererecoveredwithin thesameperiodrange.Inaddition,theoutputperiodsoftheRRcstarstendtobelonger thantheinputperiods.Thenegativetailshowninthe Pdistribution(theleftpanelin themiddleofFigure4-8)forthearticialRRcstarsofAndXIwascausedmainlydueto thisbiasintheRRcperiods.Thisresultrevealsthatthereisconsiderableuncertaintyin thepropertiesofindividualRRcstarsinAndXI. Toinvestigatethedegreeofmis-identicationsintheRRcregime,weperformeda comparativeanalysisbetweenthebest-tlightcurvesandtherst-overtonemodelight curvesforthoseunclassiedRRLcandidatesfoundintheprevioussection.Observing cadenceandphasecoveragearethetwomostimportantfactorsforaccurateperiod measurements(Y10)andthesefactorsalsohaveasignicantroleindetermining whichtypeoflightcurveprovidesthebestt.Photometricerrorsalsoinuencethe appearanceofthemeasuredlightcurves.Largephotometricerrorseasilydeform theoriginalshapeofalightcurveandcaninduceawrongdescriptionforthegiven lightvariation.IfaoriginallyRRcstarwereonlymis-identiedasafundamentalmode pulsator,thentherst-overtonemode(RRc)templatesshouldyieldalmostsame best-tsolutions(e.g.periodandamplitude)withacomparablegoodnessoftas comparedtothebestttingRRabtemplate.FromFigure4-10,weseethatthemajority ofunclassiedRRLstarsexhibitreasonablygoodqualityoftbothinthefundamental andrst-overtonemodes.Hence,weconcludethattheseunclassiedRRLsintheRRc regimeareinfactRRcstars.Therearetwoexceptionstothis-V02195&V02221, whichshowsignicantlydifferentsolutionsintheresultantperiodsforeachtypeof pulsationmode.Wesuspectthattheymaybealiasedfromouranalysis.Therefore,the correctedcensusofRRcstarsineachgalaxyis =5,and1forAndXIandAndXIII respectively. 112

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InordertoestimatetheerrorsoftheindividualRRLperiods,weperformedthe followingstatisticaltestintroducedinY10.FromthearticialRRLlists,werandomly drawthesamenumberofarticialRRLstarsasourobservedRRLsineachgalaxy(And XI:10(RRab)and5(RRc);AndXIII:8(RRab)and1(RRc))tocalculateanaverage Pvalueforeachdrawnsample.Thisramdomsamplingmethodisatypeofprobabilty weightedsamplinganddifferentfromthebootstrappingrandomreplicationinthesense thatwedrawawholesamplefromaknownparentpopulationwithoutreplications.We constructthedistributionof < > valuesforeachpulsationmodebyiteratingthis probabilitysampling10000times.Figure4-11illustrates < > distributionsofthe articialRRLstarsforAndXIandAndIIIalongwiththebest-tGaussiandistributions. The1! errorsofthebest-tGaussiansaregoodapproximationstothestandard deviationsofeach < > distribution.Therefore,thestandarderrors( / )subject totheindividualRRLperiodsinouranalysisare = 0.038and = 0.022 daysfortheRRLcandidatesfoundinAndXI.ForAndXIIIRRLcandidatesthese valuesbecome = 0.051and = 0.022days.Theexactlysamemethod wasappliedfortheestimationoftheerrorsintheamplitude.Weobtained = 0.027and = 0.024magfortheAndXIRRLcandidates.ForAnd XIII,theseerrorvaluesare = 0.087and = 0.033mag. ThisstatisticaltestsuggeststhattheRRccandidatesaresubjecttorelativelyhigher errorsintheirindividualperiodsandamplitudesascomparedtotheRRabcandidates. Howeverwefoundnosignifcantbiasesinourdeterminationofthemeanperiodsand amplitudes.Henceweassumethatthealiasdonotaffecttheresultsintheremainderof ouranalysis. 113

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Figure4-8. TheresultsfromoursyntheticlightcurvesimulationfortheAndXIdata.Top panelsillustratethedifference( P= )betweentheoutputperiod andtheinputperiodasafunctionoftheinputperiodfortwodifferent pulsatingmodes.Lowerpanels(middle&bottom)describethedistributions ofthedeviationoftheoutputperiodandamplitudefromtheinputvalues. Oursimulationrevealsthattheresultantperiodsfromouranalysismight haveasignicantaliasingintheRRcregimeascomparedtotheRRab regime. 114

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Figure4-9. TheresultsfromoursyntheticlightcurvesimulationforAndXIII.The simulationshowsthatthealiasingissueislesssignicantfortheAndXIII RRLcandiatesascomparedtotheAndXIRRLs. 115

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Figure4-10. Thecomparisonsbetweenthebest-tlightcurvesandtheRRctemplate tsfortheunclassiedRRLcandidates. 116

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Figure4-11. ThedistributionsoftheoutputperioddeviationforsyntheticRRabandRRc stars.Thedashedlinesillustratethebest-tGaussiansforeach distribution. < > and representthepeakandthestandarddeviation oftheGaussiantrespectively. 117

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4.4.3Period-Amplitude(P-A)Diagrams TheP-ArelationsoftheRRLpopulationsinAndXIandAndXIIIarepresentedin Figure4-12.Forcomparison,wegeneratedcontouredP-AdiagramsfortheRRLstars inthespheroid(orinnerhalo;S09, # 5kpc),andahaloeld(Brownetal.2004 (B04), # 11kpc;hearafterBrowneld)ofM31.ThecontourplotfortheM31outer halowasscaledupabout5timesinordertoseeitstrendmoreclearly.TheRRLsstars (opensymbols)discoveredinAndXIandAndXIIIfromouranalysisareoverplotted onthetopofthesecontouredP-Adiagrams.TwosolidlinesrepresentingOosterhoffI (OoI)andII(OoII)ducialsfortheGalacticGlobularClusters(Clement2000)arealso plotted.SincetheamplitudesoftheM31RRLstarsinthesetwopreviousstudieswere determinedintheACS/F606Wpassband,weappliedan8%incrementintheamplitudes ofeachM31RRLinordertoconvertF606WamplitudeintoVbandamplitude(B04; S09). FromFigure4-12,weseethattheP-ArelationsoftheRRabstarsinAndXIand AndXIIIagreefairlywellwiththegeneraltrendofthesestarsintheM31outerhalo, whiletheRRccandidatesinbothdSph'sareobviouslyshiftedtowardthelongerperiod directionwithrespecttotheM31RRcstars.ThemeanRRabperiodsforAndXIand AndXIIIare < > =0.621 0.026(error1) 0.022(error2)daysand0.648 0.026(error1) 0.022(error2)days,respectively,whilefortheM31outerhalo,this valuebecomes0.594days(B04).The"error1"valuerepresentsthestandarderrorof themeanandthe"error2"valueistheerrorsubjecttotheindividualperiodcalculated fromoursyntheticlightcurvesimulations.ThediscrepancyinthemeanRRabperiods betweentheM31haloandthesetwodSph'sismainlyduetothelackofshortperiod RRabpopulationswithhighamplitudesinAndXIandAndXIII. TobetterunderstandthecharacteristicsoftheRRLpopulationsofthesetwo dSph's,wecomparedtheP-ArelationsofAndXIandAndXIIIwiththoseoffourother AndromedadSph's(AndI&III(P05);AndII(P04);AndVI(P02)).Figure4-13presents 118

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theP-ArelationsoftheseAndromedadSph's.Accordingtothiscomparison,theP-A relationsoftheRRLstarsinAndXIandAndXIIIshowtheclosestresemblancetothat ofAndIIIamongthesefourAndromedadSph's.TheRRabstarsinAndIIIappearto trackthegeneraltrendoftheBrowneldRRabstars.ThelackofshortperiodRRab starswithhigheramplitudesandthelocationsofRRcstarsintheP-ArelationofAndIII RRLsaresimilartothecharacteristicsoftheRRLpopulationsinAndXIandAndXIII. ItisinterestingtoseethatAndIIIistheleastluminousgalaxyamongthesefourdSph's anditsmeanmetallicity( < / > =1.7)iscomparabletothoseofAndXIandAnd XIII( < / > =1.74; < / > =1.75,seesection4.5).Weseethatthe similarbehaviorintheP-ArelationsamongthesethreedSph's(AndIII,AndXI,andAnd XIII)andtheirsimilarglobalpropertiesarerelated.FromFigure4-13,wealsoobserve thattheP-ArelationsofthesefourAndromedadSph'sareasdiverseastheircomplex starformationhistories.BroaddistributionsofRRabperiodsforeachAndromedadSph alsoreectsignicantmetallicitydispersionsinthesegalaxiesindicatingthatthese AndromedadSphgalaxieshavelikelyexperiencedextendedandcomplexchemical enrichmenthistoriesduringthecourseoftheirevolution.Anoticeablediscrepancy revealedinthecontouredP-Arelationsbetweentheinnerhalo(S09)andahaloeld (B04)ofM31isalsoveryintriguing.AsrstrecognizedintheworkofS09,based onthefactthatthecensusofRRLpopulationsinbothstudies(B04&S09)arequite complete,thesedifferentP-ArelationsoftheRRLstarsresidingatdifferentdistances fromtheM31centerappeartobegenuine.Assumingthisassertionistrue,wecarefully suggestapossibliltythattheRRLpopulationsintheM31halomayalsoexhibittheir owndichotomyinthesensethattheentirecanonicalOosterhoffdichotomyoftheMW RRLswouldbeshiftedtowardtheshorterperiodregimeandthegapbetweenthetwo distinctiveM31RRLpopulationsintheP-Adiagrambecomesmuchnarrowerthanthat oftheP-ArelationsfortheMWRRLs. 119

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Figure4-12. TheP-ArelationsofRRLcandidates(opencircles)ofAndXIandAndXIII areoverplottedontopofthecontouredP-ArelationsoftheM31haloRRLs (leftpanels,S09:innerhalo, # 5kpc;rightpanels,B04:Browneld, # 11kpc).SolidlinesrepresenttheducialsofOosterhoffIandIIGGC (Clement2000). 120

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4.5Metallicity M06derivedthemeanmetallicitiesofAndXIandAndXIIIbyinterpolatingbetween Padovaisochrones(Giradietal.2004)ontoptheCFHT/MagaCamsurveydata.The estimatedmeanmetallicityvaluesare < / > =1.3and1.4dexforAndXIand AndXIIIrespectivelywithinanerrorof 0.5dex.Mostrecently,fromtheirKeck/DEIMOS andSUBARU/SuprimeCamstudyofthefaintM31satellites,C10estimatedmetallicities ofindividualRGBstarsinthesetwodSph'sbyusingisochroneinterpolationas wellastheCalciumIItripletspectra.Fortheisochroneinterpolation,theyused Dartmouthisochrones(Dotteretal.2008)insteadofusingPadovaisochrones.The meanmetallicitiesobtainedbyapplyingthesetwodifferentmethodsconvergedat < / > =2.0 0.2dexforbothAndXIandAndXIII.C10explainedthatthe relativelyhighervaluesofthemeanmetallicityforthesedSph'sinthepreviouswork ofM06wereprobablycausedbytheuseofPadovaisochrone,whichsystematically producemoremetal-richvaluesintheMegaCamltersthanotherisochronemodels. WeestimatedthemetallicitiesofAndXIandAndXIIIbyusingtheperiod-amplitude-metallity relationshipforRRabstarsderivedbyAlcocketal.(2000)fromMACHOproject.The relationisgiveninthefollowingequation: / TheestimatedmeanmetallicityoftheRRabstarsinAndXIis < / > =1.75 0.12(error1) 0.13(error2).ForAndXIIIthisvaluebecomes < / > =1.74 0.12(error1) 0.14(error2).Error1representsthestandarderrorofthemean, whileerror2istheamountoferrorpropagatedfromthedeterminationofindividual periodsandamplitudesoftheRRLcandidates.Thus,thetotalerrorsinourmetallicity determinationsdescribedbythequadraturesumoferror1anderror2are 0.18dex forbothAndXIandAndXIII.Forreference,the erroroftheAlcocketal.(2000) relationshipisabout # 0.3dex.Todoublecheckthevalidityofourestimates,we independentlycalculatedthemeanmetallicityofthesedSph'sbyusingtheSindex 121

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Figure4-13. ThecomparisonsofP-AdiagramsfortheM31dSphgalaxies. 122

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(Hartwick1968;Savianeetal.2000).TheSindexisaRGBslopeoriginallydened bythelineconnectingtwopointsoftheRGBonthe(B-V,V)plane:therstoneatthe leveloftheHB,andtheotheroneat2.5magbrighterthantheHB.Savianeetal.(2000) redenedthisrelationshipinthe(VI,V)planebyadjustingthesecondpointto2.0mag brighterthanHB.Themetallicity-SindexrelationshipcalibratedbySavianeetal.(2000) isgiveninthefollowingform: / = % Figure4-14illustratesourmeasurementsofSindicesforAndXIandAndXIII. (VI)colorsofRGBsatV(HB)andV(HB-2.0)werecalculatedfromtheleastsquare tofaquadraticpolynomialtotheRGBsofeachgalaxy.Byusingthemetallicity-S indexrelationshipabove,weobtained[Fe/H]=1.70and1.63dexforAndXIandAnd XIIIrespectively.ThemetallicityestimationsforbothAndXIandAndXIIIfromRGB slopeshowexcellentagreementwiththeRRLmetallicities.Itisworthmentioninghere thatweareawareofacaveatabouttheuseoftheMACHOrelationship(Alcocketal. 2000).AccordingtoCacciarietal(2005),thismethodcanunderestimatethemetallicity especiallyfortheRRLsthathavesignicantlyevolvedfromthezero-agehorizontal branch.ThisevolutionaryeffectgenerallyraisestheluminosityofRRLstars.Then,the pulsationperiodoftheseevolvedRRLsbecomeslonger,asaresultyieldingarelatively lowermetallicity.Ourmetallicityestimationsfromthesetwocompletelyindependent methodsagreeverywellanddifferbyonly < 0.1dex.Thereforeweconcludethatthis evolutionaryeffectofRRLsdoesnotnegativelyimpactourmetallicitydetermination obtainedfromtheMACHOrelationshipforAndXIandAndXIII. 4.6Distance ConsideringthebrightestRGBstarconrmedbytheirKeck/DEIMOSspectroscopy asaproxyofthetipofRGB(TRGB)foreachgalaxy,C10setdistancerangesof 610770kpc,and750940kpcforAndXIandAndXIIIrespectively.Forthiscalculation, theyassumedthatthebrightestDEIMOSstarisfoundwithin0.5magoftheTRGB.C10 123

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Figure4-14. TheillustrationofSindexmethodforthemetallicitymeasurement(Saviane etal.2000).TheredsolidlinesrepresentRGBducialsforeachgalaxy derivedfromtheleastsquaretofaquadraticpolynimial.Thepoints markedasacrossaretheVmagnitudeofRGBattheHBlevelandthatof RGBat2.0magbrighterthanHBlevelrespectively. alsoprovideddistancesofAndXIandAndXIIIestimatedbyutilizingHBmagnitudes. Inthiscase,thedistancesofAndXIandAndXIIIbecome # 830kpc,and910kpc, respectively. WeattempttorenethedistancesofAndXIandAndXIIIbyusingtheRRL candidatesthatareawellknownpopulationIIstandardcandle.Thereddeningvalueof E(B-V)=0.08isadopttedfromtheGalacticExtinctionmapofSchlegeletal(1998)for bothAndXIandAndXIII.ThemeanVmagnitudeof11RRabcandidatesfoundinAnd XIis < > =25.31 0.02.Byapplyingtheextinctionlaw,Av=3.1E(B-V)=0.248, weobtainedameanintrinsicVmagnitudeofAndXIRRabstars < > =25.06 0.02.ThentheabsoluteVmagnitudeofeachAndXIRRabstariscalculatedusing 124

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themetallicity-luminosityrelationshipforRRabstars, =0.23[Fe/H]+0.93,from Chaboyer(1999).ThisyieldsameanabsoluteVmagnitudeof < > =0.53 0.05.Givenerrorrepresentsthequadraturesumofthestandarderrorofthemean(0.03 mag)andtheamountoferrorpropagatedfromourmetallicitydetermination(0.04mag). ThusweobtainthemeanabsolutedistancemodulusforAndXIis =24.54 0.05.ThisplacesAndXIatadistanceof # 810 18kpc,whichisoutsideofthe distancerangeof610770kpcobtainedfromTRGBmethod,butagreeswellwiththe distanceof830kpcestimatedbytheHBmagnitudeinthepreviousworkofC10. ForAndXIII,theapparentmeanVmagnitudeof8RRabcandiatesis < > =25.49 0.02.EmployingonceagaintheChaboyer(1999)equationfortheRRab metallicity-luminosityrelation,wend < > =0.53 0.05.Thisgivesadistance modulusof =24.71 0.05(D # 875 18kpc)forAndXIII,showingexcellent agreementwiththepreviousestimationdonebyC10. 4.7Discussion Theluminosity-metallicity(L-M)relationsoftheLocalGroupdwarfsatellitesreects theintrinsicpropertiesofdwarfgalaxiesandcontainssignicantimplicationsforthe mechanismofgalaxyformationandtheenvironmentalconditionspresentduringthe earlyepochsofstarformation(Harbecketal2005;Bovill&Ricotti2009). Thestandardsenariosofgalacticchemicalenrichment(Larson1974;Tinsley &Larson1979;Dekel&Silk1986)expectthataL-Mrelationshouldbeestablished indwarfgalaxies.Indeed,thisL-Mrelationwasuncoveredbytheobservationsand comparativestudiesoftheLocalGroupdwarfsatellites(Caldwelletal.1992;Grebel& Guhathakurta1999;Grebeletal.2003(G03))inthemannerthatmoreluminous(i.e. moremassive)galaxiesappeartobemoremetal-richwhilelessluminous(i.e.less massive)galaxiestendtobemoremetal-poor.ThisobservationalL-Mtrendagreesvery wellwiththetheoreticalpredictionsthatattheearlystageofgalaxyformation,galactic windstriggeredbysupernovaexplosionsmoreeffectivelyremovedtheinterstellar 125

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medium(ISM)inthevicinityoffaintgalaxies(i.e.lessmassiveorshallowerpotential wells)sothatlessmetalsshouldbetrappedinthesedwarfgalaxies(Savianeetal. 2008)becausethesefaintgalaxiesarelesscapableofretainingthemetals.TheL-M relationsoftheLocalGroupdwarfgalaxiesalsorevealedthefundamentaldifferences andpossiblecorrelationsbetweendIrrsanddSphs(Skillman&Bender1995;Richer etal.1998;Mateo1998;G03).Fromtheircomparativestudyofthecompilationof40 nearbydwarfgalaxiesG03observedthefactthatinthemetallicity-luminosityrelations, theoldstellarpopulationsofdIrrsaresystematicallymoremetal-poorascompared tothoseofdSphsatthesameluminosity(i.e.present-daydIrrsareatleast10times brighterinluminositythanpresent-daydSphsatagivenmetallicity).Thisindicatesthat thegasdecientdSphsinwhichstarformationhasbeeninadormantstate,should bemoreeffectivelyenrichedthandIrrs,whichcurrentlyexhibiton-goingstarformation. Basedonthepresent-dayluminosity,HIgascontent,andthemodestratesofon-going starformationofthedIrrs,G03concludedthatmostofthepresent-daydIrrsinthe LocalGroupcannotbefadedenoughtoevolveintodSphsoveraHubbletime.Hence, thedIrrsarenotlikelyprecursorsofthedSphsandthesetwoclassesofgalaxiesare fundamentallydifferentstellarsystemsthatexperiencedifferentpathsintheirevolution. WithnewlydeterminedmetallicitiesfromtheRRLperiods,weplottedAndXIand AndXIIIontheL-MrelationsoftheLocalGroupdwarfgalaxiesinFigure4-15.The absoluteVmagnitudesofAndXIandAndXIIIwereadoptedfromthepreviouswork ofC10.Among40nearbygalaxiesinthecompilationofG03,weonlyinclude34Local Groupdwarfsatelliteswithin1.5MpcfromtheMilkyWay(MW).TheL-Mrelationfor 8recentlydiscoveredultra-faintdwarf(uFd)satellitesoftheMWwereobtainedfrom therecentworkofNorrisetal.(2010).Thedependentvariableofthisplotrepresents themeanmetallicityoftheoldstellarpopulationsineachgalaxywhiletheindependent variableisintegratedabsoluteVmagnitudeofthedwarfgalaxies.Tobetterunderstand thisplot,adifferentsymbolwasusedforeachclassofdwarfgalaxy(solidcircles(dIrr); 126

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opencircles(dSph);opentriangles(dE);openstars(dIrr/dSph,transitiontype);solid squares(ultrafaintdwarf)).FromFigure4-15weseethatwithinatypicalmetallicity error( < / > # 0.4dex),awellestablishedL-Mrelationshipcontinuesfromthe brightestdIrranddEtothefaintestdwarfsatellite,Segue1,despiteanoticablegap betweenthefaintendofthecanonicaldwarfgalaxiesandthebrightendofthenewly discoverdultra-faintdwarfsatellites.Wealsoobservethewellknownfeaturesinthe L-MrelationshipthatdSphsaremoremetal-richthanthedIrrsatthesameabsolute Vmagnitude,whilethetransitiontypedwarfgalaxies(dIrr/dSph:Phoenix,DDO 210,LGS3,andAntlia)showsimilarcharacteristicsasdSphs(Skillman&Bender 1995;Richeretal.1998;Mateo1998,andG03).Ourestimatesofthemetallicity ( < / > =1.75; < / > =1.74)tendtolocateAndXIandAnd XIIIslightlyofffromtheaverageL-Mrelationascomparedwiththepreviouswork ofC10( < / > =-2.0forbothAndXIandAndXIII).Howeverbothgalaxiesstill appeartofollowthegeneraltrendsofthisL-Mrelationwithintheerrorofthemetallicity determinations. TheobservedpropertiesofthenewlydiscovereduFdgalaxies,suchassize, surfacebrightness,masstolightratio,andL-Mrelationcanbeexplainedinthe contextof"thetidaldisruptionscenario"ofthedSphformationwhichsuggeststhatthe present-dayfaintgalaxieswereoncemuchmoremassivebutlostsignicantmassvia tidalinteractionswiththeirgianthostgalaxies(e.g.UsarMinordSph:Martinez-Delgado etal.2001;Mayeretal.2001).However,thistidalscenariocannotaccountforall thepropertiesofuFdgalaxies,especiallytheverymetal-poornatureofsomeofuFd galaxies.IfthedSphsformedinmassivehalos,thedeepgravitationalpotentialwellof themassivehaloseffectivelycontainsmetals.Hence,thissetsupalowerlimitofthe metallicityforthedSphgalaxies.Thecontinuouslydecreasingmetallicitypatternfrom thebrightdIrrsand/ordEsallthewaytotheuFdsatellitesintheL-Mrelationsmay implythatthesenewlyfounduFdgalaxieswereoriginallylessmassivestellarsystems 127

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formedinlowmassdarkmatterhaloswithlessmetalsinwhichmostofstarsmustform beforetheendofreionization( < < ;Bovill&Ricotti2009;Walkeretal.2009; Salvadori&Ferrara2009).IntermsoftheabsoluteVmagnitude,AndXI( =6.9) andAndXIII( =6.7)appeartoresideintheuFdregime(C10).Asmentioned above,theirmetallicitiesseemtoberelativelyhigherthantheaverageL-Mrelationsat givenluminosities.ThisopensupthepossibilitythatthesetwofaintdSphmaybetidal remnantsfromtheinteractionswiththeirgianthost,M31orpre-reionizationfossilsin whichmetallicitywasenrichedbyalatephasegasaccretionandstarformationwell afterreinoization,atredshiftz < 12(Ricotti2009).However,consideringthefactthatthe absoluteVmagnitudesofAndXIandAndXIIIarethelowerlimitsoftheirluminosities (M06),wealsocannotignoreanotherpossibilitythatthesefaintdSphcouldbecanonical dSphgalaxies.Therefore,theverdictaboutthetrueoriginsofAndXIandAndXIIIis stilltentative.Tobetterunderstandthetruenatureofthesegalaxies,weneedaccurate observationsoftheircircularvelocities( )andtheirorbitalmotionaroundM31. 4.8Summary WepresentacomprehesivestudyofthestellarpopulationsintwofaintM31dwarf satellites,AndXIandAndXIIIusingdeeparchivalimagesfromHST/WFPC2.Based ontheanalysisoftheHBmorphologyandthepropertiesofRRLstars,weobtainthe followingresults: ThecharacteristicfeaturesintheVICMDsofAndXIandAndXIII,suchassteep &narrowRGB,bluishHB,andalmostnon-existingRCaredistinctfromthegeneral CMDpatternsofmoreluminousdwarfsatellitesintheLocalGroup.AndXIandAnd XIIIappeartobepurelyoldandmetal-poorstellarsystemsandmayhaveexperienced relativelysimplestarformationhistoriesascomparedwiththeirluminouscounterpartsin theLocalGroup. WediscoveredRRLpopulationsinbothAndXI( )andAndXIII ( )byusingournewtemplatelightcurvettingroutine(RRFIT).TheP-A 128

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Figure4-15. Luminosity-metallicity(L-M)relationsoftheLocalGroupdwarfgalaxies. ThedatawereobtainedfromthecompilationofGrebel,Gallagher,& Harbeck(2003)forthecanonicaldwarfsatellites( < ).FortheuFd systems,thedatawastakenfromtherecentworkofNorrisetal.(2010). AndXIandAndXIIIareshownasmarkedboxes.ThemetallicityrelationappearstobeverywellestablishedfromthebrightestdE,M32to thefaintestMWsatellite,Segue1.Thereisanoticeablegaparound = 6 # 8.AndXIandAndXIIIseemtollthisgapbuttheyexhibitrelatively highermetallicitiesthanthemeanL-MrelationatgivenabsoluteV magnitudes.Thetypicalerrorinthemeanmetallicityisabout # 0.30.4 dex. 129

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relationsofRRLstarsinthesetwoM31dwarfsatellitesappeartofollowtheP-Atrend oftheM31outerhaloRRLpopulation.Inaddition,ourcomparativeanalysisoftheP-A relationsfortheRRLstarsintheM31halosmayrevealthattheM31RRLpopulations seemtoexhibittheirownP-Adichotomyinthesensethattheentirepatternofthe canonicalOosterhoffdichotomyfortheMWRRLsappearstobeshiftedtowardtheshort perioddirectionandthegapbetweentwodistinctRRLpopulationsbecomesnarrower. ThemetallicitiesofRRabstarswerecalculatedviatheP-A-[Fe/H]relationshipof Alcocketal.(2000).Theobtainedmetallicities( / ; / )areconsistentwiththevaluescalculatedfromtheRGBslopeindicatingthatour measurementsarenotsignicantlyaffectedbytheevolutionaryeffectofRRLstars. ThedistancetoeachgalaxywascalculatedusingtheabsoluteVmagniutdes ofRRabstars.Wend =24.54forAndXIandthisvaluebecomes =24.71forAndXIII.Ourresultsagreeverywellwiththemeasurementsfromthe previousstudies(M06,C10). TheL-MrelationsofAndXIandAndXIIIfollowthegeneraltrendoftheL-Mrelation fortheLocalGroupdwarfgalaxiesandappeartollthegapbetweenthefaintendofthe canonicaldSphsandthebrightendofnewlydiscovereduFdsystems.Themetallicities ofAndXIandAndXIIIseemtoberelativelyhigherthantheaveragemetallicityof uFdsystemsatthesameluminosityindicatingthattheyusedtobemoremassive systemsbuthavelostsignicantmassviatidalinteractionwiththeirgianthost,M31or pre-ionizationfossilsinwhichmetallicitywasenrichedalatephasegasaccreationand starformationwellafterreionization(z # 12).However,thesignicantuncertainties intheintegratedabsoluteVmagnitudesofAndXIandAndXIIImightholdanother possibilitythatthesedwarfgalaxiesbelongtothecanonicalLocalGroupdSphsystems. 130

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BIOGRAPHICALSKETCH Soung-ChulYangwasborninahotsummerdayinSeoulKorea.Inhischildhood, hewasahappykidwholovedtospendmostoftimeintheplaygroundwithfriends.He alwayslovesmountains,creeksandtrees.Helovesanimals,birds,butteresandbittles. Especially,Helovesnightsky-allkindsofstarsandgalaxies.Andaboveall,heloves Godwhocreatedhim,allofthesebeautifulnatures,andtheendlessuniversewithfullof wonders. 137