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The Stellar Populations of M33's Outer Regions

Permanent Link: http://ufdc.ufl.edu/UFE0021708/00001

Material Information

Title: The Stellar Populations of M33's Outer Regions
Physical Description: 1 online resource (248 p.)
Language: english
Creator: Barker, Michael K
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: chemical, color, diagram, evolution, formation, galaxies, galaxy, history, m33, magnitude, star, stars
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: The fossil record of galaxy evolution is encoded in the ages, chemical compositions, kinematics, and spatial distributions of stellar populations. Therefore, one of the best ways to test predictions of galaxy formation simulations is to study these properties in real populations. To that end, we have obtained VI photometry with the Advanced Camera for Surveys on the Hubble Space Telescope for three fields in M33's outskirts located at deprojected radii of ~ 9 - 13 kpc. The color-magnitude diagrams (CMDs) reveal a mixed stellar population whose youngest constituents have ages no greater than ~ 100 Myr and whose oldest members have ages of several Gyr or more. The presence of stars as massive as 3 - 5 solar masses is consistent with global star formation thresholds in disk galaxies but could argue for a threshold in M33 that is on the low end of observational and theoretical expectations. The metallicity gradient as inferred by comparing the observed red giant branch to the Galactic globular clusters is consistent with M33's inner disk gradient traced by several other studies. The radial stellar scale length increases with age in a manner similar to that of the vertical scale height of several nearby late-type spirals. We also present a detailed analysis of the star formation history (SFH) of these fields by modeling the observed CMDs as linear combinations of individual synthetic populations with different ages and metallicities. We find that the mean age and metallicity increase and decrease with radius, respectively. Allowing age and metallicity to be free parameters and assuming star formation began ~ 14 Gyr ago, we find that the mean age of all stars and stellar remnants increases from ~ 6 Gyr to ~ 8 Gyr and the mean global metallicity decreases from ~ -0.7 to ~ -0.9. The random errors on the age and metallicity estimates are, respectively, ~ 1.0 Gyr and ~ 0.15 dex. By comparing the results obtained with two sets of stellar tracks and test populations with known SFH we have estimated the systematic errors to be 1.0 Gyr and 0.2 dex. Lastly, we develop a chemophotometric approach to modeling CMDs that involves simultaneously coupling the chemical evolution equations with the synthetic CMD method. Applying this technique to our innermost field in M33, we find that the canonical closed box model fails to reproduce the observed distribution of stars in the CMD. Models with an exponentially declining inflow rate from the time of galaxy formation exhibit similar discrepancies, but to a lesser extent. Instead, the best inflow models have a significant fraction of gas inflow taking place ~ 3 - 7 Gyr ago and a very small fraction ( < 10%) taking place within the last 3 Gyr. A small outflow rate within ~ 2 times the star formation rate is preferred. Stars formed over 8 Gyr ago have a mean alpha/Fe of ~ 0.2 +/- 0.1 and stars forming today have alpha/Fe ~ -0.1 +\- 0.1. The mean alpha/Fe of all stars ever formed is ~ 0.1 +/- 0.1. The predictions of our models for the present-day star formation rate, gas mass, and oxygen abundance in M33 generally compare favorably to independent observations.
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 Michael K Barker.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Sarajedini, Ata.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2008-06-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021708:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021708/00001

Material Information

Title: The Stellar Populations of M33's Outer Regions
Physical Description: 1 online resource (248 p.)
Language: english
Creator: Barker, Michael K
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: chemical, color, diagram, evolution, formation, galaxies, galaxy, history, m33, magnitude, star, stars
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: The fossil record of galaxy evolution is encoded in the ages, chemical compositions, kinematics, and spatial distributions of stellar populations. Therefore, one of the best ways to test predictions of galaxy formation simulations is to study these properties in real populations. To that end, we have obtained VI photometry with the Advanced Camera for Surveys on the Hubble Space Telescope for three fields in M33's outskirts located at deprojected radii of ~ 9 - 13 kpc. The color-magnitude diagrams (CMDs) reveal a mixed stellar population whose youngest constituents have ages no greater than ~ 100 Myr and whose oldest members have ages of several Gyr or more. The presence of stars as massive as 3 - 5 solar masses is consistent with global star formation thresholds in disk galaxies but could argue for a threshold in M33 that is on the low end of observational and theoretical expectations. The metallicity gradient as inferred by comparing the observed red giant branch to the Galactic globular clusters is consistent with M33's inner disk gradient traced by several other studies. The radial stellar scale length increases with age in a manner similar to that of the vertical scale height of several nearby late-type spirals. We also present a detailed analysis of the star formation history (SFH) of these fields by modeling the observed CMDs as linear combinations of individual synthetic populations with different ages and metallicities. We find that the mean age and metallicity increase and decrease with radius, respectively. Allowing age and metallicity to be free parameters and assuming star formation began ~ 14 Gyr ago, we find that the mean age of all stars and stellar remnants increases from ~ 6 Gyr to ~ 8 Gyr and the mean global metallicity decreases from ~ -0.7 to ~ -0.9. The random errors on the age and metallicity estimates are, respectively, ~ 1.0 Gyr and ~ 0.15 dex. By comparing the results obtained with two sets of stellar tracks and test populations with known SFH we have estimated the systematic errors to be 1.0 Gyr and 0.2 dex. Lastly, we develop a chemophotometric approach to modeling CMDs that involves simultaneously coupling the chemical evolution equations with the synthetic CMD method. Applying this technique to our innermost field in M33, we find that the canonical closed box model fails to reproduce the observed distribution of stars in the CMD. Models with an exponentially declining inflow rate from the time of galaxy formation exhibit similar discrepancies, but to a lesser extent. Instead, the best inflow models have a significant fraction of gas inflow taking place ~ 3 - 7 Gyr ago and a very small fraction ( < 10%) taking place within the last 3 Gyr. A small outflow rate within ~ 2 times the star formation rate is preferred. Stars formed over 8 Gyr ago have a mean alpha/Fe of ~ 0.2 +/- 0.1 and stars forming today have alpha/Fe ~ -0.1 +\- 0.1. The mean alpha/Fe of all stars ever formed is ~ 0.1 +/- 0.1. The predictions of our models for the present-day star formation rate, gas mass, and oxygen abundance in M33 generally compare favorably to independent observations.
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 Michael K Barker.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Sarajedini, Ata.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2008-06-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021708:00001


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Therearemanypeoplewhohavecontributedtothiswork,eitherdirectlyorindirectly.First,itisagreatpleasuretothankmyadvisor,Dr.AtaSarajedini,forguidingme,answeringallmyquestions,havinghighexpectationsyetdemonstratingpatiencewhenprogresswasslow,andforprovidingmewithexceptionalresearch,travel,andobservingopportunities.MysincereappreciationgoestotheLatexthesistemplatetechnicians:Suvrath,Dave,andJulianwhosehardworkhassavedthesanityofseveralstudentsincludingmyself.IalsowishtothankMichelleandDavidforsupport,encouragement,advice,andmanydeliciousmeals.ThanksalsogotoAaronforinvaluablehelpwithresearch,forbeingthebestoceroomate,andforyearsofadeptsoftballleadership.Iwouldn'thavesurvivedtheseyearsifitweren'tformyfellowgraduatestudentsandfriendsandallthefuntimesandlaughingwehaveshared.Myfriends,KhurramandAlex,thoughfarinphysicalterms,havealwaysbeenthereforme.SomeofmyworkhasbenetedgreatlyfromuseoftheUFHighPerformanceComputingCenterandIwishtothankthestathereformaintainingthatresource.Mycollaborators,DougGeislerandPaulHarding,haveprovidedmanyusefulcommentsonourpapers.Last,butcertainlynotleast,everythinghasbeenpossiblethankstomyparents.Theirunendingsupport,encouragement,advice,patience,andlisteningskillshavemeantsomuchtomeandshouldbeamodelforfamilieseverywhere. 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 7 LISTOFFIGURES .................................... 9 LISTOFSYMBOLS .................................... 14 ABSTRACT ........................................ 16 CHAPTER 1INTRODUCTION .................................. 18 2DEEPACSIMAGINGOFM33'SOUTERREGIONS .............. 24 2.1ObservationsandPhotometry ......................... 26 2.1.1ACS ................................... 26 2.1.2WFPC2 ................................. 28 2.2ArticialStarTests ............................... 29 2.3Color-MagnitudeDiagrams ........................... 31 2.4StellarSurfaceDensity ............................. 35 2.5MetallicityDistributionFunctions ....................... 38 2.6MetallicityGradient .............................. 39 2.7Discussion .................................... 42 2.8Conclusions ................................... 48 3STARFORMATIONHISTORY ........................... 62 3.1Method ..................................... 65 3.2Results ...................................... 70 3.2.1Padovatracks .............................. 70 3.2.2Teramotracks .............................. 74 3.3Discussion .................................... 76 3.4Conclusions ................................... 81 4INFLOWHISTORYANDCHEMICALEVOLUTION .............. 109 4.1ChemicalEvolutionEquations ......................... 114 4.2Method ..................................... 118 4.3Results ...................................... 122 4.3.1ClosedBoxModels ........................... 122 4.3.2InowandOutowModels ....................... 124 4.4Discussion .................................... 127 4.4.1ComparisontoObservationsinM33 .................. 128 5

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......................... 131 4.4.3ImplicationsfortheFormationoftheGalaxy'sHalo ......... 132 4.5Conclusions ................................... 136 5CONCLUSIONS ................................... 169 5.1Summary .................................... 169 5.2Discussion .................................... 171 5.3FutureWork ................................... 174 APPENDIX ATESTINGTHEMETHOD ............................. 177 BTESTINGTHECHEMOPHOTOMETRICMETHOD .............. 196 REFERENCES ....................................... 235 BIOGRAPHICALSKETCH ................................ 248 6

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Table page 2-1Observationlog .................................... 50 2-2Variationinscalelengthwithage .......................... 50 3-1FittedparametersofSFHsolutionsusingthePadovatracks ........... 84 3-2BasicresultsofSFHsolutionsusingthePadovatracks .............. 84 3-3SFHofA1usingthePadovatracks ......................... 85 3-4SFHofA2usingthePadovatracks ......................... 85 3-5SFHofA3usingthePadovatracks ......................... 85 3-6AgeCDFofA1usingthePadovatracks ...................... 86 3-7AgeCDFofA2usingthePadovatracks ...................... 86 3-8AgeCDFofA3usingthePadovatracks ...................... 86 3-9AMRofA1usingthePadovatracks ........................ 87 3-10AMRofA2usingthePadovatracks ........................ 87 3-11AMRofA3usingthePadovatracks ........................ 87 3-12ZCDFofA1usingthePadovatracks ........................ 88 3-13ZCDFofA2usingthePadovatracks ........................ 88 3-14ZCDFofA3usingthePadovatracks ........................ 88 3-15FittedparametersofSFHsolutionsusingtheTeramotracks ........... 89 3-16BasicresultsofSFHsolutionsusingtheTeramotracks .............. 89 3-17SFHofA1usingtheTeramotracks ......................... 90 3-18SFHofA2usingtheTeramotracks ......................... 90 3-19SFHofA3usingtheTeramotracks ......................... 90 3-20AgeCDFofA1usingtheTeramotracks ...................... 91 3-21AgeCDFofA2usingtheTeramotracks ...................... 91 3-22AgeCDFofA3usingtheTeramotracks ...................... 91 3-23AMRofA1usingtheTeramotracks ........................ 92 7

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........................ 92 3-25AMRofA3usingtheTeramotracks ........................ 92 3-26ZCDFofA1usingtheTeramotracks ....................... 93 3-27ZCDFofA2usingtheTeramotracks ....................... 93 3-28ZCDFofA3usingtheTeramotracks ....................... 93 4-1Adoptedchemicalyieldsandsolarabundances ................... 138 4-2ResultsofthechemophotometricmethodusingthePadovatracks ........ 138 4-3FittedstarformationandoutowecienciesusingthePadovatracks ...... 138 4-4ResultsofthechemophotometricmethodusingtheTeramotracks ........ 139 4-5FittedstarformationandoutowecienciesusingtheTeramotracks ...... 139 A-1Resultsoftestingthecanonicalmethod ....................... 179 B-1Resultsoftestingthechemophotometricmethod .................. 198 B-2Fittedstarformationandoutoweciencies .................... 198 8

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Figure page 2-1ImageshowingM33 .................................. 51 2-2Thedierencebetweeninputandoutputmagnitude ................ 52 2-3Completenessrateasafunctionofinputmagnitude ................ 52 2-4CMDofeldA1 ................................... 53 2-5CMDofeldA2 ................................... 53 2-6CMDofeldA3 ................................... 54 2-7CMDofA1withisochrones ............................. 54 2-8Ageandmetallicityconstraints ........................... 55 2-9Close-upofRCregionofA1 ............................. 55 2-10CMDofA1withtheRGBridgelines ........................ 56 2-11CMDofeldW1 ................................... 56 2-12CMDofeldW2 ................................... 57 2-13CMDofeldW3 ................................... 57 2-14SurfacedensityofRGBstars ............................ 58 2-15CMDforasubsampleofHubbleDeepFieldimages ................ 58 2-16CMDofA1andthesixboxes ............................ 59 2-17Relativesurfacedensityofstars ........................... 59 2-18Radialstellarscalelengthasafunctionofage ................... 60 2-19GeneralizedhistogramoftheRGBmetallicitydistributionfunction ....... 60 2-20RGBmetallicitygradientinM33 .......................... 61 3-1SFHresultsforA1usingthePadovatracks .................... 94 3-2SameasFigure 3-1 butforA2 ............................ 95 3-3SameasFigure 3-1 butforA3 ............................ 96 3-4SFHresultsforA1usingthePadovatracksandafterexcludingtheregionI>27 97 3-5SameasFigure 3-4 butforA2 ............................ 98 9

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3-4 butforA3 ............................ 99 3-7ComparisonofSFHresults .............................. 100 3-8Exploringparameterspacebyhand ......................... 101 3-9SFHresultsforA1usingtheTeramotracks .................... 102 3-10SameasFigure 3-9 butforA2 ............................ 103 3-11SameasFigure 3-9 butforA3 ............................ 104 3-12SameasFigure 3-7 butfortheTeramotracks ................... 105 3-13SameasFigure 3-8 butfortheTeramotracks ................... 106 3-14CMDofeldA1(graypoints)withCMDofTerzan7overplotted ........ 107 3-15V-bandstellarmass-to-lightratioinM33 ...................... 107 3-16AMRofM33(points)comparedtotheSV,LMC,andSMC ........... 108 4-1Schematicdiagramshowingtherelationships .................... 140 4-2Flowcharthighlightingthemainsteps ....................... 140 4-3ConstructionofamodelCMD ............................ 141 4-4ClosedboxmodelusingthePadovatracks ..................... 142 4-5ExponentialinowmodelusingthePadovatracks ................. 143 4-6SameasFigure 4-5 butfortheSandageinowmodel ............... 144 4-7SameasFigure 4-5 butforthedoubleexponentialinowmodel ......... 145 4-8SameasFigure 4-5 butforthetruncatedinowmodel .............. 146 4-9SameasFigure 4-5 butforthefreeinowmodel .................. 147 4-10ClosedboxmodelusingtheTeramotracks ..................... 148 4-11ExponentialinowmodelusingtheTeramotracks ................. 149 4-12SameasFigure 4-11 butfortheSandageinowmodel .............. 150 4-13SameasFigure 4-11 butforthedoubleexponentialinowmodel ......... 151 4-14SameasFigure 4-11 butforthetruncatedinowmodel .............. 152 4-15SameasFigure 4-11 butforthefreeinowmodel ................. 153 4-16FurtherdetailsoftheclosedboxmodelusingthePadovatracks ......... 154 10

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4-16 butfortheexponentialinowmodel ............. 155 4-18SameasFigure 4-16 butfortheSandageinowmodel .............. 156 4-19SameasFigure 4-16 butforthedoubleexponentialinowmodel ......... 157 4-20SameasFigure 4-16 butforthetruncatedinowmodel .............. 158 4-21SameasFigure 4-16 butforthefreeinowmodel ................. 159 4-22FurtherdetailsoftheclosedboxmodelusingtheTeramotracks ......... 160 4-23SameasFigure 4-22 butfortheexponentialinowmodel ............. 161 4-24SameasFigure 4-22 butfortheSandageinowmodel .............. 162 4-25SameasFigure 4-22 butforthedoubleexponentialinowmodel ......... 163 4-26SameasFigure 4-22 butforthetruncatedinowmodel .............. 164 4-27SameasFigure 4-22 butforthefreeinowmodel ................. 165 4-28OxygenabundancesinM33 ............................. 166 4-29ComparingchemicalmodelsforM33,theSV,LMC,andSMC .......... 167 4-30ComparingchemicalmodelsforM33toobservationalestimates ......... 168 A-1Test1:Optimal .................................... 180 A-2Test2:Optimal .................................... 181 A-3Test3:Teramo .................................... 182 A-4Test4:f=0:8 .................................... 183 A-5Test5:f=0:1 .................................... 184 A-6Test6:x=2:0 ................................... 185 A-7Test7:x=3:4 ................................... 186 A-8Test8:Optimal .................................... 187 A-9Test9:Teramo .................................... 188 A-10Test10:f=0:8 .................................... 189 A-11Test11:f=0:1 .................................... 190 A-12Test12:x=2:0 ................................... 191 A-13Test13:x=3:4 ................................... 192 11

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................................... 193 A-15Test15:Optimal ................................... 194 A-16Test16:-0.05Voset ................................ 195 B-1Test1:Closedbox .................................. 199 B-2Test1:Exponentialinow .............................. 200 B-3Test1:Sandageinow ................................ 201 B-4Test1:Doubleexponentialinow .......................... 202 B-5Test1:Truncatedinow ............................... 203 B-6Test1:Freeinow .................................. 204 B-7Test2:Closedbox .................................. 205 B-8Test2:Exponentialinow .............................. 206 B-9Test2:Sandageinow ................................ 207 B-10Test2:Doubleexponentialinow .......................... 208 B-11Test2:Truncatedinow ............................... 209 B-12Test2:Freeinow .................................. 210 B-13Test3:Closedbox .................................. 211 B-14Test3:Exponentialinow .............................. 212 B-15Test3:Sandageinow ................................ 213 B-16Test3:Doubleexponentialinow .......................... 214 B-17Test3:Truncatedinow ............................... 215 B-18Test3:Freeinow .................................. 216 B-19[=Fe]vs:[Fe=H]relationofTest1:Closedbox .................. 217 B-20[=Fe]vs:[Fe=H]relationofTest1:Exponentialinow .............. 218 B-21[=Fe]vs:[Fe=H]relationofTest1:Sandageinow ................ 219 B-22[=Fe]vs:[Fe=H]relationofTest1:Doubleexponentialinow .......... 220 B-23[=Fe]vs:[Fe=H]relationofTest1:Truncatedinow ............... 221 B-24[=Fe]vs:[Fe=H]relationofTest1:Freeinow .................. 222 12

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.................. 223 B-26[=Fe]vs:[Fe=H]relationofTest2:Exponentialinow .............. 224 B-27[=Fe]vs:[Fe=H]relationofTest2:Sandageinow ................ 225 B-28[=Fe]vs:[Fe=H]relationofTest2:Doubleexponentialinow .......... 226 B-29[=Fe]vs:[Fe=H]relationofTest2:Truncatedinow ............... 227 B-30[=Fe]vs:[Fe=H]relationofTest2:Freeinow .................. 228 B-31[=Fe]vs:[Fe=H]relationofTest3:Closedbox .................. 229 B-32[=Fe]vs:[Fe=H]relationofTest3:Exponentialinow .............. 230 B-33[=Fe]vs:[Fe=H]relationofTest3:Sandageinow ................ 231 B-34[=Fe]vs:[Fe=H]relationofTest3:Doubleexponentialinow .......... 232 B-35[=Fe]vs:[Fe=H]relationofTest3:Truncatedinow ............... 233 B-36[=Fe]vs:[Fe=H]relationofTest3:Freeinow .................. 234 13

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ACSAdvancedCameraforSurveysAGBAsymptoticgiantbranchAMRAge-metallicityrelationCDFCumulativedistributionfunctionCDMColddarkmatterCEHChemicalevolutionhistoryCMDColor-magnitudediagramdIrrDwarfirregularDPADelayedproductionapproximationdSphDwarfspheroidalGGCGalacticglobularclusterHBHorizontalbranchHSTHubbleSpaceTelescopeIFHInowhistoryIFRInowrateIGMIntergalacticmediumIMFInitialmassfunctionIRAInstantaneousrecyclingapproximationISMInterstellarmediumLGLocalGroupLMCLargeMagellanicCloudMDFMetallicitydistributionfunctionMSMainsequenceMSTOMainsequenceturnoPNePlanetarynebulaeRCRedclump 14

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Eggenetal. ( 1962 ,hereafterELS62).Theseauthorsstudiedthekinematicsandcolorsof200dwarfstarsinthesolarvicinity.Theyfoundthatastar'sorbitaleccentricity,angularmomentum,andvelocityperpendiculartotheGalaxy'splane(W-velocity)werecorrelatedwithitscolor.Bluestarstendedtohavehighereccentricities,lowerangularmomenta,andhigherW-velocities.TheauthorsintrepretedthistobeevidencethattheGalaxycollapsedmonolithicallyoutofaprotogalacticgascloud.Sincecolorwasaproxyformetallicity,starswiththelowestmetallicitiesformedduringthecollapse,whichoccurredonafree-falltimescale(tff=p Kant ( 1969 ). 18

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ELS62 remainedpopularformanyyears,butastheamountofobservationaldataincreased,alternativestookshape.Ofparticularimportancewastheworkof Searle&Zinn ( 1978 ,hereafterSZ78)whostudiedthemetallicitiesandhorizontalbranch(HB)morphologiesoftheGalaxy'sglobularclustersystem.Theyfoundthatclusterslocatedbeyond8kpchadawiderangeofmetallicitiesatalldistances,consistentwithnometallicitygradient,andthat,unliketheinnerhaloclusters,theseouterclustersexhibitedadiversityofHBmorphologiesatagivenmetallicity.AfterconsideringotherclusterparametersbesidesmetallicitythatwouldaecttheHBmorphology, SZ78 concludedthatclusteragewasthedominant2ndparameterandthattheouterhaloclustershadanagespreadof109years.Thesefactsled SZ78 toproposeascenarioinwhichtheinnerhalocollapsedonafreefalltimescale(asin ELS62 )buttheouterhalowasbuiltupoveralongertimescalethroughthechaoticaccretionofsmallprotogalacticgaseousfragments.Thesefragmentslostkineticenergy,formedstarsandclusters,experiencedchemicalenrichment,andeventuallydisrupted.TheremaininggasinthefragmentsfellontotheGalaxy'sdiskwhilethestarsandclustersreacheddynamicalequilibriumintheouterhalo.Intheyearssince,evidencehasaccumulatedthatvisiblegalaxiesresideinmuchmoremassivehalosofdarkmatter(DM),whichdominatesthemassoftheUniverse.ThecurrentlyfavoredcandidateforDMistheweaklyinteractingmassiveparticle,ofwhichcolddarkmatter(CDM)isthemostsuccessfultype.InmoderncosmologicalsimulationsofstructureformationwithCDM,thesmallestDMdensityperturbationsintheearlyUniversearethedensestandcollapserst( Peebles 1982 ).Thesesubhalosmergewitheachother,formingsuccessivelylargerhalosinahierarchicalbottom-upfashionanalagoustotheaccretionscenarioof SZ78 .Gaswithinthesesubhaloscoolsradiativelyandcollapsesasthemergingtakesplace,althoughtheextenttowhichthisoccursiscontroversial.Thesesimulationshavebeenverysuccessfulatreproducingobservationsonscalesofgalaxyclustersorlarger,butsomewhatlesssoonscalesofindividualgalaxies( Bahcall 19

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1999 ; Baugh 2006 ).Forexample,earlysimulationssueredfromtheproblemof\overcooling,"inwhichgascoolingwastooecientintheearlyuniverse.Thisresultedinpresent-daydiskgalaxiesthatweretoosmall,hadtoolittlespecicangularmomentum,hadanexcessivelydominantoldspheroid,andhadtoomuchhalosubstructure(e.g., Navarro&White 1994 ; Navarro&Steinmetz 1997 ).However,theextenttowhichtheseandotherproblemswererelatedtoresolutioneects,poortreatmentofgasphysics,orafundamentalawinthenatureoftheDMorcosmologicalparameterswasnotclear.ModernsimulationsintheconcordanceCDMcosmogony,whichhasanonzerocosmologicalconstant,havemetwithmoresuccess.ThisisprimarilybecauseadvancementincomputingpowerhasenabledgreatermassandforceresolutionandabettertreatmentofgasheatingfromtheUVbackground,stellarwinds,andsupernovae(e.g., Abadietal. 2003 ; Sommer-Larsenetal. 2003 ; Governatoetal. 2004 2007 ).Thesesimulationspredictthatagalaxy'spresent-daymorphologyisastrongfunctionofitsmass,environment,andmassaccretionhistory.MassivespiralgalaxiesliketheMilkyWaylocatedintheeldorloosegroupsexperiencedaninitialperiodofheavybombardmentbysmallergalaxiessimilartothefragmentsproposedby SZ78 .Theirlastmajormergeroccured&8Gyragoandsincethattimetheyhavegrownthroughaccretionofcooledgasandafewadditionaldwarfgalaxieswhosestarsmostlyendupintheouterhalo.Higherdensityenvironmentsormoreactivemerger/accretionhistoriesarelikelytoresultinmoreprominentspheroidsandearliermorphologies.ItwascommonlyheldthatintheCDMscenario,individualdiskgalaxiesforminside-out,resultinginpresent-daydisksthatgetyoungerwithradius,butwiththenewestsimulations,thesituationisnotsosimple.Forexample, Sommer-Larsenetal. ( 2003 ,hereafterSL03)presentadetailedanalysisoftwodiskgalaxiesoutofmanythatformedinacosmologicalsimulation.Oneoftheseformedinside-out,buthasverylittleagegradientwithameanstellarageof78Gyr(disregardingthebulge).Theothergalaxyformedoutside-in,withameanageincreasingfrom4Gyrat2diskscalelengths 20

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Abadietal. ( 2003 ,hereafterA03)runacosmologicalsimulationandselectforfurtherstudyonemassivespiralwhichdoeshaveathinandthickdisk.Theyndmostofthestarsinthethindiskactuallyformedinsituoverthelast8Gyrviathesmooth,fairlyconstantaccretionofcoldgasoriginatinginaccretedsatellitesordenselaments.Thethindiskmeanageis7GyratR=1kpcand3GyratR=20kpc(or4diskscalelengths).Starsinthethickdiskformedinsatellitesthatmergedwiththeparentgalaxypriorto8Gyrago,sothiscomponenthasanolderageof1011Gyr.Consideringthethinandthickdisksandthespheroidtogether,allstarshaveameanageof9Gyrthatremainsroughlyconstantwithradius.Whattheseandothersimulationsshowisthatthefossilrecordofagalaxy'sevolutionisencodedintheages,chemicalcompositions,kinematics,andspatialdistributionsofitsstars.Therefore,oneofthebestwaystotestsimulationpredictionsistostudythesepropertiesinrealpopulations.Theeldofgalacticpaleontologyseekstomeasurethesepropertieswiththegoalofunderstandinggalaxyformationandevolutionand,inparticular,therolesofgasows,tidalinteractions,satelliteaccretion,andenergeticfeedback(fromsupernovae,stellarwinds,orAGN).Tothatend,galacticpaleontologistsemploymanytechniquessuchassyntheticCMDttingandchemicalevolutionmodeling.Theseparticularmethodsareusedtoextractstarformationhistoriesandchemicalenrichmenthistoriesfromcolor-magnitudediagrams(CMDs),elementalabundances,andgasfractionsinnearbygalaxies.Inaddition,itisnowbecomingpossibletochemicallytagindividualstarsinourownGalaxybymeasuringtheiratmosphericelementalabundancesandtracethembacktotheiroriginalformationsites( Freeman&Bland-Hawthorn 2002 ). 21

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Mateo 1998 ; Belokurovetal. 2007 ).TheLGmassisdominatedbytheGalaxy,withatotalbaryonicplusDMmassof1012M,andM31,anotherearlytypespiralofcomparablemass(e.g., Klypinetal. 2002 ,butseealso Gottesmanetal. ( 2002 )whoargueforasomewhatsmallerM31mass).Eachofthesegalaxieshostsasystemof20knownmuchsmallersatellitegalaxies,themoststudiedofwhicharedwarfspheroidalsanddwarfirregularseachwithtotalmassoforder107M( Mateo 1998 ).TheonlyotherspiralgalaxyintheLGisM33,whichhasatotalmassof1011M( Corbelli 2003 ).M33istheclosestthingtoa\puredisk"galaxythatexistsintheLG.Thebulgeissosmallthatitsveryexistenceiscontroversial( Corbelli&Walterbos 2007 ,andreferencestherein),thereisnodetectablecentralsupermassiveblackhole( Gebhardtetal. 2001 ; Merrittetal. 2001 ),andthehaloluminosityislessthanafewpercentofthediskluminosity( Fergusonetal. 2007 ).TheouterHIdiskiswarped,buttherearenootherunambiguoussignsofinteractionsorrecentmassivesatelliteaccretionsuchasinM31( Fergusonetal. 2007 ; Ibataetal. 2007 ).Forthesereasons,M33providesauniquelaboratoryforstudyingrelativelyisolateddiskevolution.Inthisstudy,weexaminethestellarpopulationsofM33'soutskirtsusingphotometryobtainedwiththeAdvancedCameraforSurveysontheHubbleSpaceTelescope.InChapter 2 ,wedescribethephotometricreductionprocedureandpresenttheresultingCMDs.Weprovidearstestimateoftherangeofagesandmetallicitiesthatcouldbepresentintheseelds.Wegoontoanalyzethestructuraldistributionofstarsanditscorrelationwithage.InChapter 3 ,wederivethestarformationhistoryandage-metallicityrelationinM33'soutskirtsbyemployingthesyntheticCMDttingmethod.ThismethodenablesustorecoverbroadtrendsinthestarformationrateandmetallicityevolutionandtoestimatethemeanageandmetallicityinM33.Building 22

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4 .ThisapproachinvolvessimultaneouslycouplingthechemicalevolutionequationswiththesyntheticCMDmethod.Altogether,theseresultscontributetoourcensusoftheLG,ourknowledgeofstellardynamicsandstarformationinlowdensityenvironments,thestructureofdiskgalaxies,andourinterpretationofCMDs.Inaddition,theyprovideusefulobservationalconstraintsontheoreticalsimulationsofgalaxyformationthatattempttoreproducethepropertiesofpresent-daygalaxies. 23

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deVaucouleurs 1963 ),itisalsotheonlyotherknownspiralintheLGbesidestheGalaxyandM31.Therefore,understandingM33'sevolutionisanimportantsteptowardsunderstandingtheevolutionofspiralgalaxiesingeneral.Unlikeitslarger,moremassivespiralcounterpartsintheLG,M33hasalate-typemorphology(HubbletypeofScd).Likemostlate-typespirals,ithasarelativelylowtotalmassof1011MincludingtheDMhalo( Corbelli 2003 )andhightotalgasmassfractionof0:20:4includingatomicandmolecularhydrogenandhelium( Garnett 2002 ; Corbelli 2003 ).Someempiricalandtheoreticalstudiespredictsuchgalaxiestohaveevolutionaryhistoriesdierentfromthoseofearliermorphologicaltypes(e.g., Scannapieco&Tissera 2003 ; Garnett 2002 ; Ferrerasetal. 2004 ; Dalcantonetal. 2004 ; Heavensetal. 2004 ).Hence,M33potentiallyprovidesacontrastingviewofgalaxyevolutiontothatprovidedbytheGalaxyandM31.Theouterdisksofspiralgalaxiesareuniqueenvironmentsforseveralreasons.Theyareoftencharacterizedbywarps,ares,andothereectsofgasinfallorgravitational 24

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Fergusonetal. ( 1998 )discoveredHIIregionsorganizedinspiralarmsoutto2opticalradiiinthreelate-typediskgalaxies.TherecentdiscoveryofextendedUVdisksinseveralgalaxiesfurtherraisestheimportanceofspiralstructureindrivingstarformationintheouterregionsofthesegalaxies( GildePazetal. 2005 ).Inaddition,theUVandcosmic-raybackgroundsaswellasfeedbackfrommassivestarscouldbemoreimportantregulatorsofstarformationinthetenuousgasofouterdisksthanininnerdiskswheredensemolecularcoresarereadilyshieldedfromdissociationandionization.Thestellarpopulationsintheoutskirtsofdiskgalaxiescancontainimportantcluestotheinterplaybetweentheseprocesses.Furthermore,theytellusaboutthegalacticcollapsehistory,conditionsintheearlyhalo,andtheprogressionofsubsequentstarformation( Freeman&Bland-Hawthorn 2002 ).Forexample,thedisktruncationseeninopticalsurfacephotometryofmanygalaxiescouldbeassociatedwiththemaximumspecicangularmomentumofthebaryonsintheprotogalaxy(e.g., vanderKruit 1987 ; Pohlenetal. 2000 ; deGrijsetal. 2001 )orwithacriticalgasdensityforstarformation(e.g., Naab&Ostriker 2006 ).In Tiedeetal. ( 2004 ,hereafterPaperI)weusedground-basedphotometryreachingthehorizontalbranchtostudythemetallicityandspatialdistributionofstarsinM33'soutskirts.TheprimaryconclusionwasthatthemetallicitygradientwasconsistentwiththatofM33'sinnerdiskimplyingthatthediskextendsouttoadeprojectedradiusofatleastRdp10kpc.Thepresentpaperisanaturalfollow-upto PaperI becauseweusedeeperphotometryobtainedwiththeAdvancedCameraforSurveys(ACS)onboardthe 25

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3 ,wepresentadetailedanalysisofthestarformationhistoryofthisregionbasedontheACSdata.Thischapterisorganizedasfollows.Inx wedescribetheobservationsandphotometricreductionprocedure.WepresentanddiscusstheresultingCMDsinx .Inx weinvestigatethestellarsurfacedensity.Theninx andx wederivethemetallicitydistributionfunctionsandcomparethemtomeasurementsreportedintheliteratureinthecontextofM33'smetallicitygradient.Finally,inx andx wediscusstheimplicationsandsummarizetheresults.Inthisandallsubsequentchapters,unlessotherwisenoted,agemeanslookbacktime(i.e.,timefromthepresent).Weexpressabundanceratiosusingtheusualnotation,where[Xi=Xj]log(Xi=Xj)log(Xi=Xj).Theglobalmetallicityis[M/H]log(Z=H)log(Z=H)log(Z=Z)andweadoptZ=0:019.ForM33'sdistance,inclination,andpositionangleweassume,respectively,86728kpc( PaperI ; Galletietal.2004 ),56,and23( Corbelli&Schneider 1997 ; Regan&Vogel 1994 ). 2.1.1ACSWemakeuseofobservationsobtainedwithACSduringCycle11programGO-9479.Threeeldswereobservedatprojectedradiiofapproximately200300southeastofM33'snucleusorRdp913kpc.ThelocationsoftheeldsareshowninFigure 2-1 .Eacheldwasobservedforatotalof760sand1400sintheF606WandF814Wlters,respectively.TheobservationsforeachlterweredividedintotwoCR-SPLITexposurestoallowidenticationandmaskingofcosmicrays.Noditheringwascarriedout.Henceforth,wewillrefertotheACSeldsasA1,A2,andA3inorderofincreasinggalactocentricdistance.TheobservationsaresummarizedinTable 2-1 .ThedatawereretrievedfromtheSpaceTelescopeScienceInstitute(STScI)aftergoingthroughthestandardCALACSpipelineand\on-the-y"processing.This 26

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Sarajedinietal. ( 2006 )fordetailsofthePSF-makingprocedure.WefoundthatPSFphotometryresultedinCMDswithfeaturesthatweremoreclearlydenedthanthoseresultingfromsmallaperturephotometry.ForeachM33eldwerstusedSourceExtractor( Bertin&Arnouts 1996 )toidentifysources,DAOPHOTtomeasureaperturemagnitudes,andALLSTARtomeasurePSFmagnitudes.Thisprocesswasrepeatedontheresultingsubtractedimagetocatchanystarsthatweremissed.ThenweinputthestarlistsintoDAOMASTERtoderiveprecisespatialcoordinatetransformationsbetweentheframesineachlter.Thisallowedustocoaddalltheframestoproduceonesinglemasterimageforeacheld.ThismasterimagewasthenrunthroughtwoiterationsofSExtractor,DAOPHOT,andALLSTARasbefore.TheresultinglistofobjectsandindividualCR-SPLITexposureswereinputintoALLFRAMEtoobtainthenalPSFmagnitudes( Stetson 1987 ; Stetson&Harris 1988 ; Stetson 1993 1994 ).Wederivedmeanaperturecorrectionsfrom50100bright,isolatedstarsinA1.Thestandarddeviationsoftheaperturecorrectionsrangedfrom0:020:03magwhilethestandarderrorofthemeanwasalways<0:01mag.TherewerenotenoughbrightstarstoderivereliableaperturecorrectionsinA2andA3.SincetheACSeldsoverlapped,weidentied200starsincommonbetweenA1andA2and40betweenA2andA3.FromthesestarswecalculatedmeanosetstobringthePSFmagnitudesofA2andA3onto 27

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Riess&Mack ( 2004 ).Thesecorrectionswereusually<0:005mag.ToconverttheaperturemagnitudestothestandardUBVRIsystem,weusedthetheoreticaltransformationof Siriannietal. ( 2005 ).Theseauthorsquoteanuncertaintyof0.05magforthistransformationwhichweadoptastheuncertaintyinthephotometriczero-pointinthepresentstudy.Toreducespuriousdetections(e.g.incompletelymaskedcosmicrays,backgroundgalaxies,noise,etc.)wemadecutsonthenalcatalogaccordingtothefollowingcriteria.AnobjectwaskeptifitwasdetectedonallCR-SPLITexposures,if<3ofthemedianatitsmagnitude,sharp<3ofthemediansharpatitsmagnitude,jsharpj0:5,anderror<2timesthemedianerroratitsmagnitude.TheparametermeasuresthequalityofthePSFtandsharpmeasuresthesharpnessorspatialextentoftheobject.Therewere22415,7666,and3337starsinthenalcatalogsforA1A3,respectively. 2-1 showsthelocationsoftheeldswhichwillbereferredtoasW1,W2,andW3inorderofincreasinggalactocentricdistance.Table 2-1 containstheexposureinformation.WeelectedtouseHSTphot( Dolphin 2000 )ratherthanDAOPHOTtoobtainPSFphotometry.Ourexperiencehasbeenthattheformerissuperiorincomputationaleciencybutthelatterissuperiorinphotometricdepth.SincetheWFPC2exposuretimesarerelativelyshorttheextraphotometricdepth(0:10:2mag)gainedbyusingDAOPHOTwasnotworththeextracomputationaltime. 28

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3 .Thisensuredamoreecientandcompletesamplingoftheerrorandcompletenessfunctionsbecauseitfocusedonregionswherethetruestellarcolorsandmagnitudesareexpectedtolie.Intotal,1106articialstarsweregeneratedforeacheld.ThearticialstarswereinsertedintotheoriginalframesusingthesamePSFsthatweusedtophotometertheoriginalframes.Weplacedthestarsonaregulargridsuchthatthespacingbetweenthemwas2.1PSFttingradii(42pixels).Thisdistancewaschosen 29

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Stetson&Harris 1988 ).Thismethodusesmoreinformation(likethepositionsofallthestarsontheimage)toidentifythearticialstarsanddoesnotrequireamaximumacceptableshiftinpositionormagnitudeforrecoveredstars.Thislastpointiscrucialtoproperlysamplethetailsoftheerrordistributions.InFigure 2-2 weshowthedierencebetweeninputandoutputmagnitudeasafunctionofinputmagnitudeforallrecoveredstarsineldA1.Thegraypointsaretheindividualarticialstarswhiletheblacksquaresanderrorbarsrepresentthemedianandstandarddeviationinbins0.4magwide.ThisgureshowshowastarislikelytogetredistributedintheCMDifoneknowswhereitoriginatesbeforethemeasurementprocess.Formostofthemagnituderangecoveredineachband,thereisnosignicantdierencebetweentheinputandoutputmagnitudes.However,starswithinputmagnitudesVin&27:5orIin&27:0tendtoberecoveredsystematicallybrighterthantheirtruemagnitudes.Sincetheeldsarenotverycrowded,thissystematicerrorislargelycausedbyPoissonnoiseinthenumberofunresolvedM33starsperpixelandinthenumberofphotonsreachingthedetector.Starsareequallylikelytoexperiencepositiveandnegativeuctuationsbutatthefaintendstarsexperiencingnegativeuctuationsmay 30

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Stetson&Harris 1988 ; Gallartetal. 1996 ; Bellazzinietal. 2002b ).InFigure 2-3 weshowthevariationofthecompletenessratewithinputmagnitudeandcolorforA1.Thesolid,dotted,anddashedlinescorrespondtothecolorranges0:5<(VI)<0:5,0:5<(VI)<1:5,and1:5<(VI)<2:5,respectively.IntheV-band,thecompletenessreaches50%atVin27:428:2whileintheI-band,thecompletenessreaches50%atIin26:227:0.AtconstantImagnitude,thecompletenessdecreaseswithcolorbecausetheVmagnitudegetsfainter.AtconstantVmagnitude,thecompletenessincreaseswithcolorbecausetheImagnitudegetsbrighter.Thecompletenessrisesrapidlyfromthefaintendand,duetoourdetectionrequirementsandthepresenceofcosmicraysandbadpixels,levelsoat90%atVin26:0andIin25:0.TheerrorsandcompletenessratesforA2andA3aresimilartowithin3%overmostofthemagnituderange(i.e.,crowdingisnotastronglimitingfactor). 2-4 { 2-6 .Qualitatively,theybearsomeresemblancetotheCMDsofM33'sinnerdiskwhichwereobtainedwithWFPC2andpresentedin Sarajedinietal. ( 2000 ).ThemostprominentfeaturesinallthreeCMDsaretheredclump(RC)atI24.4andredgiantbranch(RGB)whosebrighteststarsreachacolorof(VI)2.FieldA1alsocontainsasignicantblueplumeofyoungermainsequence(MS)starsat(VI)0andaredsupergiant(RSG)sequence(sometimesreferredtoasthe\verticalclump")extendingfromthetopoftheRCandadjacenttotheRGB.TheCMDforeldA1isreproducedinFigure 2-7 withisochronesfrom Girardietal. ( 2002 )overplottedassumingaforegroundreddeningofE(VI)=0:060:02( Mould&Kristian 1986 ; Sarajedinietal. 2000 )andextinctionAI=1:31E(VI)( vonHippel&Sarajedini 1998 ).Wenotethatusingtherelationsof Siriannietal. ( 2005 )foraG2starresultsinE(F606WF814W)=0:04andAF814W=1:35E(VI).Thepairofisochrones 31

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Sarajedinietal. ( 2006 )estimatedatypicaldiskreddeningofE(VI)=0:3basedonM33RRLyraeslocatedatRdp130.ReddeningvaluesthatlargeineldA1wouldbesurprisinggiventhatitislocatedalmost3timesfartherout.However,littleisknownaboutthedistributionofdustinM33sowecannotruleoutsomecontributiontotheMSwidthduetodust.The28GyrisochronesinFigure 2-7 indicateanagespreadofseveralGyrcouldaccountformuchoftheRGBwidth.However,metallicityhasalargereectonthecoloroftheRGBthanage.Becauseofthewell-knownage-metallicitydegeneracy,multiplecombinationsofageandmetallicityareconsistentwiththepositionoftheRGB.Togetaroughideaofwhichagesandmetallicities,wetaGuassiantothecolordistributionofallstarsinA1withabsolutemagnitudesintherange3:7
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Girardietal. ( 2002 )isochroneswhicharedisplayedassolidlines.Thedottedlinesrepresentthe1widthoftheobserveddistribution.InterpolatingbetweenthetheoreticallinesbyeyeweestimatethatthebulkoftheRGBstarsinA1couldhavemetallicitiesintherange1:3<[M=H]<0:8atanageof14.1Gyrand0:8<[M=H]<0:4at2Gyr.Thesetwoagesare,respectively,theapproximatemaximumandminimumpossibleagesforrstascentRGBstarsandareconstrainedbytheageoftheUniverseandthetimeatwhichtheRGBphasetransitionoccurs( Ferraroetal. 1995 ; Barkeretal. 2004 ).InA2theconsistentrangesare1:7<[M=H]<0:8at14.1Gyrand1:1<[M=H]<0:4at2Gyr.TherearenotenoughstarsinA3toreliablytaGaussianusingthesameprocedure.Theselimitsareveryapproximateaswehaveonlyusedthecentral68%oftheRGBstars.Inaddition,thepresenceofasymptoticgiantbranch(AGB)starscouldcauseanunderestimateofthemetallicitybecausetheyliejusttotheleftofrst-ascentRGBstarsofthesameageandmetallicity.WehavealsoonlyusedasmallportionoftheRGBwhoseoverallshapedependsonchemicalcompositionandage.Chapter 3 hasamorethoroughanalysiswhichincludestheseeects.ThecolorandmagnitudeoftheRCarealsosensitivetotheageandmetallicityofitsconstituentstars.InFigure 2-9 weshowaclose-upoftheRCregioninA1withmeantheoreticalvaluesfrom Girardi&Salaris ( 2001 )asafunctionofmetallicityandage.Thecurveshavemetallicitiesof1:3,0:7,and0:4fromlefttoright,respectively.Thesymbolsoneachcurverepresent5dierentages.Theopencirclescorrespondto1Gyr,squaresto2Gyr,trianglesto5Gyr,starsto8Gyr,andlledcirclesto12Gyr.Thecrossshowstheobservedmeanabsolutemagnitude(0:41)anddereddenedcolor(0:94).Thisgureprovidesevidencefortheexistenceofstars25Gyroldwithasmalldependenceonmetallicity.Ifthemeanmetallicityis0:7thenanageof5Gyrispreferredbutifthemetallicityis0:4then2Gyrispreferred.ThemeanRCmagnitudeandcolorforA2are,respectively,0:40and0:92whileforA3theyare0:38and0:92.Thisindicates 33

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Girardi&Salaris 2001 ).Indeed,thereisalsoasequenceofstarsextendingfromtheRCtowardbluercolorsandfaintermagnitudeswhichliesjustabovethe12Gyrpointonthe[M/H]={1.3curve.Withsuchfewstarsitishardtosaywhetheritisjustarandomgroupingorthehorizontalbranch(HB)ofanolderandmoremetal-poorpopulation.Finally,thisgurealsonicelyshowsthatthelefthalfoftheRCcancontainstarsyoungerthan1Gyr.TheRGBridgelinesofGalacticglobularclusters(GGCs)M92,NGC6752,and47Tucfrom Brownetal. ( 2005 )areoverplottedontheCMDofA1inFigure 2-10 .TheGGCdatawasoriginallyintheACSinstrumentalsystembutwehavetransformedthemusingtheprescriptionandclusterparametersoutlinedin Brownetal. ( 2005 )andusingthesametransformationsthatweappliedtotheM33data.TheGGCridgelinesspanthewidthofM33'sRGBindicatingthattheoldeststarsinA1mostlikelyhavemetallicitiesbetween[Fe/H]=1:54(NGC6752)and0:70(47Tuc).Thisempiricalcomparisonisinagreementwithwhatwefoundaboveusingthe Girardietal. ( 2002 )modelsanddemonstratesthatnoseriouserrorshavebeenintroducedinthetransformationtotheground-basedltersystem.TheHBlociofthesamethreeGGCsarealsoplottedinFigure 2-10 .StarsintheblueHBtailat(VI)0belongtobothM92andNGC6752whiletheredHBat(VI)0:9belongsto47Tuc.ThebulkofM33'scoreheliumburningstarsarebrighterthanthoseof47TucprovidingfurtherevidenceforapopulationyoungerthantheGGCs.However,asnotedpreviously,thefaintestportionofM33'sRCcouldcontainstarsasoldas47Tuc.Becauseofitsmagnitudeandcolorrange,theyoungMSmakesitdiculttoconrmorruleoutcompletelythepresenceofablueHBtailinM33similartothatof 34

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2-11 { 2-13 displaytheCMDsforthethreeWFPC2elds.DuetotheshorterexposuretimeinF606W,thelimitingmagnitudeisabout2magnitudesbrighterthanintheACSelds.MostoftheCMDfeaturesarewashedoutexceptfortheRGB.Becauseoftheshallowerphotometricdepthandfewernumberofstars,wedonotusetheWFPC2CMDsinanypartofthisstudyexceptintheanalysisofstellarsurfacedensity. 2-14 .ThestarswereselectedtoliebetweenthelinesinFigures 2-11 { 2-13 (notethatthelinesarenotshowninFigures 2-4 { 2-6 forclarity).EachACSeldwasdividedintofourradialbins(representedbydiamonds)whereaseachWFPC2eldwastreatedinitsentirety(representedbysquares).SinceW1coincideswithA3,theWFPC2eldswerebroughtontothecompletenessscaleoftheACSeldsbynormalizingthesurfacedensityinW1tothatinA3.ThisavoidsmakinguncertainestimatesofthedieringcompletenessratesbetweentheACSandWFPC2eldswithintheRGBselectionregion.However,usingtherawWFPC2densitiesdoesnotchangetheresults.Hence,W1isnotshowninFigure 2-14 norisitincludedinthetsbelow.TheerrorbarsreectthePoissonuncertaintynormalizedbytheactualareaobservedineachradialbin.Notethatwehaveneglectederrorbarsindeprojectedradiusduetothenitethicknessofthedisk. Sethetal. ( 2005 )observedasampleofedge-onlate-typespiral 35

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Corbelli&Schneider ( 1997 )tatilted-ringmodeltotheHIdistributionandfoundthatthepositionanglechangesfrom+20to15overtheregionwehaveobserved.Whetherthestellardiskfollowsthischangeisunclear.Anexponentialprolewasttotheobserveddistributioninaleast-squaressenseanditisshownasthedottedlineinFigure 2-14 .Thescalelengthofthetis4:900:10.ThesurfacedensityinW3showsasignicant(3)deviationfromtheexponentialprole.Toassessthelevelofcontaminationfrombackgroundgalaxiesandforegroundstarswereducedasubsampleofimages(2ineachlter)oftheHubbleDeepFieldusingthesametechniqueandthresholdsthatwereappliedtoM33.TheresultingCMDisshowninFigure 2-15 andcontains7objectsintheRGBselectionregion.Therefore,weestimatethesurfacedensityofbackgroundgalaxiesandforegroundstarstobe1arcmin2.Includingthisconstantosetinthetreducestheexponentialscalelengthto4:700:10.ThesolidlineinFigure 2-14 representsthesumoftheexponential(dashed)andoset(dot-dashed).Thelastpointstillshowsanexcessofstarsbutonlyatthe1:8level.IfthisexcessisnotduetoPoissonianuctuationsthenitcouldrepresentatransitiontoamoreextendedstellarcomponent,apointtowhichwereturninx .TheK-bandsurfacebrightnessscalelengthofM33hasbeenmeasuredtobe5:805:90( Regan&Vogel 1994 ; Simonetal. 2006 ).Whendealingwithintegratedlight,theK-bandisgenerallythoughttobeabettertraceroftheoldRGB(age&2Gyr)stellardistributionthanopticalbands.However, Sethetal. ( 2005 )foundthattheK-bandlightintheirsampleoflowmass,latetypespiralswasdominatedbyyoungerredsupergiantsandAGBstars.Also, Regan&Vogel ( 1994 )foundasystematicdecreaseinM33'ssurfacebrightnessscalelengthwithwavelength.Theyusedasimpletoymodelwhichascribedthistrendtotheabsorbingeectsofdust.Theirmodelneglectedtheeectsofforward 36

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Regan&Vogel ( 1994 )and Simonetal. ( 2006 ).Hence,ifM33'sdensityproleisnotasingleexponentialthenthedierencebetweenourmeasurementswouldbeexpected.Indeed, Roweetal. ( 2005 )surveyedM33'sluminousstellarpopulationsandfoundaclearbreakinthecarbonstarproleatRdp350.Whiletheydidnotmakeanyexponentialtstotheirproleweestimatebyeyethatoutsidethisradiusthescalelengthoftheirproleisremarkablyclosetoourresult.Thispictureisconrmedby Fergusonetal. ( 2007 )whoconductedawideeldsurveyofM33withtheIsaacNewtonTelescope.TheyreportasimilarbreakintheRGBdensityproleataboutthesameradiusfoundby Roweetal. ( 2005 )andbeyondwhichthescalelengthissimilartowhatwehavefound.In PaperI ,wefoundthatmassiveMSstarsweremoreconcentratedtowardM33'snucleusthanAGBstarswhichinturnweremoreconcentratedthanRGBstars.Thisimpliedaprogressioninthestellarscalelengthwithage.InspectionoftheCMDspresentedherealsosuggeststhatthedensityofstarsintheyoungMSdeclinesfasterthanthedensityofRGBstars.ToinvestigatethisinmoredetailweselectedseveralregionsoftheCMDonthebasisthateachregionprobesdierentageranges.Usingtheresultsfromx wefoundthatcontoursofconstantagerunroughlydiagonallysincethemainsequenceturno(MSTO)andSGBmovetowardfainterandreddermagnitudeswithage.Figure 2-16 showstheregionsweselected.Theboundarieswerechosentoroughlyfollowlinesofconstantageandthesizeswerechosenasacompromisebetweentheneedforgoodnumberstatisticsandasmallrangeofagesineachbox.Thefaintlimitwaschosentoavoidtheregionwheresystematicmagnitudeerrorsdominateandtominimize 37

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Gallartetal. ( 1999 )usedasimilarapproachtoisolatedierentagerangesinstudyingthestarformationhistoryofLeoI.Table 2-2 liststhemeanage(averagedoverallthreeelds)andscalelengthforeachboxandtheirstandarddeviations.InFigure 2-17 weshowtherelativestellarsurfacedensityofeachboxforeldsA1A3.Thereisatrendofdecreasingconcentrationastheboxesgetfainter,and,hence,older.Wetanexponentialproletoeachbox'sstellardistributionspanningallthreeelds.Figure 2-18 displaysthebehaviorofthescalelengthwithmeanage.Thecurvedlinesshowthreepower-lawrelationsoftheformh=3twith=0:1;0:3;0:5.Theformoftheserelationsissomewhatarbitraryandweshowthecurvesonlyforreference.Theverticalerrorbarsarethestatisticaluncertaintiesinthescalelengthfromtheleast-squaresttingprocedure.Thehorizontalerrorbarsrepresentthespreadoftheagesineachbox.Thepreciseagesprobablyrepresentthelargestsourceofuncertaintyinthisplot.They-errorsarefairlyuniformbutthex-errorsincreasedramaticallyfortheoldestboxes.Thisisbecausethestellarisochronesgetmorephotometricallydegeneratewithage.Comparisonofthepower-lawrelationssuggeststhat0:1..0:3butwerefrainfrommakingamorepreciseestimationduetotheinherentsystematicuncertainties.Wediscusspossibleinterpretationsinx PaperI ,weemploythe Savianeetal. ( 2000 )gridofRGBducialstoconstructthemetallicitydistributionfunction(MDF)ofeacheld.ThoseauthorsusedalargehomogeneousphotometricdatabaseofGGCstoderiveafunctionwhichhasoneparameter,[Fe/H],thatspeciestheshapeoftheRGB.IfanRGBstar'sabsolutemagnitudeanddereddenedcolorareknown,thenthefunctioncanbesolvedforthestar'smetallicity.Tominimizecontaminationfromforegroundstars,AGBstars,andredsupergiants,werestrictthepresentanalysistostarsintheregion1:0(VI)02:2 38

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2-19 asthesolid-linegeneralizedhistogramsfromtoptobottom,respectively.ThesewereconstructedbyassigningaunitGaussiantoeachstarwithastandarddeviationequaltothestar'smetallicityuncertainty.Themedianmetallicityis1:14,1:23,and1:30whiletheinterquartilerangeis0.4,0.6,and0.6dex.Thedashedlinerepresentsthe\instrumentalresponse,"namelytherecovereddistributionforatestpopulationhavingasinglemetallicity( Bellazzinietal. 2002a ).Thetestpopulationconsistedof2000starswhoseinputmagnitudesreproducedtheobservedRGBluminosityfunctionandwhosecolorsreproducedtheSavianeetal.RGBridgelinefor[Fe/H]=1:1.Thestandarddeviationoftherecovereddistributionis0.04dexandrepresentsthetotalintrinsicrandomerrorintroducedduringtheentiremeasuringprocessfromthephotometricreductiontothemeasurementofmetallicities.Wendthatwhenthe1uncertaintiesinthedistanceandreddeningareaddedinquadraturetheyintroduceasystematicerrorof0:1dex. 2-20 summarizestheseothermeasurements.Theopentriangleisbasedontheresultsof Stephens&Frogel ( 2002 ,SF02)whoimagedthecentral2200ofM33withGeminiNorth.Theyobtainednear-IRphotometryandfromtheslopeoftheRGBcalculatedameanmetallicityof0:260:27(rand).Thelledcirclesaretheresultsof Kimetal. ( 2002a ,K02),whoobtainedVIphotometryof10WFPC2eldslocatedthroughoutthedisk(Rdp16kpc).Theyfoundmedianmetallicitiesrangingfrom0:6to0:9withatypicalerrorof0.09dex.Itisnotclearwhethertheirquotederrorsarerandomorsystematic.Theopencirclescorrespondtotheresultsof Galletietal. ( 2004 ,G04),who 39

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PaperI (PI)afterapplyingamissingfactorofcos(DEC)intheoriginalcalculationofdeprojectedradii.ThisdoesnotaectanyoftheconclusionsofPIorthispaper.Theerrorbarsdemonstratethe\instrumentalresponse."Alargesurveycoveringprojectedradiiof260600wasconductedby Brooksetal. ( 2004 ,B04)whofoundapeakmetallicityof1:270:04(rand)whichisshownastheopen(downward-pointing)triangle. Davidge ( 2003 ,D03)imagedaeldatRdp720andfoundevidenceforanexcessnumberofstarsrelativetoacontroleldwhichheintrepretedasAGBandRGBstarsinM33.HemeasuredtheRGBmetallicitytobe[Fe/H]=1:00:3(rand)0:3(sys)whichisshownasanopensquare.Weshowonlytherandomerrortobemoreconsistentwiththeotherpoints.Thelledtrianglesrepresenttheresultsofthepresentstudywhiletheerrorsarethe\instrumentalresponse"discussedintheprevioussection.ThestarsymbolsinFigure 2-20 correspondto9haloglobularclustersofM33.Theirmetallicitieswereestimatedby Sarajedinietal. ( 2000 ,S02)usingWFPC2VIphotometryandtheslopesoftheclusterRGBs.TheerrorsfortheclustersarerandomerrorspropagatedthroughtherelationsbetweenRGBcolor,slope,andmetallicity.Themeanmetallicityoftheseclustersis1:270:11(rand).Recently, Sarajedinietal. ( 2006 )studiedtheRRLyrae(RRL)populationinanACSeldlocatedatRdp150.TheyfoundthattheRRLmetallicitydistributionexhibitedapronouncedpeakat[Fe/H]1:3whichtheyinterpretedasevidenceforaeldhalopopulation.ThedashedlineinFigure 2-20 thereforerepresentsthehaloofM33(includingclustersandeldstars).M33'sdiskpresumablyhasadierentstarformationhistoryfromitshalosoatransitionfromonetotheothercouldbeobservableasachangeintheapparentRGBmetallicitygradient.ThedottedlineinFigure 2-20 isthettotheinnerdiskelds(lledcircles)from K02 whilethesolidlineistheirtwhichexcludedtheinnermosttwo 40

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PaperI ,wefoundthatthemetallicitygradientwasconsistentwiththeinnerdiskgradient.InthepresentstudywendthatthesamegradientextendsouttoRdp=500.Pastthisradiusthereappearstobeaatteninginthegradientbutthesituationissomewhatuncertain. Brooksetal. ( 2004 )interpretedtheireldtobedominatedbyahalopopulationbecauseoftheshallowsurfacedensityprolewithapower-lawslopeof1:47andbecausetheirmetallicitymatchedthehaloglobularclusters.Likewise, Davidge ( 2003 )suggestedtheAGBandRGBstarshefoundweretheeldcounterpartstothehaloGCswhichmayhaveformedoveratimescaleofseveralGyr(seealso Sarajedinietal. ( 2000 )).Unfortunately,theseanalysesreliedheavilyupontheadoptedlevelofcontaminationfromforegroundGalacticstarsandbackgroundgalaxies.OnlymoreprecisemeasurementsofRGBmetallicitiesatradiipastRdp=600coulddetermineifthediskgradientcontinuesoutwardoriftheslopeattensoutasmightbeexpectedforahalo(orthick-disk)population.SuchmeasurementscouldrequirelargeareastoobtainastatisticallysignicantsampleofRGBstars.Finally,thereareseveralimportantconsiderationstonotewhileexaminingFigure 2-20 .First,wehaveusedourducialM33distance,inclination,andpositionangleandthecentersoftheeldsstudiedtodeterminetheirdeprojecteddistances.Becausethe Davidge ( 2003 ), Brooksetal. ( 2004 ),and Galletietal. ( 2004 )eldswererelativelylarge,itwouldbemoreaccuratetoplottheirpositionsaccordingtothemeanRAandDECoftheRGBstarsintheirelds.DependingonthegeometryoftheireldsrelativetoM33'snucleus,thiscouldhavetheeectofmovingtheminwardtosmallerradiibecauseofthenegativestellardensitygradient.Mostimportantly,allofthemeasurementspresentedinFigure 2-20 comparedM33'sRGBstarstotheGGCswhichareold(12Gyr)andcontainenhancementsinthe-elementabundance([=Fe]0:3).Aspointedoutby Salaris&Girardi ( 2005 ),theRGBsofgalaxieswithcompositestellarpopulations,suchastheLMCandSMC, 41

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3 wemodelthestarformationhistoryofeldsA1A3usingstellarevolutionarytrackswith[=Fe]=0:0andwendthatthetruemetallicityis0:4dexhigherbutthemetallicitygradientthroughtheeldsisroughlyunchanged.Fromthe Girardietal. ( 2002 )isochronesweestimatethatapproximatelyhalfofthisosetisduetothelower-elementabundanceandhalfisduetoayoungermeanage(68Gyr).Iftheouterregionswereasyoungas2Gyr,thetotalosetwouldamountto0:6dex.CurrentlythereisnoinformationonthestarformationhistoryofM33'sinnerdisksoitispossibletheRGBmetallicitygradientoveritsentirediskisshallowerorsteeper.However,itisunlikelythatanagegradientcanmimictheapparentmetallicitydierenceof0:8dexbetweenM33'scentralandouterregionsbecausethelatterarenotyoungenough. Kennicutt ( 1989 )and Martin&Kennicutt ( 2001 )arguethatitisgovernedbygravitationalinstabilityasparameterizedbytheToomreQparameter.Thisparameterdependsonthelocalepicyclicfrequencyandgasvelocitydispersion.Itaccuratelypredictsthecriticalradiusformanyhighsurfacebrightnessgalaxiesbutfailsforsomelow-massspiralslikeM33(R=290)wherelargeportionsofthediskarebelowthethresholdgasdensitybutactivelyformingstars. Corbelli ( 2003 )usedmeasurementsofthegaskinematicsinM33toderiveanextensiverotationcurveandmassmodel.ShefoundthattheToomrecriterioncould 42

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Martin&Kennicutt 2001 ).WhatimplicationsdoourresultshaveforthestarformationthresholdinM33?Wenotedinx thateldA1containsstars35MwhileA2andA3containstars34M.ThesemassivestarscanbenoolderthantheirMSlifetimesof100400MyrandunlesswehavecoincidentallyobservedthemattheendoftheirMSphasesthentheyareprobablyevenyounger.ThisfactisdirectevidenceforrecentstarformationatRdp350500inapparentdisagreementwithM33'sstarformationthresholdradiusof290.Itispossiblethatthesemassivestarsactuallyformedatsmallerradiiandhavesincemigratedoutward.Giventheiryoungages,however,thereprobablyhasnotbeensucienttimeforthistooccur.Couldstarformationbeongoingtodayinourelds? Boissieretal. ( 2006 )usedGALEXimagestostudytheradialvariationofstarformationin43spiralgalaxies.IncludedintheirsamplewasM33whoseFar-UVproleextendedouttoRdp430,wellpastthethresholdradiusmeasuredwithH.Indeed,nearlyallofthegalaxiesintheirsampledisplayedsimilarbehaviorleadingtotheconclusionthatstarformationisongoingtodayintheoutskirtsofthesegalaxiesbutatlevelstoolowtoproduceanyionizingstars.TheUVcontinuum,however,issensitivetothestarformationrateintegratedoverthelast100Myr.Incontrast,theHobservationstracethestarformationrateoverthelast20Myr( Kennicutt 1998 ).Therefore,itispossiblethattherearenoionizingstarsalivetodaybecausestarformationended20100Myrago.ThislattersencariocouldexplainourobservationsofyoungstarsinM33'soutskirtsbeyondtheHthresholdradiusand,therefore,savetheapplicabilityoftheToomreQparametertoM33.However,wewouldstillneedtoexplainhowstarformationcouldhave 43

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Corbelli ( 2003 )theazimuthallyaveragedHIcolumndensityis3:0,2:0,and1:5Mpc2atthecentralradiiofeldsA1,A2,andA3,respectively.ComplexitiesintheHIdistributioncancausesystematicandrandomerrorswhenperformingazimuthalaveragesevenindetailedtilted-ringmodels.SuchisthecaseinM33'souterdiskwhereresidualsbetweenthemodelandobserveduxatdierentpositionangleswithinaringcanvarybyafactorof2( Corbelli&Schneider 1997 ).Azimuthallyaveragedcolumndensitiesarewhatarecommonlyreportedintheliteratureforothergalaxiessoweusethemhereaswell.Thehighresolutionaperturesynthesismapof Newton ( 1980 )showsthattheHIdensitythroughoutoureldsisbelowthelowestcontourwhichcorrespondsto4:3Mpc2.Theamountofmoleculargasinoureldsisdiculttoascertainbutitisunlikelytocontributesignicantlytothetotalgascontent.OureldslieoutsidetheGMCsurveyof Engargiolaetal. ( 2003 )andareatthelimitofthesensitivityandcoverageoftheCOmapspresentedby Heyeretal. ( 2004 ).TheoutermostreliablepointintheirmapisatRdp240wheretheH2columndensityis0:6Mpc2.ThiscanbetakenasaroughupperlimitforoureldsconsideringthattheCOtoH2conversionfactormaybedierentintheouterdiskwherethemetallicityislower.AcrucialpointtoconsideriswhetherthegasdensityinoureldscouldhavebeensignicantlygreaterjustafewhundredMyrago.Thispossibilityisactuallyruledoutbythelowstarformationraterequiredtoexplainthesmallnumberofyoung,massivestarsobserved.FromthestarformationhistoriescalculatedinChapter 3 ,wendthatthemeanstarformationrateinthepast400Myrhasbeen<0:04Mpc2Gyr1.Thus,nomorethan0:02Mpc2couldhavebeenconvertedtostarsinthattime. 44

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( 2003 )calculatedthevariationinthethresholddensitywithradiusinM33.Accordingtoherplots,theToomrecriterionpredictsathresholddiskdensitythatdropsfrom7to6Mpc2acrosseldsA1A3whereastheshearratecriterionpredictsathresholdthatisapproximatelyconstantat5Mpc2.Therefore,afewhundredMyragothegasdensitywasbeloweitherthreshold.Corbelli'smassmodelpredictsthegastodominatethebaryonicmassintheseouterregionssoitisalsounlikelythatthestellarmasscontributessignicantlytothetotaldisksurfacedensity.Ontheotherhand,thedarkmatterdensitywithinthediskisaboutequaltothegasdensity.Hence,includingdarkmatterinthetotaldiskdensitycanexplaintherecentstarformationineldA1butnotA2orA3.Agrowingbodyofevidencehassuggestedthataconstantthresholdgasdensityof310Mpc2describestheextentofstarformingdisksequallywellifnotbetterthanaradiallyvaryingthresholdliketheToomreQparameterorshearratecriterion( Skillman 1987 ; Tayloretal. 1994 ; Fergusonetal. 1998 ; Martin&Kennicutt 2001 ).ThephysicalbasisforsuchathresholdcouldberelatedtotheminimumpressureneededfortheformationofacoldgasphaseintheISM( Elmegreen&Parravano 1994 ; Schaye 2004 ).IfsuchaconstantthresholdappliestoM33thenourresultsimplyitis.3Mpc2andcouldbeassmallas1Mpc2.Indeed, Boissieretal. ( 2006 )traceM33'sFar-UVproleouttogasdensitiesof12Mpc2.Afterthischapterwaspublished,DavidThilkerkindlyprovideduswithHImeasurementsinoureldsthatweretakenwiththeVeryLargeArrayandGreenBankTelescope.Thesedatashowthat,ataresolutionof500pc,themeanprojectedHIsurfacedensitydecreasesfrom1.1Mpc2inA1to0.3Mpc2inA3.Atahigherresolutionof100pc,theprojectedHIsurfacedensityis1.4Mpc2inA1and0.7Mpc2inA3,whichreectsthefactthatthereisstructureonscales<500pc.Sincethedeprojectedsurfacedensitycanonlybesmaller,thesemoreaccuratevaluesputtighter 45

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Naab&Ostriker 2006 ).ThismeansthattheoldeststarsweobservetodayshouldhavethesmallestscalelengthincontrasttoourresultswhichshowtheoppositetrendinM33.Thisseemstosuggestanoutside-informationscenario.AdierentinterpretationisthatweareobservingatransitionbetweentwodistinctcomponentsinM33,likeadisk/thick-diskordisk/halo.ThiswouldexplainwhythenumberofRGBstarsineldW3islargerthanpredictedbyasimpleexponentialplusbackgroundmodel.Ifthisiscorrect,theneldA3couldhaveanon-negligiblethick-disk/halocomponentwhichmightexplainwhyitsmetallicitymatchesthatofM33'shalo.Interestingly,theM-starprolemeasuredby Roweetal. ( 2005 )showsaatteningatapproximatelythesamelocationaseldsA2A3furtherhintingatasecond,moreextendedcomponent.M33'shalowasrecentlyisolatedkinematicallyby McConnachieetal. ( 2006 )whoanalyzedKeckDEIMOSspectraof280starslocated380alongthemajoraxis.Theseauthorsfoundevidenceforthreedistinctkinematiccomponents:adisk,halo,andanintermediatecomponentwhichtheyhypothesizedcouldbeatidalstreaminM33.Itisunclearhowtheintermediatecomponentwouldaectourresultsbecause,ifitisastream,itmightnotgothroughourelds.Thehalocomponent,however,wouldbepresentinoureldsalthoughit'sprecisecontributionisuncertain.Oureldslieataboutthesame 46

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McConnachieetal. ( 2006 )buttheyareontheminoraxissothehalo-to-diskratiocouldbelargerdependingonthetruehalodensitydistribution.Complicatingthepictureisthepossibilityofdiskorbitalheatingmechanisms.Theseprocessesmust,atsomelevel,modifythestellarage,metallicity,anddensitygradientsputinplacebystarformationregardlessofwhetheritprogressesinside-outorvice-versa(e.g., Lepineetal. 2003 ; Sellwood&Binney 2002 ; Wielenetal. 1996 ).Theclassicalmechanisminvolvesgravitationalencountersbetweenstarsandgiantmolecularcloudsofmass106M( Spitzer&Schwarzschild 1953 ).Thisprocesshasbeenshowntoheatthestellardiskataratewheretheverticalandradialvelocitydispersionsarerelatedbyz/R/twhere0:25andz=R0:7( Lacey 1984 ; Villumsen 1985 ).Unfortunately,observationsintheGalaxyindicatethat1)therearetoofewGMCswiththerequisitemass( Lacey 1984 ),2)0:5( Wielen 1977 ),and3)z=R0:5( Hanninen&Flynn 2002 ).Inresponse,othermechanismshavebeenproposed,fromheatingbyspiralarmstomassivehaloblackholespassingthroughthedisk( Lacey&Ostriker 1985 ).Theformerismostpromisingbecausetheoreticalsimulationspredict0:2..0:5fortheresultingheatingrate( DeSimoneetal. 2004 ).It'sbiggestproblem,though,isthatspiralwaveshavenoeectontheheatingrateintheverticaldirectionand,thus,cannotexplainwhytheheatingratehasthesametimedependenceintheradialandverticaldirections.ItnowappearsthatsomecombinationoftheseprocessestakesplacewithspiralwavesdoingmostoftheheatingandGMCsredistributingsomeoftheradialpeculiarvelocitiesintotheverticaldirection(e.g., Carlberg 1987 ).Thepreciserelativecontributionspresumablydependonthecharacteristicsofthegalaxyinquestion,likethemassspectrumofGMCsandthestrength,number,pitchangle,andlifetimeofspiralarmsandotherirregularitiesinthepotentiallikebarsandaccretedsatellites.Animportantpieceofthepuzzlecomesfrom Sethetal. ( 2005 ).Afteranalyzingtheverticaldistributionofstarsinsixlate-typespiralstheyfoundthatthescaleheight 47

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Sethetal. ( 2005 )usedthisproportionalitytoshowthatiforbitaldiusionisresponsiblefortheirresultsthentheheatingrateintheverticaldirectionmustbesignicantlylessthanintheGalaxy,namely<0:15.TheseresultsareintriguinglysimilartowhatwehavefoundinM33fortheradialdirectionandpointtoacommonorigininalllate-typespirals. Sethetal. 2005 ).WeareunabletosaywhetherthisbehaviorisduetotheorbitaldiusionofstarsastheyageortointrinsicvariationsinSFHwithradius.Giventheexponentialradialdistribution,metallicitygradient,andmixedagespresentinoureldsitislikelythestarsbelongpredominantlytoM33'sdisk.Thiswouldmean 48

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49

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Observationlog FieldDate(UT)FilterExposureTime(s)R.A.(J2000.0)Decl.(J2000.0) A12003-1-12F606W238001:35:1830:28:58A12003-1-12F814W270001:35:1830:28:58A22003-1-12F606W238001:35:3230:28:06A22003-1-12F814W270001:35:3230:28:06A32003-1-12F606W238001:35:4630:27:02A32003-1-12F814W270001:35:4630:27:02W12003-1-12F606W214001:35:4230:26:16W12003-1-12F814W250001:35:4230:26:16W22003-1-12F606W214001:35:5630:25:25W22003-1-12F814W250001:35:5630:25:24W32003-1-12F606W214001:36:1030:24:20W32003-1-12F814W250001:36:1030:24:20 Table2-2. Variationinscalelengthwithage BoxAge(Gyr)(Gyr)h(arcmin)(arcmin) 10.350.151.920.2220.620.582.980.2731.901.793.550.1844.313.004.090.1456.023.404.560.1466.793.454.860.18 50

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ImageshowingM33andtheapproximatelocationsandsizesoftheregionsobservedwithACSandWFPC2.NorthisupandEastistotheleft.Theimagedimensionsare1onaside. 51

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ThedierencebetweeninputandoutputmagnitudeforallrecoveredarticialstarsineldA1(graypoints).Eachlledsquareanderrorbargivesthemedianerroranditsstandarddeviation.A)V-band.B)I-band. Figure2-3. CompletenessrateasafunctionofinputmagnitudeineldA1fortheinputcolorranges0:5<(VI)<0:5(solid),0:5<(VI)<1:5(dotted),and1:5<(VI)<2:5(dashed).A)V-band.B)I-band. 52

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CMDofeldA1.ThemainfeaturesaretheRCatI24.4,theRGBextendingfromtheRCtobrightermagnitudes,andtheblueplumeofyoungerMSstarsat(VI)0. Figure2-5. SameasFigure 2-4 butforeldA2. 53

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SameasFigure 2-4 butforeldA3. Figure2-7. CMDofA1withisochronesfromGirardietal.(2002)overplotted.Theisochroneshaveametallicityof[M/H]=0:7andagesof100Myr,398Myr,and1.0,2.0,5.0,and7.9Gyrfromtoptobottom,respectively.Thethreehorizontallinesmarkthe100MyrMSlocationsof5,4,and3Mfromtoptobottom,respectively. 54

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Ageandmetallicityconstraintsfromthedereddenedcolor(dashedlines)andwidth(dottedline)oftheRGBinA1.ThesolidlinesarethepredictionsoftheGirardietal.(2002)isochrones. Figure2-9. Close-upofRCregionofA1withmeantheoreticalRCvaluesfromGirardi&Salaris(2001)asafunctionofmetallicityandage.Thecurveshaveglobalmetallicitiesof1:3,0:7,and0:4fromlefttoright,respectively.Theopencirclescorrespondto1Gyr,squaresto2Gyr,trianglesto5Gyr,starsto8Gyr,andlledcirclesto12Gyr.ThecrossmarkstheobservedmeanmagnitudeandcoloroftheRC. 55

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CMDofA1withtheRGBridgelinesandHBlociofGGCsM92([Fe/H]=2:14),NGC6752([Fe/H]=1:54),and47Tuc([Fe/H]=0:70)overplotted. Figure2-11. CMDofeldW1.Starsbetweenthelineswereusedtostudythestellarsurfacedensity. 56

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SameasFigure 2-11 butforW2. Figure2-13. SameasFigure 2-11 butforW3. 57

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SurfacedensityofRGBstarsasafunctionofdeprojectedradius.ThediamondscorrespondtoeldsA1{A3andthesquarescorrespondtoeldsW2andW3.TheerrorbarsarePoissonerrorsscaledbytheareaobservedineachradialbin.Thedottedlineshowsanexponentialttoallthepointswhilethesolidlineshowsanexponentialplusconstantmodel(dashed+dot-dashed). Figure2-15. CMDforasubsampleofHubbleDeepFieldimages.Objectsbetweenthelineswereusedtoestimatecontaminationfrombackgroundgalaxiesandforegroundstars. 58

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CMDofA1andthesixboxesusedtostudytheagedependenceoftheradialscalelength. Figure2-17. RelativesurfacedensityofstarsineachboxshowninFigure 2-16 59

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Radialstellarscalelengthasafunctionofage.EachpointandhorizontalerrorbaristhemeanandstandarddeviationofstellaragesforeachboxshowninFigure 2-16 .Theverticalerrorbarsaretherandomuncertaintiesinthescalelengthsfromtheleast-squarests.Threearbitrarypower-lawrelationswhereh=3tareshownforcomparison. Figure2-19. GeneralizedhistogramoftheRGBmetallicitydistributionfunctionineldA1(top),A2(middle),andA3(bottom).Thedashedcurveshowsthe\instrumentalresponse." 60

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RGBmetallicitygradientinM33.Thedottedandsolidlinesare,respectively,thetsfromK02toallthelledcirclesandallbuttheinnertwowherecrowdingwassevere.ThedashedlinerepresentsM33'shalometallicity(seetextfordetails). 61

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ELS62 ,theages,kinematics,andchemicalcompositionsofstellarpopulationsintheGalaxyhaveprovedcrucialtoourunderstandingofitsevolution(see Freeman&Bland-Hawthorn ( 2002 )forarecentreview).Bythesametoken,suchvitalstatisticsarereshapingourviewofnearbygalaxies,especiallythoseintheLG(e.g., Sarajedinietal. 2000 ; Harbecketal. 2001 ; Fergusonetal. 2002 ; Brownetal. 2003 ; Lanfranchi&Matteucci 2004 ; Coleetal. 2005 ).AcriticaltoolinthisadvancementistheCMD.BycomparingtheobserveddistributionofstarsinaCMDwiththepredictionsofstellarevolutionarytheoryonecanestimatetheiragesandmetallicities.Forstarclusters,suchacomparisonisstraightforwardrelativetothemorecomplextaskofdisentanglingtheagesandmetallicitiesofstarsinthegeneraleld.Nevertheless,thestudyofeldpopulationshasprogressedtremendouslydueinparttoadvancesinCMDanalysistechniquesand,inparticular,thetechniqueofsyntheticCMDtting.CentraltothistechniqueistheuseoftheoreticalstellarevolutionarytrackswithwhichonecangenerateamodelCMDforanyarbitrarystarformationhistory(SFH).ThemodelCMDcanthenbecomparedtotheobservedCMDtoseehowcloselytheymatchand,thus,howcloselythemodelSFHmatchesthetrueSFH.VariousformsofthistechniquehavebeenappliedtogalaxiesthroughouttheLGrevealingavarietyofSFHs(e.g. Tosietal. 1991 ; Bertellietal. 1992 ; Aparicioetal. 1997 ; Dohm-Palmeretal. 1997 ; Tolstoyetal. 1998 ; Gallartetal. 1999 ; Hernandezetal. 2000 ; Olsen 1999 ; Milleretal. 2001 ; Wyder 2003 ; Skillmanetal. 2003 ; Harris&Zaritsky 2004 ; Holtzmanetal. 1999 ; Martnez-Delgadoetal. 1999 ; Dolphin 2002 ).Surprisingly,though,ithasyettobeappliedintherefereedliteraturetoM33,thethirdmostmassivegalaxyintheLG.M33isalate-typespiralgalaxymakingittheonlyotherknownspiralintheLG 62

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Mould&Kristian ( 1986 ,hereafterMK86).TheyusedVIphotometryofaeld200southeastalongM33'sminoraxiscorrespondingtoadeprojectedradiusofRdp10kpc.BecausethiseldwaslocatedoutsidetheopticalradiusofM33'sdisk,itwasassumedthattheywouldbesamplingthehalopopulation.BycomparingtheobservedRGBtoempiricalRGBsofGGCs,theyestimatedtheRGBstarsintheireldtohaveameanmetallicityofh[Fe=H]i=2:20:8.TheyconcludedthatthehaloeldpopulationofM33containsstarsasmetal-poorasthemostmetal-poorGGCs.Since MK86 ,moststellarmetallicityestimatesinM33haveutilizedRGBstarsinasimilarmanner. Stephens&Frogel ( 2002 )resolvedtheRGBofM33'snucleusinthenear-infraredandmeasuredametallicityof0:26. Kimetal. ( 2002a )measuredthemetallicityatseveraldierentlocationsthroughouttheinnerdiskandfoundittodecreaselinearlywithgalactocentricradiusfrom0:6to0:9. Brooksetal. ( 2004 )and Davidge ( 2003 )measuredmetallicitiesof1:3and1:0,respectively,inthefarouterregionsofM33possiblysamplingthehalo.In PaperI ,weusedground-basedphotometryreachingthehorizontalbranch(HB)tostudythemetallicityandspatialdistributionofstarsinaeldcoincidentwiththatstudiedby MK86 .WithmoreaccuratephotometryweconcludedthattheRGBmetallicitywasactually1:0.Inaddition,themetallicitygradientwasconsistentwiththatfoundby Kimetal. ( 2002a )implyingthatthisregionwasdominatedbydiskratherthanhalostars.ComparitivelylittleisknownabouttheagesofM33'sstellarpopulations.Theagesareimportantbecausenotonlydotheytellusaboutthetemporalandspatialprogressionofstarformationbuttheyalsocouldaectthemetallicityestimatessummarizedabove.ImplicitinthoseestimatesistheassumptionthattheRGBstarshavethesamemeanageastheGGCs(i.e.12Gyr).Thisassumptionisnecessarybecauseoftheage-metallicity 63

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Salaris&Girardi 2005 ). Sarajedinietal. ( 2000 )presentedCMDsfor10ofM33'shaloglobularclustersandthebackgrounddiskpopulations.Surprisingly,8ofthe10clustersshowedredHBmorphologies,indicatingthattheyarepossiblysignicantlyyoungerthan12Gyr.ThediskCMDsrevealedmixedpopulationsinawiderangeofevolutionarystatessuggestingstarformationinthediskhasoccurredoveralongtimespan.Therefore,itiscertainlypossiblethatM33'shaloanddiskredgiantsdonothavethesameageastheGGCs.Inadditiontostellaragesandmetallicities,thelargescalespatialdistributionofM33'seldstarscanalsoprovidecluestothesystem'sstructureandevolution. Roweetal. ( 2005 )mappedthedistributionofdierenttypesofstarsfromyoung,unevolvedMSstarstoolderAGBandRGBstars.Theyfoundtheyoungeststarstobeconcentratedinspiralfeatureswhiletheoldeststarsweremoreevenlydistributedthroughoutthediskdemonstratingthemigrationofstarsfromtheirbirthsites. Roweetal. ( 2005 )alsousednarrow-bandphotometrytomaptheAGBpopulationsandfoundthecarbonstardensityproletoextendouttoadeprojectedradiusofRdp500600whereitappearedtoatten.TheM-starprolewasqualitativelysimilarwithanunambiguousatteningatRdp450whichtheyattributedtoforegroundstarsalthoughwenotethatthedensitycontinuedtodeclineouttoRdp900perhapsindicatingamoreextendedcomponent.Finally,theyconcludedthattheratioofC-starstoM-stars,whichisaroughtracerofmetallicity(butsee Cionietal. ( 2006 )foradiscussionofageeects)attensoutatRdp120.Theypointoutthatsuchaatteningisconsistentwithviscousdiskformationmodelswhichpredictgasintheouterdisktobewellmixedduetoradialgasows.ObservationstakenwithACSonHSTwerepresentedinChapter 2 .Thesedatacoveredthreecolineareldslocatedatprojectedradiiof20300southeastofM33'snucleus,theinnermostofwhichoverlappedwiththeeldstudiedin PaperI .Theeld 64

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2 .InthepresentstudyweusethesamedatapresentedinChapter 2 tomakequantitativeestimatesoftheSFHs.Thischapterisorganizedasfollows.Inx wedescribeourimplementationofthesyntheticCMDttingmethod.TheresultsofapplyingthismethodtotheACSdataarepresentedinx .Wediscusstheresultsandtheirimplicationsinx andx .Lastly,inAppendix A wetesttheaccuracyofthemethodanditsrobustnessagainsterrorsintheinputparameters. Aparicio&Gallart 2004 ).Weuse5metallicitybins0.3dexwideovertheinterval1:7[M=H]0:2and9agebinsofwidth0.25dexintherangelog(age)=7.90-10.15(79.4Myr-14.1Gyr).Thischoiceofageandmetallicitybinningissimilartowhathasbeenusedinotherstudieswithphotometryofcomparabledepth( Wyder 2001 ; Dolphinetal. 2003 ).Itisacompromisebetweenprecision,accuracy,andcomputationaleciency.Smallerbinscouldincreaseaccuracyatthecostoflosingprecision,increasingnoiseinthesolution,andincreasingcomputationaltime( Olsen 1999 ; Dolphin 2002 ).Theagebinsarespacedlogarithmicallybecausetheinherentprecisiondecreaseswithage.Thisoccursfortworeasons.First,thephotometricerrorsandincompletenessrateincreasewithmagnitudeandtheMSTOgets 65

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Kroupaetal. ( 1993 )withtheonlydierencebeingtheirlow-massslopeis1:3.Theslopeofthelowmassend(.0:8M)onlyaectsthenormalizationoftheSFHbecausethesestarsliebelowourdetectionlimit.Sinceweareobservingasmallrangeofmassesatanygivenagewecannotusefullyconstraintheslopeathighermasses. Gallartetal. ( 1999 )summarizerecentobservationalevidenceforf=0.4andq=0.6soweadoptthosevaluesinthepresentstudy.RatherthanholdthedistanceandextinctionconstantwesolveforthemsimultaneouslywiththeSFH.ThisamountstoshiftingthemodelCMDsindierentdirectionsandaccountsforzero-pointerrorsinthetheoreticalisochronesandbolometriccorrections.Wevarythedistanceovertherange(mM)0=24:5024:80instepsof0.10mag.ThisrangeencompassesmostofM33'sdistancemeasurementsintheliterature( Galletietal. 2004 ).TheextinctionisvariedovertherangeAV=0:100:25instepsof0.05mag.Thisrangeincludesthe Schlegeletal. ( 1998 )valueofAV=0:15andalsoallowsforsomeextinctioninternaltoM33.FortheextinctionlawweadoptAI=1:31E(VI)andE(VI)=0:06asinPaperI( Cardellietal. 1989 ; vonHippel&Sarajedini 1998 ).Wewouldliketovarythephysicalingredientsgoingintothetheoreticalisochronessincetheyprobablyrepresentthelargestpossiblesourcesoferror.Suchingredients 66

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Girardietal. 2000 )andTeramo( Pietrinfernietal. 2004 )isochronestransformedtotheobservationalplanewiththe Castelli&Kurucz ( 2003 )UBVRIJHKLbolometriccorrectionlibrary.Ideally,wewouldworkentirelyinthenativeACS/WFCltersystem.IAC-STARhasanHSTbolometriccorrectionlibraryfrom Origlia&Leitherer ( 2000 )butitdoesnotincludeF606Wand,strictlyspeaking,itappliesonlytoWFPC2.Asdiscussedin Siriannietal. ( 2005 )theWFPC2andACSltertransmissioncurvesarenotidentical.Thus,weareforcedtoworkintheUBVRIsystemusingthesynthetictransformationof Siriannietal. ( 2005 ).Inourexperiencethusfar,wehavefoundgoodagreementbetweenHSTandground-baseddataintheUBVRIsystemforseveralGalacticglobularclusterswith[Fe/H].1:5. Mackeyetal. ( 2006 )foundnosignicantsystematicerrorsaftertransformingtotheground-basedsystemACS/WFCphotometryoftwoLMCclusterswithmetallicitiessimilartothemajorityofourM33stars([Fe/H]1:0)althoughitshouldbenotedtheyusedF555W,whichismoresimilartotheJohnsonV-bandthanF606W.Athighermetallicitiesthesituationcouldbedierent.Ourinvestigationshavefoundtentativeevidenceforaconstantosetof0:05maginVwhencomparing47Tuc([Fe/H]0:7)ACSphotometrytoindependentground-baseddata.OntheRGB,thisosettranslatesintoanuncertaintyof0:1dexand1:5Gyratametallicityof1:0.Thisosetisequaltotheuncertaintyofthephotometriczero-pointofthe Siriannietal. ( 2005 )synthetictransformation.Consideringourcoarsebinningschemeinage,metallicity,andintheCMDplane(asdenedbelow)andgiventhatalargefraction 67

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A wherewetatestpopulationaftermanuallyinsertingaVmagoset.WeemployedStarFISH( Harris&Zaritsky 2001 )tosimulatetheeectsofobservationalerrorsinthesyntheticCMDsandtosearchforthebest-tmodelCMD.ThearticialstartestsdescribedinChapter 2 allowustoaccuratelyquantifythephotometricerrorsandcompletenessrateasfunctionsofbothmagnitudeandcolor.Eachmodelstarisassociatedwithanearbyarticialstar.Ifthearticialstarwasrecovereditsmagnitudeshiftsareassignedtothemodelstarotherwisethemodelstarisdiscarded.EachsyntheticCMDcontains1106starsbeforethesimulationofobservationalerrors.ThecoecientsinthelinearcombinationofsyntheticCMDsareproportionaltothestarformationrates(SFRs)attheirrespectiveagesandmetallicities.StarFISHusesadownhillsimplexalgorithmtosolveforthecoecientsbyminimizingattingstatistic.Wereferthereaderto Harris&Zaritsky ( 2001 )formoredetailsofthealgorithm.ThemodelanddataCMDsaredividedintosquarebins0.1magonasideandthenumberofmodelanddatastarsineachbingointocalculatingthettingstatistic.Sincewearecountingstarsinbins,thestatisticweuseisthenegativelog-likelihoodratioforaPoissondistributiongivenby=2Pimini+niln(ni=mi)wheremiandniarethenumberofmodelanddatastarsinCMDbini,respectively.Thepropertiesofthisparameterhavebeendiscussedinvariousstudies(e.g., Mighell 1999 ; Hauschild&Jentschel 2001 ; Dolphin 2002 ).Forlargemiitiswellapproximatedbythecommonlyused2.IncludedinthelinearcombinationofsyntheticCMDsisabad-pointCMDwhichwettocosmicrays,hotpixels,foregroundstars,andotherobjectsintheobservedCMDthatcannotbereproducedbyIAC-STAR(seealso Dolphin ( 2002 )).Thishastheformofauniformdistributionthatcontributes0:05\stars"toeachCMDbinresultingin120 68

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Gallartetal. ( 1999 )and Wyder ( 2001 ),theglobalbest-tmodelistheweightedaverageofallacceptableindividualsolutions,eachofwhichcorrespondstoaparticularcombinationofdistanceandreddening.Asolutionisacceptableifitlieswithin1ofthebest-t.ForeachindividualsolutionStarFISHcalculatestheerrorsontheSFRsbymovingthroughtheparameterspaceinmanydierentdirectionsuntilthettingstatisticchangesby1.Thus,theerrorsrepresentuncorrelatedandcorrelatederrorsbetweentheamplitudes.Theerrorsoftheindividualbest-tsolutionareaddedinquadraturewiththespreadofallacceptablesolutions.Inthiswaytheerrorsoftheglobalbest-treectcorrelationsbetweenage,metallicity,distance,andreddening.Thequalityofthetismeasuredbytheparameter,Q,whichisthedierencebetweenanditsexpectationvalueinunitsofitsstandarddeviation.TheexpectationvaluedependsonthemodelbutisapproximatelyequaltothenumberofCMDbinscontributingtothetminusthenumberoffreeparameterswhichincludeanynonzeroSFHamplitudes(typically25)plusdistanceandextinction.TheQparametermeasuresthelikelinessofthedatabeingrandomlydrawnfromthemodel( Dolphin 2002 ).Onlyforcomparisonpurposeswealsocalculate2ofthebest-tdenedby2=Pi(nimi)2=miand2=2=,whereisthenumberofsignicantCMDbinsminusthenumberoffreeparameters.StudiesapplyingthesyntheticCMDttingmethodtorealstellarpopulationstypicallyndvaluesforQand2intherange15( Dolphin 2002 ; Harris&Zaritsky 2004 ; Gallartetal. 1999 ; Skillmanetal. 2003 ; Dolphinetal. 2003 ; Wyder 2001 2003 ).InAppendix A wedemonstratetheeectivenessofthemethodonseveraltestpopulations.Inparticular,weexaminehowerrorsinthevariousinputparametersaecttheaccuracyoftherecoveredSFHandhowtheycontributetosystematicerrorsintheresults.Suchtestsarecriticaltounderstandingthestrengthsandlimitationsofthemethodandhowtointerprettheresults. 69

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3.2.1PadovatracksWeappliedthetechniquedescribedintheprevioussectiontoeldsA1A3.Figures 3-1 presenttheresultsusingthePadovatracks.Ineachgure,panelAshowstheSFHand1errorsasexplainedbefore.InpanelBweshowtheagecumulativedistributionfunction(ageCDF).PanelCdisplaystheage-metallicityrelation(AMR)whereeachpointisthemeanmetallicityofallstarsformedinthecorrespondingagebin.Thehorizontalerrorsdenotetheagebinwidth.PanelDisthemetallicitycumulativedistributionfunction(ZCDF)ofallstarseverformed.TheverticallinesinpanelsBandDcorrespondtothemeanageandmetallicityofallstarsandstellarremnantsandthe1condenceintervals.AlsoshownaretheE)dataCMD,F)modelCMD,G)residuals,andH)signicance.ThedataandmodelCMDsareHessdiagrams(2-Dhistograms)onalogarithmicscale.Theresidualsareonascalewhere3isblackand+3iswhiteandpositiveresidualsmeanthemodelistoohigh.Uponinspectionofthesolutions,weseethatthemodelCMDsunderpredictthenumberofstarsfainterthanI=27.ThisindicatesanapproximatelyconstantnumberofcontaminantsatI>27duetonon-stellarsourceslikeunresolvedbackgroundgalaxiesandspuriousnoiseartifacts.ThiscontaminationismuchlessthanthenumberofrealstarsinA1butbecomesmoresignicantinA2andA3.TheTeramoCMDsshowedthesamediscrepancymakingitunlikelythatthestellartracksarethecause.AsatestwerepeatedtheentirephotometricreductionprocedureandarticialstartestsforA3usingmorestringentdetectionrequirements.ThisallowedustorepeattheSFHanalysisforA3whichwefoundtoyieldbetteragreementbetweenthemodelanddataCMDsbutthemodelstillslightlyunderpredictedthenumberofstarsatthefaintend.TheresultingSFHwasnearlyidenticaltothatproducedafterexcludingI>27intheoriginaldataset(seebelow)becausethereislittleinformationthereanywaytoconstrainthesolution.Since 70

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3-4 { 3-6 .ThelargestdiscrepanciesoccurintheRCandHBwherethemodeloverpredictsthenumberofstars.DisagreementsintheRCandHBarecommon(e.g., Dolphinetal. 2003 ; Wyder 2001 2003 )andoftenduetouncertaintiesinthestellarevolutionarytracks.InA1andA2,themodelalsounderpredictsthenumberofstarsjustabovetheRCpossiblyindicatingaproblemwiththeAGBbump.InA3thesediscrepanciesarenotassignicantwhichcouldreectalesscomplexSFHrelativetoA1andA2.Table 3-1 givesthetqualityandmeandistanceandextinctionforeacheldtogetherwiththeir1uncertainties.Table 3-2 liststhemeanage,metallicity,andV-bandmass-to-lightratio,M=LV,andtheir1condenceintervals.Tables 3-3 { 3-14 showtheSFH,ageCDF,AMR,andZCDFforeacheld.TofacilitatecomparisonbetweenthethreeeldsweshowtheirresultstogetherinFigure 3-7 .Ineachgraph,A1isthesolidline,A2thedottedline,andA3thedashedline.TheerrorbarshavebeenomittedforclaritybuttheyarethesameasinFigures 3-4 { 3-6 .TheSFHsarequalitativelysimilarwhichisnotsurprisingsincetheCMDsaresimilar,too.A1showsanenhancementoftheSFRduringtheperiod2.54.5Gyragobyafactorof3overthemeanSFRofallages.Becauseofthelargeagebinsemployed,thisdoesnotnecessarilymeanthetrueSFHpeakedattheseexactages(seeAppendix A ).ThisisfollowedbyadeclineintheSFRuntil250MyragoatwhichtimetheSFRincreases.Thismightsuggestaburstofstarformation(SF)inthelast250MyrbuttheyoungestfewagebinsaredominatedbysmallnumberstatisticssotheSFRsarenotwellconstrained(seeAppendix A ).Moreimportantly,theSFRintheyoungestfewagebinscouldbeoverestimatediftherearestarspresentinthedatawithages.80Myr,theyoungestagecoveredinthesyntheticCMDs.Forexample,ifthetrueSFRoverthepast140MyrhasbeenconstantthentheSFRintheyoungestbincouldbeoverestimated 71

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A ).Itismoreinstructivetoaveragethemetallicityattheseyoungages.Whenwedothiswendthatthemeanmetallicityforages2:5Gyris0:53,0:67,and0:69withastandarderrorinthemeanof0:07dex.Hence,wecansaywith95%condencethatthemeanmetallicityofA1atyoungagesishigherthanthatinA2andA3butA2isconsistentwithA3.AsaconsistencycheckonthesolutionswecanexploretheparameterspacebyhandusingthesyntheticCMDswith(mM)0=24:60andAV=0:20.PanelAofFigure 3-8 showswhathappenstothetquality,Q,whenweadoptanexponentiallydecreasingorincreasingSFHandvarythetimescale,.Positive(negative)timescalescorrespondtoadecreasing(increasing)SFRsinceformationtime.Thediamonds,asterisks,andsquaresrepresentA1,A2,andA3,respectively.Foreacheldwehaveset=1;2;4;6;10;20,and30andwenormalizethemodelCMDtohavethesametotalnumberofstarsasthedataCMDinthettedregion.TheblacklinescorrespondtosyntheticCMDswithmetallicities 72

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Dolphin 1997 ).PanelCexploresthedurationofstarformationforaconstantSFRstartingatlog(t=yr)=10:15(14.1Gyr).Thedurationissuccessivelyincreasedinstepsof0.25dex.Weseethattheoptimaldurationis1.5dexinA1and1.25dexinA2andA3.ThisfurthersupportsthecaseforalongereraofstarformationinA1thaninA3. 73

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3-8 makesiteasiertounderstandtheglobalbest-tsolutionsforA1andA2whichshowanenhancementintheSFRat2:54:5GyrwithapproximatelyconstantSFRatotheragesandadropintheaverageSFRoverthepast1Gyr. 3-9 { 3-11 displaytheglobalsolutionsobtainedwiththeTeramotracks.Table 3-15 givesthetqualityandmeandistanceandextinctionforeacheldtogetherwiththeir1uncertainties.Table 3-16 liststhemeanage,metallicity,andV-bandmass-to-lightratio,M=LV,andtheir1condenceintervals.Tables 3-17 { 3-28 showtheSFH,ageCDF,AMR,andZCDFforeacheld.ThereareseveralstrikingdierencesbetweentheTeramoandPadovasolutions.First,theenhancementatintermediateagesoccursovertwocontiguousagebinsfrom2:58Gyrratherthanjustonebin.InA1,thestrengthoftheenhancementisabout70%smallersinceitlastsforalongertimespanandthetotalnumberofstarsmustbeconserved.Inaddition,alargerfractionofstarsformedby5Gyrago:70%versus50%forthePadovatracks.AnotherdierencebetweentheTeramoandPadovasolutionsisthattheRCareaintheTeramomodelCMDprovidesabetterttothedata.Interestingly,though,the 74

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Gallartetal. 2005 ).AlthoughtheextendedHBdoesnotappeartosignicantlyconstributetotheresiduals,thelargewidthoftheoldestagebinmayhaveforcedthemodeltoincludeveryoldstars(&12Gyr)thatmightnotbeinthedata.Were-ranthettingroutinebutchangedtheoldestagebintohaveawidthoflog(t)=0:15sotheoldeststarsincludedinthemodelwere11.22Gyrold.Asexpected,theHBmorphologyoftheresultingtswasredderandsimilartothePadovaresultsintheprevioussectionbutthetqualitieswerenobetterandtheSFHwasnotsignicantlychanged.OnenotabledierencebetweentheTeramomodelCMDsanddataCMDsisthatthemodelscontainanexcessofstarsontheRGB.ThisisaknownissuewiththeTeramomodelswhichpredictRGBlifetimesthataretoolong(by25%).ThisresultsinanRGBluminosityfunctionwithtoomanystarswhencomparedtoothersetsofmodelsandGalacticglobularclusters( Gallartetal. 2005 ).SincethisdiscrepancyonlyaectsthenumberofstarsontheRGB,itprobablyonlyaectsthetotalintegratedluminosityandtheabsolutenormalizationoftheSFR(i.e.,amodelthatinherentlyoverpredictsthenumberofRGBstarswouldrequireasmallerSFRtoreproducethesamenumberofobservedRGBstarscomparedtoamodelwithnooverprediction).Sometimeafterthischapterwaspublished,IAC-STARwasupdatedwiththenewestversionoftheTeramotracks.UsingthesenewtracksdoesnotsignicantlychangetheresultsbecausethedierencesbetweenthenewandoldTeramotracksaremuchsmallerthanthedierencesbetweenthePadovaandTeramotracks.Wenotethatthebest-tdistancemodulusis0:1maggreaterfortheTeramotracksthanforthePadovatracksyetthebest-textinctionvaluesaresimilar.Thisunderscoresthefactthatdistancesandextinctionsobtainedwiththistechniquearesubjecttosystematicerrorsinthestellarevolutionarytracks.Theseerrorscandependonlter,age,andmetallicityamongotherfactors( Wyder 2003 ). 75

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3-12 .DespitethedierencesfromthePadovasolutions,theyexhibitsimilartrendsbetweenthethreeelds.ThestrengthoftheenhancementatintermediateagesdecreasesrelativetotheSFRatolderages.Consequently,themeanageoftheeldsincreasesfrom6:50+0:460:51GyrinA1to8:09+0:971:24GyrinA3.Themeanmetallicitydecreasesfrom0:66+0:110:11to0:89+0:180:18.TheapparentlackofevolutionintheAMRbetweenthetwooldestbinsdoesnotnecessarilyweakenthevalidityofthemodelnordoesitnecessarilymeantherewasnochangeinthetrueAMR.AsshowninAppendix A ,variationsbetweenadjacentbinsmustbeconsideredwithcaution.Figure 3-13 showsagainthattheTeramotrackspredictsimilartrendsbetweentheeldsasthePadovatracksalthoughsomespecicdetailsaredierent.Thepreferredexponentialtimescaledecreasesfrom10GyrinA1to46GyrinA3.TheratioofrecentSFRtopastSFRis0:10:2inA1andconsistentwithzeroinA2andA3.Thedurationofstarformationdecreasesfrom11:3dexinA1to0:71:0dexinA3.Finally,thepreferredageincreasesfromlog(age/yr)=9:5inA1tolog(age/yr)=9:8inA3. 3-14 .ThisgureshowstheCMDofeldA1asgraypointswiththeCMDofglobularclusterTerzan7asblackpoints.TheTer7datacomefrom Sarajedini&Layden ( 1997 )andwehaveplottedonlystarswithinthecentral8000oftheclustercenter.Mostoftheblackpointsbluerthan(VI)0:8areGalacticeldstars.Ter7belongstotheSagittariusdwarfgalaxyandisestimatedtohaveametallicity[Fe/H]=0:820:15andtobe6Gyryoungerthan47Tuc( Sarajedini&Layden 1997 ).TheRCandRGBofTer7closelymatchthoseofM33conrmingourgeneralresultthatM33'soutskirtsare68Gyroldwithmetallicitiesof0:7to0:9. Ciardulloetal. ( 2004 )conductedaphotometricandspectroscopicsurveyofplanetarynebulae(PNe)throughoutM33.Theyestimatedthediskmasssurfacedensityunder 76

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Regan&Vogel ( 1994 )withacentralAVof0.9. Ciardulloetal. ( 2004 )foundthattheV-bandmass-to-lightratioofthestellarcomponentincreasesfrom0:3to1:5overthefaceofthedisk.WeshowtheirresultsassquaresinFigure 3-15 aftertransformingtoaGalaxy-M33distanceof867kpc( PaperI ; Galletietal.2004 ).TheM=LVvaluesforeldsA1A3derivedfromourSFHanalysisareshownascircles(Padova)andtriangles(Teramo).ThisprovidesaniceconsistencycheckonourSFHresultsbecauseM=LVdependsheavilyonageandtoalesserextentonmetallicity.Forinstance,thePadovasyntheticCMDscoveringmetallicitiesfrom0:8to0:5haveanM=LVthatincreaseswithagefrom0.16to3.57.TherelativeproportionsofdierentagesintheSFHsaectboththenormalizationofM=LVanditschangewithradius.TheagreementbetweenthetwosetsofdatathusprovidesindependentsupportthatourSFHresultscontainareasonablemixofagesandmetallicities.Morefundamentally,theagreementsupportstheIMFweusedincalculatingtheSFHs.Recallthatthelow-massexponent(M0:5M)was1:35.Ifwesteepenitto2:00thenM=LVincreasesby20%withoutaectingtheSFHs.Aatterlow-massslopeof0:70woulddecreaseM=LVby10%.ChangingtheIMFslopeathighermassescouldaecttheSFHsandresultingM=LVinanon-trivialway.However,itisunlikelythatwejusthappenedtopickaparticularformoftheIMFwhichyieldsasimilarM=LVRdprelationasthePNekinematics.Therefore,itseemsthattheIMFinM33'soutskirtsissimilartotheGalaxy'sorisatleastshallowerthanaSalpeterformatthelowestmasses.Takenatfacevalue,Figure 3-15 alsosuggeststhatthemeanageofM33'sentirestellardiskincreaseswithradius.Allelsebeingequal,thecorrelationbetweenageand 77

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Fall&Efstathiou 1980 ; Moetal. 1998 ).Thesizesofdiskgalaxiesareobservedtodecreasewithredshiftinroughaccordancewithmodelpredictions( Fergusonetal. 2004 ).Furthermore,galacticdisksinthelocalUniversegenerallybecomebluerwithincreasingradiuswhichisusuallyinterpretedasadecreasingmeanage( deJong 1996 ; Bell&deJong 2000 ).Doestheinside-outbuild-upofdarkmatterhalosnecessarilyresultinstellardiskswhosemeanagesatthepresentepochdecreasewithradius?Thequestionisdiculttoanswerbecauseitrequiresincorporatingthehighlyuncertainphysicsofbaryoniccollapse,starformation,andfeedbackintotheresultsofhierarchicalcosmologicalsimulations( Silk 2003 ).AsexplainedinChapter 1 ,thesesimulationsformdisksthatgrowbothinside-outandoutside-in.Mostothertheoreticalpredictionsfortherunofmeanagewithradiuscomefromsimpleanalyticorsemi-analytictreatmentsofthebaryonicphysics(e.g., Molla&Daz 2005 ; Naab&Ostriker 2006 ).Thesestudiesdopredictthemeanstellaragetodecreasewithradiusundertheinside-outhierarchicalframework.However,thetreatmentsoftheprocessesmaybreakdownintheoutskirtsofdisksorthevariousassumptions 78

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Debattistaetal. ( 2006 )showedthatbarscanleadtosignicantmassredistributionbothwithinandawayfromtheplaneofadiskgalaxy.Thisresulthighlightstheimportanceofsecularevolutioninmodifyingdiskstructure.Alternatively,starformationcouldbegininaninside-outfashionbutitcouldbetruncatedoutside-inproducingapositiveagegradientbecausetheinnerregionswouldbeformingstarsforalongerperiodoftime.Ontheobservationalside,thenature,ubiquity,andinterpretationofnegativediskcolorgradientsisnotentirelyclear. MacArthuretal. ( 2004 )examinedopticalandnear-IRcolorgradientsforalargesampleofgalaxiesandderivedluminosity-weightedmeanageandmetallicityprolesfromstellarpopulationsynthesismodels.Theyfoundevidenceforaradialdependenceofagegradientsinthesensethattheinnerregionsshowedgenerallysteepergradientsthantheouterregions.Inaddition,somegalaxiesdisplayedinectionpointsintheiragegradients. Tayloretal. ( 2005 )foundamorphologicaldependenceofcolorgradientssuchthatearly-typesystemstendedtogetbluerwithradiuswhereaslate-typespiral,irregular,peculiar,andmerginggalaxiestendedtogetredderwithincreasingradius.Theyattributedthistomegers,accretions,andinteractionstriggeringradialinowsofgasandcentrallyconcentratedstarbursts.TheyalsofoundthatgalaxieswithfaintabsoluteB-bandmagnitudesweresomewhatmorelikelytogetredderwithradiusthantheirbrightercounterparts.Ontheotherhand, Jansenetal. ( 2000 )foundnocolorgradientdependenceonmorphologicaltypebutanevenstrongertrendwithB-bandmagnitude.Theyconcludedthatstarformationtendstooccurintheouterregionsofluminousgalaxiesbutintheinnerregionsoffaintersystems.HowdoesM33comparewiththeresultsofthesestudies?Becauseofitslargeangularextentintheskyandlowsurfacebrightness,M33'scolorgradientsarenotwellknown. 79

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( 1981 )carriedoutUBVRIphotoelectricmeasurementsofthecentral130andfoundthediskcolorstochangelittlewithradiusexceptfor(UB)whichisheavilyinuencedbydust.The2MASSLargeGalaxyAtlas( Jarrettetal. 2003 )reports(JKS)asincreasingfrom0:8to1.0overtheinner90. Regan&Vogel ( 1994 ),ontheotherhand,found(JK)todecreasefrom1:0to0.8overthesameregion.Thecauseofthediscrepancyisnotclearbutitcouldarisefromuncertaintiesintheskysubtraction.Inanycase,ourSFHresultspredictintegratedcolorsof(VI)1:0,(BI)1:7,and(JK)0:8inM33'souterdisk.ThesevaluesareinreasonableagreementwiththepublishedmeasurementsbutitwouldbeworthwhiletoupdateandextendtheradialcoverageofM33'ssurfacephotometry.SuchdatacouldprovideindependentconstraintsonSFHanalysessimilartoourown.ItisinterestingtocompareourresultsforM33'sAMRtothatofotherwell-studiedsystems.InFigure 3-16 ,thegraysolidlinesshowtheAMRsoftheSmallandLargeMagellanicClouds(SMCandLMC,orMCs),andthesolarvicinity(SV).FortheMCswehaveusedtheburstingmodelsof Pagel&Tautvaisiene ( 1998 )whichincludeinowandnon-selectivegalacticwinds.TheseauthorstunedtheparametersoftheirmodelstomatchtheobservedabundancesofMCclustersandsupergiants.Theabruptchangeintheenrichmentrateat3Gyrisduetoaburstinstarformationpossiblycausedbyaninteractionbetweentheclouds.TheSVmodelistakenfrom Twarog ( 1980 )whousedtheabundancesofalargesampleofnearbyFdwarfsasconstraints.Thismodelincorporatedaninitialmetallicityof1:0andaconstantSFRandinowrateoverthedisklifetime.TheexistenceandnatureofanAMRintheSVisamatterofsomedebate. Edvardssonetal. ( 1993 )and Feltzingetal. ( 2001 )foundtheAMRtohavealargeintrinsicscatter(0:2dex)withtheoldeststarsbeingbothmetal-poorandmetal-rich.Subsequentstudieshavesincechallengedtheirresultscitingsampleselectioneectsorbiasesintheagedeterminationsasthecause( Garnett&Kobulnicky 2000 ; Rocha-Pintoetal. 2000 ; Kotonevaetal. 2002 ; Pont&Eyer 2004 ; Rocha-Pintoetal. 2006 ).Inany 80

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Rocha-Pintoetal. 2000 ).ThepointsinFigure 3-16 showtheAMRswederivedforeldA1(circles),A2(triangles),andA3(squares).ThePadovaresultsareshowninpanelAwhiletheTeramoresultsareshowninpanelB.BecausetheAMRattheyoungestagesisdominatedbysmallnumberstatistics,wehaveaveragedthe6youngestagebinswhichcoverages.2:5Gyr.Figure 3-16 demonstratesthatthelevelofenrichmentinM33'souterdiskhasbeenintermediatebetweentheSMCandLMCbutperhapssomewhatclosertothelatter.Indeed,iftheSMCandLMChadcontinuedtoevolvequiescentlyratherthanexperienceburstsat34Gyrthentheirpresent-daymetallicitieswouldhavebeencloseto0:9and0:5,respectively.InthatcaseM33'souterdiskwouldhaveresembledtheLMCevenmore.Finally,ourresultsimplyapresent-dayglobalmetallicityof0:5inM33'souterdiskwhichisingoodagreementwiththeresultsof Urbanejaetal. ( 2005 ).Theseauthorsconductedadetailedspectralanalysisof10B-typesupergiantstarsthroughoutM33basedonnon-LTEmodelatmospheresincludingtheeectsofstellarwinds.Theyfound[M/H]intheirstellarsampletodecreasefromabout0.0nearM33'snucleustoabout0:5atRdp=330justinteriortoeldA1. 81

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2 exceptforazero-pointosetof0:4dex.HalfofthisosetisduetotheyoungermeanageofM33comparedtotheGGCsandhalfisduetothelower-elementabundance([/Fe]=0)ofthestellartracks(seealso Salaris&Girardi ( 2005 )).Wecautionthattheageandmetallicitygradientsdonotnecessarilycontinueintotheinnerdisk.However,thestellarM=LVimpliedbyourresultsisconsistentwithextrapolationoftheindependentestimatesof Ciardulloetal. ( 2004 )forregionsinteriorto 82

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2 ,wefoundthatthestellarscalelengthincreaseswithageinaroughlypower-lawfashionreminiscentofwhathasbeenobservedintheverticaldirectioninsixlow-massspirals( Sethetal. 2005 ).Thisbehaviorcouldbecausedbytheorbitaldiusionofstarsastheyage.Therefore,theSFHwehavederivedinthepresentstudycouldreectasuperpositionofstarformationandlaterdynamicalprocesseswhichacttoredistributestarsinthedisk.Anysimilaranalysescarriedoutonotherstellarpopulations,especiallythoseofdiskgalaxies,couldfacesimilaruncertainties. 83

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FittedparametersofSFHsolutionsusingthePadovatracks FieldQ2 AV Table3-2. BasicresultsofSFHsolutionsusingthePadovatracks Field Age(Gyr)hi(Gyr)lo(Gyr) [M=H]hilo 84

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SFHofA1usingthePadovatracks AgeRangeSFRhilo Note.{Theunitsare104Myr1. Table3-4. SFHofA2usingthePadovatracks AgeRangeSFRhilo Note.{Theunitsare104Myr1. Table3-5. SFHofA3usingthePadovatracks AgeRangeSFRhilo Note.{Theunitsare104Myr1. 85

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AgeCDFofA1usingthePadovatracks AgeRangeM=Mtothilo Table3-7. AgeCDFofA2usingthePadovatracks AgeRangeM=Mtothilo Table3-8. AgeCDFofA3usingthePadovatracks AgeRangeM=Mtothilo 86

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AMRofA1usingthePadovatracks AgeRange[M=H]hilo Table3-10. AMRofA2usingthePadovatracks AgeRange[M=H]hilo Table3-11. AMRofA3usingthePadovatracks AgeRange[M=H]hilo 87

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ZCDFofA1usingthePadovatracks [M/H]RangeM=Mtothilo Table3-13. ZCDFofA2usingthePadovatracks [M/H]RangeM=Mtothilo Table3-14. ZCDFofA3usingthePadovatracks [M/H]RangeM=Mtothilo 88

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FittedparametersofSFHsolutionsusingtheTeramotracks FieldQ2 AV Table3-16. BasicresultsofSFHsolutionsusingtheTeramotracks Field Age(Gyr)hi(Gyr)lo(Gyr) [M=H]hilo 89

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SFHofA1usingtheTeramotracks AgeRangeSFRhilo Note.{Theunitsare104Myr1. Table3-18. SFHofA2usingtheTeramotracks AgeRangeSFRhilo Note.{Theunitsare104Myr1. Table3-19. SFHofA3usingtheTeramotracks AgeRangeSFRhilo Note.{Theunitsare104Myr1. 90

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AgeCDFofA1usingtheTeramotracks AgeRangeM=Mtothilo Table3-21. AgeCDFofA2usingtheTeramotracks AgeRangeM=Mtothilo Table3-22. AgeCDFofA3usingtheTeramotracks AgeRangeM=Mtothilo 91

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AMRofA1usingtheTeramotracks AgeRange[M=H]hilo Table3-24. AMRofA2usingtheTeramotracks AgeRange[M=H]hilo Table3-25. AMRofA3usingtheTeramotracks AgeRange[M=H]hilo 92

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ZCDFofA1usingtheTeramotracks [M/H]RangeM=Mtothilo Table3-27. ZCDFofA2usingtheTeramotracks [M/H]RangeM=Mtothilo Table3-28. ZCDFofA3usingtheTeramotracks [M/H]RangeM=Mtothilo 93

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SFHresultsforA1usingthePadovatracks.A)SFH.B)AgeCDF.C)AMR.D)ZCDF.E)DataCMD.F)ModelCMD.G)Residuals.H)Signicance. 94

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SameasFigure 3-1 butforA2. 95

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SameasFigure 3-1 butforA3. 96

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SFHresultsforA1usingthePadovatracksandafterexcludingtheregionI>27.A)SFH.B)AgeCDF.C)AMR.D)ZCDF.E)DataCMD.F)ModelCMD.G)Residuals.H)Signicance. 97

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SameasFigure 3-4 butforA2. 98

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SameasFigure 3-4 butforA3. 99

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ComparisonofSFHresultsforA1(solid),A2(dotted),andA3(dashed).A)SFH.B)AgeCDF.C)AMR.D)ZCDF. 100

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Exploringparameterspacebyhand.Eachgraphshowshowthetqualityvarieswithaparticularparameter.A)Exponentialtimescale.B)RatioofmeanrecentSFRtooldSFR.C)Starformationduration.D)Agebin.Thepointsymbolsarediamonds,asterisks,andsquaresforeldsA1,A2,andA3,respectively.Graylinesshowtheresultofdecreasingthemetallicity(seetextfordetails). 101

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SFHresultsforA1usingtheTeramotracks.A)SFH.B)AgeCDF.C)AMR.D)ZCDF.E)DataCMD.F)ModelCMD.G)Residuals.H)Signicance. 102

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SameasFigure 3-9 butforA2. 103

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SameasFigure 3-9 butforA3. 104

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SameasFigure 3-7 butfortheTeramotracks. 105

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SameasFigure 3-8 butfortheTeramotracks. 106

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CMDofeldA1(graypoints)withCMDofTerzan7overplotted(blackpoints). Figure3-15. V-bandstellarmass-to-lightratioinM33.SquaresrepresentthedatabasedonPNekinematics(Ciardulloetal.2004).CirclesandtrianglescorrespondtotheSFHresultsforeldsA1A3usingthePadovaandTeramomodels,respectively. 107

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AMRofM33(points)comparedtotheSV,LMC,andSMCshownasgraylines.FieldsA1,A2,andA3correspondtocircles,triangles,andsquares,respectively.A)Padovaresults.B)Teramoresults. 108

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Freeman&Bland-Hawthorn 2002 ).Another,equallyimportantmethod,ischemicalmodeling,whosegoalistoreproducetheelementalabundancedistributionofasystembysimulatingitsSFHandCEH.Forexample,theevolutionofthe-elements(O,Ne,Mg,Si,S,Ca,Ti)relativetoiron,commonlyplottedas[/Fe]vs.[Fe/H],isanextremelyusefultooltodiagnosethetimescaleofstarformation.Thisisbecausethe-elementsareproducedmainlyinthehydrostaticburningphasesandexplosivedeaths(supernovaetypeII,orSNeII)ofmassivestars(M&8M),whichhaveshortlifetimes(.107yr).Themajorityofiron,ontheotherhand,iscreatedinsupernovaetypeIa(SNeIa),mostofwhichoccuronamuchlongertimescaleof1Gyr.Theseeventsarethoughttobethethermonuclearexplosionsofcarbon-oxygenwhitedwarfsinbinarysystems.ASNIacanoccurafterawhitedwarfreachestheChandrasekharlimitof1.4MbyaccretingmatterfromacompanionstarthathaslleditsRochelobeorbymergingwithanotherwhitedwarf( Greggio 2005 ).Becauseofthedierentnucleosyntheticsitesandproductiontimescalesofthe-elementsandiron,theirabundanceratiotellsusabouttherelativeimportanceofSNeIIvs.SNeIaandtheeciencyofstarformation.Starswithhigh[/Fe]ratiosformedoutofgasenrichedmostlybySNeII(acanonicalvaluefortheejectaofatypicalSNII 109

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Aparicioetal. ( 1997 )derivedtherstSFHoftheLGdwarfgalaxy,LGS3,fromCMDttingandusedthechemicalevolutionequationstoseehowmuchgasinowandoutowwasrequiredtomatchtheirresults. Carigietal. ( 2002 )computedthechemicalevolutionoffourdwarfspheroidal(dSph)satellitesoftheGalaxy.Asexternalconstraints,theseauthorsusedtheSFHsofthesegalaxiesderivedby Hernandezetal. ( 2000 )fromaCMDttingmethod. Dolphin ( 2002 )calculatedtheSFHsof6dSphGalacticsatellitesusingsyntheticCMDtting,andthen Lanfranchi&Matteucci ( 2003 2004 )adoptedhisSFHsasinputstotheirchemicalevolutionmodelsforthesamegalaxies.Similarly, Fenneretal. ( 2006 )modeledthechemicalevolutionoftheSculptordSphusingtheSFHderivedby Dolphinetal. ( 2005 )fromaCMDanalysis.Lastly,afteradoptingtheSFHderivedby Wyder ( 2001 2003 ), Carigietal. ( 2006 )modeledtheevolutionofNGC6822inacosmologicalframework.Conversely,theresultsofchemicalmodelingcanbeusedasinputstoCMDtting.Forexample, Pagel&Tautvaisiene ( 1998 ,hereafterPT98)modeledthechemicalevolutionoftheLMC,adoptinggasinowandnonselectivegalacticwinds.TheseauthorstunedthemodelparameterstomatchtheobservedabundancesofclustersandsupergiantstarsintheLMC.SomesubsequentstudiesadoptedtheLMC'sAMRtoderiveitsSFHfromCMDandluminosityfunctiontting(e.g., Holtzmanetal. 1999 ; Smecker-Haneetal. 2002 ).AlltheaformentionedstudiescombinedCMDttingandchemicalmodelinginatwo-stepprocess,inwhichtherststepwasdoneindependentlyofthesecond.However,thetwostepsareinextricablylinkedbecauseanincreaseintheSFRspeedsupthechemicalenrichment.Gasowsintooroutofthesystemcanchangethiscouplingmaking 110

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Bickeretal. 2004 ; Boissier&Prantzos 2001 ,andreferencestherein).Particularlyrelevantforthepresentstudy,whichisconcernedwitharesolvedpopulation,istheworkof Ikuta&Arimoto ( 2002 )and Yuk&Lee ( 2007 ). Ikuta&Arimoto ( 2002 )computedafewclosedboxevolutionmodelsforseveralGalacticdSphs.TheyperformedaqualitativecomparisonoftheirmodelCMDand[Mg/Fe]vs.[Fe/H]relationwithwhatwasobservedandfoundareasonableagreement,buttheyhadtoinvokegasstrippingviarampressureortidalshockstoreconcilethepresentdaygasfractionoftheirclosedboxmodels(97%)withtheobservedvalues(0%). Yuk&Lee ( 2007 )improveupontheworkof Ikuta&Arimoto ( 2002 )byquantitativelyttingaclosedboxchemicalmodeltotheCMDofIC1613,arelativelyisolatedLGdwarfirregulargalaxy.TheirmodelSFHandAMRareingoodagreementwithpreviousindependentdeterminationsbasedonthecanonicalCMDttingmethod,lendingsupporttoboththeoldandnewmethods.Moreover,theirpredictedpresent-dayoxygenabundanceisconsistentwiththeobservedvalue.TheseworksrepresentasignicantimprovementoverpreviousstudiesofresolvedstellarpopulationsbecausetheyincorporateCMDttingandchemicalmodelingsimultaneously.Nevertheless,therearemanylinesofevidencethatsuggestgalaxiesdonotevolveasclosedboxes.Asoriginallyhypothesizedby Larson ( 1974 )andexempliedbythe Ikuta 111

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( 2002 )results,gasoutowscouldexplainthelackofgasindSphsdespitetheirlowmetallicities(seealso Lanfranchi&Matteucci ( 2004 )).OtherevidenceforgasoutowsincludestheabundancesofmetalsintheIGM( Edge&Stewart 1991 ; Mushotzky&Loewenstein 1997 ),themass-metallicityrelationofgalaxiesatlowandhighredshift(e.g., Garnett 2002 ; Tremontietal. 2004 ; Pilyuginetal. 2004 ; Erbetal. 2006 ),extendedextra-planarHIgasinspirals( Fraternalietal. 2004 ; Oosterlooetal. 2007 ),highvelocityclouds(HVCs)withnearsolarmetallicity( vanWoerden&Wakker 2004 ; Wakker 2001 ; Richteretal. 2001 ),extra-planaropticalandX-rayemissionaroundstarburstgalaxies( Heckmanetal. 1990 ; Lehnert&Heckman 1996 ; Martinetal. 2002 ; Stricklandetal. 2004 ),andvelocityshiftsofhigh-ionabsorptionlinesindampedLyman-systems( Foxetal. 2007 )andLymanbreakgalaxiesatz34(e.g., Pettinietal. 2001 ; Adelbergeretal. 2003 ).Foramoredetailedreview,werefertheinterestedreaderto Veilleuxetal. ( 2005 ).Evidenceforgasinowsincludestheso-calledG-dwarfproblem,whichisthefactthatthemetallicitydistributionfunctionoflowmass,longlivedstarsobservedintheSVandinmanyothergalaxiesistoonarrowandcontainstoofewmetalpoorstarscomparedtotheclosedboxmodel(e.g., Tinsley 1975 ; Rocha-Pinto&Maciel 1996 ; Sethetal. 2005 ; Jrgensen 2000 ; Wyse&Gilmore 1995 ; Harris&Harris 2002 ; Kochetal. 2006 ; Sarajedini&Jablonka 2005 ; Mouhcineetal. 2005 ; Wortheyetal. 2005 ).GasinowoverseveralGyrisrequiredtotthechemicalabundances,gasmassfraction,andextendedSFHoftheSV(e.g., Chiappinietal. 2001 ; Portinarietal. 1998 ).Otherevidenceincludesthekinematicsofextra-planarHIgasinsomespirals( Fraternali&Binney 2006 ),lowmetallicitiesofsomeHVCs( Wakkeretal. 1999 ; Richteretal. 2001 ),highvelocityOVIabsorptionalongvarioussightlinesthroughtheGalaxy'shalo( Sembachetal. 2003 ),andthenonmonotonicSFHsoflowmassgalaxies( Heavensetal. 2004 ).Therearetheoreticalexpectationsforgasinows,aswell.CosmologicalsimulationsofgalaxyformationintheCDMframeworkpredictdiskgalaxiestoformfromthesmooth 112

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Abadietal. 2003 ; Sommer-Larsenetal. 2003 ; Governatoetal. 2004 2007 ).Thisgascouldcooloutofareservoirofhothalogas( Sommer-Larsenetal. 2003 ; Kaufmannetal. 2006 ; Maller&Bullock 2004 )orbeaccretedontothehalofromtheIGM.Thisideaissupportedbytherecentdiscoveryofahot(T106K)gaseoushaloaroundthequiescentmassivespiral,NGC5746( Pedersenetal. 2006 ).Thisgasistoohottobeheatedbysupernovaeinthediskandthedisksupernovarateistoolowtohavecreatedthereservoirthroughtheoutowofdiskgas.Finally,theoreticalsimulationssuggesttheneedforextendedaccretionofdilutegastokeepdisksfrombeingdestroyedafterasuccessionofminormergerswithmassratiosof4:1andevenupto10:1( Bournaudetal. 2007 ).Despiteallthisevidence,theprecisenatureandimportanceofgasowsintheevolutionofgalaxiesisstilluncertain.Tohelpimprovethesituation,inthepresentpaper,wedevelopachemophotometricCMDttingmethodasanextensiontothecanonicalmethodusedinChapter 3 ,butwiththegoalofexaminingtheroleofgasowsinM33'sevolution.Following Ikuta&Arimoto ( 2002 ),wesolvethechemicalevolutionequationstoobtainaself-consistentSFHandAMR.WeimproveupontheirworkbyallowingforgasinowandoutowandbyecientlysearchingthefullvolumeofparameterspacetomakeadetailedandquantitativettotheobservedCMD.ThephotometricdataweuseinthischapterandthereductionprocedurewerepresentedinChapter 2 .Insummary,threecolineareldslocatedinprojection20300southeastofM33'snucleuswereobservedwiththeAdvancedCameraforSurveysonboardtheHubbleSpaceTelescope.TheeldnamesweredesignatedA1,A2,andA3inorderofincreasinggalactocentricdistance.InChapter 3 ,wecomputedtheSFHsfortheseeldsusingtheclassicalsyntheticCMDttingmethodwithageandmetallicityasfreeparameters.BecauseeldsA2andA3mayhaveanon-negligiblecontributionfromM33'shaloorthick-disk(seeChapter 3 foradiscussion),werestrictourselvestoanalyzingeldA1inthischapter. 113

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,weoutlinethechemicalevolutionequations,whichformthebackboneofourmodels.Wedescribeinx howwelinktheseequationswiththesyntheticCMDttingmethodtobuildaself-consistentmodelCMD.Inx ,wepresenttheresultsofttingclosedboxandinow/outowmodelstothedata.Inx ,wecomparesomepredictionsofourbesttmodelstoindependentobservationsinM33,wecompareourresultstootherchemicalmodelsoftheSV,LMC,andSMC,andwediscusssomeimplicationsfortheformationoftheGalaxy'shalo.Wesummarizeourresultsinx Pagel&Tautvaisiene ( 1995 ,hereafterPT95).TheseauthorssuccessfullyappliedtheDPAinconjunctionwiththeIRAtomodelthechemicalevolutionoftheSVand,later,theMagellanicClouds( PT98 ).IntheDPA,thereisadelaytime,d,betweenthebirthofastellargenerationandtheresultingSNeIaexplosions.OurmodelstracktheelementsO,Mg,Si,Ca,Ti,andFe.Tominimizetheeectofuncertaintiesintheyieldofanyoneparticular-element,wefocusontheirsum,whichwerefertoas.Wedonotfollowcarbonandnitrogenbecausetheyhaveasignicantcontributionfromlonglivedlowandintermediatemassstars,forwhichtheIRAandDPA 114

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Tinsley ( 1980 )and PT95 ,theequationsofchemicalevolutionundertheIRAandDPAcanbeexpresssedas dt=fI(t)fO(t)(4{1) vandenHoek&Groenewegen ( 1997 )(usingavariablemasslosseciency)and Portinarietal. ( 1998 ).Wendthat,averagedoverallmetallicities,R=0:235fora Kroupaetal. ( 1993 )IMF.WenoteinpassingthattheprecisevalueofRisinconsequentialbecausethefactor(1R)canbeabsorbedintothestarformationeciencyparameter,,describedbelow.However,weexplicitlyincludeittobemoreconsistentwithpreviousstudies.Equations 4{1 { 4{4 representconservationoftotal,gaseous,stellar,andelementalmass.TherstterminEquation 4{4 representsthemassofelementithatisoriginallypresentinthegasandlosttostarformation,pluswhatisinstantaneouslyreturnedbythe 115

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4{4 representstheinstantaneousrestitutionrateofnewlysynthesizedelementiwhilethethirdtermisthedelayedrestitutionofnewlysynthesizedelementi(fromSNeIa),whichiszerofort
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Schmidt ( 1959 ),whofoundthatstarformationratetracedgasdensityintheGalaxy, Kennicutt ( 1998 )measuredmeangasmassesandSFRswithintheopticalradiiof60normalspiralsandwithinthecentralregionsof30starburstgalaxiesandfound=0:250:07and=1:400:15 Gottesman&Weliachew 1977 ; Wong&Blitz 2002 ; Kennicuttetal. 2007 ; Boissieretal. 2003 ; Misiriotisetal. 2006 ).InM33, Heyeretal. ( 2004 )measured=3:30:07and=0:00350:066usingtheinfraredluminositytomeasuretheSFR. Boissieretal. ( 2006 )measuredM33'sultravioletsurfacebrightnessandplottedtheSFRproleagainstthegasproleandweestimatebyeyethattheyobtainedasimilarvalueforas Heyeretal. ( 2004 ),butasmallervalueforbyafactorof3.Thecauseofthevariationsamongthedierentmeasurementsisunclearbuttheycouldarise,inpart,fromnon-axisymmetricprolesoruncertaintiesintheextinctioncorrection,theCO=H2conversionfactor,theuxcalibration,andtheconversiontoSFR.Thevariationsmayalsobeduetointrinsicpropertiesofthegalaxies,asthereissomeevidencethatmolecule-richgalaxies,typicallymassivespiralsandstarbursts,havelowervaluesthanmolecule-poorgalaxies,typicallylowsurfacebrightnessanddwarfsystems.Interestingly,M33fallsintothislattercategorywithatotalmolecularfractionof0:1( Corbelli 2003 ).

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Murgiaetal. 2002 ; Matthewsetal. 2005 ; Leroyetal. 2005 ; Gardanetal. 2007 ).Indeed,thestudiesmentionedabovealsofoundthat,whenconsideringthemoleculargasalone,1:4,withmuchlessgalaxy-to-galaxyvariationthanwhenconsideringthetotaloratomicgas.Itisbeyondthescopeofthepresentstudytotrackthetimeevolutionofthemoleculargasfraction,butthisisonepossibleavenueforfutureimprovement.Inanycase,weadopt=3:3andallowtovarybetween0.0001and10.0.Adopting=1:4doesnotsignicantlychangeourresultsbecauseg1throughoutmostofthesystem'sevolution.Figure 4-1 showsadiagramintendedtohighlight(inasimpliedway)theprocessestheoccurcontinuouslythroughoutthemodelevolution.Solidblackanddashedredarrowsdepict,respectively,positiveandnegativecorrelations.GasinowdepositsgasintothesystemanddrivesSFviatheKennicutt-Schmidtlaw.Becausetheinowinggasisprimordial,theISMmetallicityisalwaysbelowwhatitwouldbewithoutinow.About25%ofthegasthatgoesintomakingeachstellargenerationisinstantaneouslyreturnedtotheISMbystellarwindsandSNeII,while75%islockedupintostellarremnantslikewhitedwarfs,neutronstars,andblackholes.TheSFenrichestheISMinmetals,butalsodrivesanoutowofgasoutofthesystem.Thus,allelsebeingequal,thepresenceofagasoutowquenchestheSFR,slowsthechemicalenrichment,andsupressesthemetallicitybelowwhatitwouldbewithoutoutow.TheISMmetallicitygenerallyincreaseswithtimeduetostellarnucleosynthesis,butashort,rapidincreaseintheinowratecandecreasetheISMmetallicitytemporarily.Intheabsenceofallgasows,aninitialgasreservoirmustbepresenttostartSF,whichcontinuouslydeclinesthereafter. 4-2 ,weshowaowchartdepictingthemethodusedinthischapter,whichaddsseveralsteps(toprowenclosedinadashedbox)asafront-endtothecanonicalmethodusedinChapter3(bottomrow).Westartwithasetofmodelparameters(,, 118

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4{1 ).Theseequationsareintegratedusinga4th-orderRunge-Kuttamethodwithatimestepof2106yr.Thenumericalintegrationwascheckedagainstseveralanalyticalsolutionsandtheagreementwasfoundtobeexcellent.Thechemicalevolutionmodelspeciesthetotalandgasmasssurfacedensities,SFR,andabundancesofthevariouselementsasfunctionsoftime.Theage-metallicityplaneisdividedintologarithmicbinsofwidth0.25dexinageand0.3dexinmetalabundance.Tocoverthisplane,weusethesamesetofsyntheticCMDsasinChapter3,eachofwhichrepresentsthepredictedphotometricdistributionofstarsinagebinjandmetallicitybink.Wecalculatethetotalstellarmass,Mj,formedinagebinj(thedeprojectedareaoftheACSeldis106pc2)andthecorrespondingmass-weightedmeanglobalmetallicity,h[M=H]ij,usingEquation 4{6 describedbelow.ThisinformationgoesintocomputingtheamplitudesofthesyntheticCMDs,ajk.Oncetheamplitudesareinhand,therestoftheprocessisalmostidenticaltoChapter 3 .ThemodelCMDisdividedintosquarebins0.1magonasideandthevalueofmodelCMDbiniisalinearsummationofthisbininallthesyntheticCMDs(i.e.,overallageandmetallicitybins).ThemodelisthencomparedtothedatausingthemaximumlikelihoodratioforaPoissondistribution,(see 3.1 ).Themodelparametersarechangedandthewholeprocessrepeatsuntilisminimized.TofurtherillustratetheconstructionofamodelCMDwiththisnewmethod,Figure 4-3 showstheresultsofanexponentialinowmodelttothedata(see 4.3.2 ).InpanelA,thecyanlineistheSFR,theblacksolidlineistheinowrate(dividedby10),andtheblackdottedlineistheoutowrate.TheotherpanelsshowB)[Fe/H],C)[/Fe],andD)[M/H]asfunctionsoftime.Inallpanels,theredlineshowsthemeanvalueforeachagebin.PanelDalsoshowsthesyntheticCMDage-metallicitybinboundariesasverticalandhorizontalblacklines.Thus,eachrectangularregionrepresentsaparticularsyntheticCMD.Thecoloringofeachregionsigniesforthisparticularmodelhowmuchstellarmass 119

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3 ,weusetheprogram,StarFISH( Harris&Zaritsky 2001 ),tosolveforthebesttparameters.Thistime,however,wealsousethegeneticalgorithm,PIKAIA( Charbonneau 1995 ),toecientlysearchthefullvolumeofparameterspace.Briey,thisalgorithmrandomlygeneratesaninitialpopulationofsolutions,whichisevolvedthroughsuccessivegenerationsundertheactionofnaturalselection,breeding,inheritance,andrandommutationtondtheglobalsolution.WeranPIKAIAfor200generationsinthesteady-state-replace-randomreproductionmodewithcreepmutationenabledand50individualsineachgeneration.Then,thedownhillsimplexroutineofStarFISHwasstartedfromthebesttsolutionfoundbyPIKAIA.Thishybridapproachprovedmoreecientatlocatingtheglobalsolutionthaneithermethodindividually.Becausewewerenolongersolvingfortheamplitudesofthebasispopulations,wehadtomodifythewayStarFISHcalculatedthecondenceintervals.Foreachparameter,wetooksmallstepsinthepositiveandnegativedirectionsawayfromitsoptimumvalue.Aftereachstep,weallowedthedownhillsimplextoreconvergewhileholdingthatparameterxedandallowingtheotherstovary.Theprocesswasrepeateduntilthe1limitofthettingstatisticwasreached.ToestimatethesystematicerrorsinthestellarevolutionarytrackswecreatedtwosetsofsyntheticCMDsusingthe Girardietal. ( 2000 )and Pietrinfernietal. ( 2004 )trackswhichwedesignateasPadovaandTeramo(alsoreferredtoasBaSTIintheliterature),respectively.Theconversionfromthetheoreticaltotheobservationalplaneisaccomplishedwiththe Castelli&Kurucz ( 2003 )libraryofbolotmetriccorrections. 120

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VandenBergetal. 2006 ; Pietrinfernietal. 2006 ; Dotteretal. 2007b ). Salarisetal. ( 1993 )foundthat-enhancedtracksandisochronesarewellreproducedbysolar-scaledoneswiththesameglobalmetallicityprovidedtheenhancementsaresimilarforallthe-elements.SubsequentstudiesdemonstratedthatthisresultbeginstobreakdownforZ&0:003(e.g. Salaris&Weiss 1998 ; Salasnichetal. 2000 ; VandenBergetal. 2000 ; Kimetal. 2002b ).Wehavecheckeditsapplicabilityusingseveralofthemostrecentisochronedatabases( Pietrinfernietal. 2006 ; Dotteretal. 2007b ; VandenBergetal. 2006 )andwendthatovertherangeofages,[Fe/H],and[/Fe]mostappropriateforourdata,asolar-scaledisochroneintheIvs:(VI)planeiswithin0:1magofan-enhancedisochronewiththesameglobalmetallicity.Therefore,weaccountfor-elementenhancementsbycalculatingtheglobalmetallicityfollowingtheformalismof Salarisetal. ( 1993 )and Piersantietal. ( 2007 ). [M=H]=[Fe=H]+log(a10[=Fe]+b)(4{6)InEquation 4{6 ,a=Pi(Xi=Z)0:7fori=O,Ne,Mg,Si,S,Ca,andTiandb=1a.Notethatthisrelationimplicitlyassumesnoenhancementsinelementsother 121

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4{6 tounderestimate[M/H]byonly0:1dex.Theeectwouldbeevensmallerforanyotherheavyelementssincetheycompriseamuchsmallermassfractionofallmetalsthancarbon.Inanycase,ourconclusionsareinsensitivetotheprecisevalueofthecorrectionfactorto[Fe/H]inEquation 4{6 becauseitgenerallyamountsonlyto<0:2dex.Inprinciple,thebolometriccorrections,colortransformations,andevolutionarylifetimesalsodependon[/Fe],butinpractice,ourdataarenotsignicantlyaectedbythesedependencies. Cassisietal. ( 2004 )provedthatthebolometriccorrectionsandcolortransformationsdependnegligiblyon[/Fe]inthevisualandnear-infraredpasspands. Dotteretal. ( 2007a )investigatedtheeectofabundancevariationsonstellarevolutionarymodelsandfoundthatwhen[=Fe]=0:3,theMSlifetimeisdecreasedby5%.Wehavecomparedthesolar-scaledand-enhancedTeramotracks,whichhave[=Fe]0:4( Pietrinfernietal. 2006 ),andwendthat,ingeneral,theevolutionaryphaselifetimesdierby.10%.Theseeectsarelikelytobeevensmallerforourdatasincewederive0:2.[=Fe].0:2foralmostallages.InAppendix B ,wepresentsometestsofthemethod.Thesetestsareimportantforunderstandingitsstrengthsandlimitations.ThemostrobustlyrecoveredquantitiesaretheageCDF,AMR,ZMDF,inowCDF,outoweciency,and[/Fe]vs.[Fe/H]relation.TheinowCDFismostaccurateatages.7Gyr. 4.3.1ClosedBoxModelsWebeginbytestingthecanonicalclosedboxmodelinwhichtheinowandoutowratesareidenticallyzero.Thesystemisinitiallycomposedentirelyofgas.ThetotalmassremainsconstantthroughoutitsevolutionwhilethegasmassandSFRdecreasemonotonicallywithtime. 122

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4-4 andFigure 4-10 displaytheglobalsolutionsfortheclosedboxmodelusingthePadovaandTeramotracks,respectively.Inthesegures,thesameinformationisplottedasinFigure 3-4 sothattheseresultscanbedirectlycomparedtotheresultsofChapter 3 .Tables 4-2 { 4-5 listthetqualitiesandparametersofthesolutions.Thetqualitiesoftheclosedboxsolutionsare>20worsethanthesolutionsofChapter 3 ,whichhadnoconstraintsonageandmetallicity.Thisisnotsurprisingsinceourclosedboxmodelhasonlytwofreeparameters,namely,thestarformationeciencyandthetotalmass.However,aswewillseebelow,theadditionofgasinowandoutowsignicantlyimprovesthetswithonly24morefreeparameters,indicatingthisregioninM33probablydidnotevolveasaclosedbox.Becauseofthereducednumberoffreeparameters,thecondenceintervalsoftheclosedboxsolutionsaresignicantlysmallerthanthoseoftheChapter 3 solutions.Thisdemonstratesthatthechemicalevolutionequationscanbeusedtoalleviatetheage-metallicitydegeneracyinherentinbroad-bandstellarcolors.TherearetwosignicantdiscrepanciesbetweenthemodelanddataCMDsthatarecommontoboththePadovaandTeramoresults.First,themodelspredicttoomuchstarformationatages.1GyrwhichcausesanoverabundanceofmodelMSstarsontheblueplumeat(VI)0:0.Second,themodelCMDshavetoofewstarsinaregioncenteredat(VI)0:5andI26:5.IntheglobalsolutionsofChapter 3 ,thisregionisdominatedbystarswithages28Gyr,indicatingtheclosedboxmodelshavetoolittlestarformationattheseages.Therearealsoseveraldiscrepanciesthatdependonwhichtracksareused.First,theRGBofthePadovamodelistooblue,indicatingameanmetallicitythatistoolow.TheTeramomodelRGB,ontheotherhand,appearsslightlytoowide,possiblyindicatinganexcessivelylargemetallicityspread,andithastoomanystarsoverall.ThisoverabundanceofRGBstarsischaracteristicoftherstversionoftheTeramotracksemployedbyIAC-STARandwasalsonotedinChapter 3 .SometimeafterChapter 3 123

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3 solution.Therefore,theclosedboxmodelhasanincorrectdistributionofstellaragesat18Gyr.Finally,wenotethattheTeramoCMDshavetoomanystarsontheblueHB.SincetheblueHBispopulatedbytheoldeststarsthismeansthatthereistoomuchstarformationattheoldestages.Theproblemcould,inprinciple,arisefromthemetallicityoftheoldestagebinbeingtoolowbutsinceitisalreadyclosetothesolutioninChapter 3 ,whichdoesnothavesuchalargediscrepancy,thisprobablyisnotthecase. ,thereisampleevidencethatgalaxiesingeneraldonotalwaysevolveasclosedboxes.AnexponentialinowrateisoneofthesimplestandmostcommonformsusedintheliteraturesoitisinstructivetoseehowwellitcanexplainM33'sstellarpopulations.Accordingly,wesolvedfortheinowtimescaleandtheinitialinowrate.Wealsoincludedgasoutowbyallowinganonzerooutoweciency,w.Figure 4-5 andFigure 4-11 showtheresultsusingthePadovaandTeramotracks,respectively.Thebesttinowhistory(IFH)dividedbyafactorof10isplottedasagraylineinpanelAandtheinowCDFisplottedasagraylineinpanelB.Themodelswithexponentialinowandoutowprovidebettertstothedatathantheclosedboxmodelsbuttheystillshowlargediscrepancieswiththedata.Infact,theproblemswiththesemodelsareverysimilartothoseoftheclosedboxmodels,buttheseverityofthedisagreementshasbeenlessened.Hence,thereisstilltoomuchstarformationatages.1Gyrandtoolittleintherange28Gyr.Thetqualitiesare15worsethantheChapter 3 solutions. 124

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vandenBosch 2002 ; Wechsleretal. 2002 ).Withthisinmind,wealsoinvestigatedanotherfunctionfortheinowrate(IFR)whichhasadelayedmaximum,fI(t)/texp(t2=22),whereisthetimebetweenwhentheinowstartsandwhenitpeaks.Thisfunction,whichwerefertoasSandageinow,wasrstusedby Sandage ( 1986 )todescribethevariationinSFHwithgalaxymorphologyandlaterexplicitlypresentedby MacArthuretal. ( 2004 ).WefoundthatusingthisfunctionfortheIFRimprovedthetqualitiesovertheexponentialIFR.TheresultsareplottedinFigure 4-6 andFigure 4-12 forthePadovaandTeramotracks,respectively.Byshiftingthebulkoftheinowtowardyoungerages,itallowsformorestarformationatcorrespondinglyyoungerages.Inspiteofthisimprovement,thesolutionsstillexhibitsimilardiscrepanciesastheexponentialinowmodels,buttoalesserdegree.Thetqualitiesare9worsethantheChapter 3 solutions.ThemaindrawbackoftheexponentialandSandagefunctionsisthattheIFRtodaycannotbevariedindependentlyoftheIFRatintermediateages(28Gyr).ThesefunctionsjustdonotprovideenoughfreedomtodescribethetrueIFHwhichmaynotbeadequatelycharacterizedbyjusttwoparameters.Theseresultsledustotrythreelessrestrictiveinowmodels.Therstwasadoubleexponentialmodeldescribedbyfourparameters:agrowingtimescale,adecayingtimescale,atransitiontimebetweenthegrowinganddecayingmodes,andtheIFRatthetransitiontime.Thesecondwasatruncatedmodeldescribedbyfourparameters:theinitialIFR,theIFRatamodeltimeof7Gyr,atruncationtimewhentheinowends,andtheIFRatthetruncationtime.Inthethirdmodel,whichwecalledfreeinow,weapproximatedthetrueIFHwithadiscretefunctionbydividingtheentireagerangeinto4binseachwithapossiblydierentbutconstantIFR.Weexperimentedwithdierentbinningschemesandsettleduponareasonablecompromisebetweenthedesiretohave 125

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B ,weshowthattheseinowfunctionscanreasonablycapturebroadtrendsinthetrueIFHandchemicalevolution.ThesolutionsusingthesethreeinowmodelsarediplayedinFigures 4-7 { 4-9 and 4-13 { 4-15 forthePadovaandTeramotracks,respectively.Thefreeinowmodelsprovidethehighestqualityts.However,thedouble-exponentialandtruncatedinowmodelsare<1worseandexhibitqualitativelysimilarresults.ThediscrepanciesbetweenmodelanddataexhibitedpreviouslywiththeexponentialandSandageinowmodelsarealmostcompletelyerased.MostofthediscrepanciesthatdoremainaresimilartothoseexhibitedbythesolutionsinChapter 3 ,leadingustoconcludethattheyaremostlycausedbyinaccuraciesinthestellartracks.However,thetqualitiesare24worsethantheChapter 3 solutions.Thisdierencecouldarisefromtheapproximationsmadeinproducingthechemicalevolutionmodelsandtheuncertaintiesinherentinthestellaryields.Second,ageandmetallicityarenolongercompletelyfreeparameterssoerrorsinthestellartrackscannotbeaseasilyhiddenbyarbitrarycombinationsofageandmetallicity.Third,radialmixingcouldcauseaninowandoutowofstars( Roskaretal. 2007 )andcouldleadtoametallicityspreadthatsystematicallyvarieswithage( Sellwood&Binney 2002 ).ThelargestdierencebetweenthePadovaandTeramosolutionsisthatthelatterexhibitmetallicites0:2dexhigheratallages.ThePadovaandTeramosolutionsinChapter 3 didnothaveaslargeadierenceintheAMRandZCDF.Webelievethisismostlyduetothemetallicityofthe6.2GyragebinintheTeramosolutionbeing0.3dexlargerthaninChapter 3 .TheoverallfasterenrichmentoftheTeramosolutionscomparedtothePadovasolutionsrequireshigherttedvaluesof.Inacoupleoftheinowmodels, 126

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3 solutions.First,theyhave5060%ofthegasaccretiontakingplacebetween3and7Gyrago.Anythinglesswouldproducetoofewintermediate-agestars.Second,atmost10%ofthegaswasaccretedinthelast3Gyr.AnyamountinexcessofthatwouldleadtoarecentSFRthatistoohighandproducetoomanyyoungstarsontheblueplumeMSat(VI)0:0.Third,theoutoweciencyistypically10:5,whichisrelativelysmallcomparedtowhathasbeenestimatedfordwarfgalaxiesintheLG( Lanfranchi&Matteucci 2004 ; Carigietal. 2006 ).Finally,theresultsfortheSFH,ageCDF,AMR,andZCDFaresimilartotheChapter 3 solutions.ThislendssupporttoourconclusionsinChapter 3 ,andsuggeststheyarenotsignicantlyaectedbyunphysicalcombinationsofageandmetallicity. 4-16 { 4-21 and 4-22 { 4-27 summarizesuchpredictionsusingthePadovaandTeramotracks,respectively.Ineachgure,panelAshowsthegasmassinblacklinesandtotalmassingraylinesaveragedovereachagebin.Themean[/Fe]and[Fe/H]ofallstarsformedineachagebinareplottedinpanelB.Thesepointsrepresentmassweightedaveragesand,therefore,areskewedtowheremostofthestellarmasswasformedwithineachagebin.Thethreehorizontallinesmarkthemean[/Fe]ofallstarseverformedandthe1bounds.PanelsCandDdisplay,respectively,theAMRandMDFofiron.TheprimarydierencebetweenthePadovaandTeramosolutionsisthatthelatterpredictsmallergasandtotalmassesandsomewhathighervaluesof[Fe/H],by0:2 127

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Tinsley 1975 1980 ).Theinowmodelsshowqualitativelysimilardetailsastheclosedboxmodelswithafewnotabledierences.Becauseofthepresenceofgasinow,thegasandtotalmassesriseintheearlyevolutionarystagesandreachamaximumseveralGyrlater.Thegasmassbeginstodeclineastheinowratebecomessmallbutstarformationandoutowcontinue.Thetotalmassdecreasesinafewcaseswhentheoutowrateexceedstheinowrate.Themean[/Fe]oftheoldestagebinis0:2inalltheinowmodelswhilethatoftheyoungestbinis0:10:1.Eventhoughthemajorityofagebinshave[/Fe]ratioslessthansolar,themajorityofthestellarmassisformedintheoldestthreebins,sothatthemean[/Fe]ofallstarseverformedis0:1foralltheinowsolutions.Notethatthe[/Fe]vs.[Fe/H]relationisnotalwayssingle-valued,since[/Fe]canincreasewithtimedependingonthepreciseinterplaybetweengasows,theSFR,andtheSNIaexplosionrate(see 4.4.2 ).Finally,theAMRsoftheinowsolutionsaresomewhatmoremetal-richthantheclosedboxsolutionsandtheMDFsaregenerallymorenarrow. 128

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Corbelli&Schneider 1997 ).Achangeof10intheinclinationwouldchangethesurfacedensitybyapproximately0:2Mpc2.Thus,consideringonlytherandomandinclinationuncertainties,thePadovaandTeramosolutionsareconsistentwiththeobservationsatthe1and2levels,respectively.ThedierencebetweenthePadovaandTeramosolutionsis0:2Mpc2andgivessomeindicationofthesystematicerrorsduetouncertaintiesinthestellartracks.ThetestsinAppendix B showthatourmodelstendtounderpredictthemasssurfacedensity,whichisconsistentwithwhatwendhere.Thepresent-daySFRisaquantitythatisrelativelyeasytomeasureingalaxiesandthereforeprovidesausefulcheckonourresults.UsingGALEXnear-UVandfar-UVimagesofM33,Boissieretal.(2007;privatecommunication)computedtheUVsurfacebrightnessineldA1andthenconvertedthattoaSFRusingtherelationin Kennicutt ( 1998 ),whichisaslightlymodiedversionoftheonerstpresentedin Madauetal. ( 1998 ).TheinfrareddatausedtoestimateextinctionwasofpoorqualityatthisdistanceinM33,sotheSFRcouldonlybeconstrainedtotherange0:60:9Myr1,wherethelowerlimitcorrespondstozeroextinctionandtheupperlimitcorrespondstoanextinctionofAFUV=0:49.ThechiefsourcesofuncertaintyintheselimitsarethattheUVux-SFRcalibrationwasbasedontheoreticalisochroneandspectrallibrariesandthereforesubjecttoalltheuncertaintiesinherentinthoseandthatitassumedaSalpeterIMF.Accordingto Madauetal. ( 1998 ),adoptingaScaloIMF( Scalo 1986 ),whichismoresimilartotheformwehaveused,theresultingSFRwouldbe50%smaller.Therefore,thelimitsabovebecome0:30:5Myr1,whichareingoodagreementwithourpredictionsof0:4and0:3Myr1forthePadovaandTeramofreeinowsolutions,respectively. 129

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Magrinietal. ( 2007 )compiledanextensivecatalogofpreviouslymeasuredabundancesinHIIregions,typeA-Bsupergiantstars,andPNe.TheHIIregionsandsupergiantsprobethepresent-dayabundancewhereasthePNecouldprobetheabundanceatolderages.Themasses,andhencelifetimes,ofthePNeprogenitorsarenotknownwithgreatcertainty.Thesampleof Magrinietal. ( 2007 )coversonlythebrightesttwomagnitudesofthePNeluminosityfunction,soitcouldbebiasedtowardthehighmassendoftheprogenitormassrange(1M.M.5M).Therefore,theprogenitorsofthe Magrinietal. ( 2007 )sampleprobablyhadMSlifetimeslessthanafewGyr.MostoftheHIIregionabundancesinthe Magrinietal. ( 2007 )compilationweremadefromdirectTemeasurements,whichisgenerallyconsideredthemostreliablemethod.Eightobjectshaveatleasttwoindependentmeasurementsandthreeofthoseobjectshavethreeindependentmeasurements.Theoxygenabundancescompiledby Magrinietal. ( 2007 )areplottedinFigure 4-28 andwehavealsoaddedtherecentabundancesderivedby Viironenetal. ( 2007 )for60HIIregionsbasedonthelog(H=[SII]6717+6731)vs.log(H=[NII]6583)diagnosticdiagram.ThesolidlinesinpanelArepresenttheirlineartandmeanresidualaboutthatt.ThepredictionsofthePadovaandTeramofreeinowsolutionsforthepresent-dayabundanceareshownasthelledandopenstars,respectively.OurpredictionsareconsistentwiththeabundancesofsupergiantsandPNebutarehigherthantheoutermostHIIregions.Somestudieshavearguedthattheoxygengradientisnotconstantbutattensoutwithincreasingradius( Magrinietal. 2007 ; Viironenetal. 2007 ).Ourpredictionsareabout12higherthanwhatwouldbeinferrediftherewerenogradientbeyondRdp300.ItisnotclearifthisdiscrepancyreectsaproblemwithourpredictionsortheHIIregionabundances.ThedatainFigure 4-28 suggestthelatterexplanationbecausetheHIIregionabundancesaresystematicallylowerthansupergiantsandPNeby0:2dex. 130

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4-29 ,wecomparetheevolutionof[/Fe]inM33tothechemicalevolutionmodelsoftheSV,LMC,andSMCpresentedin PT95 and PT98 .Theselatterthreemodelshavebeencitedoftenintheliteraturebecauseoftheirsimplicityandabilitytoreproduceobservationsfairlywell.Theblackandmagentasolidlinesshow,respectively,thefreeinowsolutionsusingthePadovaandTeramotracks.Thelledpointsarethemeanvaluesineachagebin(panelBofFigures 4-21 and 4-27 ).InspectionofFigure 4-29 revealsthatM33's[/Fe]vs.[Fe/H]relationisnotexactlythesameastheothersystems,buttheprecisedetailsshownbythelinesarenotaswellconstrainedasthemeanvaluesofeachagebin.ThelinesserveasagoodstartingpointforcomparingM33toothersystemsandunderstandingthebehaviorofthe[/Fe]vs.[Fe/H]relationaslongaswerememberthattheoverallshapeismorerobust,ascanbeseenbyexaminingallacceptableinowsolutions(Figures 4-19 { 4-21 andFigures 4-25 { 4-27 ).Becausewehaveusedalmostidenticalchemicalevolutionequationsandidenticalstellaryieldsas PT95 and PT98 ,ourmodelsshowasimilaroverallbehaviorinresponsetogasows.ThediscontinuitiesintherelationforeachsystemcanbetracedbacktotheinterplaybetweentheSFR,IFR,andthedelayedinjectionofironintotheISMfromSNeIa.Therefore,thedierencesbetweentherelationsariseprimarilyfromdierencesintheSFHandIFH.IntheIRA,theabundanceratioofanytwoelementsisaconstantdeterminedbytheratiooftheirnucleosyntheticyields.Thus,initially,[=Fe]=log(y=yFe)log(X=XFe)0:4,whereyandXaresummationsoverO,Mg,Si,Ca,andTi.After1.3Gyrhaveelapsed,theDPAbeginsoperatingastherstSNIainjectironintotheISMandproducetherstdownturn,or\knee",intherelation.ThelocationofthiskneeisdependentontheSFR,whichdependsontheIFRandoutowrate(seeFigure 4-1 ).The 131

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4-9 ),2)acorrespondingincreaseintheSFRwhichraises[/Fe],and3)thesubsequentdropin[/Fe]duetoSNIa.TheTeramomodelexperiencesamuchsmallerloopbecauseitdoesnothaveaslargeanincreaseintheIFR(seetheIFHinPanelAofFigure 4-15 ). Freeman&Bland-Hawthorn 2002 ).OneexampleofthisapproachhasbeenthequesttounderstandandidentifytheprogenitorsoftheGalaxy'sstellarhaloeldpopulationbycomparingitschemicalabundancestoothersystems(seetherecentreviewby Geisleretal. ( 2007 )andreferencestherein).RecallfromChapter 1 ,thatthehierarchicalpictureofgalaxyformationpredictsthatlargeDMhalosarebuiltupfromtheaccretion/mergingofsmallersubhalossimilartotheprotogalacticfragmentsproposedby SZ78 .InthecaseoftheGalaxy,themostobviouscandidatesforthesesubhalosareitsdSphsatellites(andotherLGmembersbesidesM31).Asexplainedindetailby Geisleretal. ( 2007 )andreferencestherein,theGalaxy'seldhalopopulationischemicallydistinctfromtheothersystems,indicatingthattheformerwasnotbuiltupfromthelatter.Inparticular,thedSphsandotherLGgalaxiesarecharacterizedby[/Fe]ratioslowerthanmostoftheGalaxy'shalo.ThisiscommonlyinterpretedtomeanthattheSFRinthedSphswaslowerand,therefore,therewasnotenoughtimetoreachhighmetallicitiesbeforeSNeIacontributedsignicantamountsofiron.ItisinterestingtocompareourresultsforM33'souterdisktothespectroscopicmeasurementsinotherLGsystems.SuchanexerciseplacesourresultsintothecontextoftheLGasawholeandhassomeimplicationsfortheformationoftheGalaxy'shalo.To 132

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4-30 ,wesummarizethehigh-resolutionspectroscopicmeasurementsof[/Fe]and[Fe/H]inthesesystems.ThisgureisthesameasFigure12in Geisleretal. ( 2007 )exceptthatwehaveaddedthePadovaandTeramofreeinowsolutionsastheblackandmagentasolidlines,respectively.Wereferthereaderto Geisleretal. ( 2007 )foramoredetailedexplanationthantheonewegivebelowandforalistofallthereferencespresentingthedata.ThecolorgreeninFigure 4-30 correspondstoeldstarsintheGalaxy'shalo,whileothercolorscorrespondtostarsinotherLGsystems,mostlysatellitesoftheGalaxy. Grattonetal. ( 2003 )examinedasampleof146starsintheSVwithaccurateparallaxes,radialvelocities,andpropermotions.ByassumingamassdistributionfortheGalaxy,theyintegratedthestellarorbitsbackwardsintimeanddividedthesampleintothindisk,\dissipativecollapse,"and\accretion"componentsbasedonorbitaleccentricity,apogalacticdistance,rotationvelocity,andmaximumdistanceabovetheGalacticplane.Thegreensolidlinerepresentsthedissipativecollapsecomponent,whichtheseauthorspostulatedformedduringthedissipativecollapseoftheGalaxy'sgaseoushaloasoriginallyoutlinedby ELS62 .ThiscomponentischaracterizedbyanetpositiverotationvelocityabouttheGalacticcenter.Thegreenstarsrepresenttheaccretioncomponent,possiblyoriginatingintheaccretedsubhalospredictedbyhierarchicalCDMmodels.ThiscomponenthasnegligiblenetrotationorasmallnegativenetrotationabouttheGalacticcenter.Exceptforthelledsquares,theothergreenpointsinFigure 4-30 representothersamplesofhalostarsselectedfortheirunusualkinematicsand/ororbitalelements(i.e.,retrograderotation,largeeccentricity,etc.)andthereforerepresentcandidatesfororiginatinginchaoticallyaccretedsubhalos.Thelledgreensquareswereselectedsimplyfortheirlowmetallicities.ThebluepointsrepresentstarsinthedSphGalacticsatellites,thecyanpointsareLMCstars,yellowpointsarestarsindwarfirregulargalaxies,andredpointsarestarsintheSaggitariusdSph(Sgr).Typicalrandommeasurementuncertaintiesareindicatedinthebottomleftcorner. 133

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Geisleretal. ( 2007 )thatsomeoftheaccretedGalactichalostarsoriginatedinhighmassdwarfsystemslikeSgrasopposedtotheirlowermasscounterpartslikethedSphs.Furthermore,basedonitssimilaritywithM33(seealsoFigure 4-29 ),wespeculatethatasystemliketheLMCcouldhavecontributedstarstothehalo,aswell.NotethatthecyantrianglesinFigure 4-30 refertoredgiantsin4oldLMCclusters,whichmaynotberepresentativeofitsentiremetal-poorclusteroreldpopulations.AlthoughwehavelittleinformationonM33'sinnerdiskevolution,thepresenceofametallicitygradient( Magrinietal. 2007 )andawidevarietyofagesinferredfromCMDs( Sarajedinietal. 2000 )hintatanextendedSFHwithafasterenrichmenttakingplaceinM33'sinnerdisk.Therefore,wehypothesizethatthekneeinthe[/Fe]vs.[Fe/H]relationinM33'sinnerdiskoccursatahighermetallicitythanintheouterdisk.Thisbringsustoanotherkeypoint:candidateaccretionhalostarswithdierent[/Fe]butthesame[Fe/H]didnotnecessarilyoriginateindierentobjects.Inotherwords,the-elementandironabundancesalonedonotnecessarilyprovideenoughinformationtotagindividualhalostarstouniqueprogenitors.Thisisbecausetheinnerregionsofaprotogalacticfragmentcouldhavebecomeenrichedwithmetalsfasterthantheouterregions.Therefore,the 134

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Zentner&Bullock ( 2003 )usedasemianalyticmodeltoexaminethesurvivaloforbitingsubhalosintheGalaxy'spotential.TheypresentedtheorbitalevolutionforthreedierentsubhaloseachaccretedontotheGalaxy'shalo8Gyragowiththesameinitialorbittypicalofsuchhalos 135

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Harbecketal. 2001 ; Winnick 2003 ; Tolstoyetal. 2004 ; Kochetal. 2006 ; Stetsonetal. 1998 ; Bellazzinietal. 2005 ; Battagliaetal. 2006 ; Fariaetal. 2007 ; Komiyamaetal. 2007 ; McConnachieetal. 2007 ),intheSgrstream( Bellazzinietal. 2006 ; Chouetal. 2007 ),NGC6822( deBlok&Walter 2006 ),andinM33( Roweetal. 2005 ,Chapter 2 ,Chapter 3 ).Inmostcases,theinnerregionsofthegalaxiesaremoremetalrichand/orolderthantheouterregions.Theevolutionofmetallicitygradientsindiskgalaxiesisamatterofsomedebate,withsomestudiespredictingthegradienttoincreasewithtimeandotherspredictingtheopposite( Magrinietal. 2007 ,andreferencestherein).TheevolutionarymodelofM33presentedin Magrinietal. ( 2007 )predictsthemetallicitygradienttohavebeensteeperinthepast.MeasurementsofthespatiallyresolvedSFHandCEHoftheselowmassgalaxiescouldhelpusunderstandiftheycandevelopchemicalgradientsintherstfewGyroftheirlivesorifsuchgradientswerepresentinthegasfromwhichtheyformed.Thepreliminaryresultsof Rizzietal. ( 2004 )and Gallartetal. ( 2005 )indicatetheformerpossibilitycouldhaveappliedtoCarina,Sculptor,Sextans,andFornax. 136

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137

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Adoptedchemicalyieldsandsolarabundances Elementyiyi;dXai; ( 1989 ). Table4-2. ResultsofthechemophotometricmethodusingthePadovatracks ModelQ2 AV Table4-3. FittedstarformationandoutowecienciesusingthePadovatracks Model log()hilo 138

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ResultsofthechemophotometricmethodusingtheTeramotracks ModelQ2 AV Table4-5. FittedstarformationandoutowecienciesusingtheTeramotracks Model log()hilo 139

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Schematicdiagramshowingtherelationshipsbetweenthemaincomponentsofthechemicalevolutionmodel.Solidblackanddashedredarrowsindicate,respectively,positiveandnegativecorrelations.Seetextfordetails. Figure4-2. Flowcharthighlightingthemainstepsofthenewchemophotometricmethod,whichconsistsofaddingseveralsteps(toprow)asafront-endtothecanonicalmethod(bottomrow)usedinChapter 3 .Seetextfordetails. 140

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ConstructionofamodelCMD.Inallpanels,theredlineshowsthemeanvalueofthecyanlineineachagebin.A)TheSFR(cyanline),outowrate(dottedblackline),andIFRdividedby10(solidblackline).B)[Fe/H]vs.time.C)[/Fe]vs.time.D)[M/H]vs.time(cyanline)andsyntheticCMDage-metallicitybinboundaries(blacklines).OrangehatchedboxesrepresentCMDamplitudesofzero.Grayscaleboxesrepresentthecontinuumofnonzeroamplitudeswherewhiteistheminimumandblackisthemaximum. 141

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ClosedboxmodelusingthePadovatracks.A)SFH.B)AgeCDF.C)AMR.D)ZCDF.E)DataCMD.F)ModelCMD.G)Residuals.H)Signicance. 142

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ExponentialinowmodelusingthePadovatracks.A)SFH(blacklines)andIFH(graylinesanddividedby10).B)AgeCDF(blacklines)andinowCDF(graylines).C)AMR.D)ZCDF.E)DataCMD.F)ModelCMD.G)Residuals.H)Signicance. 143

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SameasFigure 4-5 butfortheSandageinowmodel. 144

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SameasFigure 4-5 butforthedoubleexponentialinowmodel. 145

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SameasFigure 4-5 butforthetruncatedinowmodel. 146

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SameasFigure 4-5 butforthefreeinowmodel. 147

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ClosedboxmodelusingtheTeramotracks.A)SFH.B)AgeCDF.C)AMR.D)ZCDF.E)DataCMD.F)ModelCMD.G)Residuals.H)Signicance. 148

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ExponentialinowmodelusingtheTeramotracks.A)SFH(blacklines)andIFH(graylinesanddividedby10).B)AgeCDF(blacklines)andinowCDF(graylines).C)AMR.D)ZCDF.E)DataCMD.F)ModelCMD.G)Residuals.H)Signicance. 149

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SameasFigure 4-11 butfortheSandageinowmodel. 150

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SameasFigure 4-11 butforthedoubleexponentialinowmodel. 151

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SameasFigure 4-11 butforthetruncatedinowmodel. 152

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SameasFigure 4-11 butforthefreeinowmodel. 153

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FurtherdetailsoftheclosedboxmodelusingthePadovatracks.A)Evolutionofgas(black)andtotal(gray)mass.B)[/Fe]vs.[Fe/H]relation.C)AMR.D)MDF. 154

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SameasFigure 4-16 butfortheexponentialinowmodel. 155

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SameasFigure 4-16 butfortheSandageinowmodel. 156

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SameasFigure 4-16 butforthedoubleexponentialinowmodel. 157

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SameasFigure 4-16 butforthetruncatedinowmodel. 158

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SameasFigure 4-16 butforthefreeinowmodel. 159

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FurtherdetailsofclosedboxmodelusingtheTeramotracks.A)Evolutionofgas(black)andtotal(gray)mass,B)[/Fe]vs.[Fe/H]relation,C)AMR,andD)MDF. 160

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SameasFigure 4-22 butfortheexponentialinowmodel. 161

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SameasFigure 4-22 butfortheSandageinowmodel. 162

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SameasFigure 4-22 butforthedoubleexponentialinowmodel. 163

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SameasFigure 4-22 butforthetruncatedinowmodel. 164

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SameasFigure 4-22 butforthefreeinowmodel. 165

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OxygenabundancesinM33.Inallthreepanels,thelledandopenstarsarethePadovaandTeramofreeinowmodels,respectively.A)HIIregions.B)AandBsupergiantstars.C)PNe.Seetextfordetails. 166

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ComparingchemicalmodelsforM33,theSV,LMC,andSMC.Theblackandmagentalinesarethefreeinowsolutionswhilethelledpointsarethemeanvaluesineachagebin. 167

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ComparingchemicalmodelsforM33toobservationalestimatesofindividualstarsinvariousLGsystems.ThePadovaandTeramofreeinowmodelsareshownasblackandmagentalines,respectively.GreensymbolsandlinecorrespondtotheGalactichalo,bluesymbolstoGalacticdSphsatellites,cyansymbolstotheLMC,yellowstarstodIrrs,andredsymbolstoSgr.Theerrorbarsinthelowerleftcornerrepresenttypicalrandommeasurementuncertainties.Seetextfordetails. 168

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Sethetal. 2005 ).WeareunabletosaywhetherthisbehaviorisduetotheorbitaldiusionofstarsastheyageortointrinsicvariationsinSFHwithradius.WehavealsoconductedadetailedanalysisoftheSFHoftheseM33eldsbyapplyingthesytheticCMDttingmethod.Togainabetterunderstandingofthesystematicerrorswehaveconductedtheanalysiswithtwodierentsetsofstellartracks,PadovaandTeramo,somethingwhichhasrarelybeendoneintheliteraturebefore.Theprecisedetailsoftheresultsdependonwhichtracksareusedbutwecanmakeseveralconclusionsthatarefairlyrobustdespitethedierences.AllowingageandmetallicitytovaryasfreeparametersandassumingSFbegan14Gyrago,wendthat,inA1,themeanSFR80800Myragowas30%ashighasthelifetime-averagedSFR,inA2itwas10%ashigh,andinA35%ashigh.Thefractionofstarsformedby4.5Gyragoincreasesfrom65%inA1to80%inA3.The 169

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Lacey&Ostriker 1985 ; Lin&Pringle 1987 ; Portinari&Chiosi 2000 ).GasowingintothesystemfromoutsidethediskcouldoriginateinHIcloudssimilartothoseobservedaroundtheGalaxy,M31,andM33( Wakkeretal. 1999 ; Richteretal. 2001 ; Westmeieretal. 2007 ).Wealsoallowforgasoutowatarateproportionaltothestarformationrate.Comparedtothecommonmethodofallowingageandmetallicitytobefreeparameters,thisscenarioyieldsamorephysicallyself-consistentSFHwithfewer 170

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1 ,weoutlinedsomerecentstudieswhichpresentedresultsofnumericalgalaxyformationsimulations.Mostofthesestudieshavefocusedonmassiveearly-typespiralgalaxies.ThesesimulatedgalaxieshavemoreprominentspheroidsthanM33,andintheCDMframeworkthisisusuallyinterpretedtomeantheyhadmoreactivemerger/accretionhistoriesandtheiraccretedsatelliteswereonaveragemoremassive( Zentner&Bullock 2003 ).Forthesereasons,comparingourM33resultsdirectlytothesimulationsrequiressomecare,butisstillworthwhilebecausedisksareexpectedtoformlargelyfromthesmoothaccretionofcooledgas,regardlessoftheirmass.WehavealreadypresentedevidencethatM33'sdiskdominatesoveritsspheroidineldA1,sowewillimplicitlyfocusonthateldinwhatfollows.Thegalaxypresentedby A03 hasavirializeddarkhalomassof1012M,abaryonicmassof1011M,andaspheroid-to-diskmassratioof2.IfM33hasnothickdisk,thenitismostappropriatetocompareourresultthatM33'soutskirtsare6Gyr 171

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A03 'ssimulatedgalaxy,whoseoutskirtsare3Gyrold.ThisisinterestingbecausenumericalsimulationsofstructureformationpredictthatlessmassiveDMhalosexperienceanearlierpeak(i.e.,atgreaterlookbacktime)inthemassaccretionrate( Wechsleretal. 2002 ; vandenBosch 2002 ).Therefore,wewouldnaivelyexpectM33'shalotohaveexperiencedanearlierpeakrelativetotheGalaxy,andconsequentlytohavealargerpresent-daymeanstellarage.However,thetheoreticalmassaccretionhistoryappliesonlytotheDMratherthantothebaryonsandonlytotheentirehaloratherthantoanysmallregionofthedisklikewhatwehaveobservedinM33.Thenumericalsimulationsalsopredictasignicantscatterinthemassaccretionrateamonghalosofsimilarpresent-daymass.Thiscouldexplainwhythetwodiskgalaxiesof SL03 havemassesandmorphologiessimilartothoseof A03 ,butthemeanstellaragesintheoutskirtsare8and6.5Gyr.Indeed, A03 reportthatthegasaccretionrate(ontothecenteroftheDMhalo)overthelast8Gyrisapproximatelyconstantwhereasoverthesametimespan SL03 reportanexponentiallydecliningrate.However,itisalsolikelythatdierencesinthetreatmentofgasphysicscontributetothedierentresultsof A03 and SL03 .Thispointishighlightedbytheresultsof Okamotoetal. ( 2005 ),whofoundthatgivenidenticalinitialconditions,earlyandlate-typediskgalaxiescouldariseinthesameDMhalofromdierencesinthemodeofstarformationandstrengthoffeedback.Perhapsmoreimportantly,theeectsoffeedbackfromsupernovaeandstellarwindshavebeenshownintheoreticalsimulationstoresultinatop-downprogressionofSFingalaxieswhichoccurssimultaneouslywiththebottom-upprocessofDMstructureformation(e.g., Governatoetal. 2007 ).Thismeansthatlessmassivegalaxiesshouldhaveonaverageyoungerstellarpopulations,inqualitativeagreementwiththe\downsizing"observedinsurveysoflowandhighredshiftgalaxies(e.g., Cowieetal. 1996 ; Heavensetal. 2004 ; Baueretal. 2005 ; Juneauetal. 2005 ; CidFernandesetal. 2007 ; Perez-Gonzalezetal. 2007 ).Hence,ontheoreticalandempiricalgrounds,themeanstellarageofM33shouldactuallybesmallerthantheGalaxy.Whetherthisappliesat 172

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Heavensetal. 2004 ; CidFernandesetal. 2007 ).Usingradiallyresolvedintegratedspectra, MacArthuretal. ( 2004 )foundthatthemeanagemeasuredat1near-infraredscalelengthcorrelateswithgalaxymass,butinM33thisdistancecorrespondstoRdp60,whichissignicantlyclosertothenucleusthanourelds. Dalcanton&Bernstein ( 2002 )uncoveredevidenceforubiquitousthickdisksinbulgelessdiskgalaxies.IfM33doeshaveathickdisk,thenweshouldcompareourresultstothetotaldiskof A03 becausewecouldbeseeingasuperpositionofM33'sthinandthickdisksalongthelineofsight. A03 donotreporttheageoftheirgalaxy'stotaldisk,butitmustbebetween3and9Gyrintheoutskirtssincethesearethemeanstellaragesinthethindiskaloneandinallcomponents(includingthespheroid),respectively.OurSFHsolutionsdonothaveenoughresolutiontodisentanglethetwocomponentsinM33iftheyexist,sothedierencebetweenourresultandthatof A03 couldarisefromadierentthin-to-thickdiskmassratioinadditiontoallthepossibilitiesalreadydiscussedabove.Oneexceptiontothetrendofsimulatingmassiveearly-typediskgalaxiesistheworkof Robertsonetal. ( 2004 ).TheseauthorsemployedadierenttreatmentofSFandfeedbackfrompreviousstudies,onewhichincludedamulti-phaseISM.Theypublishedtherstexampleofabulgelessgalaxyformedinacosmologicalsimulationandwhichalsoshowedanexponentialsurfacebrightnessprole.Theirdiskgalaxyhadavirializedmassof1011Mandabaryonicmassof1010M.TheirgalaxywassignicantlyolderandmoremetalrichthanM33,withameanstellarageincreasingfrom7:5Gyrinthecenterto10Gyrintheoutskirtswhilethemeanstellarmetallicitydecreasedfrom0:1to0:1.Thisdiscussionhighlightsthefactthatdetailsofthemassaccretionhistoryandgasphysics,particularlythemodeandstrengthofSFandstellarfeedbackandthestructureoftheISM,areimportantfactorsaectingthepresent-daypropertiesofdisk 173

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4 .ThemostsignicantimprovementwillberelaxingtheIRAandDPAtoaccountmoreaccuratelyforthedelayedinjectionofcertainelements,likeC,N,andFe,andthedependenceofstellaryieldsonmetallicity.Thiswouldrequiresignicantlymorecomputingtime,butcouldbefeasiblewiththeparallelizedversionofPIKAIA.Itwouldalsobeinterestingtoallowthestarformationeciencytovarywithtimeasmightbeexpectedifthephysicalpropertiesofthestarformingregionschangewithtime.Inprinciple,anytimedependentparameterofthechemicalevolutionmodelcanbesolvedforinapiecewisefashionaswedidfortheIFHinthefreeinowsolutions,butcaremustbetakentoensurewellconstrainedsolutions.WealsointendtoexploresmallerageandmetallicitybinsforthesyntheticCMDsanddierentrecipesforcalculatingtheCMDamplitudes.Itmightbepossibletoaccountforinowandoutowofstars,aswell.Asdiscussedin 4.2 ,theSFRcouldbemorecloselytiedtothemoleculargasthanthetotalgas,soaprescriptionforcalculatingthemoleculargasfractionateachtimestepmightprovideamoreaccuratemodel.OtherobservationalconstraintsthatwouldbeusefultohaveinthefuturewouldbespectroscopicabundancesofM33'sRGBstarstobecomparedwiththeresultsofourchemicalmodels.M33'sdistancecurrentlyplacesitbeyondthelimitforhigh-resolutionspectroscopywith8-10mclasstelescopesbutseveralgroupsarecurrentlyobtaininglow-resolutionspectroscopyoftheCaIItripletinthenear-infrared.Inthefuture,wecouldtsuchobservationalconstraintssimultaneouslywiththeCMD.Afundamentalquestionwouldthenbe,howdoesoneweightthedierentdatapointstobettedinrelationtotheCMD?Overthepastdecade,muchworkhasfocusedonstudyingtheevolutionofthesolarneighborhood.Onecommonstrategyhasusedthechemicalevolutionequationstoreproduceobservationalconstraints,likethegasfraction,G-dwarfmetallicitydistribution,andchemicalabundances(e.g. Portinarietal. 1998 ; Chiappinietal. 2001 ).Another 175

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Bertelli&Nasi 2001 ; Cignonietal. 2006 ).Wewillunifythesetwoapproachesintoasinglecomprehensivemodelbyapplyingthechemophotometricmethod,whichcanconstraintheinowhistoryratherthanassumeaparticularform,likeanexponential,asisoftendone.ThechemophotometricmethodwillbeparticularlyusefulappliedtoM31anditssystemofsatellites,whichprovideanothertestinggroundforthehierarchicalgalaxyformationmodels.ThesegalaxiesaretoofarawaytoobtainhighresolutionspectroscopicelementalabundancesofRGBstarswiththecurrentgenerationoftelescopes.Withthechemophotometricmethoditispossibletoextractthesamechemicalabundanceinformationfrombroad-bandphotometryreachingseveralmagnitudesbelowtheRC.WewillalsobeabletocomparetheinferredIFHsofthesesystemstothemassaccretionhistoriespredictedbynumericalcosmologicalsimulations.Awidearealcoverageofthesesystemswouldbenecessarytofullysampletheirhalos. 176

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A-1 { A-13 wheretheguretitlestellthetruevalueofthevariedparameter.\Optimal"testshavetheparametersheldattheirtruevalues.AlltestpopulationsweregeneratedwiththePadovatracksexceptforthosetitled\Teramo"whichweregeneratedwiththeTeramotracks.ThePadovasyntheticCMDswereusedtoteverytestpopulation.ThepanelsintheseguresarethesameasinFigure 3-1 butwealsoshowthetrueSFH,ageCDF,AMR,andZCDFasdottedlines.Theverticaldottedlinesrepresentthetruemeanageandmetallicityofallstarseverformed.Lastly,Table A-1 liststhetquality,distance,andextinctionforeachtest.Ingeneral,theagreementbetweentherecoveredSFH,distance,andextinctionandtheirtruevaluesisgood.Theerrorbarsarerealisticindicatorsofthetypicaldeviations.Evenwhenthetruebinaryfractionisaslowas0.1orashighas0.8thesolutionisquiteaccurate.Whenx=2:0asmallerfractionofmassineachgenerationislockedupinlow-massstarssothetotalmassformedisunderestimated.Ontheotherhand,whenx=3:4,alargerfractionofmassislockedupinlow-massstarssothetotalmassisoverestimated.Despitethesenormalizationdierences,theageCDF,AMR,andZCDFarerecoveredaccuratelyandtherearenolargeresidualsbetweenthemodelanddataCMDs.Therefore,themethodisstableagainstreasonableerrorsinthebinaryfractionandIMFgiventhedepthofourphotometry.Duetotherelativelylargeagebinsemployedinthepresentanalysis,thepeakintherecoveredSFHcanbesignicantlydierentfromthepeakinthetrueSFH.Forexample,eveninthebest-casescenariowhereallinputparametersarecorrect,Test8showsthatonecouldmistakenlyconcludeapeakintheSFRatages4:58:0Gyrwheninfactthepeakisat910Gyr.Similarly,thelargeagebinslimittheconclusionsthatcanbemaderegardingthe\burstiness"oftheSFH.Anyburstofshorterdurationthanthecorrespondingagebinwillbedistributedthroughouttheentirebin.EvenintheoptimalcasesadjacentbinscanhavethesameSFRormetallicityleadingonetothinkthatthesequantitiesareconstantwhentheyaretrulychanging.Therefore,cautionisrequiredwheninterpretingbin-to-binvariationsandmoreweightmustbegiventothenetchangeoverseveralbins.However,theageCDFisrecoveredquiteaccuratelyandisrelativelyinsensitivetoerrorsinforx.Hence,conclusionsbasedontheageCDFareingeneralmorerobustthanthosebasedonthedierentialSFH( Holtzman 2002 ).Sincetheage-sensitivesub-giantbranchforages&5GyrliesfainterthanI=27,thereisnotasmuchinformationavailabletodistinguishbetweentheoldesttwoagebins.Therefore,thesebinsaremoresusceptibletotheage-metallicitydegeneracyandtheyshouldbeconsideredwithcaution.Thetestsshowthatthelargestdeviationsoftenoccurinthesebinsbuttheyaretypicallywithintheerrorbars. 177

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Dolphinetal. 2003 )butiftherearefewstarspopulatingthelatterthenthemetallicityatages<1Gyrishardtoconstrain.Thelargestinaccuraciesinthesolutionscomefromerrorsinthestellartracks.Tests3and9showthatimperfectionsinthetrackscancausedeviationslargerthanthe1errorsalthoughnearlyallthedeviationsare<2.TheCMDregionsthataretpoorlymayonlycontainasmallrangeofagesormetallicities,thusaectingasmallportionoftherecoveredSFH.Thestrongcorrelationsbetweenadjacentage/metallicitybins,though,maycauseerrorsinonebintoleakintootherbins.Moreimportantly,therearemultipleCMDregionswiththesameagesandmetallicitiessoifoneregionistpoorlythentheotherscanstilldrivethesolutiontowardagoodt(providedtherearenoerrorsinthoseotherregions).Thestellartracksaremoreaccurateatsomeagesandmetallicitiesthanothers.Therefore,theaccuracyoftherecoveredSFHdependsonthetrueSFHitself.WeinvestigatedseveralotherCMDbinningschemesforTests3and9including0.25magsquarebinsandrectangularbinslongerinthecolordimension.WealsotriedmaskingouttheRCregionfromthetstoseeifthatwasthemainsourceoferror.Inallcasesthesolutionsweresomewhatlessaccuratethanintheoriginalbinningscheme.Thisagreeswiththendingsof Dolphin ( 2002 )thatincreasingtheCMDbinsizedecreasessensitivityandthattheRCcancontainvitalageandmetallicityinformationevenwhenitisnotperfectlymodeled.Finally,inthelasttestwehaveappliedanosetof0:05magtotheV-bandofthesimulateddatastarswith[M=H]>0:8.Suchametallicity-dependentosetcouldarisefromanimperfecttransformationtotheground-basedphotometricsystem.Thesolutionisalmostunaected.Allquantitiesarerecoveredaccurately.TheonlysystematicerroroccursintheAMRwherethemetallicitiyisunderestimatedby0:1dexfor[M=H]>0:8.Nevertheless,thisdierenceisstillwithinthe1errorsofthesolution.Thesetestsshowthatthemethodcanreliablyextractusefulinformationsuchastheageandmetallicitydistributionsofallstarseverformed.Thisholdsevenwhenthebinaryfractionandhigh-massIMFslopearereasonablydierentfromthevalueswehaveassumed.Errorsinthetracksthemselvesmakethelargestcontributiontooursystematicerrorswhichwecanquantifybycomparingtheresults(fortherealdataandtestdata)obtainedwiththePadovaandTeramotracks.Weestimateconservativesystematicuncertaintiesof15%intheageCDF,1:0Gyrinthemeanage,and0:2dexintheAMRandmeanmetallicity.Theseestimatesdonotincludevariationsinthe-elementabundancesorerrorsinthebolometriccorrections. 178

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Resultsoftestingthecanonicalmethod TestQ2 AV 179

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Test1:Optimal.Thedottedlinesshowthetruevaluesandthesolidlinesshowtherecoveredvalues.SeeAppendixAfordetails.A)SFH.B)AgeCDF.C)AMR.D)ZCDF.E)DataCMD.F)ModelCMD.G)Residuals.H)Signicance. 180

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Test2:Optimal. 181

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Test3:Teramo. 182

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Test4:f=0:8. 183

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Test5:f=0:1. 184

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Test6:x=2:0. 185

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Test7:x=3:4. 186

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Test8:Optimal. 187

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Test9:Teramo. 188

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Test10:f=0:8. 189

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Test11:f=0:1. 190

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Test12:x=2:0. 191

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Test13:x=3:4. 192

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Test14:Optimal. 193

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Test15:Optimal. 194

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Test16:-0.05Voset. 195

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4 .WetthreetestpopulationswithdierentIFHsandinputparameters,usedEquations 4{1 { 4{4 todeterminethecorrespondingSFHsandAMRs,andthenusedIAC-STARtomaketheproperCMDs.Test1haslog()=1:30andanexponentialIFHwithtimescale,=5Gyr,Test2haslog()=0:70andaSandageIFHwithtimescale,=5Gyr,andTest3wasgeneratedwithlog()=1:0andaburstyfreeinowrate.Eachtestpopulationwasgeneratedwithw=1:0,(mM)0=24:68andAV=0:18,andthesameIMF,binaryfraction,andminimumbinarymassratiothatwasusedtomakethesyntheticCMDs.Themetallicityspreadwasuniformoverawidthof0:15dex.TheSFRwasnormalizedtoproduce10;000observedstars.EachtestpopulationwasmadeandtwiththePadovasyntheticCMDsandweappliedtheclosedboxandallveinowmodelsdescribedinChapter 4 .TheresultsareshowninFigures B-1 { B-36 .ThetitleofeachgurereferstowhichIFHmodelwasappliedtothesimulatedtestdata.ThepanelsintheseguresarethesameasinFigure 4-4 andFigure 4-16 exceptthatthedottedlinesinallpanelsshowthetruevalues.WealsoshowthetrueIFH(dividedby10)andinowCDFassolidgraylines(withouterrorbars)inFigures B-1 { B-18 .Table B-1 liststhetquality,distance,andextinctionforeachtestandTable B-2 liststherecoveredvaluesforlog()andw.Ingeneral,theagreementbetweentherecoveredSFH,AMR,distance,andextinctionandthetruevaluesisgood.SimilaragreementwasfoundinChapter 3 whenageandmetallicitywerefreeparameters.Itisreassuringthattheincorporationofthechemicalevolutionequationsandthecorrespondingreductioninfreeparametershasnotdiminishedthemethod'saccuracyforrecoveringtheSFHandAMR.ManyofthesamecaveatsthatwediscussedinAppendix A applyhere,too.Inparticular,theageCDFisgenerallymoreaccuratethanthedierentialSFHbecauseitislesssensitivetoanticorrelationsbetweenbinsanderrorsinthebinaryfractionorIMF.ThelargeagebinscanwashoutSFburstsandcausesignicant(afewGyr)deviationsbetweenthetimeoftherecoveredSFRpeakanditstruetime.Bin-to-binvariationsintheSFHandAMRshouldbeconsideredwithcautionbutthenetchangeoverseveralbinsisgenerallymoreaccurate.OnedierencebetweenthetestshereandinAppendix A isthatheretherecoveredSFHandAMRatages<1Gyrdonotshowthesamelargedeviationsfromthetruevalues.SuchdeviationsinAppendix A wereduetosmallnumberstatisticsandtherelativelymetallicity-independentpositionoftheyoungMS.Thechemicalevolutionequationshelpensureagainstsuchdeviationsbyconstrainingthepossiblemetallicitiesateachage.Forexample,attheyoungestages,itisverydiculttoproduceverylowmetallicitieswithalowSFR(seeninAppendix A )becausethelargeinoweventneededtolowerthemetallicitywouldalsosignicantlyincreasetheSFRabovewhatisobserved.WithrespecttotheIFH,thesetestsshowthattheinowCDFisgenerallymoreaccuratethanthedierentialIFH.ThisisbecausethenormalizationoftheIFHcanbeosetwhiletheoverallshaperemainsthesame,asinthecaseofTest2:Sandageinow.TheleastaccuratesolutionsoccurwhentheadoptedfunctionalformoftheIFHisvery 196

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197

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Resultsoftestingthechemophotometricmethod TestQ2 AV TableB-2. Fittedstarformationandoutoweciencies Test log()hilo 198

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Test1:Closedbox.Dottedblackandsolidblacklinesshowthetrueandrecoveredvalues,respectively.SeeAppendixBfordetails.A)SFH(blacklines)andtrueIFH(graylinewithouterrorbars).B)AgeCDF.C)AMR.D)ZCDF.E)DataCMD.F)ModelCMD.G)Residuals.H)Signicance. 199

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Test1:Exponentialinow.Dottedblackandsolidblacklinesshowthetrueandrecoveredvalues,respectively.SeeAppendixBfordetails.A)SFH(blacklines),recoveredandtrueIFH(graylineswithandwithouterrorbars,respectively)dividedby10.B)AgeCDF(blacklines)andrecoveredandtrueinowCDF(graylineswithandwithouterrorbars,respectively).C)AMR.D)ZCDF.E)DataCMD.F)ModelCMD.G)Residuals.H)Signicance. 200

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Test1:Sandageinow.SamepanelsasFigure B-2 201

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Test1:Doubleexponentialinow.SamepanelsasFigure B-2 202

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Test1:Truncatedinow.SamepanelsasFigure B-2 203

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Test1:Freeinow.SamepanelsasFigure B-2 204

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Test2:Closedbox.SamepanelsasFigure B-1 205

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Test2:Exponentialinow.SamepanelsasFigure B-2 206

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Test2:Sandageinow.SamepanelsasFigure B-2 207

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Test2:Doubleexponentialinow.SamepanelsasFigure B-2 208

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Test2:Truncatedinow.SamepanelsasFigure B-2 209

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Test2:Freeinow.SamepanelsasFigure B-2 210

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Test3:Closedbox.SamepanelsasFigure B-1 211

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Test3:Exponentialinow.SamepanelsasFigure B-2 212

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Test3:Sandageinow.SamepanelsasFigure B-2 213

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Test3:Doubleexponentialinow.SamepanelsasFigure B-2 214

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Test3:Truncatedinow.SamepanelsasFigure B-2 215

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Test3:Freeinow.SamepanelsasFigure B-2 216

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[=Fe]vs:[Fe=H]relationofTest1:Closedbox.Dottedlinesshowthetruevalues.A)Evolutionofgas(black)andtotal(gray)mass.B)[/Fe]vs.[Fe/H]relation.C)AMR.D)MDF. 217

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[=Fe]vs:[Fe=H]relationofTest1:Exponentialinow.SamepanelsasFigure B-19 218

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[=Fe]vs:[Fe=H]relationofTest1:Sandageinow.SamepanelsasFigure B-19 219

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[=Fe]vs:[Fe=H]relationofTest1:Doubleexponentialinow.SamepanelsasFigure B-19 220

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[=Fe]vs:[Fe=H]relationofTest1:Truncatedinow.SamepanelsasFigure B-19 221

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[=Fe]vs:[Fe=H]relationofTest1:Freeinow.SamepanelsasFigure B-19 222

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[=Fe]vs:[Fe=H]relationofTest2:Closedbox.SamepanelsasFigure B-19 223

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[=Fe]vs:[Fe=H]relationofTest2:Exponentialinow.SamepanelsasFigure B-19 224

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[=Fe]vs:[Fe=H]relationofTest2:Sandageinow.SamepanelsasFigure B-19 225

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[=Fe]vs:[Fe=H]relationofTest2:Doubleexponentialinow.SamepanelsasFigure B-19 226

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[=Fe]vs:[Fe=H]relationofTest1:Truncatedinow.SamepanelsasFigure B-19 227

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[=Fe]vs:[Fe=H]relationofTest1:Freeinow.SamepanelsasFigure B-19 228

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[=Fe]vs:[Fe=H]relationofTest3:Closedbox.SamepanelsasFigure B-19 229

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[=Fe]vs:[Fe=H]relationofTest3:Exponentialinow.SamepanelsasFigure B-19 230

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[=Fe]vs:[Fe=H]relationofTest3:Sandageinow.SamepanelsasFigure B-19 231

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[=Fe]vs:[Fe=H]relationofTest3:Doubleexponentialinow.SamepanelsasFigure B-19 232

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[=Fe]vs:[Fe=H]relationofTest3:Truncatedinow.SamepanelsasFigure B-19 233

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[=Fe]vs:[Fe=H]relationofTest3:Freeinow.SamepanelsasFigure B-19 234

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SeveraleventsthroughoutMichaelBarker'schildhoodledhimtoastronomy.Onemorningwhenhewas5yearsold,hisparentswokehimupbeforesunriseanddraggedhimtosomeremotelocationwheretheyspiedHalley'scometasitapproachedperihelion.Severalyearslater,theyvisitedtheU.S.NavalObservatorywheretheylearnedabouttheatomicclockandlookedatMarsthroughagiantrefractortelescope.Inmiddleschool,theyattendedanopenhouseatUniversityofMaryland'steachingobservatory.Later,Michaeltookanastronomycourseinhighschool,whichwashisfavoriteduringthoseentirefouryears.Afterthat,heknewhewantedtopursueastronomy.MichaelbeganhisundergraduateeducationatUniversityofMarylandin1997.Beginninghissophomoreyear,heworkedparttimefortheSmallBodiesNodeofthePlanetaryDatasystem.Thisjobinvolvedarchivingspacecraftdatafrompastandpresentmissions,makingsurethisdatametPDSstandards,andmaintainingthesoftwareusedforthesetasks.Inhisjuniorandsenioryears,hewrotehisastronomyhonorsthesisoncosmologicalconstraintsfromrotationcurvesoflowsurfacebrightnessgalaxiesunderthesupervisionofDr.StacyMcGaugh.Hegraduatedin2001withaB.S.inAstronomyandPhysicswithhighhonorsinastronomy.Inthesummeraftergraduating,hewasaninternatNASAGoddardSpaceFlightCenterwhereheconductedresearchwithDr.EliDwekontheconnectionbetweenthecosmicinfraredandradiobackgrounds.Michael'sgraduatecareeratUniversityofFloridabeganinAugust2001andtwoyearslaterheearnedhisM.S.inAstronomy.UnderthetutelageofDr.AtaSarajedini,hisMaster'sThesisexaminedvariationsinstarformationhistoryandtheredgiantbranchtip.Duringhisgraduatecareer,MichaelwasabletotraveltoArizona,Mexico,Chile,andSpaingainingobservingexperienceandattendingconferences.UponcompletionofhisPh.D.program,MichaelwillstartapostdoctoralresearchpositionatUniversityofEdinburgh,Scotland. 248