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Gravitational Microlensing in the Milky Way with the Hubble Space Telescope and OGLE-III

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Gravitational Microlensing in the Milky Way with the Hubble Space Telescope and OGLE-III Gravitational Microlensing in the Milky Way with the Hubble Space Telescope and OGLE-III A thesis submitted to The University of Manchester for the degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences 2007 Szymon Kozłowski School of Physics and Astronomy 2 GRAVITATIONAL MICROLENSING IN THE MILKY WAY Contents List of Figures 7 List of Tables 9 Abstract.................................... 11 Declaration .................................. 13 CopyrightStatement ............................. 14 Dedication................................... 15 Acknowledgements .............................. 16 TheAuthor .................................. 18 SupportingPublications. 19 1 Introduction 23 1.1 TheGalaxy–MilkyWay ........................ 23 1.1.1 The Galactic bulge / bar .................... 24 1.1.2 DarkmatterintheGalactichalo . 25 1.1.3 TowardabetterunderstandingoftheGalaxy . 26 1.2 Microlensingsurveys . 27 1.2.1 TheOGLE,MACHO,EROSandMOAcollaborations . 27 1.2.2 Follow-upsurveys .. .. .. .. .. .. .. 29 1.2.3 Microlensing surveys toward the Andromeda Galaxy (M31) . 29 1.3 Gravitationalmicrolensing . 30 1.3.1 Basics.............................. 30 SZYMON KOZŁOWSKI 3 CONTENTS 1.3.2 Theopticaldepth........................ 36 1.4 DataAnalysisTechniques. 36 1.4.1 Profilesofstars ......................... 36 1.4.2 Aperturephotometry . 38 1.4.3 Signal-to-NoiseRatio . 39 1.4.4 Profilephotometry(andastrometry) . 40 1.4.5 FittingPSFs(models)tothedata. 40 1.4.6 DifferenceImageAnalysis . 42 2 Resolving blending in the microlensing surveys with the HST 47 2.1 Abstract................................. 47 2.2 Introduction............................... 48 2.3 HST andOGLEimagesanddatareduction. 49 2.3.1 Searching for OGLE microlensing events in the HST archive . 49 2.3.2 HST andOGLEdata ...................... 51 2.4 Analysis................................. 53 2.5 Microlensing parameters from photometry and astrometry ...... 59 2.6 Discussion................................ 64 2.7 Conclusions............................... 68 3 HST proper motions in the Galactic centre 69 3.1 Abstract................................. 69 3.2 Introduction............................... 70 3.3 HST imagesanddatareduction . 71 3.3.1 Imagereductions ........................ 74 3.3.2 ObjectcataloguesandPSFfitting . 75 3.4 Estimating transverse motions of the Galactic bulge stars ....... 76 3.4.1 Relativepropermotionsandtheirdispersions . ... 76 3.4.2 Astrometricerrors . 77 3.5 Results.................................. 80 4 GRAVITATIONAL MICROLENSING IN THE MILKY WAY CONTENTS 3.5.1 Propermotiondispersions . 81 3.5.2 Anisotropyandcovariance . 82 3.5.3 Comparisonswithpreviouswork . 84 3.6 Discussion................................ 87 3.6.1 Distanceandpopulationtrends. 87 3.6.2 StellarvelocityellipsoidoftheGalacticbar . .... 89 3.7 Summaryandconclusions . 90 4 Direct detection of a microlens 93 4.1 Abstract................................. 93 4.2 Introduction............................... 94 4.3 MicrolensingeventMACHO-95-BLG-37 . 95 4.3.1 HST astrometryandphotometry . 96 4.3.2 Microlensinglightcurverevisited . 98 4.4 Microlensinglightcurvemodels . 101 4.4.1 Colours ............................. 102 4.4.2 Parallaxconstraints. 102 4.5 Resolution of the microlensing system into lens and source ...... 103 4.5.1 Identifyingthelens . 105 4.5.2 Proper motion, Einstein ring radius and relative parallax . 106 4.6 Microlensingscenariosandthelensmass . 107 4.6.1 Bluelensscenario . 108 4.6.2 Redlensscenario. 109 4.6.3 Thelensmassestimates . 109 4.7 Discussion................................ 112 5 The Optical Depth in OGLE–III 115 5.1 Abstract................................. 115 5.2 Introduction............................... 116 5.3 Data................................... 117 SZYMON KOZŁOWSKI 5 CONTENTS 5.4 Software................................. 118 5.4.1 Templates............................ 119 5.4.2 Pipeline............................. 120 5.4.3 SimulationoftheOGLE–IIIimages . 122 5.4.4 Calibrations........................... 124 5.4.5 Searchengine.......................... 125 5.4.6 Thecatalogueoflightcurves. 127 5.5 Calculationoftheopticaldepth. 128 5.5.1 Thenumberofmonitoredstars. 128 5.5.2 Thetimescaleofanevent. 131 5.5.3 Detection efficiency ...................... 131 5.5.4 Themicrolensingeventsfortheopticaldepth . 133 5.5.5 Results ............................. 134 5.6 Discussionandfuturework. 135 6 Summary and future work 147 6.1 Summaryoftheworkpresentedinthisthesis . 147 6.2 Futurework............................... 149 References 152 6 GRAVITATIONAL MICROLENSING IN THE MILKY WAY List of Figures 1.1 Thesideviewofagravitationallens . 31 1.2 Agravitationallensasseenonthesky . 33 1.3 Standardmagnificationcurves . 34 1.4 Trajectories of a lensed source for given impact parameters...... 35 1.5 Difference between the SoDoPhot andDIAphotometry. 44 2.1 Comparison between the OGLE and HST images ........... 56 2.2 Comparison between the OGLE and HST images ........... 57 2.3 HST viewontheanalysedblends. 58 2.4 Lightcurvesfortheanalysedevents . 65 3.1 Spatialdependenceofpropermotiondispersions . ..... 81 3.2 Spatial dependence of anisotropy ratio and covariance term...... 82 3.3 Comparison of the HST andOGLE–IIdata. 84 3.4 Cut-off HST imagesfortheoutliers. 85 3.5 Colour-magnitude diagram and relative proper motions . ....... 87 3.6 Histogramsofrelativepropermotions . .. 88 3.7 Average relative proper motions and dispersions of stars in Baade’s Window................................. 88 4.1 HST imagesoftheMACHO-95-BLG-37eventlocation . 96 4.2 Light curveof the MACHO-95-BLG-37 eventfrom the DIA . .. 98 SZYMON KOZŁOWSKI 7 LIST OF FIGURES 4.3 Colour-magnitude diagram of stars around the MACHO-95-BLG-37 eventlocation .............................. 107 4.4 Photometricsolutionsfor the lens distance and mass . ...... 111 5.1 Asingleframefromthesimulations. 123 5.2 TheDSSimageoftheBLG206field . 129 5.3 Luminosityfunctions for Baade’s Windowand BLG206 . 130 5.4 Thedetection efficiencycurves .. .. .. .. .. .. 132 5.5 Lightcurvesofmicrolensingevents . 140 5.6 Lightcurvesofmicrolensingevents . 141 5.7 Lightcurvesofmicrolensingevents . 142 5.8 Lightcurvesofmicrolensingevents . 143 5.9 Lightcurvesofthetwobinarymicrolensingevents . ..... 143 5.10 A sample of four OGLE–III microlensing events which did not pass thesearchcriterion. 144 5.11 Lightcurves of artificial microlensingevents . ....... 145 5.12 Sample light curves of variable stars from the database......... 146 8 GRAVITATIONAL MICROLENSING IN THE MILKY WAY List of Tables 2.1 Logofthe HST archiveimages.. .. .. .. .. .. .. 51 2.2 InformationabouttheOGLE–IIIevents . 55 2.3 PhotometryoftheOGLE–IIIevents . 60 2.4 Photometry of the OGLE–III events (continuation of Table2.3). .. 61 2.5 Fit parameters for the seven microlensing events . ...... 66 3.1 The HST propermotionmini-survey:data . 72 3.2 The HST proper motion mini-survey: data (continuation of Table 3.1) 73 3.3 Resultsofthepropermotionmini-survey . .. 79 3.4 Results of the proper motion mini-survey (continuation ofTable3.3) . 80 3.5 Comparison of the proper motion dispersions from Kuijken and Rich (2002)andourreanalysisofthesamedata . 86 4.1 HST astrometry ............................. 99 4.2 HST photometry............................. 99 4.3 Microlensinglightcurvemodel. 101 4.4 HST kinematicsofstarsAandB . 108 5.1 All measured optical depths toward the Galactic bulge . ....... 117 5.2 Calibrationparametersofthetemplateimages . ..... 122 5.3 Microlensing events used for the optical depth calculation. .. .. 138 5.4 Microlensing events used for the optical depth calculation (continua- tionofTable5.3) ............................ 139 SZYMON KOZŁOWSKI 9 LIST OF TABLES 10 GRAVITATIONAL MICROLENSING IN THE MILKY WAY The University of Manchester ABSTRACT OF THESIS submitted by Szymon Kozłowski for the Degree of Doctor of Philosophy and entitled Gravitational Microlensing in the Milky Way with the Hubble Space Telescope and OGLE-III. August 2007 Gravitational lensing is a powerful tool for astronomers to study the Universe. It occurs on both cosmological and local (Galactic) scales. This thesis focuses on observational studies of Galactic microlensing, which, as I will show, have significant impact on studies of the Galactic structure and the mass function of lenses in the Milky Way. The first chapter provides a basic treatment of gravitational lensing and of the data analysis procedures used throughout this thesis. The next chapter is devoted to the investigation of blending issues. The ground-based microlensed stars (blends) are re- solved into separate components using the Hubble Space Telescope (HST). With Dif- ference Image Analysis, seven microlensed stars are recognised. Blending fractions are calculated from the HST images and compared with the fractions derived from light curve fitting. Chapters 3 and 4 present my studies of HST two-epoch images of 37 Galactic bulge fields; this work has been published in Monthly Notices of the Royal Astronomical Society and the Astrophysical Journal. The superb resolution of the HST allows the measurement of stellar positions with milli-arcsecond accuracy. Using the two-epoch images, I build a catalogue of stellar proper motions for 26,000 stars. For each field I calculate dispersions from the rel- ∼ ative proper motions. Small gradients in these proper motion dispersions and in the anisotropy are clearly detected. For the first time, a covariance in the longitudinal and latitudinal motions is discovered. These results will provide strong
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