Gravitational Lensing : Models and Astrophysical Applications

다국어 초록 (Multilingual Abstract)

This dissertation is an investigation of gravitational lens models and detailed analyses of the Tensing properties of three astrophysically interesting multiply-imaged quasi-stellar objects (QSOs) Q2237+0305, Q0957+561, and H1413+1143. A general-form power-law elliptical mass distribution is considered as a model for a Tensing object, and a Fourier series expansion technique is applied to obtain semi-analytical expressions for the deflection and magnification due to the general power-law mass model. Investigating more sophisticated lens models permitted by most recent and comprehensive sets of data, the following astrophysical/cosmological results are derived. For Q2237+0305, Tensing properties of the elliptical mass model with varying radial index are calculated, and similarities and quantitative differences between the elliptical lens model and a pseudo-elliptical lens model (a power-law sphere plus shear) are highlighted. For Q0957+561, the elliptical mass model and a power-law sphere are used to model the Tensing galaxy and cluster respectively, as motivated by recent Hubble Space Telescope (HST) imaging of the galaxy and weak Tensing observations of the cluster. The lens model for Q0957+561 gives a best-fit to present observational constraints and yields a Hubble constant of H_(o) = 57^(+19)_(-16) (95% confidence) km s^(-1) Mpc^(-1). For H1413+1143, recent data from HST WFPC1,2, NICMOS, and FOS are used to explore possible lens models. Analyses of two-component lens models (namely, two-galaxy and galaxy+cluster) indicate that at least the continuum source region is microlensed. The broad emission line region could also be microlensed. However, information from present observations are not sufficient to draw any conclusions on the leasing nature of the broad emission line region or its size scale.

목차 (Table of Contents)

• Abstract = iii
• Contents = viii
• Chapter1 Introduction = 1
• 1.1 Introduction to the Problem = 1
• 1.2 Historical Background = 3
• 1.3 Gravitational Lensing: Basic Theory and Observational Status = 6
• 1.4 Astrophysical Applications of Gravitational Lensing = 11
• 1.5 Summary of Main Chapters = 15
• 1.5.1 Gravitational Lensing: A Fast and Exact Series Approach (Chapter 2) = 16
• 1.5.2 A Model Grid for Q2237+0305 and Relation to Observational Constraints (Chapter 3) = 16
• 1.5.3 A Determination of the Hubble Constant Using Q0957+561 (Chapter 4) = 17
• 1.5.4 New Lens Models of the Cloverleaf QSO H1413+1143 (Chapter 5) = 18
• Chapter2 Gravitational Lensing: A Fast and Exact Series Approach = 19
• 2.1 Introduction = 19
• 2.2 Mathematical Formulation = 22
• 2.2.1 Definition of the Deflection Potential Series = 22
• 2.2.2 The Projected Surface Mass Density = 24
• 2.2.3 The Deflection Angle and Magnification Factor = 26
• 2.3 Critical Curves and Caustics of Power-Law Lenses = 31
• 2.4 Discussion and Conclusion = 35
• Chapter3 A Model Grid for Q2237+0305 and Relation to Observational Constraints = 45
• 3.1 Introduction = 45
• 3.2 Lens Model and Method = 49
• 3.3 Results = 51
• 3.4 Discussion and Summary = 58
• Chapter4 A Determination of the Hubble Constant Using Q0957+561 = 65
• 4.1 Introduction = 65
• 4.2 Summary of Current Observational Constraints = 69
• 4.3 An Observationally Motivated Model of the Lens = 74
• 4.4 Results of Fitting the Model to the Observational Constraints: Bounds on the Hubble Constant = 77
• 4.5 An Updated Result with a New Blob Magnification Ratio = 86
• 4.6 Discussion = 89
• Chapter5 New Lens Models of the Cloverleaf QSO H1413+1143 = 97
• 5.1 Introduction = 97
• 5.2 Review of the Power-Law Elliptical Mass Model = 99
• 5.3 Gravitational Lens Models of the Cloverleaf = 100
• 5.3.1 Single Galaxy Lens Models: Isolated = 104
• 5.3.2 Single Galaxy Lens Models: With External Tidal Perturbation = 106
• 5.3.3 Two-Galaxy Lens Models = 107
• 5.3.4 Galaxy+Cluster Lens Models: A Model-Dependent Bound on the Mass of the Lensing Galaxy = 114
• 5.3.5 BEL/Continuum Ratio and a Size-Scale Constraint on the BEL Region = 118
• 5.4 Discussion = 121
• Chapter6 Summary and Comments on Future Work = 126
• Bibliography = 131