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Introduction to gravitational lensing : with Python examples / / Massimo Meneghetti
Introduction to gravitational lensing : with Python examples / / Massimo Meneghetti
Autore Meneghetti Massimo <1974->
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (417 pages)
Disciplina 523.112
Collana Lecture Notes in Physics
Soggetto topico Gravitational lenses
Astrophysics
Galaxies
ISBN 3-030-73582-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Acknowledgments -- Contents -- About the Author -- Part I Generalities -- 1 A Brief History of Gravitational Lensing -- 1.1 Corpuscular Theory of Light -- 1.2 The Einstein Revolution -- 1.3 How to Prove the Deflection of Light? -- 1.4 The Eddington Expeditions -- 1.5 Following Intuitions -- 1.6 First Observational Discoveries -- 1.7 The First Microlensing Observations -- 1.8 The Detection of Weak Lensing -- References -- 2 Light Deflection -- 2.1 Deflection of a Light Corpuscle -- 2.2 Deflection of Light According to General Relativity -- 2.2.1 Fermat Principle and Light Deflection -- Deflection in the Perturbed Minkowski's Space-Time -- Effective Refractive Index -- Deflection Angle -- Born Approximation -- 2.2.2 Deflection of Light in the Strong Field Limit -- 2.3 Deflection by an Ensemble of Point Masses -- 2.4 Deflection by an Extended Mass Distribution -- 2.5 Python Applications -- 2.5.1 Light Deflection by a Black-Hole -- 2.5.2 Light Deflection by an Extended Mass Distribution -- References -- 3 The General Lens -- 3.1 Lens Equation -- 3.2 Lensing Potential -- 3.3 First Order Lens Mapping -- 3.3.1 First Order Lensing of a Circular Source -- 3.4 Magnification -- 3.5 Lensing to the Second Order -- 3.5.1 Complex Notation -- 3.6 Time Delay Surface -- 3.6.1 Gravitational and Geometrical Time Delays -- 3.6.2 Multiple Images and Magnification -- 3.6.3 Examples -- Axially Symmetric Lenses: One-Dimensional Case -- Axially Symmetric Lenses: Two-Dimensional Case -- Elliptical Potentials -- 3.6.4 General Considerations -- 3.7 Python Applications -- 3.7.1 Implementing a Ray-Tracing Algorithm -- 3.7.2 Derivation of the Lensing Potential -- 3.7.3 Lensing Maps -- 3.7.4 Critical Lines and Caustics -- 3.7.5 Shear and Flexion -- 3.7.6 Full Ray-Tracing Simulation and Time Delay Surface -- 3.7.7 Lensing by Numerically Simulated Mass Distributions.
References -- Part II Applications -- 4 Microlenses -- 4.1 The Point-Mass Lens -- 4.1.1 Deflection Angle and Lensing Potential -- 4.1.2 Lens Equation -- 4.1.3 Multiple Images -- 4.1.4 Critical Lines, Caustics, and Magnification -- 4.1.5 Source Magnification -- 4.1.6 Microlensing Cross Section -- 4.2 Microlensing Light-Curve -- 4.2.1 Light-Curve Fitting -- 4.3 Microlensing Parallax -- 4.3.1 Orbital Parallax -- 4.3.2 Satellite Parallax -- 4.3.3 Terrestrial Parallax -- 4.4 Astrometric Microlensing -- 4.5 Photometric Microlensing: Optical Depth and Event Rates -- 4.5.1 Optical Depth -- Optical Depth of an Exponential Disk -- 4.5.2 Event Rate -- 4.6 Results from MACHO Searches -- 4.7 Multiple Point Masses -- 4.7.1 Generalities -- Deflection Angle -- Lens Equation -- Critical Lines -- 4.7.2 Binary Lenses -- Lens Equation -- Critical Lines and Caustics -- Multiple Images -- Image Magnifications and Light-Curves -- 4.8 Planetary Microlensing -- 4.8.1 Perturbations of the Central Caustic -- 4.8.2 Perturbations of the Planetary Caustic -- 4.8.3 Perturbations of the Resonant Caustic -- 4.8.4 Perturbations of the Inner and Outer Images -- 4.8.5 Analysis of the Light-Curve in a Planetary Caustic Crossing Event -- 4.8.6 Planetary Microlensing Detections -- 4.9 Python Applications -- 4.9.1 Standard Microlensing Light-Curve -- 4.9.2 Fitting the Standard Light-Curve -- 4.9.3 Distribution of Microlensing Event Timescale -- 4.9.4 Astrometric Microlensing Effect -- 4.9.5 Critical Lines and Caustics of a Binary Lens -- 4.9.6 Solving the Lens Equation of the Binary Lens -- 4.9.7 Light-Curve in a Binary Microlensing Event -- References -- 5 Extended Lenses -- 5.1 Circular, Axially Symmetric Lenses -- Critical Lines and Caustics -- Einstein Radius -- Tangential and Radial Magnification of the Images -- 5.2 Power-Law Lens -- 5.2.1 Lenses with 1< -- n< -- 2.
Critical Lines and Caustics -- Multiple Images -- Image Magnification -- 5.2.2 Lenses with n > -- 2 -- 5.2.3 Singular Isothermal Sphere -- 5.3 Softened (Non-singular) Isothermal Lenses -- 5.4 Elliptical Lenses -- 5.4.1 Singular Isothermal Ellipsoid -- Convergence -- Lensing Potential -- Deflection Angle -- Shear -- Critical Lines -- Caustic and Cut -- Multiple Images -- Distortion and Parity of the Images -- 5.4.2 Softened (Non-singular) Elliptical Models -- 5.4.3 Pseudo-Elliptical Models -- 5.5 Other Profiles -- 5.5.1 The Navarro-Frenk-White Model -- 5.5.2 The Dual Pseudo-Isothermal Mass Distribution -- 5.6 External Perturbations -- 5.7 Multiple Mass Components -- 5.8 Time Delays -- 5.9 Mass-Sheet Degeneracy -- 5.10 Multiple Lens Planes -- 5.11 Python Applications -- 5.11.1 Numerical Solution of the Lens Equation -- Multiple Images by a SIE Lens -- 5.11.2 Triangle Mapping -- 5.11.3 SIS Lens in an External Shear -- 5.11.4 Multiple Lens Planes -- References -- 6 Lensing by Galaxies and Clusters -- 6.1 Strong Lensing by Galaxies and Galaxy Clusters -- 6.1.1 Scale of the Lensing Events -- 6.1.2 Strong Lensing Cross-Section -- 6.1.3 The Quest for Strong Lensing Galaxies -- 6.1.4 Strong Lensing by Galaxy Clusters -- 6.1.5 Lens Inversion -- Parametric Reconstruction Algorithms -- Simultaneous Reconstruction of Source and Lens -- Complex Parametric Models -- Free-Form Reconstruction Algorithms -- 6.2 Weak Lensing by Galaxy Clusters -- 6.2.1 The Principle -- 6.2.2 Ellipticity Measurements -- 6.2.3 Tangential and Cross Component of the Shear -- 6.2.4 Aperture Mass Densitometry -- 6.2.5 The Kaiser and Squires Inversion Algorithm -- 6.2.6 Challenges in Shear Measurements -- Intrinsic Source Ellipticity -- Effects of the Point-Spread-Function -- 6.2.7 Redshift Dependence of the Signal -- 6.2.8 Limitations of the Methods.
6.3 Applications of Lensing by Galaxies and Galaxy Clusters -- 6.3.1 The Nature of Dark Matter -- 6.3.2 The Interplay Between Dark Matter and Baryons -- 6.3.3 Cosmic Telescopes -- 6.3.4 Cosmological Applications -- 6.4 Python Applications -- 6.4.1 Parametric Strong Lensing Mass Reconstruction -- Simulating a Lens -- Lens Modeling -- Using More Constraints -- Optimization in the Source Plane -- 6.4.2 Parametric Weak Lensing Mass Measurement -- Weak Lensing Measurements -- Fit of the Tangential Shear Profile -- 6.4.3 The Kaiser-Squires Inversion Algorithm -- References -- 7 Lensing by Large-Scale Structure -- 7.1 Light Propagation Through an In-homogeneous Universe -- 7.1.1 Deflection of Light -- 7.1.2 Effective Convergence -- 7.1.3 Limber's Equation and the Convergence Correlation Function -- 7.1.4 Effective Lensing Potential, Lensing Jacobian, Shear -- 7.2 Cosmic Shear -- 7.2.1 Shear Correlation Functions -- 7.2.2 Shear in Apertures and Aperture Mass -- 7.2.3 E- and B-modes -- 7.2.4 Cosmic Shear as a Cosmological Probe -- 7.3 Lensing of Cosmic Microwave Background -- 7.3.1 Lensing of the CMB Temperature -- 7.3.2 Lensing of the CMB Polarization -- 7.3.3 Reconstruction of the Lensing Potential -- 7.4 Python Applications -- 7.4.1 Effective Shear and Potential -- 7.4.2 Power Spectrum -- 7.4.3 Correlation Functions -- References -- Part III Appendixes -- 8 Python Mini-Tutorial -- 8.1 Installation -- 8.2 Documentation -- 8.3 Running Python -- 8.4 Your First Python Code -- 8.5 Variables -- 8.6 Strings -- 8.7 Lists -- 8.8 Tuples -- 8.9 Dictionaries -- 8.10 Blocks and Indentation -- 8.11 IF/ELIF/ELSE -- 8.12 While Loops -- 8.13 For Loops -- 8.14 Functions -- 8.15 Classes -- 8.16 Inheritance -- 8.17 Modules -- 8.18 Importing Packages -- 9 Cosmology Primer -- 9.1 The Friedmann-Lemaitre-Robertson-Walker Metric -- 9.2 Redshift -- 9.3 The Friedmann Equations.
9.4 Cosmological Parameters -- 9.5 Cosmological Distances -- 9.6 The Friedmann Models -- 9.6.1 Single Component Models -- 9.6.2 Multiple Component Models -- 9.7 Structure Formation -- 9.7.1 Linear Growth of Density Perturbations -- 9.7.2 Density Power Spectrum -- 9.7.3 Non-linear Evolution -- 9.8 Mass Function -- 9.9 Dark Energy Models -- References -- Index.
Record Nr. UNISA-996466846203316
Meneghetti Massimo <1974->  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Introduction to gravitational lensing : with Python examples / / Massimo Meneghetti
Introduction to gravitational lensing : with Python examples / / Massimo Meneghetti
Autore Meneghetti Massimo <1974->
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (417 pages)
Disciplina 523.112
Collana Lecture Notes in Physics
Soggetto topico Gravitational lenses
Astrophysics
Galaxies
ISBN 3-030-73582-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Acknowledgments -- Contents -- About the Author -- Part I Generalities -- 1 A Brief History of Gravitational Lensing -- 1.1 Corpuscular Theory of Light -- 1.2 The Einstein Revolution -- 1.3 How to Prove the Deflection of Light? -- 1.4 The Eddington Expeditions -- 1.5 Following Intuitions -- 1.6 First Observational Discoveries -- 1.7 The First Microlensing Observations -- 1.8 The Detection of Weak Lensing -- References -- 2 Light Deflection -- 2.1 Deflection of a Light Corpuscle -- 2.2 Deflection of Light According to General Relativity -- 2.2.1 Fermat Principle and Light Deflection -- Deflection in the Perturbed Minkowski's Space-Time -- Effective Refractive Index -- Deflection Angle -- Born Approximation -- 2.2.2 Deflection of Light in the Strong Field Limit -- 2.3 Deflection by an Ensemble of Point Masses -- 2.4 Deflection by an Extended Mass Distribution -- 2.5 Python Applications -- 2.5.1 Light Deflection by a Black-Hole -- 2.5.2 Light Deflection by an Extended Mass Distribution -- References -- 3 The General Lens -- 3.1 Lens Equation -- 3.2 Lensing Potential -- 3.3 First Order Lens Mapping -- 3.3.1 First Order Lensing of a Circular Source -- 3.4 Magnification -- 3.5 Lensing to the Second Order -- 3.5.1 Complex Notation -- 3.6 Time Delay Surface -- 3.6.1 Gravitational and Geometrical Time Delays -- 3.6.2 Multiple Images and Magnification -- 3.6.3 Examples -- Axially Symmetric Lenses: One-Dimensional Case -- Axially Symmetric Lenses: Two-Dimensional Case -- Elliptical Potentials -- 3.6.4 General Considerations -- 3.7 Python Applications -- 3.7.1 Implementing a Ray-Tracing Algorithm -- 3.7.2 Derivation of the Lensing Potential -- 3.7.3 Lensing Maps -- 3.7.4 Critical Lines and Caustics -- 3.7.5 Shear and Flexion -- 3.7.6 Full Ray-Tracing Simulation and Time Delay Surface -- 3.7.7 Lensing by Numerically Simulated Mass Distributions.
References -- Part II Applications -- 4 Microlenses -- 4.1 The Point-Mass Lens -- 4.1.1 Deflection Angle and Lensing Potential -- 4.1.2 Lens Equation -- 4.1.3 Multiple Images -- 4.1.4 Critical Lines, Caustics, and Magnification -- 4.1.5 Source Magnification -- 4.1.6 Microlensing Cross Section -- 4.2 Microlensing Light-Curve -- 4.2.1 Light-Curve Fitting -- 4.3 Microlensing Parallax -- 4.3.1 Orbital Parallax -- 4.3.2 Satellite Parallax -- 4.3.3 Terrestrial Parallax -- 4.4 Astrometric Microlensing -- 4.5 Photometric Microlensing: Optical Depth and Event Rates -- 4.5.1 Optical Depth -- Optical Depth of an Exponential Disk -- 4.5.2 Event Rate -- 4.6 Results from MACHO Searches -- 4.7 Multiple Point Masses -- 4.7.1 Generalities -- Deflection Angle -- Lens Equation -- Critical Lines -- 4.7.2 Binary Lenses -- Lens Equation -- Critical Lines and Caustics -- Multiple Images -- Image Magnifications and Light-Curves -- 4.8 Planetary Microlensing -- 4.8.1 Perturbations of the Central Caustic -- 4.8.2 Perturbations of the Planetary Caustic -- 4.8.3 Perturbations of the Resonant Caustic -- 4.8.4 Perturbations of the Inner and Outer Images -- 4.8.5 Analysis of the Light-Curve in a Planetary Caustic Crossing Event -- 4.8.6 Planetary Microlensing Detections -- 4.9 Python Applications -- 4.9.1 Standard Microlensing Light-Curve -- 4.9.2 Fitting the Standard Light-Curve -- 4.9.3 Distribution of Microlensing Event Timescale -- 4.9.4 Astrometric Microlensing Effect -- 4.9.5 Critical Lines and Caustics of a Binary Lens -- 4.9.6 Solving the Lens Equation of the Binary Lens -- 4.9.7 Light-Curve in a Binary Microlensing Event -- References -- 5 Extended Lenses -- 5.1 Circular, Axially Symmetric Lenses -- Critical Lines and Caustics -- Einstein Radius -- Tangential and Radial Magnification of the Images -- 5.2 Power-Law Lens -- 5.2.1 Lenses with 1< -- n< -- 2.
Critical Lines and Caustics -- Multiple Images -- Image Magnification -- 5.2.2 Lenses with n > -- 2 -- 5.2.3 Singular Isothermal Sphere -- 5.3 Softened (Non-singular) Isothermal Lenses -- 5.4 Elliptical Lenses -- 5.4.1 Singular Isothermal Ellipsoid -- Convergence -- Lensing Potential -- Deflection Angle -- Shear -- Critical Lines -- Caustic and Cut -- Multiple Images -- Distortion and Parity of the Images -- 5.4.2 Softened (Non-singular) Elliptical Models -- 5.4.3 Pseudo-Elliptical Models -- 5.5 Other Profiles -- 5.5.1 The Navarro-Frenk-White Model -- 5.5.2 The Dual Pseudo-Isothermal Mass Distribution -- 5.6 External Perturbations -- 5.7 Multiple Mass Components -- 5.8 Time Delays -- 5.9 Mass-Sheet Degeneracy -- 5.10 Multiple Lens Planes -- 5.11 Python Applications -- 5.11.1 Numerical Solution of the Lens Equation -- Multiple Images by a SIE Lens -- 5.11.2 Triangle Mapping -- 5.11.3 SIS Lens in an External Shear -- 5.11.4 Multiple Lens Planes -- References -- 6 Lensing by Galaxies and Clusters -- 6.1 Strong Lensing by Galaxies and Galaxy Clusters -- 6.1.1 Scale of the Lensing Events -- 6.1.2 Strong Lensing Cross-Section -- 6.1.3 The Quest for Strong Lensing Galaxies -- 6.1.4 Strong Lensing by Galaxy Clusters -- 6.1.5 Lens Inversion -- Parametric Reconstruction Algorithms -- Simultaneous Reconstruction of Source and Lens -- Complex Parametric Models -- Free-Form Reconstruction Algorithms -- 6.2 Weak Lensing by Galaxy Clusters -- 6.2.1 The Principle -- 6.2.2 Ellipticity Measurements -- 6.2.3 Tangential and Cross Component of the Shear -- 6.2.4 Aperture Mass Densitometry -- 6.2.5 The Kaiser and Squires Inversion Algorithm -- 6.2.6 Challenges in Shear Measurements -- Intrinsic Source Ellipticity -- Effects of the Point-Spread-Function -- 6.2.7 Redshift Dependence of the Signal -- 6.2.8 Limitations of the Methods.
6.3 Applications of Lensing by Galaxies and Galaxy Clusters -- 6.3.1 The Nature of Dark Matter -- 6.3.2 The Interplay Between Dark Matter and Baryons -- 6.3.3 Cosmic Telescopes -- 6.3.4 Cosmological Applications -- 6.4 Python Applications -- 6.4.1 Parametric Strong Lensing Mass Reconstruction -- Simulating a Lens -- Lens Modeling -- Using More Constraints -- Optimization in the Source Plane -- 6.4.2 Parametric Weak Lensing Mass Measurement -- Weak Lensing Measurements -- Fit of the Tangential Shear Profile -- 6.4.3 The Kaiser-Squires Inversion Algorithm -- References -- 7 Lensing by Large-Scale Structure -- 7.1 Light Propagation Through an In-homogeneous Universe -- 7.1.1 Deflection of Light -- 7.1.2 Effective Convergence -- 7.1.3 Limber's Equation and the Convergence Correlation Function -- 7.1.4 Effective Lensing Potential, Lensing Jacobian, Shear -- 7.2 Cosmic Shear -- 7.2.1 Shear Correlation Functions -- 7.2.2 Shear in Apertures and Aperture Mass -- 7.2.3 E- and B-modes -- 7.2.4 Cosmic Shear as a Cosmological Probe -- 7.3 Lensing of Cosmic Microwave Background -- 7.3.1 Lensing of the CMB Temperature -- 7.3.2 Lensing of the CMB Polarization -- 7.3.3 Reconstruction of the Lensing Potential -- 7.4 Python Applications -- 7.4.1 Effective Shear and Potential -- 7.4.2 Power Spectrum -- 7.4.3 Correlation Functions -- References -- Part III Appendixes -- 8 Python Mini-Tutorial -- 8.1 Installation -- 8.2 Documentation -- 8.3 Running Python -- 8.4 Your First Python Code -- 8.5 Variables -- 8.6 Strings -- 8.7 Lists -- 8.8 Tuples -- 8.9 Dictionaries -- 8.10 Blocks and Indentation -- 8.11 IF/ELIF/ELSE -- 8.12 While Loops -- 8.13 For Loops -- 8.14 Functions -- 8.15 Classes -- 8.16 Inheritance -- 8.17 Modules -- 8.18 Importing Packages -- 9 Cosmology Primer -- 9.1 The Friedmann-Lemaitre-Robertson-Walker Metric -- 9.2 Redshift -- 9.3 The Friedmann Equations.
9.4 Cosmological Parameters -- 9.5 Cosmological Distances -- 9.6 The Friedmann Models -- 9.6.1 Single Component Models -- 9.6.2 Multiple Component Models -- 9.7 Structure Formation -- 9.7.1 Linear Growth of Density Perturbations -- 9.7.2 Density Power Spectrum -- 9.7.3 Non-linear Evolution -- 9.8 Mass Function -- 9.9 Dark Energy Models -- References -- Index.
Record Nr. UNINA-9910508441103321
Meneghetti Massimo <1974->  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui