Saas-Fee Advanced Course

Strong, Weak and Micro: Swiss Society for Astrophysics and Astronomy

By: P. Schneider, Christopher Kochanek, Joachim Wambsganss

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Hardcover | 5 May 2006

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The observation, in 1919 by A.S. Eddington and collaborators, of the gra- tational de?ection of light by the Sun proved one of the many predictions of Einstein's Theory of General Relativity: The Sun was the ?rst example of a gravitational lens. In 1936, Albert Einstein published an article in which he suggested - ing stars as gravitational lenses. A year later, Fritz Zwicky pointed out that galaxies would act as lenses much more likely than stars, and also gave a list of possible applications, as a means to determine the dark matter content of galaxies and clusters of galaxies. It was only in 1979 that the ?rst example of an extragalactic gravitational lens was provided by the observation of the distant quasar QSO 0957+0561, by D. Walsh, R.F. Carswell, and R.J. Weymann. A few years later, the ?rst lens showing images in the form of arcs was detected. The theory, observations, and applications of gravitational lensing cons- tute one of the most rapidly growing branches of astrophysics. The gravi- tional de?ection of light generated by mass concentrations along a light path producesmagni?cation,multiplicity,anddistortionofimages,anddelaysp- ton propagation from one line of sight relative to another. The huge amount of scienti?c work produced over the last decade on gravitational lensing has clearly revealed its already substantial and wide impact, and its potential for future astrophysical applications.

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Non-Fiction Science Physics Classical Mathematics Gravity Applied Physics Astrophysics Astronomy, Space & Time Cosmology & The Universe Relativity Physics Astronomical Observation & Observatories

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Published: 13th November 2010

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Introduction to Gravitational Lensing and Cosmology	p. 1
Introduction	p. 1
History of Gravitational Light Deflection	p. 2
Discoveries	p. 5
What is Lensing Good for?	p. 14
Gravitational Lens Theory	p. 18
The Deflection Angle	p. 18
The Lens Equation	p. 20
Magnification and Distortion	p. 23
Critical Curves and Caustics, and General Properties of Lenses	p. 25
The Mass-Sheet Degeneracy	p. 29
Simple Lens Models	p. 31
Axially Symmetric Lenses	p. 31
The Point-Mass Lens	p. 34
The Singular Isothermal Sphere	p. 36
Non-Symmetric Lenses	p. 38
The Cosmological Standard Model I: The Homogeneous Universe	p. 44
The Cosmic Expansion	p. 44
Distances and Volumes	p. 49
Gravitational Lensing in Cosmology	p. 52
Basics of Lensing Statistics	p. 54
Cross-Sections	p. 55
Lensing Probabilities; Optical Depth	p. 57
Magnification Bias	p. 58
The Cosmological Standard Model II: The Inhomogeneous Universe	p. 61
Structure Formation	p. 61
Halo Abundance and Profile	p. 71
The Concordance Model	p. 77
Challenges	p. 81
Final Remarks	p. 83
References	p. 84
Strong Gravitational Lensing	p. 91
Introduction	p. 91
An Introduction to the Data	p. 92
Basic Principles	p. 97
Some Nomenclature	p. 98
Circular Lenses	p. 101
Non-Circular Lenses	p. 112
The Mass Distributions of Galaxies	p. 121
Common Models for the Monopole	p. 125
The Effective Single Screen Lens	p. 129
Constraining the Monopole	p. 130
The Angular Structure of Lenses	p. 136
Constraining Angular Structure	p. 140
Model Fitting and the Mass Distribution of Lenses	p. 143
Non-Parametric Models	p. 150
Statistical Constraints on Mass Distributions	p. 152
Stellar Dynamics and Lensing	p. 158
Time Delays	p. 163
A General Theory of Time Delays	p. 165
Time Delay Lenses in Groups or Clusters	p. 169
Observing Time Delays and Time Delay Lenses	p. 170
Results: The Hubble Constant and Dark Matter	p. 174
The Future of Time Delay Measurements	p. 181
Gravitational Lens Statistics	p. 182
The Mechanics of Surveys	p. 182
The Lens Population	p. 185
Cross Sections	p. 192
Optical Depth	p. 193
Spiral Galaxy Lenses	p. 196
Magnification Bias	p. 197
Cosmology With Lens Statistics	p. 205
The Current State	p. 206
What Happened to the Cluster Lenses?	p. 210
The Effects of Halo Structure and the Power Spectrum	p. 216
Binary Quasars	p. 218
The Role of Substructure	p. 221
Low Mass Dark Halos	p. 230
The Optical Properties of Lens Galaxies	p. 232
The Interstellar Medium of Lens Galaxies	p. 238
Extended Sources and Quasar Host Galaxies	p. 243
An Analytic Model for Einstein Rings	p. 243
Numerical Models of Extended Lensed Sources	p. 248
Lensed Quasar Host Galaxies	p. 251
Does Strong Lensing Have a Future?	p. 255
References	p. 256
Weak Gravitational Lensing	p. 269
Introduction	p. 269
The Principles of Weak Gravitational Lensing	p. 272
Distortion of Faint Galaxy Images	p. 272
Measurements of Shapes and Shear	p. 274
Tangential and Cross Component of Shear	p. 277
Magnification Effects	p. 280
Observational Issues and Challenges	p. 281
Strategy	p. 282
Data Reduction: Individual Frames	p. 284
Data Reduction: Coaddition	p. 288
Image Analysis	p. 292
Shape Measurements	p. 295
Clusters of Galaxies: Introduction, and Strong Lensing	p. 298
Introduction	p. 298
General Properties of Clusters	p. 299
The Mass of Galaxy Clusters	p. 301
Luminous Arcs and Multiple Images	p. 304
Results from Strong Lensing in Clusters	p. 309
Mass Reconstructions from Weak Lensing	p. 315
The Kaiser-Squires Inversion	p. 316
Improvements and Generalizations	p. 317
Inverse Methods	p. 324
Parameterized Mass Models	p. 327
Problems of Weak Lensing Cluster Mass Reconstruction and Mass Determination	p. 330
Results	p. 333
Aperture Mass and Other Aperture Measures	p. 343
Mass Detection of Clusters	p. 346
Cosmic Shear - Lensing by the LSS	p. 355
Light Propagation in an Inhomogeneous Universe	p. 356
Cosmic Shear: The Principle	p. 358
Second-Order Cosmic Shear Measures	p. 360
Cosmic Shear and Cosmology	p. 366
E-Modes, B-Modes	p. 371
Predictions; Ray-Tracing Simulations	p. 377
Large-Scale Structure Lensing: Results	p. 382
Early Detections of Cosmic Shear	p. 383
Integrity of the Results	p. 384
Recent Cosmic Shear Surveys	p. 386
Detection of B-Modes	p. 392
Cosmological Constraints	p. 394
3-D Lensing	p. 397
Discussion	p. 400
The Mass of, and Associated with Galaxies	p. 404
Introduction	p. 404
Galaxy-Galaxy Lensing	p. 405
Galaxy Biasing: Shear Method	p. 416
Galaxy Biasing: Magnification Method	p. 427
Additional Issues in Cosmic Shear	p. 430
Higher-Order Statistics	p. 430
Influence of LSS Lensing on Lensing by Clusters and Galaxies	p. 436
Concluding Remarks	p. 439
References	p. 442
Gravitational Microlensing	p. 453
Lensing of Single Stars by Single Stars	p. 454
Brief History	p. 454
Theoretical Background	p. 454
How Good is the Point Lens - Point Source Approximation?	p. 458
Statistical Ensembles	p. 460
Binary Lenses	p. 461
Theory and Basics of Binary Lensing	p. 462
First Microlensing Lightcurve of a Binary Lens: OGLE-7	p. 466
Binary Lens MACHO 1998-SMC-1	p. 467
Binary Lens MACHO 1999-BLG-047	p. 471
Binary Lens EROS BLG-2000-005	p. 472
Microlensing and Dark Matter: Ideas, Surveys and Results	p. 475
Why We Need Dark Matter: Flat Rotation Curves (1970s)	p. 475
How to Search for Compact Dark Matter (as of 1986)	p. 477
Just Do It: MACHO, EROS, OGLE et al. (as of 1989)	p. 477
"Pixel"-Lensing: Advantage Andromeda!	p. 478
Current Interpretation of Microlensing Surveys with Respect to Halo Dark Matter (as of 2004)	p. 479
Microlensing toward the Galactic Bulge	p. 484
Microlensing Surveys in Search of Extrasolar Planets	p. 486
How Does the Microlensing Search for Extrasolar Planet Work? The Method	p. 486
Why Search for Extrasolar Planets with Microlensing? - Advantages and Disadvantages	p. 488
Who is Searching? The Teams: OGLE, MOA, PLANET, MicroFUN	p. 492
What is the Status of Microlensing Planet Searches so far? The Results	p. 493
When will Planets be Detected with Microlensing? The Prospects	p. 496
Note Added in April 2004 (About One Year after the 33rd Saas Fee Advanced Course)	p. 497
Summary	p. 497
Higher Order Effects in Microlensing:	p. 499
Astrometric Microlensing	p. 516
Quasar Microlensing	p. 520
Microlensing Mass, Length and Time Scales	p. 521
Early and Recent Theoretical Work on Quasar Microlensing	p. 524
Observational Evidence for Quasar Microlensing	p. 526
Quasar Microlensing: Now and Forever?	p. 534
References	p. 536
Index	p. 541
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Saas-Fee Advanced Course

Strong, Weak and Micro: Swiss Society for Astrophysics and Astronomy

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Hardcover

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