Gravitational lensing strong weak and micro

Saas-Fee Advanced Course 33 P Schneider C Kochanek J Wambsganss Gravitational Lensing: Strong, Weak and Micro Saas-Fee Advanced Course 33 Swiss Society for Astrophysics and Astronomy Edited by G Meylan, P Jetzer and P North With 196 Illustrations, 36 in Color ABC Peter Schneider Joachim Wambsganss Institut für Astrophysik und Extraterrestrische Forschung Universität Bonn Auf dem Hügel 71 D-53121 Bonn, Germany peter@astro.uni-bonn.de Zentrum für Astronomie Universität Heidelberg (ZAH) Mönchhofstr 12-14 D-69120 Heidelberg, Germany jkw@ari.uni-heidelberg.de Christopher S Kochanek Department of Astronomy The Ohio State University 4055 McPherson Lab 140 West 18th Avenue Columbus, OH 43210 USA ckochanek@astonomy.ohio-state.edu Volume Editors: Georges Meylan Pierre North Philippe Jetzer Institute of Theoretical Physics Universität Zürich Winterthurerstrasse 190 CH-8057 Zürich, Switzerland Laboratoire d’Astrophysique Ecole Polytechnique Fédérale de Lausanne (EPFL) Observatoire CH-1290 Sauverny, Switzerland This series is edited on behalf of the Swiss Society for Astrophysics and Astronomy: Soci´et´e Suisse d’Astrophysique et d’Astronomie Observatoire de Gen`eve, ch des Maillettes 51, 1290 Sauverny, Switzerland Cover picture: (Left) Matterhorn, Zermatt, Switzerland, as seen in all its usual beauty (Kurt Müller, http://photo.zermatt.ch) (Right) Another vision of the same mountain, as observed on April 2003, while suffering from the transiant phenomenon of a passing-by black hole of one Jupiter mass (with the help of B McLeod, CfA, Castle, and F Summers, STScI) Library of Congress Control Number: 2006920099 ISBN-10 3-540-30309-X Springer Berlin Heidelberg New York ISBN-13 978-3-540-30309-1 Springer Berlin Heidelberg New York This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable to prosecution under the German Copyright Law Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2006 Printed in The Netherlands The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use A X macro package Typesetting by the authors and SPI Publisher Services using a Springer LT E Cover design: design & production GmbH, Heidelberg Printed on acid-free paper SPIN: 11568278 55/3100/SPI - To the memory of Dennis Walsh (12 June 1933–1 June 2005) who, with his two colleagues Bob Carswell and Ray Weymann, discovered in 1979 the first extragalactic gravitational lens, the quasar QSO 0957+0561 Preface The observation, in 1919 by A.S Eddington and collaborators, of the gravitational deflection of light by the Sun proved one of the many predictions of Einstein’s Theory of General Relativity: The Sun was the first example of a gravitational lens In 1936, Albert Einstein published an article in which he suggested using 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 first 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 first lens showing images in the form of arcs was detected The theory, observations, and applications of gravitational lensing constitute one of the most rapidly growing branches of astrophysics The gravitational deflection of light generated by mass concentrations along a light path produces magnification, multiplicity, and distortion of images, and delays photon propagation from one line of sight relative to another The huge amount of scientific 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 The 33rd Saas-Fee Advanced Courses of the Swiss Society for Astronomy and Astrophysics, entitled Gravitational Lensing: Strong, Weak, and Micro, took place from 8–12 April, 2003, in Les Diablerets, a pleasant mountain resort of the Swiss Alps The three lecturers were Peter Schneider, Christopher S Kochanek, and Joachim Wambsganss These proceedings are provided in four complementary parts of a book on gravitational lensing P Schneider wrote Part 1, Introduction to Gravitational Lensing and Cosmology, the first draft of which was made available to all registered participants a week before the course C.S Kochanek wrote Part about Strong Gravitational Lensing, while P Schneider in Part dealt with VIII Preface Weak Gravitational Lensing, and J Wambsganss in Part about Gravitational Microlensing We are thankful to Nicole Tharin, the secretary of the Laboratoire d’Astrophysique de l’Ecole Polytechnique F´ed´erale de Lausanne (EPFL), for her continuous presence and efficient help, and to Yves Debernardi for his efficient logistic support during the course We are equally thankful to Fr´ed´eric Courbin, Dominique Sluse, Christel Vuissoz, and Alexander Eigenbrod for help in the editorial process of this book The meeting was also sponsored by the Universit´e de Lausanne, the Ecole Polytechnique F´ed´erale de Lausanne (EPFL), the Swiss Society for Astronomy and Astrophysics, the Acad´emie Suisse des Sciences Naturelles, the Fonds National Suisse de la Recherche Scientique, the Space Telescope Science Institute, the Universită at Ză urich, and the Observatoire de Gen`eve Lausanne, July 2005 Georges Meylan Philippe Jetzer Pierre North Contents Part 1: Introduction to Gravitational Lensing and Cosmology P Schneider Introduction 1.1 History of Gravitational Light Deflection 1.2 Discoveries 1.3 What is Lensing Good for? Gravitational Lens Theory 2.1 The Deflection Angle 2.2 The Lens Equation 2.3 Magnification and Distortion 2.4 Critical Curves and Caustics, and General Properties of Lenses 2.5 The Mass-Sheet Degeneracy Simple Lens Models 3.1 Axially Symmetric Lenses 3.2 The Point-Mass Lens 3.3 The Singular Isothermal Sphere 3.4 Non-Symmetric Lenses The Cosmological Standard Model I: The Homogeneous Universe 4.1 The Cosmic Expansion 4.2 Distances and Volumes 4.3 Gravitational Lensing in Cosmology Basics of Lensing Statistics 5.1 Cross-Sections 5.2 Lensing Probabilities; Optical Depth 5.3 Magnification Bias The Cosmological Standard Model II: The Inhomogeneous Universe 6.1 Structure Formation 6.2 Halo Abundance and Profile 1 14 18 18 20 23 25 29 31 31 34 36 38 44 44 49 52 54 55 57 58 61 61 71 X Contents 6.3 The Concordance Model 6.4 Challenges Final Remarks References 77 81 83 84 Part 2: Strong Gravitational Lensing C S Kochanek 91 Introduction 91 An Introduction to the Data 92 Basic Principles 97 3.1 Some Nomenclature 98 3.2 Circular Lenses 101 3.3 Non-Circular Lenses 112 The Mass Distributions of Galaxies 121 4.1 Common Models for the Monopole 125 4.2 The Effective Single Screen Lens 129 4.3 Constraining the Monopole 130 4.4 The Angular Structure of Lenses 136 4.5 Constraining Angular Structure 140 4.6 Model Fitting and the Mass Distribution of Lenses 143 4.7 Non-Parametric Models 150 4.8 Statistical Constraints on Mass Distributions 152 4.9 Stellar Dynamics and Lensing 158 Time Delays 163 5.1 A General Theory of Time Delays 165 5.2 Time Delay Lenses in Groups or Clusters 169 5.3 Observing Time Delays and Time Delay Lenses 170 5.4 Results: The Hubble Constant and Dark Matter 174 5.5 The Future of Time Delay Measurements 181 Gravitational Lens Statistics 182 6.1 The Mechanics of Surveys 182 6.2 The Lens Population 185 6.3 Cross Sections 192 6.4 Optical Depth 193 6.5 Spiral Galaxy Lenses 196 6.6 Magnification Bias 197 6.7 Cosmology With Lens Statistics 205 6.8 The Current State 206 What Happened to the Cluster Lenses? 210 7.1 The Effects of Halo Structure and the Power Spectrum 216 7.2 Binary Quasars 218 The Role of Substructure 221 8.1 Low Mass Dark Halos 230 The Optical Properties of Lens Galaxies 232 9.1 The Interstellar Medium of Lens Galaxies 238 Contents XI 10 Extended Sources and Quasar Host Galaxies 243 10.1 An Analytic Model for Einstein Rings 243 10.2 Numerical Models of Extended Lensed Sources 248 10.3 Lensed Quasar Host Galaxies 251 11 Does Strong Lensing Have a Future? 255 References 256 Part 3: Weak Gravitational Lensing P Schneider 269 Introduction 269 The Principles of Weak Gravitational Lensing 272 2.1 Distortion of Faint Galaxy Images 272 2.2 Measurements of Shapes and Shear 274 2.3 Tangential and Cross Component of Shear 277 2.4 Magnification Effects 280 Observational Issues and Challenges 281 3.1 Strategy 282 3.2 Data Reduction: Individual Frames 284 3.3 Data Reduction: Coaddition 288 3.4 Image Analysis 292 3.5 Shape Measurements 295 Clusters of Galaxies: Introduction, and Strong Lensing 298 4.1 Introduction 298 4.2 General Properties of Clusters 299 4.3 The Mass of Galaxy Clusters 301 4.4 Luminous Arcs and Multiple Images 304 4.5 Results from Strong Lensing in Clusters 309 Mass Reconstructions from Weak Lensing 315 5.1 The Kaiser–Squires Inversion 316 5.2 Improvements and Generalizations 317 5.3 Inverse Methods 324 5.4 Parameterized Mass Models 327 5.5 Problems of Weak Lensing Cluster Mass Reconstruction and Mass Determination 330 5.6 Results 333 5.7 Aperture Mass and Other Aperture Measures 343 5.8 Mass Detection of Clusters 346 Cosmic Shear – Lensing by the LSS 355 6.1 Light Propagation in an Inhomogeneous Universe 356 6.2 Cosmic Shear: The Principle 358 6.3 Second-Order Cosmic Shear Measures 360 6.4 Cosmic Shear and Cosmology 366 6.5 E-Modes, B-Modes 371 6.6 Predictions; Ray-Tracing Simulations 377 Part 4: Gravitational Microlensing 539 Mao, S 1999, A&A 350, L19 Metcalf, R.B., Madau, P 2001, ApJ 563, Metcalf, R.B., Zhao, H.S 2002, ApJ 567, Milgrom, M 2001, MNRAS 326, 126 Mineshige, S., Yonehara, A 1999, ApJ 343, 41 Mollerach, S & Roulet, E 2002 Gravitational Lensing and Microlensing, World Scientific Nemiroff, R.J 1997, ApJ 486, 693 Nemiroff, R.J., Wickramasinghe, W.A.D.T 1994, ApJ 424, L21 Nguyen, H.T., Kallivayalli, N., Werner, M.W., Alcock, C., Patten, B.M., Stern, D 2004, ApJS 154, 266 Ostensen, R et al 1996, A&A 309, 59 Ostensen, R et al 1997, A&A 126, 393 Paczy´ nski, B 1986a, ApJ 301, 502 Paczy´ nski, B 1986b, ApJ 304, Paczy´ nski, B 1996, ARA&A 34, 419 Paczy´ nski, B 1998, ApJ 494, L23 Paczy´ nski, B., Stanek, K.Z., Udalski, A., Szyma´ nski, M, Kalu˙zny, J., Kubiak, M., Mateo, M., Krzemi´ nski, W 1994, ApJ 435, L113 Pelt, J et al 1998, A&A 336, 829 Peng, E.W 1997, ApJ 475, 43 Rees, M 2003, Phil Trans Roy Soc Lond 361, 2427-2434 Refsdal, S 1964a, MNRAS 128, 295 Refsdal, S 1964b, MNRAS 128, 307 Refsdal, S., 1966, MNRAS 134, 315 Refsdal, S., Stabell, R., Pelt, J., Schild, R 2000, A&A 360, 10 Renn, J., Sauer, T., Stachel, J 1997, Science 275, 184 Reza, Y 2000, Trois Versions de la Vie, Albin Michel (Paris) Rubin, V.C 1983, Science 220, 1339 Sackett, P.D 1997, in Final Rep ESO Working Group on Detection of Extrasolar Planets, F Paresce & A Renzini (eds.), (ESO: Garching) Sackett, P.D 2001, Gravitational Lensing: Recent Progress and Future Goals, Tereasa G Brainerd & Christopher S Kochanek (eds.), (ASP: San Francisco), ASP Conf Ser # 237, p 227 Sahu, K.C 1994, Nature 370, 275, Sahu, K 2003, in The Dark Universe: Matter Energy and Gravity, M Livio (ed.), (Cambridge Univ Press: Cambridge), p 14, also astro-ph/0302325 Sanders, R.H., McGaugh, S.S 2002, A&A 40, 263 Schechter, P.L., Wambsganss, J 2002, ApJ 580, 685 Schild, R 1996, ApJ 464, 125 Schmidt, R., Wambsganss, J 1998, A&A 335, 379 Schneider, P., Weiss, A 1986, A&A 164, 237 Schneider, P., Weiss, A 1987, A&A 171, 49 Smith, M.C., Mao, S., Wozniak, P 2002a, MNRAS, 332, 962 Smith, M.C., Mao, S., Wozniak, P., Udalski, A., Szymanski, M., Kubiak, M., Pietrzynski, G., Soszynski, I., Zebrun, K 2002b, MNRAS 336, 670 540 J Wambsganss Soldner, J 1801, Berliner Astron Jahrb 1804, p 161 Spergel, D.N., Verde, L., Peiris H.V., Komatsu E., Nolta M.R et al 2003, ApJS, 148, 175 Stanek, K.Z., Mateo, M., Udalski, A., Szyma´ nski, M, Kalu˙zny, J., Kubiak, M 1994, ApJ 429, L73 Treyer, M & Wambsganss 2004, A&A 416, 19 Tsapras, Y., Horne, K., Kane, S & Carson, R 2003, MNRAS 343, 1131 Udalski A., Szymanski M., Kaluzny J., Kubiak M., Krzeminski W., Mateo, M., Preston, G.W Paczy´ nski, B 1993, Acta Astronomica 43, 289 Udalski A., Szymanski M., Mao, S., Di Stefano, R., Kaluzny J., Kubiak M., Mateo M & Krzeminski W 1994a, Astrophys J.L 436, L103 Udalski A., Szymanski M., Stanek, K.Z et al (The OGLE collaboration) 1994b, Act Astr 44, 165 Udalski A., Szymanski M., Kubiak M et al 1998, Acta Astronomica 48, 147 Udalski A 2003, Acta Astronomica 53, 291 Vanderriest, C., Schneider, J., Herpe, G., Ch`evreto n, M., Moles, M., Wl´erick, G 1989, A&A 215, Walsh, D et al 1979, Nature 279, 381 Wambsganss, J 1990, PhD thesis (Munich University), also Max-Planck Report MPA-550 Wambsganss, J., Paczy´ nski, B., Schneider, P 1990, ApJ 358, 33 Wambsganss, J., Paczy´ nski, B 1991, AJ, 102, 864 Wambsganss, J., Paczy´ nski, B 1992, ApJ 397, Wambsganss, J 1997, MNRAS 284, 172 Wambsganss, J 1998, Living Reviews in Relativity 1, No 12, http://relativity.livingreviews.org/Articles/lrr-1998-12 Wambsganss, J., Schmidt, R.W., Colley, W.N., Kundi´c, T., Turner, E.L 2000, A&A 362, L37 Witt, H.J 1993, ApJ 403, 530, Witt, H.J 1995, ApJ 449, 42 Witt, H.J., Mao, S 1995, ApJ 447, 105 Wyithe, J.S.B et al 2000a, MNRAS 315, 51 Wyithe, J.S.B et al 2000b, MNRAS 318 Wolszczan, A 1994, Science 264, 538 Wozniak, P.R et al 2000a, ApJ 529, 88 Wozniak, P.R et al 2000b, ApJ 540, 65 Wozniak, P.R et al 2001, Acta Astronomica 51, 175 Wozniak, P & Paczy´ nski, B 1997, ApJ 487, 55 Yonehara, A et al 1998, ApJ 501, 41 Yonehara, A 2001, ApJ 548, 127 Yoo, J., DePoy, D.L., Gal-Yam, A., Gaudi, B.S., Gould, A et al 2004, ApJ 603, 139 Young, P 1981, ApJ 244, 756 Index H0 , 4, 12, 13, 16, 47, 79, 98, 123, 128, 163–165, 169, 171, 174–178, 180–182, 194, 255, 300, 303, 357, 358, 397 Ω0 = Ωtot , 48 ΩCMB , 48 ΩΛ , 47–49, 64 Ωm , 47–49, 64 Ωr , 47–49, 64 Σ(ξ), 34, 36 μp , 56 σ(Δθ), 56 σ8 , 69, 70, 72, 79, 81, 311, 361, 367, 384, 385, 387, 396, 397, 400 σQ , 56 σv , 36 σtot (Q), 57 0047–2808, 160, 250 2dF Galaxy Redshift Survey, 78, 183 3-D gravitational potential, 398 lensing, 397 Abell 1689, 305, 310, 313, 315, 334, 335, 341 Abell 1705, 352 Abell 2218, 10, 17, 309 Abell 222/223, 335, 336 Abell 2390, 306, 307 Abell 370, 270, 309, 315 Abell 901/902, 335 ACS, 281, 298, 305, 313, 390 adiabatic equation, 45 affine parameter, 19 AGAPE, 478 angle deflection, 18, 461 scaled deflection, 21 angular correlation function, 423 angular diameter distance, 45, 50, 52, 53, 98, 164, 194, 271, 357 aperture mass, 315, 343, 345, 347, 363, 423 dispersion, 368, 393, 395, 420 map, 346 third-order statistics, 433 APM 08279+5255, 17, 59, 61, 94, 118, 220, 243 arc, 7, 9, 10, 15, 304, 306, 310–312, 315, 335, 341, 352 arclet, 7, 10, 270, 304, 306, 315, 441 astroid, 43 astroid curve, 114, 116, 192, 202, 245 B 0218+357, 170, 173, 174, 196, 240, 242, 531 B 1359+154, 94 B 1422+231, 156, 170, 171, 221, 243 B 1600+434, 170, 174, 177, 178, 181, 196, 531 B 1608+656, 156, 160, 170, 173, 180 B 1933+503, 94, 98, 145, 146 B 1938+666, 12 B 2108+213, 211 B-modes, 371, 372, 374, 392, 393, 433 background galaxies, 332, 393, 406, 409 baryonic matter, 129, 178, 179, 192, 211–217, 231, 300, 347 542 Index Bessel functions, 362, 364 bias factor, 430 of galaxies, 405 parameter, 418, 419, 421, 427 biasing of galaxies, 271, 416–418, 427 stochastic, 419 binary lenses, 461, 462, 465–467, 472, 484, 486, 497, 499, 505, 510 binary quasars, 218–220, 232 MGC 2214+3550, 219 PKS 1145–071, 219 QSO 2345+007, 218 binary source, 500, 505 binary stars, 465, 479, 486, 505, 521 Birkhoff theorem, 31, 71 blending, 465, 478, 499, 500, 519–521 Bremsstrahlung, 301, 302 brightness moments, 274 profile, 294 in X-rays, 302 BTC, 351, 383, 389 Butcher–Oemler effect, 300 Canopus, 473 Carswell, R.F., causal contact, 62 caustic, 25, 26, 104, 113, 115–117, 121, 201, 222, 230, 245, 247, 460, 462, 467, 473, 487, 490, 499, 505, 507, 510, 512, 522, 524, 531 fold, 26 lips, 41 tangential, 43 Cavendish, H., cB58, 17, 59, 61 cD galaxy, 299, 309 CDM, 309, 313, 314, 424 CfA redshift survey, 183 CfA-Arizona Space Telescope Lens Survey (CASTLES), 92, 96, 139, 143, 221, 253 CFH12K, 282, 386 CFHT, 282, 386 CFRS 03.1077, 160 Chandra, 303, 304, 310, 338 Deep Field South (CDF-S), 292, 293 Chang, K., 454 Charge Coupled Device (CCD), 5, 478, 500 fringes, 286, 287 mosaic, 11, 383 multi-chip, 286 chromatic effect, 14 Chwolson, O., 3, 454 Cl 0024+17, 310, 311, 340 Cl 1409+52, 315 Cl 2244−02, CLASS, clusters of galaxies, 299, 415 Abell 2218, 10, 17, 441 Abell 222/223, 335 Abell 851, 416 AC 114, 416 central cD, 299, 309 Cl 0939+4713, 417 Cl 2244−02, MG 1131+0456, MS 1054-03, 337 MS 1512+36, 59 CMB, 300, 366, 367, 400 anisotropy, 271, 366, 401, 427 temperature map, 271 CMB anisotropies primary, 77 secondary, 77 coaddition, 290, 291 COBE satellite, 69, 80 Cold Dark Matter (CDM), 15, 67, 82, 107, 128, 129, 148, 157, 178, 208, 211, 212, 220 collisionless Boltzmann equation, 63 COMBO-17, 293, 376, 391 comoving angular diameter distance, 45, 50, 52, 58, 98, 164, 194, 357 distance, 49, 50, 53 horizon, 62, 67 number density, 58, 73 observer, 45 radial coordinate, 45 radius, 73 sphere, 70 volume, 45, 46 volume element, 51 compact objects, 15, 453, 477, 486, 521, 524, 528 Index complex shear, 25 concentration parameter, 76 concordance, 79 concordance model, 77, 83 conformal gravity, 476 constant cosmological, 46 convergence, 21, 102, 308, 377 coordinates angular, 21 correlation coefficient, 422 correlation function, 65, 362, 369, 372–374, 382, 419 AGN-galaxy, 429 angular, 423 QSO–galaxy, 430 three-point (3PCF), 431–433 natural components, 432 two-point, 360, 386, 427 cosmic density fluctuations, 72 Cosmic Lens All Sky Survey (CLASS), 153, 184, 203, 206, 207, 209, 211, 231 Cosmic Microwave Background (CMB), 44, 47, 61, 69, 77, 79, 80, 82, 83 cosmic scale factor, 45 cosmic shear, 355, 358, 360, 365, 366, 375, 383, 386, 394, 401, 419 detection, 422 surveys, 434 cosmic time, 45 cosmological constant, 46 cosmological model, 366 cosmological models Einstein-de Sitter, 52, 63, 64, 72, 73 Friedmann-Lemaˆıtre, 46 cosmological parameters, 47, 77, 311, 312, 314, 360, 366, 368, 369, 392, 394, 400 ΩΛ , 323, 324, 367, 395 Ωm , 324, 367, 385, 395, 396 σ8 , 311, 361, 367, 383–385, 387, 396, 397, 400, 427 cosmological constant, 46, 80, 83 critical density, 47 curvature, 357 density parameters, 47, 49, 80 Hubble constant, 4, 12, 13, 16, 47, 79, 98, 123, 128, 163–165, 169, 171, 543 174–178, 180–182, 194, 255, 300, 303, 357, 358, 397 Hubble radius, 194 radiation density, 47 total density parameter, 48 cosmological standard model homogeneous Universe, 44 inhomogeneous Universe, 61 critical curve, 25, 26, 30, 32, 104, 113, 115–117, 121, 201, 222, 230, 245, 247, 319 radial, 32 tangential, 32 critical curves, 17, 462, 463 critical density, 47 critical surface mass density, 331 cross-section point-mass lens, 55 singular isothermal sphere, 56 crossing time, 467, 470, 483, 522 curvature of the Universe, 357 curvature parameter, 45 cusp, 26, 462, 473, 510 naked, 43 dark clusters, 353, 355 dark energy, 16, 47, 62, 83, 206, 312, 355, 366, 399–401, 404, 434, 439 Dark Matter Cold (CDM), 67, 82, 107, 128, 129, 148, 157, 178, 208, 211, 212, 220 Hot (HDM), 67, 81 dark matter, 14–16, 31, 44, 58, 62, 68, 73–75, 82, 83, 129, 136, 137, 139, 147, 155–157, 163, 175, 190, 194, 212, 214, 231, 250, 299–301, 309, 313–315, 335, 347, 366, 375, 400–402, 405, 413, 417, 422, 429, 438, 454, 460, 461, 475–477, 479, 482–484, 521, 528, 531, 533 filaments, 335 profile of galaxies, 406 dark matter distribution, 68, 300, 301, 309, 313, 315, 335, 347, 366, 375, 400, 402, 405, 417, 422, 429 dark matter halo, 38, 73, 75, 76, 126–129, 136, 137, 139, 155–157, 163, 175, 190, 212, 214, 231, 250, 314, 405, 411, 413, 415, 438, 460, 544 Index 461, 475, 477, 479, 480, 483, 484, 521, 528, 531, 533 deflection angle, 18, 19, 461 deflection potential, 22, 308, 324, 326, 358 deflector plane, 20 degeneracies, 458, 475, 490, 499, 500, 517 density contrast, 62, 64, 67, 418, 423, 431 distribution, 19, 127 fluctuations, 62, 64, 67, 81 lens number, 15, 57 parameters, 47, 49, 80 density profile de Vaucouleurs, 125, 126, 138, 158 exponential disk, 125, 126 Hernquist, 126, 127, 145, 147 Navarro, Frenk and White (NFW), 76, 103, 138, 145, 306, 313, 314, 327, 334, 349, 410, 414, 438 Sersic, 126 universal=NFW, 76, 103, 138, 145, 306, 313, 314, 327, 334, 349, 410, 414, 438 differential image (analysis), 501 dispersion aperture mass, 363, 365, 368, 393, 395, 420 of intrinsic ellipticity, 409 shear, 362, 364, 365, 368, 384, 387, 391, 395 distance, 49, 458, 461, 483, 487, 488, 499, 518 angular diameter, 45, 50, 52, 53, 98, 164, 194, 271, 357 comoving, 49, 50, 52, 53 luminosity, 51 proper, 51 distance ladder, 16 distortion, 24 doppler wobble, 488 drizzling, 290 E-modes, 371, 372, 374, 393, 433 EEWS, 495, 496, 498 Einstein angle-radius, 35, 40, 53 Einstein radius, 103, 104, 112, 120, 130, 132, 135, 140, 141, 157, 164, 170, 176, 192, 197, 218, 224, 229, 277, 305 Einstein ring, 8, 102–104, 107, 112, 139, 155, 173, 219, 233, 243, 244, 246, 247, 251 radio, 8, 11, 97 radius, 455, 461, 462, 475, 487, 496, 499, 518, 522 visible, 3, 8, 251 Einstein time, 457, 458, 466, 485, 487, 501, 503, 504, 522 Einstein, A., 3, 454 Einstein-de Sitter cosmological model, 52, 63, 64, 72, 73 ellipticity, 296, 386 complex, 274, 275 definition, 274 dispersion, 276 intrinsic, 273, 276, 281, 376 mean, 276 tangential, 278, 406 energy dark, 16, 47, 62, 83, 206, 312, 355, 366, 399–401, 404, 434, 439 vacuum, 83, 206, 312, 355, 366, 399–401, 404, 434, 439 entropy regularization, 325 equation adiabatic, 45 collisionless Boltzmann, 63 Friedmann, 45 Jeans, 158, 160, 190, 192 Poisson, 22, 30, 63 Vlasov, 63, 70 equation of state (EOS), 46 EROS, 472, 477, 481, 485 ESO Imaging Survey (EIS), 293 European Southern Observatory (ESO), 518 external shear, 39, 112, 166 Faber–Jackson relation, 187–189, 232–235, 408 Fermat potential, 22, 27, 30, 36, 54 filament, 335 fluctuation field, 68 flux conservation, 60 flux ratio anomaly, 531 fold caustic, 26 Index fold caustics, 465, 470 FORS, 282 FORS1, 350, 351, 383 Fourier mode, 67 Fourier transform, 65, 307, 308, 316, 361, 418 Friedmann equation, 45 Friedmann-Lemaˆıtre cosmological models, 46 Galactic Bulge, 458, 478, 484, 500, 501, 518 Galactic halo, 471, 481 Galactic microlensing, 453, 458 galactic microlensing events MACHO-LMC-1, 14 galaxies background, 332, 393, 406, 409 brightness moments, 274 clusters, 299 depletion, 280 distorsion, 272 faint images, 272 number density, 280, 282 galaxy cB58, 17, 59, 61 host, 8, 17 IRAS F10214, 17, 59, 61 quasar host, 95, 99, 126, 169, 180, 219, 220, 243, 245, 247, 248, 250–254, 256 galaxy biasing, 416, 417, 427 galaxy–galaxy lensing, 271, 405, 406, 409, 412, 413, 415 Gaussian random field, 66 GEMS, 292 geometrical time delay, 53 geometrically-thin lens, 19 GEST, 492 giant arcs, 304, 306, 312 cluster Abell 1689, 305 Abell 370, 270 discovery, 270 Golden Lens, 181 GOODS, 292, 293 gravitational instability, 61 gravitational time delay, 53 545 H 1413+117, 531 Harrison–Zeldovich power spectrum, 68, 81, 83 HE 0230–2130, 156 HE 0435–1223, 94, 96, 156 HE 1104–1805, 94, 95, 170, 180, 242 HE 2149–2745, 170, 174, 177, 178, 181 high magnification event, 491, 493, 496, 513 Hipparcos, 518 horizon, 67 Hot Dark Matter (HDM), 67, 81 HST, 5, 6, 8, 96, 305, 337, 390 HST 14176+5226, 160 HST 15433+5352, 160 HST Medium Deep Survey (MDS), 183 Hubble Deep Field, 276, 282, 312 Ultra Deep Field (UDF), 292 Hubble constant, 4, 12, 13, 16, 47, 79, 98, 123, 128, 163–165, 169, 171, 174–178, 180–182, 194, 255, 300, 303, 357, 358, 397 Hubble expansion, 46, 71 Hubble radius, 194 Hubble Space Telescope (HST), 5, 6, 8, 96, 305, 337, 390, 513 image parity, 24, 102, 112 image positions, 143 image separation, 35, 106 image separation distribution, 92, 215 impact parameter, 18, 456, 459, 466, 499, 501, 508, 513, 516, 519 inflation, 68 internal shear, 166 interstellar medium (ISM), 123, 143, 199, 221, 224, 232 intracluster gas, 299 medium (ICM), 299, 301, 302 intrinsic alignment, 375 alignment of galaxies, 375, 402 ellipticity, 376 dispersion, 409 orientation of galaxies, 406 invariant shear, 167 IRAS F10214, 17, 59, 61 546 Index isothermal ellipsoid, 306 mass profile, 342 isothermal ellipsoid singular (SIE), 120, 121, 136, 138, 156, 168, 245 isothermal sphere non-singular (NIS), 40 singular (SIS), 36, 102–104, 107, 120, 121, 134, 135, 168, 203 Jacobi matrix, 272, 357, 380 Jacobian matrix, 23–25, 27, 32, 40, 41 Jeans equation, 158, 160, 190, 192 Jodrell/VLA Astrometric Survey (JVAS), 5, 209 JVAS, JWST, 441 K-correction, 51 Kaiser–Squires inversion, 316, 322, 344 Kepler law, 475 keplerian rotation, 475 Klimov, Yu.G., KSB method, 296, 297, 383 Lagrangian perturbation theory, 70 Laplace, P.-S., Large Magellanic Cloud (LMC), 460, 467, 477–479, 482, 483, 513, 518 large-scale structure (LSS), 70, 78, 300, 436 lensing by, 271, 333, 355, 357, 382 mass distribution, 348 of the cosmic matter field, 355 Las Campanas, 493 lens, 3, 15 as a natural telescope, 16 axially symmetric, 31 centrally condensed, 34 circular, 101 compact objects, 15 cross-section, 55 elliptical, 44 ellipticity, 112 geometrically thin, 19 isothermal sphere, 31, 36, 40, 107 mass, 14 mass distribution, 121, 123–125, 128, 137, 141, 143, 145, 152, 153, 159–161, 175, 190, 233, 237, 243, 250 multi screen, 129 non-symmetric, 38 number density, 15, 57 point-mass, 31, 34, 102, 105, 455, 457, 458, 461, 499, 516, 524 power-law, 102, 104 quadrupole, 38, 40 rotating, 505, 506 Schwarzschild, 56 single screen, 129 lens equation, 20, 101, 104, 143 lens models, 97 lens number density, 15, 57 lens plane, 20 lensed galaxies 0047–2808, 160, 250 CFRS 03.1077, 160 lensed optical quasars survey, 184 lensed quasars APM 08279+5255, 17, 59, 61, 94, 118, 220, 243 B 0218+357, 170, 173, 174, 196, 240, 242, 531 B 1359+154, 94 B 1422+231, 156, 170, 171, 221, 243 B 1600+434, 170, 174, 177, 178, 181, 196, 531 B 1608+656, 156, 160, 170, 173, 180 B 1933+503, 94, 98, 145, 146 B 1938+666, 12 B 2108+213, 211 H 1413+117, 531 HE 0230–2130, 156 HE 0435–1223, 94, 96, 156 HE 1104–1805, 94, 95, 170, 180, 242 HE 2149–2745, 170, 174, 177, 178, 181 HST 14176+5226, 160 HST 15433+5352, 160 MG 0414+0534, 94, 99 MG 1131+0456, 97, 100 MG 1549+3047, 160 MG 1654+13, 11 MG 2016+112, 94, 99, 160 Index PG 1115+080, 5, 94, 95, 142, 160, 168–171, 174, 176–178, 181, 247, 252 PKS 1830–211, 170, 196 PMN 1632–0033, 97, 100 PMN J0134–0931, 94 PMN J1632–0033, 94, 147 PMN J2004–1349, 196 QSO 0957+561, 5–7, 13, 24, 139, 145, 147, 148, 160, 162, 169, 170, 174, 178, 180, 256, 453, 527 QSO 2237+0305, 9, 10, 123, 148, 160, 161, 183, 196, 227, 453, 527 RX J0911+0551, 155, 156, 169–171, 173, 174, 178 RX J1131–1231, 94, 96 SBS 1520+530, 170, 174, 177, 178, 181 SDSS 1004+4112, 211 Liebes, S., light element abundances, 78 light propagation, 356 light travel time, 164 lightcurve, 457, 462, 465, 466, 477, 479, 486, 487, 495, 496, 499, 501, 524, 528, 534 limb darkening, 499, 507, 510 Limber’s equation, 359 line-of-sight velocity dispersion, 408 distribution, 301 linear bias factor, 69 linear growth factor, 63 Link, F., 454 Liouville theorem, 23 lips caustic, 41 Lodge, O.J., LSS lensing, 357, 436 B-modes, 371, 372, 374, 392, 393 E-modes, 371, 372, 374, 393 luminosity distance, 51 luminosity function Schechter, 61, 185–187, 194, 195 Ly-α forest, 79 M31, 478 MACHO, 467, 477, 479, 484, 528 MACHO-LMC-1, 14 547 magnification, 9, 10, 17, 23, 25, 35, 59, 102, 103, 280, 304, 310, 319, 327, 328, 332, 338, 339, 342, 429, 455, 464, 465, 487, 499, 516, 522, 533 likelihood, 326 magnification bias, 55, 58, 152, 182, 184, 197, 198, 200, 201, 203–205, 220, 238, 240, 319, 428 magnification tensor, 23, 101 Mandl, R., mass determination, 333 dimensionless, 280 distribution, 309, 315 Abell 2218, 309 Abell 370, 309 isothermal, 342 large-scale structure, 348 of galaxies, 405 map, 320 mean surface density, 279 reconstruction, 282, 315, 323, 333, 337, 343, 416 Abell 1689, 334 Abell 1705, 352 Abell 222/223, 336 Cl 0024+17, 340 MS 1054-03, 339 surface density, 279, 307, 316, 322, 326, 338, 358 critical, 331 mass distribution, 120, 121, 123–125, 128, 137, 141, 143, 145, 152, 153, 159–161, 175, 190, 233, 237, 243, 250 mass distribution substructure, 122, 144, 148, 221, 224, 225, 227, 228, 230, 231 mass profile of galaxies, 405 mass ratio, 462, 464, 472, 486, 488, 490, 494, 495, 507, 510 mass spectrum, 73 mass-sheet degeneracy, 29, 30, 39, 57, 113, 133, 169, 315, 319, 328, 330, 343, 398 mass-to-light ratio, 128, 129, 143, 155, 157, 161, 175, 178, 186, 233, 250, 300, 333, 337, 414, 418 matter 548 Index baryonic, 129, 178, 179, 192, 211–217, 231 dark, 14–16, 31, 44, 58, 62, 68, 73–75, 82, 83, 129, 136, 137, 139, 147, 155–157, 163, 175, 190, 194, 212, 214, 231, 250, 299–301, 309, 313–315, 335, 347, 366, 375, 400–402, 405, 413, 417, 422, 429, 438, 461, 475–477, 483, 484, 528, 531, 533 luminous, 14 Mattig relation, 52 MEGA, 478 MegaCam, 282, 284, 404 metric Robertson-Walker, 45 MG 0414+0534, 94, 99 MG 1131+0456, 7, 97, 100 MG 1549+3047, 160 MG 1654+13, 11 MG 2016+112, 94, 99, 160 MGC 2214+3550, 219 MicroFUN, 486, 492, 496 microlensing, 453 astrometric, 488, 489, 501, 516, 531 binary lenses, 461, 462, 465–467, 472, 484, 486, 497, 499, 505, 510 binary source, 500, 505 blending, 465, 478, 499, 500, 519–521 caustic, 460, 462, 467, 473, 487, 490, 499, 505, 507, 512, 522, 524, 531 critical curves, 462, 463 degeneracies, 458, 475, 490, 499, 500, 517 detection efficiency, 480, 485, 493 direct imaging, 513 Einstein ring radius, 455, 461, 462, 475, 487, 496, 499, 518, 522 Galactic, 453, 458, 484 high magnification event, 478, 491, 493, 496, 513 impact parameter, 456, 459, 466, 491, 499, 501, 508, 513, 516, 519 lightcurve, 457, 462, 465, 466, 477, 479, 486, 487, 495, 496, 499, 501, 524, 528, 534 magnification, 455, 464, 465, 487, 499, 516, 533 observables, 457 optical depth, 460, 477, 479, 481, 484, 500, 524 parallax, 475, 494, 499, 501, 504, 505, 514, 517, 518 pixel lensing, 478 planet, 472, 486–488, 493, 497 point lens, 458 point source, 458 probability, 460, 470, 471, 488, 489 quasar, 453, 520, 521, 524, 526, 531, 534 self lensing, 471, 481, 483 source size, 464, 475, 507, 519, 528, 531, 534 statistics, 460, 478, 489, 492, 531 stellar, 454–456, 459, 462, 465, 472, 479, 483, 484, 492, 497, 520 substructures, 531 time scale, 457, 458, 466, 467, 479, 484, 485, 487, 499, 501, 503, 504, 522 microlensing event EROS BLG-2000-005, 472 MACHO 1998-SMC-1, 467 MACHO 1999-BLG-047, 471 MACHO 95-BLG-30, 519 MACHO 97-BLG-28, 510 MACHO 97-BLG-41, 506 MACHO LMC-5, 513 MACHO-99-SMC-1, 471 MOA 2003-BLG-53, 497 OGLE 2003-BLG-235, 497 OGLE-1999-BUL-19, 504 OGLE-1999-BUL-23, 513 OGLE-1999-CAR-1, 503 OGLE-2002-BLG-055, 494 OGLE-2003-BLG-170, 495 OGLE-2003-BLG-194, 495 OGLE-2003-BLG-262, 510 OGLE-7, 466 sc33 4505, 505 microlensing experiment AGAPE, 478 EROS, 472, 481, 485 GEST, 492 MACHO, 467, 471, 477, 479, 484 MEGA, 478 MicroFUN, 486, 492, 496 MOA, 478, 486, 492, 496 Index MPF, 492 OGLE, 477, 484, 486, 492, 496, 535 PLANET, 472, 477, 486, 492, 496, 507 WeCAPP, 478 microlensing in quasars, 9, 453, 520, 521, 524, 526, 531, 534 microlensing in the Galaxy, 13 Milky Way, 459, 460, 471, 477–479, 483, 484, 486, 490 MIT/Greenbank Survey, 184 Mitchell, J., 2, MOA, 478, 486, 492, 496 moments, 274 MOND, 476 Moore profile cusp, 103, 107, 110, 127, 218 MPF, 492 MS 0302+17, 335 MS 1008-1224, 342 MS 1054-03, 337, 339 MS 1512+36, 59 multi screen lens, 129 multi-deflection, 381 multiple images criteria, 28 multiple lens-plane, 380, 382 naked cusp, 43 natural components of the 3PCF, 432 neutralino, 82 neutrinos, 48, 67, 78, 81 NFW density profile, 76, 103, 138, 145, 306, 313, 314, 327, 334, 349, 410, 414, 438 non-parametric models, 150 non-singular isothermal sphere (NIS), 40 null geodesic, 49 number counts of galaxies, 347, 423 background, 342 number counts of images, 319, 327, 339 number of images, 27 OGLE, 466, 477, 484, 486, 492, 496, 505, 535 OmegaCAM, 282, 403 optical depth, 57, 194–198, 205, 228, 242, 460, 477, 479, 481, 484, 500, 524 549 Optical HST Snapshot Lens Survey, 208 optical tidal matrix, 356 parallax, 475, 494, 499, 501, 504, 505, 514, 517, 518 parameter concentration, 76 curvature, 45 shape, 67 parity, 24, 102, 112, 277, 455, 456, 464, 533 Parkes-MIT-NRAO Lens Survey (PANELS), 184, 209 PG 1115+080, 5, 94, 95, 142, 160, 168–171, 174, 176–178, 181, 247, 252 photometric redshift, 351, 392 pixel lensing, 478 PKS 1145–071, 219 PKS 1830–211, 170, 196 Planck satellite, 367 plane deflector, 20 lens, 20 source, 20 PLANET, 472, 486, 492, 496, 507 planet, 475 microlensing, 18, 472, 486–488, 493, 497 PMN 1632–0033, 97, 100 PMN J0134–0931, 94 PMN J1632–0033, 94, 147 PMN J2004–1349, 196 point-mass lens, 31, 105 point-spread function (PSF), 283, 294, 296 affecting shape of faint galaxies, 269 anisotropy, 292, 294, 295, 354, 382, 385, 388, 390, 394 corrections, 412, 440 seeing, 283 size of, 281 stability, 298 Poisson equation, 22, 30, 63 power spectrum, 66, 67, 72, 360, 361, 365, 368, 377, 382, 383, 399, 419 3-D, 399 550 Index normalisation, 69, 70, 72, 79, 81, 311, 361, 367, 384, 385, 387, 396, 397, 400 power-law lens, 102, 104 Press–Schechter approach, 71, 73, 74 projected ellipticity, 375 proper distance, 51 proper volume element, 51 QSO, 427 QSO 0957+561, 5–7, 13, 24, 139, 145, 147, 148, 160, 162, 169, 170, 174, 178, 180, 256, 453, 527 QSO 1422+231, 17 QSO 2237+0305, 9, 10, 123, 148, 160, 161, 183, 196, 227, 453, 527 QSO 2345+007, 218 QSO-galaxy association, 428 quasar, radio-loud (RLQ), 252 radio-quiet (RQQ), 251, 252 binary, 218–220, 232 brightness profile, 521 continuum emitting region, 527 microlensing, 9, 453, 520, 521, 524, 526, 531, 534 size, 521, 534 structure, 534 variability, 527, 531 radial velocity (method of), 488, 490 radiation density, 47 radio-loud quasar (RLQ), 252 radio-quiet quasar (RQQ), 251, 252 random field, 64 Red Cluster Sequence (RCS), 332, 423 survey, 312, 392, 409, 410, 424 Red-Sequence Cluster Survey (RCS), 409 redshift distribution of galaxies, 387, 392 reduced shear, 24, 25, 30, 39, 276, 277, 295, 296, 317, 318, 330, 382 Refsdal, S., 4, 454 relative velocity, 456, 458, 501, 504, 514, 522 resonant lensing, 487 Robertson-Walker metric, 45 robotic telescopes, 535 rotating lens, 505, 506 rotation curves, 475 RX J0911+0551, 155, 156, 169–171, 173, 174, 178 RX J1131–1231, 94, 96 SAAO, 473 saddle point image, 533 satellite COBE, 69, 80 WMAP, 70, 77, 80 satellite galaxies, 94 SBS 1520+530, 170, 174, 177, 178, 181 scale factor, 45 scaled deflection angle, 21 Schechter luminosity function, 61, 185–187, 194, 195 Schwarzschild radius, 3, 18 SCUBA, 304 SDSS 1004+4112, 211 seeing, 283 self lensing, 471, 481, 483 SExtractor, 292 shape parameter, 67 Shapiro effect, 53 shear, 23–25, 32, 77, 102, 317, 322 3PCF, 432 complex, 25 correlation function, 372 cosmic, 271, 350, 351, 355, 358, 360, 365, 366, 375, 383, 386, 394, 401, 419 detection, 422 cross components of, 277, 278 dispersion, 362, 364, 365, 368, 384, 387, 391, 395 estimate, 321 external, 39, 112, 166 internal, 166 invariant, 167 mean tangential, 279, 406 reduced, 24, 25, 30, 39, 276, 277, 295, 296, 317, 318, 330, 339, 382 survey, 388 systematic uncertainty, 296 tangential, 277, 278 tidal, 112 single screen lens, 129 Index singular isothermal ellipsoid (SIE), 120, 121, 136, 138, 156, 168, 245 singular isothermal sphere (SIS), 36, 102–104, 107, 120, 121, 134, 135, 158, 168, 203, 279, 334, 410 Sloan Digital Sky Survey (SDSS), 79, 183, 200, 206, 207, 221, 411, 413, 426, 427 Small Magellanic Cloud (SMC), 460, 467, 471, 478, 481, 483, 518 SNAP, 404 solar eclipse, Soldner, J., 454 source counts, 280 source plane, 20 source redshift distribution, 92 Space Interferometry Mission (SIM), 518, 531 star spots, 499, 507, 513 statistics two-point, 373 stellar lens, 454–456, 459, 462, 465, 479, 483, 492, 497, 520 STIS, 298, 390 stochastic biasing, 419 structure formation, 61 substructure mass distribution, 122, 144, 148, 221, 224, 225, 227, 228, 230, 231 supercluster, 337 Abell 901/902, 335, 398 MS 0302+17, 335 supernovae high-redshift, 78 Type Ia, 78, 80 Suprime-Cam, 282 survey, 387 surface mass density, 19, 30, 358 κ, 279, 307, 316, 322, 326, 338, 356, 358, 397 absolute, 30 critical, 21, 29, 53 dimensionless, 21 homogeneous, 29 local, 339 mean, 32 microlensing, 460 normalized, 522 smooth, 27 551 survey 2dF galaxy redshift, 78, 183 CfA redshift, 183 CfA-Arizona Space Telescope Lens (CASTLES), 92, 96, 139, 143, 221, 253 Cosmic Lens All Sky (CLASS), 153, 184, 203, 206, 207, 209, 211, 231 HST Medium Deep (MDS), 183 Jodrell/VLA Astrometric (JVAS), 5, 209 lensed optical quasars, 184 MIT/Greenbank, 184 Optical HST Snapshot Lens, 208 Parkes-MIT-NRAO Lens (PANELS), 184, 209 Sloan Digital Sky (SDSS), 79, 183, 200, 206, 207, 221 tangential caustic, 43 temperature fluctuations, 61 temperature map of the universe, 271 theorem Birkhoff, 31, 71 Liouville, 23 magnification, 28 odd-number, 27, 35, 37 Poincar´e–Hopf index, 27 tidal shear, 112 time delay, 4, 12, 143, 164–166, 527 geometrical, 53 gravitational, 53 total, 53 total density parameter, 48 total time delay, 53 transfer function, 67 transit (of planet), 488 Tully–Fisher relation, 187–189, 408 two-point statistics, 373 uniform critical sheet, 102 vacuum energy, 47, 62, 83, 206, 312, 355, 366, 399–401, 404, 434, 439 vacuum energy density, 47 velocity dispersion, 36, 159 Very Large Array (VLA), 5, 6, 221, 282 Very Large Telescope (VLT), 9, 282 552 Index Very Large Telescope Interferometry (VLTI), 518 Very Long Baseline Interferometry (VLBI), 5, 6, 144, 147, 148, 180, 221, 229 virial equilibrium, 73, 301 virial mass, 128, 160, 218, 235 virial radius, 73, 76, 128, 160, 218, 235 virial theorem, 163 VIRMOS-DESCART, 376, 386, 387, 389, 397, 424 VISTA, 331, 404 Vlasov equation, 63, 70 volume element comoving, 51 proper, 51 von Soldner, J., 2, VST, 403 weight function, 295, 345, 349 Weymann, R.J., WFI, 282, 288, 294, 353 geometric distortion, 289 WFPC2, 298, 390 wide field imaging BTC, 351, 383, 389 CFH12K, 282, 386 MegaCam, 282, 284, 404 OmegaCAM, 282, 403 SNAP, 404 Suprime-Cam, 282 VISTA, 331, 404 VST, 403 WFI, 282, 288, 294, 353 geometric distortion, 289 WIRCAM, 331 WMAP, 300, 366, 367, 397, 427 WMAP satellite, 70, 77, 80 Walsh, D., weak lensing detection, 278 general, 269, 271 mass reconstruction, 323 observations, 282, 292 of the CMB, 272 signal-to-noise, 278, 281, 342, 347, 349 weak shear survey, 388 WeCAPP, 478 X-ray, 301, 337, 343 cluster, 333 mass, 310, 341 observations, 310 temperature, 338 XMM, 303, 304, 338 YALO, 473 Young diagram, 38 Zwicky, F., 3, 54, 299, 300 Index 553 ... wrote Part about Strong Gravitational Lensing, while P Schneider in Part dealt with VIII Preface Weak Gravitational Lensing, and J Wambsganss in Part about Gravitational Microlensing We are thankful... as SL (Strong Lensing, Kochanek, 2005, Part of this book), WL (Weak Lensing, Schneider, 2005, Part of this book), and ML (MicroLensing, Wambsganss, 2005 Part of this book) Gravitational lensing. .. in Microlensing: 499 Astrometric Microlensing 516 Quasar Microlensing 520 7.1 Microlensing