Gravitational Lenses

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Springer Science & Business Media, Oct 19, 1999 - Science - 560 pages
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Light observed from distant objects is found to be deflected by the gravitational field of massive objects near the line of sight - an effect predicted by Einstein in his first paper setting forth the general theory of relativity, and confirmed by Eddington soon afterwards. If the source of the light is sufficiently distant and bright, and if the intervening object is massive enough and near enough to the line of sight, the gravitational field acts like a lens, focusing the light and producing one or more bright images of the source. This book, by renowned researchers in the field, begins by discussing the basic physics behind gravitational lenses: the optics of curved space-time. It then derives the appropriate equations for predicting the properties of these lenses. In addition, it presents up-to-date observational evidence for gravitational lenses and describes the particular properties of the observed cases. The authors also discuss applications of the results to problems in cosmology.
 

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Contents

Introduction
1
112 The period 19191937
3
113 The period 19631979
6
114 Post1979
9
12 Outline of the book
11
13 Remarks about notation
21
Basic facts and the observational situation
25
22 The general lens
29
Multiple light deflection
281
91 The multiple lensplane theory
282
912 The magnification matrix
285
913 Particular cases
287
92 Time delay and Fermats principle
288
93 The generalized quadrupole lens
291
Numerical methods
295
101 Roots of onedimensional equations
296

23 The magnification factor
33
24 Observing gravitational lens systems
41
241 Expectations for point sources
42
242 Expectations for extended sources
46
25 Known gravitational lens systems
47
251 Doubles
48
252 Triples
60
253 Quadruples
64
254 Additional candidates
71
255 Arcs
72
256 Rings
77
257 A rapidly growing list of candidates
84
259 Gravitational lenses and cosmology
89
Optics in curved spacetime
91
32 Locally approximately plane waves
93
33 Fermats principle
100
34 Geometry of ray bundles
104
342 Optical scalars and their transport equations
106
35 Distances based on light rays Caustics
110
36 Luminosity flux and intensity
115
Derivation of the lens equation
119
42 Approximate metrics of isolated slowly moving noncompact matter distributions
121
43 Light deflection by quasistationary isolated mass distributions
123
44 Summary of FriedmannLemaitre cosmological models
127
45 Light propagation and redshiftdistance relations in homogeneous and inhomogeneous model universes
132
452 Redshiftdistance relations
134
453 The DyerRoeder equation
137
46 The lens mapping in cosmology
143
47 Wave optics in lens theory
150
Properties of the lens mapping
157
52 Magnification and critical curves
161
53 Time delay and Fermats principle
166
54 Two general theorems about gravitational lensing
172
542 Generalizations
176
543 Necessary and sufficient conditions for multiple imaging
177
Lensing near critical points
183
61 The lens mapping near ordinary images
184
62 Stable singularities of lens mappings
185
621 Folds Rules for truncating Taylor expansions
186
622 Cusps
192
623 Whitneys theorem Singularities of generic lens maps
197
63 Stable singularities of oneparameter families of lens mappings metamorphoses
198
631 Umbilics
199
632 Swallowtails
203
633 Lips and beaktobeaks
207
634 Concluding remarks about singularities
211
64 Magnification of extended sources near folds
215
Wave optics in gravitational lensing
217
72 Magnification near isolated caustic points
220
73 Magnification near fold catastrophes
222
Simple lens models
229
81 Axially symmetric lenses
230
812 The Schwarzschild lens
239
813 Disks as lenses
240
814 The singular isothermal sphere
243
815 A family of lens models for galaxies
244
816 A uniform ring
247
82 Lenses with perturbed symmetry Quadrupole lenses
249
821 The perturbed Plummer model
252
822 The perturbed Schwarzschild lens ChangRefsdal lens
255
83 The two pointmass lens
261
832 Two point masses with arbitrary mass ratio
264
834 Generalization to N point masses
265
84 Lenses with elliptical symmetry
266
841 Elliptical isodensity curves
267
842 Elliptical isopotentials
268
843 A practical approach to nearly elliptical lenses
271
85 Marginal lenses
274
86 Generic properties of elliptical lenses
277
862 Imaging properties
278
102 Images of extended sources
298
103 Interactive methods for model fitting
299
104 Grid search methods
300
105 Transport of images
302
106 Ray shooting
303
107 Constructing lens and source models from resolved images
307
Statistical gravitational lensing General considerations
309
111 Crosssections
310
1111 Multiple image crosssections
311
1112 Magnification crosssections
313
112 The random star field
320
1121 Probability distribution for the deflection
322
1122 Shear and magnification
328
1123 Inclusion of external shear and smooth matter density
330
1124 Correlated deflection probability
334
1125 Spatial distribution of magnifications
337
113 Probabilities in a clumpy universe
344
114 Light propagation in inhomogeneous universes
348
1141 Statistics for light rays
350
1142 Statistics over sources
364
115 Maximum probabilities
366
Statistical gravitational lensing Applications
371
121 Amplification bias and the luminosity function of QSOs
373
1212 QSO source counts and their luminosity function
378
122 Statistics of multiply imaged sources
380
1221 Statistics for pointmass lenses
381
1222 Statistics for isothermal spheres
385
Symmetric lenses
395
Asymmetric lenses
399
1225 Lens surveys
401
1231 Observational challenges
404
1232 Mathematical formulation of the leasing problem
407
1233 Maximal overdensity
408
1234 Lens models
411
1235 Relation to observations
415
Astrophysical discussion
419
1241 Lensinduced variability
421
1242 Microlensing in 2237+0305
425
1243 Microlensing and broad emission lines of QSOs
429
1244 Microlensing and the classification of AGNs
433
Detailed discussion
435
1252 Observational hints of amplification bias
444
1253 QSOgalaxy associations revisited
447
126 Distortion of images
448
127 Lensing of supernovae
453
128 Further applications of statistical lensing
456
1282 Recurrence of 7ray bursters
460
1283 Multiple imaging from an ensemble of galaxies and the missing lens problem
461
Gravitational lenses as astrophysical tools
467
131 Estimation of model parameters
468
1311 Invariance transformations
471
determination of Ha is not possible unless
473
1313 Application to the 0957+561 system
476
132 Arcs in clusters of galaxies
483
1322 The nearly spherical lens
485
1323 Analysis of the observations arcs as astronomical tools
492
1324 Statistics of arcs and arclets
498
133 Additional applications
501
1332 Scanning of the source by caustics
504
1333 The parallax effect
508
1334 Cosmic strings
509
1335 Upper limits to the mass of some QSOs
511
1336 Gravitational lensing and superluminal motion
512
134 Miscellaneous topics
513
1342 Light deflection in the Solar System
514
References
517
Index of Individual Objects
545
Subject Index
547
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Page 540 - Stocke, JT, Liebert, J., Gioia, IM, Griffiths, RE, Maccacaro, T., Danziger, IJ, Kunth, D.
Page 540 - ... Springer- Verlag, in press. Smette, A., Surdej, J., Shaver, PA, Foltz, CB, Chaffee, FH, Weymann, RJ, Williams, RE, Magain, P.: 1991, Astrophys. J., in press. Soucail, G., Mellier, Y., Fort, B., Hammer, F., Mathez, G.: 1987, Astron. Astrophys. 184, L7. Steidel, CC, Sargent, WLW: 1991, Astron. J., in press. Surdej, J., Magain, P., Swings, J.-P., Borgeest, U., Courvoisier, TJ-L., Kayser, R., Kellermann, KI, Kuhr, H., Refsdal, S.: 1987, Nature 329, 695.
Page 539 - SMETTE, A., SURDEJ, J., SHAVER, PA, FOLTZ, CB, CHAFFEE, FH, WEYMANN, RJ, WILLIAMS, RE & MAGAIN, P. 1992, A spectroscopic study of UM 673 A and B - On the size of Lya clouds, ApJ, 389, 39.
Page 542 - On Riemannian spaces with spherical symmetry about a line, and the conditions for isotropy in general relativity.

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Modern Cosmology
Scott Dodelson
Limited preview - 2003
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