H0, 4, 12, 13, 16, 47, 79, 98, 123, 128, 163–165, 169, 171, 174–178, 180

Home , Abell 2218, Abell 222, Abell 2390, Abell 370

Index

H0, 4, 12, 13, 16, 47, 79, 98, 123, AGAPE, 478 128, 163–165, 169, 171, 174–178, angle 180–182, 194, 255, 300, 303, 357, deflection, 18, 461 358, 397 scaled deflection, 21 Ω0 = Ωtot,48 angular correlation function, 423 ΩCMB,48 angular diameter distance, 45, 50, 52, ΩΛ, 47–49, 64 53, 98, 164, 194, 271, 357 Ωm, 47–49, 64 aperture mass, 315, 343, 345, 347, 363, Ωr, 47–49, 64 423 Σ(ξ), 34, 36 dispersion, 368, 393, 395, 420 μp,56 map, 346 σ(Δθ), 56 third-order statistics, 433 σ8, 69, 70, 72, 79, 81, 311, 361, 367, APM 08279+5255, 17, 59, 61, 94, 118, 384, 385, 387, 396, 397, 400 220, 243 σQ,56 arc, 7, 9, 10, 15, 304, 306, 310–312, 315, σv,36 335, 341, 352 σtot(Q), 57 arclet, 7, 10, 270, 304, 306, 315, 441 0047–2808, 160, 250 astroid, 43 2dF Galaxy Redshift Survey, 78, 183 astroid curve, 114, 116, 192, 202, 245 3-D gravitational potential, 398 B 0218+357, 170, 173, 174, 196, 240, lensing, 397 242, 531 B 1359+154, 94 Abell 1689, 305, 310, 313, 315, 334, 335, B 1422+231, 156, 170, 171, 221, 243 341 B 1600+434, 170, 174, 177, 178, 181, Abell 1705, 352 196, 531 Abell 2218, 10, 17, 309 B 1608+656, 156, 160, 170, 173, 180 Abell 222/223, 335, 336 B 1933+503, 94, 98, 145, 146 Abell 2390, 306, 307 B 1938+666, 12 Abell 370, 270, 309, 315 B 2108+213, 211 Abell 901/902, 335 B-modes, 371, 372, 374, 392, 393, 433 ACS, 281, 298, 305, 313, 390 background galaxies, 332, 393, 406, 409 adiabatic equation, 45 baryonic matter, 129, 178, 179, 192, affine parameter, 19 211–217, 231, 300, 347 542 Index

Bessel functions, 362, 364 Charge Coupled Device (CCD), 5, 478, bias 500 factor, 430 fringes, 286, 287 of galaxies, 405 mosaic, 11, 383 parameter, 418, 419, 421, 427 multi-chip, 286 biasing of galaxies, 271, 416–418, 427 chromatic effect, 14 stochastic, 419 Chwolson, O., 3, 454 binary lenses, 461, 462, 465–467, 472, Cl 0024+17, 310, 311, 340 484, 486, 497, 499, 505, 510 Cl 1409+52, 315 binary quasars, 218–220, 232 Cl 2244−02, 9 MGC 2214+3550, 219 CLASS, 5 PKS 1145–071, 219 clusters of galaxies, 299, 415 QSO 2345+007, 218 Abell 2218, 10, 17, 441 binary source, 500, 505 Abell 222/223, 335 binary stars, 465, 479, 486, 505, 521 Abell 851, 416 Birkhoff theorem, 31, 71 AC 114, 416 blending, 465, 478, 499, 500, 519–521 central cD, 299, 309 Bremsstrahlung, 301, 302 Cl 0939+4713, 417 brightness Cl 2244−02, 9 moments, 274 MG 1131+0456, 7 profile, 294 MS 1054-03, 337 in X-rays, 302 MS 1512+36, 59 BTC, 351, 383, 389 CMB, 300, 366, 367, 400 Butcher–Oemler effect, 300 anisotropy, 271, 366, 401, 427 temperature map, 271 Canopus, 473 CMB anisotropies Carswell, R.F., 5 primary, 77 causal contact, 62 secondary, 77 caustic, 25, 26, 104, 113, 115–117, 121, coaddition, 290, 291 201, 222, 230, 245, 247, 460, 462, COBE satellite, 69, 80 467, 473, 487, 490, 499, 505, 507, Cold Dark Matter (CDM), 15, 67, 82, 510, 512, 522, 524, 531 107, 128, 129, 148, 157, 178, 208, fold, 26 211, 212, 220 lips, 41 collisionless Boltzmann equation, 63 tangential, 43 COMBO-17, 293, 376, 391 Cavendish, H., 2 comoving cB58, 17, 59, 61 angular diameter distance, 45, 50, 52, cD galaxy, 299, 309 58, 98, 164, 194, 357 CDM, 309, 313, 314, 424 distance, 49, 50, 53 CfA redshift survey, 183 horizon, 62, 67 CfA-Arizona Space Telescope Lens number density, 58, 73 Survey (CASTLES), 92, 96, 139, observer, 45 143, 221, 253 radial coordinate, 45 CFH12K, 282, 386 radius, 73 CFHT, 282, 386 sphere, 70 CFRS 03.1077, 160 volume, 45, 46 Chandra, 303, 304, 310, 338 volume element, 51 Deep Field South (CDF-S), 292, 293 compact objects, 15, 453, 477, 486, 521, Chang, K., 454 524, 528 Index 543 complex shear, 25 174–178, 180–182, 194, 255, 300, concentration parameter, 76 303, 357, 358, 397 concordance, 79 Hubble radius, 194 concordance model, 77, 83 radiation density, 47 conformal gravity, 476 total density parameter, 48 constant cosmological standard model cosmological, 46 homogeneous Universe, 44 convergence, 21, 102, 308, 377 inhomogeneous Universe, 61 coordinates critical curve, 25, 26, 30, 32, 104, 113, angular, 21 115–117, 121, 201, 222, 230, 245, correlation coefficient, 422 247, 319 correlation function, 65, 362, 369, radial, 32 372–374, 382, 419 tangential, 32 AGN-galaxy, 429 critical curves, 17, 462, 463 angular, 423 critical density, 47 QSO–galaxy, 430 critical surface mass density, 331 three-point (3PCF), 431–433 cross-section natural components, 432 point-mass lens, 55 two-point, 360, 386, 427 singular isothermal sphere, 56 cosmic density fluctuations, 72 crossing time, 467, 470, 483, 522 Cosmic Lens All Sky Survey (CLASS), curvature of the Universe, 357 153, 184, 203, 206, 207, 209, 211, curvature parameter, 45 231 cusp, 26, 462, 473, 510 Cosmic Microwave Background (CMB), naked, 43 44, 47, 61, 69, 77, 79, 80, 82, 83 cosmic scale factor, 45 dark clusters, 353, 355 cosmic shear, 355, 358, 360, 365, 366, dark energy, 16, 47, 62, 83, 206, 312, 375, 383, 386, 394, 401, 419 355, 366, 399–401, 404, 434, 439 detection, 422 Dark Matter surveys, 434 Cold (CDM), 67, 82, 107, 128, 129, cosmic time, 45 148, 157, 178, 208, 211, 212, 220 cosmological constant, 46 Hot (HDM), 67, 81 cosmological model, 366 dark matter, 14–16, 31, 44, 58, 62, cosmological models 68, 73–75, 82, 83, 129, 136, 137, Einstein-de Sitter, 52, 63, 64, 72, 73 139, 147, 155–157, 163, 175, 190, Friedmann-Lemaˆıtre, 46 194, 212, 214, 231, 250, 299–301, cosmological parameters, 47, 77, 311, 309, 313–315, 335, 347, 366, 375, 312, 314, 360, 366, 368, 369, 392, 400–402, 405, 413, 417, 422, 429, 394, 400 438, 454, 460, 461, 475–477, 479, ΩΛ, 323, 324, 367, 395 482–484, 521, 528, 531, 533 Ωm, 324, 367, 385, 395, 396 filaments, 335 σ8, 311, 361, 367, 383–385, 387, 396, profile of galaxies, 406 397, 400, 427 dark matter distribution, 68, 300, 301, cosmological constant, 46, 80, 83 309, 313, 315, 335, 347, 366, 375, critical density, 47 400, 402, 405, 417, 422, 429 curvature, 357 dark matter halo, 38, 73, 75, 76, density parameters, 47, 49, 80 126–129, 136, 137, 139, 155–157, Hubble constant, 4, 12, 13, 16, 47, 79, 163, 175, 190, 212, 214, 231, 250, 98, 123, 128, 163–165, 169, 171, 314, 405, 411, 413, 415, 438, 460, 544 Index

461, 475, 477, 479, 480, 483, 484, 176, 192, 197, 218, 224, 229, 277, 521, 528, 531, 533 305 deflection angle, 18, 19, 461 Einstein ring, 8, 102–104, 107, 112, 139, deflection potential, 22, 308, 324, 326, 155, 173, 219, 233, 243, 244, 246, 358 247, 251 deflector plane, 20 radio, 8, 11, 97 degeneracies, 458, 475, 490, 499, 500, radius, 455, 461, 462, 475, 487, 496, 517 499, 518, 522 density visible, 3, 8, 251 contrast, 62, 64, 67, 418, 423, 431 Einstein time, 457, 458, 466, 485, 487, distribution, 19, 127 501, 503, 504, 522 fluctuations, 62, 64, 67, 81 Einstein, A., 3, 454 lens number, 15, 57 Einstein-de Sitter cosmological model, parameters, 47, 49, 80 52, 63, 64, 72, 73 density profile ellipticity, 296, 386 de Vaucouleurs, 125, 126, 138, 158 complex, 274, 275 exponential disk, 125, 126 definition, 274 Hernquist, 126, 127, 145, 147 dispersion, 276 Navarro, Frenk and White (NFW), intrinsic, 273, 276, 281, 376 76, 103, 138, 145, 306, 313, 314, mean, 276 327, 334, 349, 410, 414, 438 tangential, 278, 406 Sersic, 126 energy universal=NFW, 76, 103, 138, 145, dark, 16, 47, 62, 83, 206, 312, 355, 306, 313, 314, 327, 334, 349, 410, 366, 399–401, 404, 434, 439 414, 438 vacuum, 83, 206, 312, 355, 366, differential image (analysis), 501 399–401, 404, 434, 439 dispersion entropy regularization, 325 aperture mass, 363, 365, 368, 393, equation 395, 420 adiabatic, 45 of intrinsic ellipticity, 409 collisionless Boltzmann, 63 shear, 362, 364, 365, 368, 384, 387, Friedmann, 45 391, 395 Jeans, 158, 160, 190, 192 distance, 49, 458, 461, 483, 487, 488, Poisson, 22, 30, 63 499, 518 Vlasov, 63, 70 angular diameter, 45, 50, 52, 53, 98, equation of state (EOS), 46 164, 194, 271, 357 EROS, 472, 477, 481, 485 comoving, 49, 50, 52, 53 ESO Imaging Survey (EIS), 293 luminosity, 51 European Southern Observatory (ESO), proper, 51 518 distance ladder, 16 external shear, 39, 112, 166 distortion, 24 doppler wobble, 488 Faber–Jackson relation, 187–189, drizzling, 290 232–235, 408 Fermat potential, 22, 27, 30, 36, 54 E-modes, 371, 372, 374, 393, 433 filament, 335 EEWS, 495, 496, 498 fluctuation field, 68 Einstein angle-radius, 35, 40, 53 flux conservation, 60 Einstein radius, 103, 104, 112, 120, 130, flux ratio anomaly, 531 132, 135, 140, 141, 157, 164, 170, fold caustic, 26 Index 545 fold caustics, 465, 470 H 1413+117, 531 FORS, 282 Harrison–Zeldovich power spectrum, 68, FORS1, 350, 351, 383 81, 83 Fourier mode, 67 HE 0230–2130, 156 Fourier transform, 65, 307, 308, 316, HE 0435–1223, 94, 96, 156 361, 418 HE 1104–1805, 94, 95, 170, 180, 242 Friedmann equation, 45 HE 2149–2745, 170, 174, 177, 178, 181 Friedmann-Lemaˆıtre cosmological high magnification event, 491, 493, 496, models, 46 513 Hipparcos, 518 Galactic Bulge, 458, 478, 484, 500, 501, horizon, 67 518 Hot Dark Matter (HDM), 67, 81 HST, 5, 6, 8, 96, 305, 337, 390 Galactic halo, 471, 481 HST 14176+5226, 160 Galactic microlensing, 453, 458 HST 15433+5352, 160 galactic microlensing events HST Medium Deep Survey (MDS), 183 MACHO-LMC-1, 14 Hubble galaxies Deep Field, 276, 282, 312 background, 332, 393, 406, 409 Ultra Deep Field (UDF), 292 brightness moments, 274 Hubble constant, 4, 12, 13, 16, 47, 79, clusters, 299 98, 123, 128, 163–165, 169, 171, depletion, 280 174–178, 180–182, 194, 255, 300, distorsion, 272 303, 357, 358, 397 faint images, 272 Hubble expansion, 46, 71 number density, 280, 282 Hubble radius, 194 galaxy Hubble Space Telescope (HST), 5, 6, 8, cB58, 17, 59, 61 96, 305, 337, 390, 513 host, 8, 17 IRAS F10214, 17, 59, 61 image parity, 24, 102, 112 quasar host, 95, 99, 126, 169, 180, image positions, 143 219, 220, 243, 245, 247, 248, image separation, 35, 106 250–254, 256 image separation distribution, 92, 215 galaxy biasing, 416, 417, 427 impact parameter, 18, 456, 459, 466, galaxy–galaxy lensing, 271, 405, 406, 499, 501, 508, 513, 516, 519 409, 412, 413, 415 inflation, 68 Gaussian random field, 66 internal shear, 166 GEMS, 292 interstellar medium (ISM), 123, 143, geometrical time delay, 53 199, 221, 224, 232 geometrically-thin lens, 19 intracluster GEST, 492 gas, 299 giant arcs, 304, 306, 312 medium (ICM), 299, 301, 302 cluster intrinsic Abell 1689, 305 alignment, 375 Abell 370, 270 alignment of galaxies, 375, 402 discovery, 270 ellipticity, 376 Golden Lens, 181 dispersion, 409 GOODS, 292, 293 orientation of galaxies, 406 gravitational instability, 61 invariant shear, 167 gravitational time delay, 53 IRAS F10214, 17, 59, 61 546 Index isothermal mass distribution, 121, 123–125, ellipsoid, 306 128, 137, 141, 143, 145, 152, 153, mass profile, 342 159–161, 175, 190, 233, 237, 243, isothermal ellipsoid 250 singular (SIE), 120, 121, 136, 138, multi screen, 129 156, 168, 245 non-symmetric, 38 isothermal sphere number density, 15, 57 non-singular (NIS), 40 point-mass, 31, 34, 102, 105, 455, 457, singular (SIS), 36, 102–104, 107, 120, 458, 461, 499, 516, 524 121, 134, 135, 168, 203 power-law, 102, 104 quadrupole, 38, 40 Jacobi matrix, 272, 357, 380 rotating, 505, 506 Jacobian matrix, 23–25, 27, 32, 40, 41 Schwarzschild, 56 Jeans equation, 158, 160, 190, 192 single screen, 129 Jodrell/VLA Astrometric Survey lens equation, 20, 101, 104, 143 (JVAS),5,209 lens models, 97 JVAS, 5 lens number density, 15, 57 JWST, 441 lens plane, 20 lensed galaxies K-correction, 51 0047–2808, 160, 250 Kaiser–Squires inversion, 316, 322, 344 CFRS 03.1077, 160 Kepler law, 475 lensed optical quasars survey, 184 keplerian rotation, 475 lensed quasars Klimov, Yu.G., 4 APM 08279+5255, 17, 59, 61, 94, KSB method, 296, 297, 383 118, 220, 243 B 0218+357, 170, 173, 174, 196, 240, Lagrangian perturbation theory, 70 242, 531 Laplace, P.-S., 2 B 1359+154, 94 Large Magellanic Cloud (LMC), 460, B 1422+231, 156, 170, 171, 221, 243 467, 477–479, 482, 483, 513, 518 B 1600+434, 170, 174, 177, 178, 181, large-scale structure (LSS), 70, 78, 300, 196, 531 436 B 1608+656, 156, 160, 170, 173, 180 lensing by, 271, 333, 355, 357, 382 B 1933+503, 94, 98, 145, 146 mass distribution, 348 B 1938+666, 12 of the cosmic matter field, 355 B 2108+213, 211 Las Campanas, 493 H 1413+117, 531 lens, 3, 15 HE 0230–2130, 156 as a natural telescope, 16 HE 0435–1223, 94, 96, 156 axially symmetric, 31 HE 1104–1805, 94, 95, 170, 180, 242 centrally condensed, 34 HE 2149–2745, 170, 174, 177, 178, circular, 101 181 compact objects, 15 HST 14176+5226, 160 cross-section, 55 HST 15433+5352, 160 elliptical, 44 MG 0414+0534, 94, 99 ellipticity, 112 MG 1131+0456, 97, 100 geometrically thin, 19 MG 1549+3047, 160 isothermal sphere, 31, 36, 40, 107 MG 1654+13, 11 mass, 14 MG 2016+112, 94, 99, 160 Index 547

PG 1115+080, 5, 94, 95, 142, 160, magnification, 9, 10, 17, 23, 25, 35, 59, 168–171, 174, 176–178, 181, 247, 102, 103, 280, 304, 310, 319, 327, 252 328, 332, 338, 339, 342, 429, 455, PKS 1830–211, 170, 196 464, 465, 487, 499, 516, 522, 533 PMN 1632–0033, 97, 100 likelihood, 326 PMN J0134–0931, 94 magnification bias, 55, 58, 152, 182, PMN J1632–0033, 94, 147 184, 197, 198, 200, 201, 203–205, PMN J2004–1349, 196 220, 238, 240, 319, 428 QSO 0957+561, 5–7, 13, 24, 139, 145, magnification tensor, 23, 101 147, 148, 160, 162, 169, 170, 174, Mandl, R., 3 178, 180, 256, 453, 527 mass QSO 2237+0305, 9, 10, 123, 148, 160, determination, 333 161, 183, 196, 227, 453, 527 dimensionless, 280 RX J0911+0551, 155, 156, 169–171, distribution, 309, 315 173, 174, 178 Abell 2218, 309 RX J1131–1231, 94, 96 Abell 370, 309 SBS 1520+530, 170, 174, 177, 178, isothermal, 342 181 large-scale structure, 348 SDSS 1004+4112, 211 of galaxies, 405 Liebes, S., 4 map, 320 light element abundances, 78 mean surface density, 279 light propagation, 356 reconstruction, 282, 315, 323, 333, light travel time, 164 337, 343, 416 lightcurve, 457, 462, 465, 466, 477, 479, Abell 1689, 334 486, 487, 495, 496, 499, 501, 524, Abell 1705, 352 528, 534 Abell 222/223, 336 limb darkening, 499, 507, 510 Cl 0024+17, 340 Limber’s equation, 359 MS 1054-03, 339 line-of-sight velocity surface density, 279, 307, 316, 322, dispersion, 408 326, 338, 358 distribution, 301 critical, 331 linear bias factor, 69 mass distribution, 120, 121, 123–125, linear growth factor, 63 128, 137, 141, 143, 145, 152, 153, 159–161, 175, 190, 233, 237, 243, Link, F., 454 250 Liouville theorem, 23 mass distribution substructure, 122, lips caustic, 41 144, 148, 221, 224, 225, 227, 228, Lodge, O.J., 3 230, 231 LSS lensing, 357, 436 mass profile of galaxies, 405 B-modes, 371, 372, 374, 392, 393 mass ratio, 462, 464, 472, 486, 488, 490, E-modes, 371, 372, 374, 393 494, 495, 507, 510 luminosity distance, 51 mass spectrum, 73 luminosity function mass-sheet degeneracy, 29, 30, 39, 57, Schechter, 61, 185–187, 194, 195 113, 133, 169, 315, 319, 328, 330, Ly-α forest, 79 343, 398 mass-to-light ratio, 128, 129, 143, 155, M31, 478 157, 161, 175, 178, 186, 233, 250, MACHO, 467, 477, 479, 484, 528 300, 333, 337, 414, 418 MACHO-LMC-1, 14 matter 548 Index

baryonic, 129, 178, 179, 192, 211–217, optical depth, 460, 477, 479, 481, 484, 231 500, 524 dark, 14–16, 31, 44, 58, 62, 68, parallax, 475, 494, 499, 501, 504, 505, 73–75, 82, 83, 129, 136, 137, 514, 517, 518 139, 147, 155–157, 163, 175, 190, pixel lensing, 478 194, 212, 214, 231, 250, 299–301, planet, 472, 486–488, 493, 497 309, 313–315, 335, 347, 366, 375, point lens, 458 400–402, 405, 413, 417, 422, 429, point source, 458 438, 461, 475–477, 483, 484, 528, probability, 460, 470, 471, 488, 489 531, 533 quasar, 453, 520, 521, 524, 526, 531, luminous, 14 534 Mattig relation, 52 self lensing, 471, 481, 483 MEGA, 478 source size, 464, 475, 507, 519, 528, MegaCam, 282, 284, 404 531, 534 metric statistics, 460, 478, 489, 492, 531 Robertson-Walker, 45 stellar, 454–456, 459, 462, 465, 472, MG 0414+0534, 94, 99 479, 483, 484, 492, 497, 520 MG 1131+0456, 7, 97, 100 substructures, 531 MG 1549+3047, 160 time scale, 457, 458, 466, 467, 479, MG 1654+13, 11 484, 485, 487, 499, 501, 503, 504, MG 2016+112, 94, 99, 160 522 MGC 2214+3550, 219 microlensing event MicroFUN, 486, 492, 496 EROS BLG-2000-005, 472 microlensing, 453 MACHO 1998-SMC-1, 467 astrometric, 488, 489, 501, 516, 531 MACHO 1999-BLG-047, 471 binary lenses, 461, 462, 465–467, 472, MACHO 95-BLG-30, 519 484, 486, 497, 499, 505, 510 MACHO 97-BLG-28, 510 binary source, 500, 505 MACHO 97-BLG-41, 506 blending, 465, 478, 499, 500, 519–521 MACHO LMC-5, 513 caustic, 460, 462, 467, 473, 487, 490, MACHO-99-SMC-1, 471 499, 505, 507, 512, 522, 524, 531 MOA 2003-BLG-53, 497 critical curves, 462, 463 OGLE 2003-BLG-235, 497 degeneracies, 458, 475, 490, 499, 500, OGLE-1999-BUL-19, 504 517 OGLE-1999-BUL-23, 513 detection efficiency, 480, 485, 493 OGLE-1999-CAR-1, 503 direct imaging, 513 OGLE-2002-BLG-055, 494 Einstein ring radius, 455, 461, 462, OGLE-2003-BLG-170, 495 475, 487, 496, 499, 518, 522 OGLE-2003-BLG-194, 495 Galactic, 453, 458, 484 OGLE-2003-BLG-262, 510 high magnification event, 478, 491, OGLE-7, 466 493, 496, 513 sc33 4505, 505 impact parameter, 456, 459, 466, 491, microlensing experiment 499, 501, 508, 513, 516, 519 AGAPE, 478 lightcurve, 457, 462, 465, 466, 477, EROS, 472, 481, 485 479, 486, 487, 495, 496, 499, 501, GEST, 492 524, 528, 534 MACHO, 467, 471, 477, 479, 484 magnification, 455, 464, 465, 487, MEGA, 478 499, 516, 533 MicroFUN, 486, 492, 496 observables, 457 MOA, 478, 486, 492, 496 Index 549

MPF, 492 Optical HST Snapshot Lens Survey, 208 OGLE, 477, 484, 486, 492, 496, 535 optical tidal matrix, 356 PLANET, 472, 477, 486, 492, 496, 507 WeCAPP, 478 parallax, 475, 494, 499, 501, 504, 505, microlensing in quasars, 9, 453, 520, 514, 517, 518 521, 524, 526, 531, 534 parameter microlensing in the Galaxy, 13 concentration, 76 Milky Way, 459, 460, 471, 477–479, 483, curvature, 45 484, 486, 490 shape, 67 MIT/Greenbank Survey, 184 parity, 24, 102, 112, 277, 455, 456, 464, Mitchell, J., 2, 3 533 MOA, 478, 486, 492, 496 Parkes-MIT-NRAO Lens Survey moments, 274 (PANELS), 184, 209 MOND, 476 PG 1115+080, 5, 94, 95, 142, 160, Moore profile cusp, 103, 107, 110, 127, 168–171, 174, 176–178, 181, 247, 218 252 MPF, 492 photometric redshift, 351, 392 MS 0302+17, 335 pixel lensing, 478 MS 1008-1224, 342 PKS 1145–071, 219 MS 1054-03, 337, 339 PKS 1830–211, 170, 196 MS 1512+36, 59 Planck satellite, 367 multi screen lens, 129 plane multi-deflection, 381 deflector, 20 multiple images criteria, 28 lens, 20 multiple lens-plane, 380, 382 source, 20 PLANET, 472, 486, 492, 496, 507 naked cusp, 43 planet, 475 natural components of the 3PCF, 432 microlensing, 18, 472, 486–488, 493, neutralino, 82 497 neutrinos, 48, 67, 78, 81 PMN 1632–0033, 97, 100 NFW density profile, 76, 103, 138, 145, PMN J0134–0931, 94 306, 313, 314, 327, 334, 349, 410, PMN J1632–0033, 94, 147 414, 438 PMN J2004–1349, 196 non-parametric models, 150 non-singular isothermal sphere (NIS), point-mass lens, 31, 105 40 point-spread function (PSF), 283, 294, null geodesic, 49 296 number counts of galaxies, 347, 423 affecting shape of faint galaxies, 269 background, 342 anisotropy, 292, 294, 295, 354, 382, number counts of images, 319, 327, 339 385, 388, 390, 394 number of images, 27 corrections, 412, 440 seeing, 283 OGLE, 466, 477, 484, 486, 492, 496, size of, 281 505, 535 stability, 298 OmegaCAM, 282, 403 Poisson equation, 22, 30, 63 optical depth, 57, 194–198, 205, 228, power spectrum, 66, 67, 72, 360, 361, 242, 460, 477, 479, 481, 484, 500, 365, 368, 377, 382, 383, 399, 419 524 3-D, 399 550 Index

normalisation, 69, 70, 72, 79, 81, 311, rotating lens, 505, 506 361, 367, 384, 385, 387, 396, 397, rotation curves, 475 400 RX J0911+0551, 155, 156, 169–171, power-law lens, 102, 104 173, 174, 178 Press–Schechter approach, 71, 73, 74 RX J1131–1231, 94, 96 projected ellipticity, 375 proper distance, 51 SAAO, 473 proper volume element, 51 saddle point image, 533 satellite QSO, 427 COBE, 69, 80 QSO 0957+561, 5–7, 13, 24, 139, 145, WMAP, 70, 77, 80 147, 148, 160, 162, 169, 170, 174, satellite galaxies, 94 178, 180, 256, 453, 527 SBS 1520+530, 170, 174, 177, 178, 181 QSO 1422+231, 17 scale factor, 45 QSO 2237+0305, 9, 10, 123, 148, 160, scaled deflection angle, 21 161, 183, 196, 227, 453, 527 Schechter luminosity function, 61, QSO 2345+007, 218 185–187, 194, 195 QSO-galaxy association, 428 Schwarzschild radius, 3, 18 quasar, 4 SCUBA, 304 radio-loud (RLQ), 252 SDSS 1004+4112, 211 radio-quiet (RQQ), 251, 252 binary, 218–220, 232 seeing, 283 brightness profile, 521 self lensing, 471, 481, 483 continuum emitting region, 527 SExtractor, 292 microlensing, 9, 453, 520, 521, 524, shape parameter, 67 526, 531, 534 Shapiro effect, 53 size, 521, 534 shear, 23–25, 32, 77, 102, 317, 322 structure, 534 3PCF, 432 variability, 527, 531 complex, 25 correlation function, 372 radial velocity (method of), 488, 490 cosmic, 271, 350, 351, 355, 358, 360, radiation density, 47 365, 366, 375, 383, 386, 394, 401, radio-loud quasar (RLQ), 252 419 radio-quiet quasar (RQQ), 251, 252 detection, 422 random field, 64 cross components of, 277, 278 Red Cluster Sequence (RCS), 332, 423 dispersion, 362, 364, 365, 368, 384, survey, 312, 392, 409, 410, 424 387, 391, 395 Red-Sequence Cluster Survey (RCS), estimate, 321 409 external, 39, 112, 166 redshift distribution of galaxies, 387, internal, 166 392 invariant, 167 reduced shear, 24, 25, 30, 39, 276, 277, mean tangential, 279, 406 295, 296, 317, 318, 330, 382 reduced, 24, 25, 30, 39, 276, 277, 295, Refsdal, S., 4, 454 296, 317, 318, 330, 339, 382 relative velocity, 456, 458, 501, 504, 514, survey, 388 522 systematic uncertainty, 296 resonant lensing, 487 tangential, 277, 278 Robertson-Walker metric, 45 tidal, 112 robotic telescopes, 535 single screen lens, 129 Index 551 singular isothermal ellipsoid (SIE), 120, survey 121, 136, 138, 156, 168, 245 2dF galaxy redshift, 78, 183 singular isothermal sphere (SIS), 36, CfA redshift, 183 102–104, 107, 120, 121, 134, 135, CfA-Arizona Space Telescope Lens 158, 168, 203, 279, 334, 410 (CASTLES), 92, 96, 139, 143, 221, Sloan Digital Sky Survey (SDSS), 79, 253 183, 200, 206, 207, 221, 411, 413, Cosmic Lens All Sky (CLASS), 153, 426, 427 184, 203, 206, 207, 209, 211, 231 Small Magellanic Cloud (SMC), 460, HST Medium Deep (MDS), 183 467, 471, 478, 481, 483, 518 Jodrell/VLA Astrometric (JVAS), 5, SNAP, 404 209 solar eclipse, 3 lensed optical quasars, 184 Soldner, J., 454 MIT/Greenbank, 184 source counts, 280 Optical HST Snapshot Lens, 208 source plane, 20 Parkes-MIT-NRAO Lens (PANELS), source redshift distribution, 92 184, 209 Space Interferometry Mission (SIM), Sloan Digital Sky (SDSS), 79, 183, 518, 531 200, 206, 207, 221 star spots, 499, 507, 513 statistics tangential caustic, 43 two-point, 373 temperature fluctuations, 61 stellar lens, 454–456, 459, 462, 465, 479, temperature map 483, 492, 497, 520 of the universe, 271 STIS, 298, 390 theorem stochastic biasing, 419 Birkhoff, 31, 71 structure formation, 61 Liouville, 23 substructure magnification, 28 mass distribution, 122, 144, 148, 221, odd-number, 27, 35, 37 224, 225, 227, 228, 230, 231 Poincaré–Hopf index, 27 supercluster, 337 tidal shear, 112 Abell 901/902, 335, 398 time delay, 4, 12, 143, 164–166, 527 MS 0302+17, 335 geometrical, 53 supernovae gravitational, 53 high-redshift, 78 total, 53 Type Ia, 78, 80 total density parameter, 48 Suprime-Cam, 282 total time delay, 53 survey, 387 transfer function, 67 surface mass density, 19, 30, 358 transit (of planet), 488 κ, 279, 307, 316, 322, 326, 338, 356, Tully–Fisher relation, 187–189, 408 358, 397 two-point statistics, 373 absolute, 30 critical, 21, 29, 53 uniform critical sheet, 102 dimensionless, 21 homogeneous, 29 vacuum energy, 47, 62, 83, 206, 312, local, 339 355, 366, 399–401, 404, 434, 439 mean, 32 vacuum energy density, 47 microlensing, 460 velocity dispersion, 36, 159 normalized, 522 Very Large Array (VLA), 5, 6, 221, 282 smooth, 27 Very Large Telescope (VLT), 9, 282 552 Index

Very Large Telescope Interferometry weight function, 295, 345, 349 (VLTI), 518 Weymann, R.J., 5 Very Long Baseline Interferometry WFI, 282, 288, 294, 353 (VLBI), 5, 6, 144, 147, 148, 180, geometric distortion, 289 221, 229 WFPC2, 298, 390 virial equilibrium, 73, 301 wide ﬁeld imaging virial mass, 128, 160, 218, 235 BTC, 351, 383, 389 virial radius, 73, 76, 128, 160, 218, 235 CFH12K, 282, 386 virial theorem, 163 MegaCam, 282, 284, 404 VIRMOS-DESCART, 376, 386, 387, OmegaCAM, 282, 403 389, 397, 424 SNAP, 404 VISTA, 331, 404 Suprime-Cam, 282 Vlasov equation, 63, 70 VISTA, 331, 404 volume element VST, 403 comoving, 51 WFI, 282, 288, 294, 353 proper, 51 geometric distortion, 289 vonSoldner,J.,2,3 WIRCAM, 331 VST, 403 WMAP, 300, 366, 367, 397, 427 WMAP satellite, 70, 77, 80

Walsh, D., 5 X-ray, 301, 337, 343 weak lensing cluster, 333 detection, 278 mass, 310, 341 general, 269, 271 observations, 310 mass reconstruction, 323 temperature, 338 observations, 282, 292 XMM, 303, 304, 338 of the CMB, 272 signal-to-noise, 278, 281, 342, 347, YALO, 473 349 Young diagram, 38 weak shear survey, 388 WeCAPP, 478 Zwicky, F., 3, 54, 299, 300 Index 553