1. Bernard Fort Institut d’astrophysique de Paris Gravitational lenses in the Universe ESO-Vitacura November 14, 2006

2. Part 1: Strong Lensing multiple images regime Historical lensing observations Fermat principle and lens equations Lensing by a point mass Lensing by mass distributions Galaxy and cluster lensing: astrophysical applications

3. Weak lensing principles Lensing mass reconstruction The flexion regime The cosmic shear: an overview Part 2: weak and highly singly magnified image regime November 16, 2006

4. Deflection of light Metric for the weak field approximation

5. gravitational achromatic lens Fermat principle + Equivalent to an optical index n <1

6. 1801 Soldner: are the apparent positions of stars affected by their mutual light deflection? hyperbolic passage of a photon bulet with v = c: tan (  /2) = GM/(c 2 r) 1911 Einstein: finds the correct General Relativity answer  = 4GM/(c 2 r) => and predicts 2 x the newton value A short history of lensing

7. Light deflection by the sun  = 4 G Mo / (c 2 r) = 1.75 ‘’ 1919, Eddington measures  = 1.6“ at the edge of the sun, confirming GR r Mo r

8. 1937 Zwicky: galaxies can act as lenses 1964 Refsdal: time delay and Ho 1979 Walsh & Weyman: double QSO 0957+561 CCD cameras 1887 giant arcs in cluster and first Einstein ring 1993 Macho and Eros microlensing 1995 the weak lensing regime 2000 cosmic shear measurements 2005 discovery of an extrasolar earth like planet 2010-15 the golden age of lensing History of lensing

9. Discovery of the double quasar (Walsh et al. 1984)

10. Lensing by Galaxies: HST Images An Einstein gravitational ring

11. The Giant arc in A370

12. The second giant arc Cl 2244

13. The cosmic optical bench (or multiple thin lenses) SL

14. Calculating the deflection angle geometrical term n

16. deflection angle =  equation 1

17. for weak gravitational field light propagation time is reduced in presence of a gravitational field Fermat principle yields the deflection angle  are very small => Born's approximation can be used to remember

18. The thin lens equation A Cosmic optical bench ~ Natural optical telescope

19.   OS L Dol  Time delay and thin lens t geom. =  Dol  /(2 c) = (Dos Dol / Dls) (  )^2 / (2c) t grav. = - (2/c^2)  (Dol  ) dz Fermat’s principle:  (t geom. + t grav.) = 0 gives:  – 2 (Dls/Dos) (Dol  )  (Dol  ) identifying with:  Dos +  Dls =  Dos gives:  (  ) = (2 / c^2)   (Dol  ) From Blanford and Kochanek lectures «gravitational lenses », 1986

20. Point mass M equation 2

21. Total deviation for a 2D mass distribution O S L Gpcs kpcs Surface mass density equation 3 mm

23. (1)

24. equation 3

25. Thin lens equation A

26. SO L Uniform sheet of constant mass density  o g/cm 2  =  (1-  o /  crit ) If  o =  crit  = 0 for any  The plan focuses any beams onto the observer ~ -    / 2~  o / 2  / 2 equation 4 

27. Reduced quantities critical density (g/cm 2 ) convergence = reduced surface density deflection angle

28. Reduced thin lens equation A Non-linear projection through the reduced deflection angle  s )  i ) ( 5) (6)

29. But non linear lens    From the Liege university lensing team

30. Caustic surfaces envelopes of families of rays ~ focal surfaces

31. The 2D Poisson equation 3D Poisson equation Using Green's function of the 2D Laplacian operator gives the potential from the mass distribution (3)equation 7 (10) (8)

32. Light Travel Time and Image Formation 1 image 3 images detour Time dilation Total light travel time =source

33. OLS Multiple images formation Convergence + shear ~

34. Local image properties A = Jacobian matrix of the projection  through the lens equation If the potential gradient does not vary on the image size (9)

35. to remember convergence complex shear projection matrix (10) (9)

36. Magnification matrix M (10)

37. Etherington theorem The elementary surface brightness (flux / dx.dy) on each position the source is conserved on the conjugated point of the projected image (but seeing effects). consequence: one can detect the presence of a lense only from the magnification and distortion of a geometrical shape. A lens in front of a uniform brightness distribution (or random distribution of points) cannot be seen.

38. Magnification  Abs  surface magnification Two eingen values 2 caustic lines (11) (12) from (10)

39. Convergence map only

40. Shear map: (amplitude and direction)

41. Map of a circular sources grid

42. Cylindrical projected potential radial caustic tangential caustic

43. Solving the lens equation for a point mass M Point mass lens equation  s = |  i – 1 /  i | r i1,r i2 1/r projected potential Ln (r) rsrs with angular radial coordinates in  e unit two images but one is very demagnified Einstein radius  e (13)

44. ring configuration for point mass or spherical potential Source, lens, observer perfectly aligned  ~ 1-3” for a lens galaxy  ~ 10-50” for a cluster of galaxies

45. Magnification for a point mass f1/f2 = Multi-site observations Lensing by moving star mass note that f1 / f2 = (  2 /  1) 4 1 2

46. DM = MACHOS ? Nature of DM

47. Microlensing by MACHOS (dark stars, BH,.. ) t

48. Microlenlensing event by the binary star MACHO 98

49. Microlensing an observational challenge ! Data mining: Need to distinguish microlensing from numerous variable stars. Candidate MACHOs: Late M stars, Brown Dwarfs, planets Primordial Black Holes Ancient Cool White Dwarfs <10-20% of the galactic halo is made of compact objects of ~ 0.5 M  MACHO: 11.9 million stars toward the LMC observed for 7 yr  >17 events EROS-2: 17.5 million stars toward LMC for 5 yr  >10 events (+2 events from EROS-1) To be updated!

50. Dark Halo: Microlensing results

51. searching hearth like planet

52. Spherical potential radial caustic tangential caustic

53. Spherical isothermal potentials SIS particules in thermal equilibrium everywhere (DM, stars) deviation  = constante (13) X-section ~  4

54. to remember for SIS central singularity

55. isothermal potential with core radius: SISrc deviation  ~  if  <<  c = constante if  >>  c (14)

56. Re Isothermal potential with a core radius Equivalent to a flat rotation curve Parity changes SIS

57. Universal Cold DM density profile Numerical simulations gives:  ~ 1 Navarro, Franck and White potential 1998 with (15) (16)

58. with galaxy & cluster potentials also ellipsoidal dark matter halos M(r >) converges Central part: DM+stars

59. effective deviation angle Elliptical potential q ~ ellipticity parameter

60. / Local surface magnification Back to caustics and critical lines with projected elliptical potential Locus of caustics lines in the source plan projected into critical lines in the image plan where  become infinite = 0

61. images for a non-singular elliptical lens. Radial arc Cusp arc Einstein Cross Fold arc Singly magnified image From Kneib et al 1993

63. rays caustics Caustics (focal surfaces) rays: critical points of path length (Fermat-Hamilton) field point x., z initial wavefront, h(t) t path length rays and caustics

64. caustics are physical catastrophes described by the theory of Thom and Arnold variable parameter smooth function 11 t x<0 11 t x=0 11 t x>0 critical points: ∂  1 /∂t=0

65. Multiple images of the sun on Villarica lake images are places on the water where the distance sun-water-eye is stationary

66. Multiple caustics with merging Caustics images drawn by a distant distant sun on the bottom of a swimming pool (a reverse light propagation with the sun as an observer )

67. Light curve of OGLE235 a binary system with a big jupiter like satellite Binary events was first suggested by Mao & Paczynski, 1991, ApJL, 374, 40

69. Aplication of lensing in cosmology Newtonian gravitational potential Cosmology Cosmology geometry Newtonian potential Image magnification

70. Beyond z=6 with Strong Gravitational Lenses From Kneib et al 2005

71. Measuring Ho from time delay Cuevad Tello et al; 2006 70 +/- 10 Image locationpotential modelingdelayHo

72. RCS1 giant arc sample from Gladders et al 2005 Some arcs have Einstein radius up to 50 " A1689, RCS 0224 Specific X-ray Cluster surveys

73. Modeling A370 From Kneib et al 1993

74. LENSTOOL (strong and weak regime 1993 - 2006) people who wrote part of this project ( in chronological order ): Jean-Paul Kneib (1993), Henri Bonnet, Ghyslain Golse, David Sand, Eric Jullo, Phil Marshall GRAVLENS 2005- Software for Gravitational Lensing by Chuck Keeton Lensview 2006: Software for modelling resolved gravitational lens images B. Wayth & R. Webster Many others: Rigaud, Kovner, Kochanek, Barthelmann, Gavazzi, Valls-Gabaud, Soyu.. Modelling softwares Cf: seminar Marceau Limousin November 15

75. Probing the density profile of DM halos inside ~ 10 kpcs ? 10 < r < 2-300 kpcs r -2 r > 2-300 kpcs, maybe r -3 Cf. seminar Marceau Limousin Nov 15,2006

76. Results with MS2137-23 elliptic halo => collisionless DM, Miralda-escude 96; coupling a dual modeling SL-WL with a dynamical study of stars: profile compatible with NFW simulations for r > 10 kpcs; triaxial ellipsoïd projection effect (potential twist from radial to tangential images); MOND does not work ; Bartelmann 98, Gavazzi et al. 2002, 03, 04,..)

77. Testing DM halo shape with several arc systems Several multiple image systems can probe a dark matter twist of ellipticity Gavazzi et al 2004 Internal potential external potential

78. Detection of dark Matter clumps Bonnet et al in Cl0024+1654 (WL) Weinberg & Kamionsky 2003 theoretical predictions for non virialized cluster mass still in the merging process.

79. Simulations: CDM halos are lumpy

80. (Bradac et al. 2002) Substructure  complicated catastrophes!

81. Dalal and Kochanek 2002 Fraction of the observed image brightnesses deviating from the best smooth model fit? (Dark) halo sub-structures can explain QSO anomalies ! Sub-halo analysis with simulations

82. The Einstein cross No Dark Matter at the center of the galaxy!

84. Coupling lensing and stellar dynamics Lens modelling give the mass at r Einstein and     DM Stars see the potential for r < r eff Jeans equation  M * / L  v anisotropy  =  (M * / L, , v anisotropy    spectro observation (~ potential slope  from Koopmann & Treu 2005

85. SLACS Lensing -> recovers the Ellipticals fundamental plane For isolated E (external shear perturbation < 0.035) = 1.01 +/- 0.065 rms  (r) ~ r - 2.01 +/- 0.03 near Einstein Radius (~Flat Rot.Curve) PA and ellipticity of light and DM trace each other ( M * ~75%) No evolution ( ~0.2)

86. A SL2S cosmological tests with rings ? Hypothesis: Treu's results =1. +/- 0.065 r(r) ~ r - 2.01+/-0.03 at Re ~ Flat Rot. Curve (DM light-conspiracy) R e /  L = D ol D ls /D os R e /  * = G ( , or w 0,w 1 ) Log r ReRe Lens modeling VLT spectroscopy

87. Simulations: CDM halos are lumpy typical galaxy, ~10 12 M o should contain many sub-halos corresponding to smallest satellite galaxies. Where are they? (Moore et al. 1999; Klypin et al. 1999)

88. QSO image anomalies Fact In 4-image lenses, the image positions can be fit by smooth lens models: positions determined by  i true   i smooth The flux ratios cannot; brightnesses determined by  ij true =  ij smooth +  ij sub Interpretation Flux ratios are perturbed by substructure in the lens potential. (Mao & Schneider 1998; Metcalf & Madau 2001; Dalal & Kochanek 2002).

89. Is there Halo Sub-Structure ? (e.g. Dalal and Kochanek 2001,2002) 1 image 3 images B1555 radio Images A and B should be equally bright! Micro-lensing by stars? Maybe Halo Sub-structure ?

90. Testing rotation curves (Sanders & McGaugh 2002)

91. SIS mass distribution:  ~ 1-3” for a lens galaxy  ~ 10-50” for a cluster of galaxies Where are the intermediate mass lenses ? (3’’<  < 7’’) ? Cf ESO seminar Bernard Fort November 24

92. Does it exist cosmic strings lenses?

93. SNAP  Joint Dark Energy Mission: NASA (75%) & DOE (25%) launch 2014-2015 6 years survey: super novae and weak lensing SNAP: 2m telescope, instrument FOV 1 deg 2 Imaging / spectro. one deep field (15 deg 2 ), one large field (~300 deg 2 ?) ~ 1Billlion $  DUNE (Dark Universe Explorer): similar survey but 1.2-1.5m telescope and imaging only instrument FOV 1 deg 2 ~ 300 M€ Prediction snap n ~ 4000 and 14000 strong lenses

94. JWST JWST: Le successeur de Hubble dans l’Infrarouge Un miroir de 6,6 m Lancement en 2011 mission de 5 à 10 ans INSTRUMENT MIRI Spectro-imageur, 5-28 μm  Participation française focalisée autour du banc optique de l’imageur (détecteur intégré au RAL, UK)  Responsabilité managériale de la partie française  Responsabilité « système » de l’ensemble