Gravitational lenses in the Universe

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

2. Part 1: Strong Lensingmultiple 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. Part 2: weak and highly singly magnified image regime Weak lensing principles Lensing mass reconstruction The flexion regime The cosmic shear: an overview November 16, 2006

4. Deflection of light Metric for the weak field approximation

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

6. A short history of lensing 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/(c2r) 1911 Einstein:finds the correct General Relativity answer  = 4GM/(c2r) => and predicts 2 x the newton value

7. Light deflection by the sun 1919, Eddington measures  = 1.6“ at the edge of the sun, confirming GR r  = 4 G Mo / (c2 r) = 1.75 ‘’ r Mo

8. History of lensing 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

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 SL (or multiple thin lenses)

14. Calculating the deflection angle n geometrical term

16. = a deflection angle equation 1

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

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

19. Time delay and thin lens a Dol q O S q L tgeom. = a Dol q /(2 c) = (Dos Dol / Dls) (q-b)^2 / (2c) tgrav. = - (2/c^2) f (Dol q) dz Fermat’s principle: q (tgeom. + tgrav.) = 0 gives: b= q – 2 (Dls/Dos) (Dol q) y(Dol q) identifying with: b Dos + a(q) Dls = q Dos gives: a(q) = (2 / c^2) (Dol q) y(Dol q) From Blanford and Kochanek lectures «gravitational lenses », 1986

20. Point mass M equation 2

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

23. (1)

24. equation 3

25. Thin lens equation A

26. Uniform sheet of constant mass density So g/cm2 ~ So/ 2 ~ -So/ 2 q a ~ 2 q . So/ 2 O S L b = q (1-So/Scrit) equation 4 If So = Scritb = 0 for any q The plan focuses any beams onto the observer

27. Reduced quantities critical density (g/cm2) convergence = reduced surface density deflection angle

28. Reduced thin lens equation A (6) ( 5) (qs) (qi) Non-linear projection through the reduced deflection angle

29. But non linear lens a (q) = q a q 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. 3 images detour =source 1 image Time dilation Total light travel time Light Travel Time and Image Formation

33. Multiple images formation Convergence + shear O L S ~

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

35. to remember projection matrix (10) convergence complex shear (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 m = Abs[dq/db] from (10) surface magnification (11) 2 caustic lines Two eingen values (12)

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 two images but one is very demagnified 1/r projected potential Ln (r) rs Einstein radius qe ri1,ri2 (13) qs = |qi – 1 / qi| Point mass lens equation with angular radial coordinates in qe unit

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

45. Magnification for a point mass f1/f2 = Lensing by moving star mass 1 2 Multi-site observations note that f1 / f2 = (q2 / q1)4

46. Nature of DM DM = MACHOS ?

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

48. Microlenlensing event by the binary star MACHO 98

49. Microlensing an observational challenge! • 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! Data mining: Need to distinguish microlensing from numerous variable stars.

50. Dark Halo: Microlensing results