Cosmology with Gravitational Lensing

1. Cosmology with Gravitational Lensing Richard Lieu Department of Physics University of Alabama, Huntsville

2. History • Chwolson, O., 1924, Astronomische Nachrichten221: 329

3. History • Chwolson, O., 1924, Astronomische Nachrichten221: 329 • Einstein, A., 1936, Science84, 506.

4. History • Chwolson, O., 1924, Astronomische Nachrichten221: 329 • Einstein, A., 1936, Science84, 506. • Zwicky, F., 1937, ApJ, 86, 217

5. History • Chwolson, O., 1924, Astronomische Nachrichten221: 329 • Einstein, A., 1936, Science84, 506. • Zwicky, F., 1937, ApJ, 86, 217 • Walsh,D., 1979, Nature, 279, 381.

7. Zwicky 1937, ApJ, 86, 217.

8. Gravitational deflection of light Stems from slower speed at which light travels in a gravitational field. To see why the speed is reduced, start from the Schwarzschild metric of a point mass Here c=G=1.

9. Gravitational deflection of light Stems from slower speed at which light travels in a gravitational field. To see why the speed is reduced, start from the Schwarzschild metric of a point mass Here c=G=1. Radial null geodesic

10. A’ B’ Gravitational deflection of light Stems from slower speed at which light travels in a gravitational field. To see why the speed is reduced, start from the Schwarzschild metric of a point mass Here c=G=1. Radial null geodesic B A ● y x

11. A’ B’ Gravitational deflection of light Stems from slower speed at which light travels in a gravitational field. To see why the speed is reduced, start from the Schwarzschild metric of a point mass Here c=G=1. Radial null geodesic B A ● In time , y x

12. A’ B’ Gravitational deflection of light Stems from slower speed at which light travels in a gravitational field. To see why the speed is reduced, start from the Schwarzschild metric of a point mass Here c=G=1. Radial null geodesic B A ● In time , y x

13. A’ B’ Gravitational deflection of light Stems from slower speed at which light travels in a gravitational field. To see why the speed is reduced, start from the Schwarzschild metric of a point mass Here c=G=1. Radial null geodesic B A ● In time , y x Total angle of deflection

14. Gravitational lensing ● Convergence and shear Impact parameter Unpertured ray: Perturbed ray: But, from the diagram So, we have where

15. ● Thus, an annular segment (pixel) of area will become another pixel of area after deflection. The magnification of the area is Since , we deduce that Lensed pixel Unlensed pixel

16. Complicated! But if lensing is weak we can ignore the term and also write % area magnification %Linear magnification

17. Putting back the expression for L, we have % linear magnification: If the light ray passes outside a galaxy, the deflection will be like that by a point mass, i.e. In this case zero magnification

18. Galaxy or Before lensing Unlensed pixel area=lensed pixel area After lensing

21. lensed ring Imagine a ring lying just outside the galaxy. unlensed ring

22. lensed ring Imagine a ring lying just outside the galaxy. unlensed ring What is this extra space doing here? What occupies it?

23. lensed ring Imagine a ring lying just outside the galaxy. unlensed ring What is this extra space doing here? What occupies it? Conclusion: the light passing through the galaxy must be magnified, i.e. the galaxy image is enlarged to fill the gap.

24. Only rays passing through the gravitational lens are magnified The rest of the rays are deflected outwards to make room for the central magnification (tangential shearing) How does gravitational lensing conserve surface brightness?Unlike ordinary magnifying glass, gravitational lens magnifies a central pixel and tangentially shear an outside pixel. Before Lensing After Lensing Gravitational lensing of a large source When lens is "inside" source is magnified When lens is "outside" the source is distorted but not magnified

25. Flat +ve curvature -ve curvature

26. Positive curvature: parallel rays converge, sources appear `larger’. Source distance (or angular size distance D) is `smaller’ Zero curvature: parallel rays stay parallel, sources have `same’ size Angular size distance has Euclidean value Negative curvature: parallel rays diverge, sources appear `smaller’. Angular size distanceD is `larger’ Angular magnification

27. EXAMPLES TO ILLUSTRATE THE BEHAVIOR OF PROPAGATING LIGHT where The general equation is Non-expanding empty Universe Parallel rays stay parallel Expanding empty Universe Parallel rays diverge;

28. where The general equation is Non-expanding Universe with some matter Parallel rays diverge; Expanding Universe with matter and energy at critical density Parallel rays stay parallel;

29. z=zs z=0 If a small bundle of rays misses all the clumps, it will map back to a demagnified region Let us suppose that all the matter in is clumped i.e. the voids are matter free The percentage increase in D is given by where c=1 and & are the Euclidean angular size and angular size distance of the source This is known as the Dyer-Roeder empty beam

30. What happens if the bundle encounters a gravitational lens where the meanings of the D’s is assuming Euclidean distances since mean density is ~ critical. Also the deflection angle effect is We can use this to calculate the average

31. Consider a tube of non-evolving randomly placed lenses Thus The magnification by the lenses and demagnification at the voids exactly compensate each other. The average beam is Euclidean if the mean density is critical.

35. Only rays passing through the gravitational lens are magnified The rest of the rays are deflected outwards to make room for the central magnification (tangential shearing) How does gravitational lensing conserve surface brightness?Unlike ordinary magnifying glass, gravitational lens magnifies a central pixel and tangentially shear an outside pixel. Before Lensing After Lensing Gravitational lensing of a large source When lens is "inside" source is magnified When lens is "outside" the source is distorted but not magnified

37. Test of cosmic shear • Lack of information on the intrinsic shape of the background source is a setback. • Complete Einstein rings may provide a way out.

38. A S O B

39. A’ S O B’

45. Further tests of matter distribution at low redshift • Strong lensing time delay – shear by small scale non-linear structures. • Fast GRB jets – test of large scale primordial linear perturbations.

48. A’ S O B’ Strong lensing time delay

49. HE0435-1223 (Kochanek 2006)