Weak Lensing Tomography

1. Weak Lensing Tomography Sarah Bridle University College London

2. versus • 3d vs 2d (tomography) • Non-Gaussian -> higher order statistics • Low redshift -> dark energy

3. Weak Lensing Tomography • In principle (perfect zs) Hu 1999 astro-ph/9904153 • Photometric redshifts Csabai et al. astro-ph/0211080 • Effect of photometric redshift uncertainties Ma, Hu & Huterer astro-ph/0506614 • Intrinsic alignments • Shear calibration

4. 1. In principle (perfect zs) • Qualitative overview • Lensing efficiency and power spectrum • Dependence on cosmology • Power spectrum uncertainties • Cosmological parameter constraints

5. 1. In principle (perfect zs) Core reference • Hu 1999 astro-ph/9904153 See also • Refregier et al astro-ph/0304419 • Takada & Jain astro-ph/0310125

6. Cosmic shear two point tomography  

7. Cosmic shear two point tomography  

8. Cosmic shear two point tomography q  

9. Cosmic shear two point tomography q

10. (Hu 1999)

11. (Hu 1999)

12. (Hu 1999) Lensing efficiency Equivalently: gi(zl) = ∫zl ni(zs) Dl Dls / Ds dzs i.e. g is just the weighted Dl Dls / Ds

13. (Hu 1999) Can you sketch g1(z) and g2(z)? gi(z) = ∫ zs ni(zs) Dl Dls / Ds dzs

14. Lensing efficiency for source plane?

16. (Hu 1999)

17. Sensitivity in each z bin

18. NOT

19. (Hu 1999) Why is g for bin 2 higher? • More structure along line of sight • Distances are larger gi(zd) = ∫ zs1 ni(zs) Dd Dds / Ds dzs

21. * *

22. (Hu 1999) Lensing power spectrum

23. (Hu 1999) Lensing power spectrum Equivalently: Pii(l) = ∫ gi(zl)2 P(l/Dl,z) dDl/Dl2 i.e. matter power spectrum at each z, weighted by square of lensing efficiency

24. (Hu 1999)

25. (Hu 1999) Measurement uncertainties • <2int>1/2 = rms shear (intrinsic + photon noise) • ni = number of galaxies per steradian in bin i Cosmic Variance Observational noise

26. (Hu 1999)

27. Sensitivity in each z bin

28. NOT

29. (Hu 1999)

30. Dependence on cosmology Refregier et al SNAP3 A. m = 0.35 w=-1 B. m = 0.30 w=-0.7 ? ?

31. Approximate dependence • Increase 8→A. P↓ B. P↑ • Increase zs →A. P↓ B. P↑ • Increase m →A. P↓ B. P↑ • Increase DE (K=0) →A. P↓ B. P↑ • Increase w →A. P↓ B. P↑ Huterer et al

32. Effect of increasing w on P • Distance to z • A. Decreases B. Increases

33. Fainter Accelerating m =1, no DE Decelerating (m =1, DE=0) == (m = 0.3, DE = 0.7, wDE=0) Perlmutter et al.1998 Further away

34. w=-1 Fainter, further EdS OR w=0 Brighter, closer Perlmutter et al.1998

35. Effect of increasing w on P • Distance to z • A. Decreases B. Increases • When decrease distance, lensing effect decreases • Dark energy dominates • A. Earlier B. Later

38. Effect of increasing w on P • Distance to z • A. Decreases B. Increases • When decrease distance, lensing decreases • Dark energy dominates • A. Earlier B. Later • Growth of structure • A. Suppressed B. Increased • Lensing A. Increases B. Decreases • Net effects: • Partial cancellation <-> decreased sensitivity • Distance wins

39. Approximate dependence • Increase 8→A. P↓ B. P↑ • Increase zs →A. P↓ B. P↑ • Increase m →A. P↓ B. P↑ • Increase DE (K=0) →A. P↓ B. P↑ • Increase w →A. P↓ B. P↑ Huterer et al

40. Approximate dependence • Increase 8→A. P↓ B. P↑ • Increase zs →A. P↓ B. P↑ • Increase m →A. P↓ B. P↑ • Increase DE (K=0) →A. P↓ B. P↑ • Increase w →A. P↓ B. P↑ Huterer et al Note modulus

41. Which is more important?Distance or growth? Simpson & Bridle

42. Dependence on cosmology Refregier et al SNAP3 A. m = 0.35 w=-1 B. m = 0.30 w=-0.7 ? ?

43. (Hu 1999)

44. (Hu 1999) See Heavens astro-ph/0304151 for full 3D treatment (~infinite # bins)

45. (Hu 1999)

46. (Hu 1999) Parameter estimation for z~2

47. Predict the direction of degeneracy in w versus m plane

48. Refregier et al SNAP3

49. (Hu 1999)

50. Takada & Jain