1. KIAS, Nov 5, 2014 Measuring the Cosmic Shear in Fourier Space Jun Zhang ( 张骏 ) (Shanghai Jiao Tong University) Collaborators: Eiichiro Komatsu (MPA), Nobuhiko Katayama (IPMU), Wentao Luo (SHAO), Sebastian Foucaud (SJTU) References: JZ, 2008, MNRAS, 383, 113 JZ, 2010, MNRAS, 403, 673 JZ & Komatsu, 2011, MNRAS, 414, 1047 JZ, 2011, JCAP, 11, 041 JZ, Luo, Foucaud, 2013, arXiv:1312.5514

2. Outline: Introduction & Motivation A New Idea of Measuring Cosmic Shear Some General Issues Summary

3. Outline: Introduction & Motivation A New Idea of Measuring Cosmic Shear Some General Issues Summary

4. Image credit: Wittman et al. (2000) Credit: Clowe et al. (2006) Credit: Hoekstra & Jain (2008)

5. Is dark energy simply a cosmological constant? What is the geometry / curvature of the Universe? Is General Relativity the correct theory of gravity on cosmic scales? How cold is cold dark matter? What are the density distributions / profiles of cosmic structures (Galaxies, Groups, Clusters, etc.) at different scales?...... The Scientific Goals of Weak Lensing

8. Outline: Introduction & Motivation A New Idea of Measuring Cosmic Shear Some General Issues Summary

9. Challenges LensingPSF NoisePixelation LSSTWFIRSTEUCLID Subaru HSC Opportunities DES &

10. Credit: Huterer et al. (2005)

11. Heymans et al., 2006, MNRAS, 368, 1323 Massey et al., 2007, MNRAS, 376, 13 Bridle et al., 2009, Annals of Applied Statistics, 3, 6 Kitching et al., 2011, Annals of Applied Statistics, 5, 2231 Mandelbaum et al., 2014, ApJS, 212, 5

12. Outline: Introduction & Motivation A New Idea of Measuring Cosmic Shear Some General Issues Summary

13. Seljak & Zaldarriaga, 1999

14. In the presence of an isotropic Gaussian PSF JZ, 2008

15. In the presence of an isotropic Gaussian PSF JZ, 2011

16. The Pixelation Effect Image source: internet

17. Moffat PSFGaussian PSF FWHM of both PSF = 12 The Pixelation Effect

18. Moffat PSFGaussian PSF FWHM of both PSF = 12 The Pixelation Effect Equivalent to Whittaker–Shannon (sinc) interpolation

19. The Photon Noise

20. The Photon Noise (example)

21. The Fourier-Space Shear Estimator JZ, 2010

23. The Source Poisson Noise Example: (Stacked Power Spectrum of Selected SDSS sources)

24. Removing Source Poisson Noise

25. Test Result I

26. Dithering, MultiDrizzle A. M. Koekemoer, A. S. Fruchter, R. Hook, W. Hack, 2002 HST Calibration Workshop, 337

27. Dithering: non-flat noise PS Source: Koekemoer et al. 2007 COSMOS Non-flat noise power spectrum

28. Dithering: non-flat noise PS Ave of PS of sources with Mag >25 COSMOS Non-flat noise power spectrum

29. Final Form of the Shear Estimator

30. Test Result II JZ, Luo, Foucaud, 2013

31. http://great3.projects.phys.ucl.ac.uk Galaxies PSF

33. Outline: Introduction & Motivation A New Idea of Measuring Cosmic Shear Some General Issues Summary

34.  Reduced Shear  Form of Shear Estimator  Image Quality in Fourier Space  PSF fitting

35. Reduced Shear

36. If one plans to calibrate the multiplicative factor “a+b κ ”, one should pay attention to its dependence on “ κ ”, which, though, is not known a priori in observations.

37. Reduced Shear Theorem:, JZ, 2011

38. Form of Shear Estimator Conventional Form: New Form:

39. Form of Shear Estimator Conventional Form: New Form: Nonnegative Order One ~ 0± for faint sources

40. COSMOS Image Quality in Fourier Space

41. COSMOS

42. Image Quality in Fourier Space Bad imagesGood images SDSS

43. PSF Fitting

44. Last, but not the least … How are we limited by the shape noise?

45. Outline: Introduction & Motivation A New Idea of Measuring Cosmic Shear Some General Issues Summary

46. Summary We find that it has many advantages to measure the cosmic shear using the image power spectrum in Fourier space … … It corrects for PSF model independently, with simple and rigorous math; Effects due to photon noise is removed statistically, including images processed/combined with Multidrizzle ； Accurate to the second order in shear/convergence ； Pixelation effect is not important as long as the pixel size is less than 1/3 of the FWHM of the PSF (no dithering case); No need to identify the centroid of the image ； Fast image processing ： < 10 -2 CPU seconds/Galaxy; S / N per galaxy Increased; Immune to misidentification of stars as galaxies.

47. Summary The remaining problems are: Measurement of the PSF ； Galaxy weighting ； Measurement of the correlation functions of shear ； Theoretical prediction accuracy ；......

48. Stay tuned …