1. Xi An, May 20, 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 Summary

3. Outline: Introduction & Motivation A New Idea of Measuring Cosmic Shear 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 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. Seljak & Zaldarriaga, 1999

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

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

15. The Reduced Shear

16. 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.

17. The Reduced Shear Theorem:, JZ, 2011

18. The Pixelation Effect Image source: internet

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

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

21. The Photon Noise

22. The Photon Noise (example)

23. The Fourier-Space Shear Estimator JZ, 2010

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

26. Removing Source Poisson Noise

27. Test Result I

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

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

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

31. Final Form of the Shear Estimator

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

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

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

36. Outline: Introduction & Motivation A New Idea of Measuring Cosmic Shear Summary

37. 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 seconds/Galaxy; S / N per galaxy Increased.

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

39. Stay tuned …