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:

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

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

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

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

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

Challenges LensingPSF NoisePixelation LSSTWFIRSTEUCLID Subaru HSC Opportunities DES &

Credit: Huterer et al. (2005)

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

Seljak & Zaldarriaga, 1999

In the presence of an isotropic Gaussian PSF JZ, 2008

In the presence of an isotropic Gaussian PSF JZ, 2011

The Reduced Shear

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.

The Reduced Shear Theorem:, JZ, 2011

The Pixelation Effect Image source: internet

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

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

The Photon Noise

The Photon Noise (example)

The Fourier-Space Shear Estimator JZ, 2010

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

Removing Source Poisson Noise

Test Result I

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

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

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

Final Form of the Shear Estimator

Test Result II JZ, Luo, Foucaud, 2013

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

Galaxies PSF

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

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.

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

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