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, 113JZ, 2010, MNRAS, 403, 673JZ & Komatsu, 2011, MNRAS, 414, 1047JZ, 2011, JCAP, 11, 041JZ, Luo, Foucaud, 2013, arXiv:1312.5514

Outline:

Introduction & MotivationA New Idea of Measuring Cosmic

Shear Some General IssuesSummary

Outline:

Introduction & MotivationA New Idea of Measuring Cosmic

Shear Some General IssuesSummary

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 & MotivationA New Idea of Measuring Cosmic

Shear Some General IssuesSummary

Challenges

Lensing PSF

NoisePixelation

LSST

WFIRST EUCLID

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

Outline:

Introduction & MotivationA New Idea of Measuring Cosmic

Shear Some General IssuesSummary

Seljak & Zaldarriaga, 1999

In the presence of an isotropic Gaussian PSF

JZ, 2008

In the presence of an isotropic Gaussian PSF

JZ, 2011

The Pixelation Effect

Image source: internet

Moffat PSF

Gaussian PSF

FWHM of both PSF = 12

The Pixelation Effect

Moffat PSF

Gaussian 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. 2007

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

http://great3.projects.phys.ucl.ac.uk

Galaxies

PSF

Outline:

Introduction & MotivationA New Idea of Measuring Cosmic

Shear Some General IssuesSummary

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

Reduced Shear

Reduced Shear

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

Reduced Shear

Theorem: ,

JZ, 2011

Form of Shear Estimator

Conventional Form:

New Form:

Form of Shear Estimator

Conventional Form:

New Form:

NonnegativeOrder One

~ 0± for faint sources

COSMOS

Image Quality in Fourier Space

Image Quality in Fourier Space

COSMOS

Image Quality in Fourier Space

Bad images Good imagesSDSS

PSF Fitting

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

Outline:

Introduction & MotivationA New Idea of Measuring Cosmic

Shear Some General IssuesSummary

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.

Summary

The remaining problems are:

• Measurement of the PSF；• Galaxy weighting；• Measurement of the correlation functions of shear；• Theoretical prediction accuracy；• ... ...

Stay tuned …