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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
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Outline:
Introduction & MotivationA New Idea of Measuring Cosmic
Shear Some General IssuesSummary
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Outline:
Introduction & MotivationA New Idea of Measuring Cosmic
Shear Some General IssuesSummary
![Page 4: KIAS, Nov 5, 2014 Measuring the Cosmic Shear in Fourier Space Jun Zhang ( 张骏 ) (Shanghai Jiao Tong University) Collaborators: Eiichiro Komatsu (MPA), Nobuhiko](https://reader033.vdocuments.us/reader033/viewer/2022051417/5697bfd81a28abf838caefdd/html5/thumbnails/4.jpg)
Image credit: Wittman et al. (2000)
Credit: Clowe et al. (2006)
Credit: Hoekstra & Jain (2008)
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• 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
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Outline:
Introduction & MotivationA New Idea of Measuring Cosmic
Shear Some General IssuesSummary
![Page 9: KIAS, Nov 5, 2014 Measuring the Cosmic Shear in Fourier Space Jun Zhang ( 张骏 ) (Shanghai Jiao Tong University) Collaborators: Eiichiro Komatsu (MPA), Nobuhiko](https://reader033.vdocuments.us/reader033/viewer/2022051417/5697bfd81a28abf838caefdd/html5/thumbnails/9.jpg)
Challenges
Lensing PSF
NoisePixelation
LSST
WFIRST EUCLID
Subaru HSC
Opportunities
DES
&
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Credit: Huterer et al. (2005)
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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
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Outline:
Introduction & MotivationA New Idea of Measuring Cosmic
Shear Some General IssuesSummary
![Page 13: KIAS, Nov 5, 2014 Measuring the Cosmic Shear in Fourier Space Jun Zhang ( 张骏 ) (Shanghai Jiao Tong University) Collaborators: Eiichiro Komatsu (MPA), Nobuhiko](https://reader033.vdocuments.us/reader033/viewer/2022051417/5697bfd81a28abf838caefdd/html5/thumbnails/13.jpg)
Seljak & Zaldarriaga, 1999
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In the presence of an isotropic Gaussian PSF
JZ, 2008
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In the presence of an isotropic Gaussian PSF
JZ, 2011
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The Pixelation Effect
Image source: internet
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Moffat PSF
Gaussian PSF
FWHM of both PSF = 12
The Pixelation Effect
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Moffat PSF
Gaussian PSF
FWHM of both PSF = 12
The Pixelation Effect
Equivalent to Whittaker–Shannon (sinc) interpolation
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The Photon Noise
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The Photon Noise (example)
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The Fourier-Space Shear Estimator
JZ, 2010
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The Source Poisson Noise
Example:
(Stacked Power Spectrum of Selected SDSS sources)
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Removing Source Poisson Noise
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Test Result I
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Dithering, MultiDrizzle
A. M. Koekemoer, A. S. Fruchter, R. Hook, W. Hack, 2002 HST Calibration Workshop, 337
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Dithering: non-flat noise PS
Source: Koekemoer et al. 2007
COSMOS
Non-flat noise power spectrum
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Dithering: non-flat noise PS
Ave of PS of sources with Mag >25
COSMOS
Non-flat noise power spectrum
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Final Form of the Shear Estimator
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Test Result II
JZ, Luo, Foucaud, 2013
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http://great3.projects.phys.ucl.ac.uk
Galaxies
PSF
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Outline:
Introduction & MotivationA New Idea of Measuring Cosmic
Shear Some General IssuesSummary
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Reduced Shear Form of Shear Estimator Image Quality in Fourier Space PSF fitting
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Reduced Shear
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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.
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Reduced Shear
Theorem: ,
JZ, 2011
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Form of Shear Estimator
Conventional Form:
New Form:
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Form of Shear Estimator
Conventional Form:
New Form:
NonnegativeOrder One
~ 0± for faint sources
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COSMOS
Image Quality in Fourier Space
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Image Quality in Fourier Space
COSMOS
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Image Quality in Fourier Space
Bad images Good imagesSDSS
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PSF Fitting
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Last, but not the least …How are we limited by the shape noise?
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Outline:
Introduction & MotivationA New Idea of Measuring Cosmic
Shear Some General IssuesSummary
![Page 46: KIAS, Nov 5, 2014 Measuring the Cosmic Shear in Fourier Space Jun Zhang ( 张骏 ) (Shanghai Jiao Tong University) Collaborators: Eiichiro Komatsu (MPA), Nobuhiko](https://reader033.vdocuments.us/reader033/viewer/2022051417/5697bfd81a28abf838caefdd/html5/thumbnails/46.jpg)
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.
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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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Stay tuned …