kias, nov 5, 2014 measuring the cosmic shear in fourier space jun zhang ( 张骏 ) (shanghai jiao...
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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
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 …