Weak%20Lensing%20Flexion%20Alalysis%20by%20HOLICs

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Weak Lensing Flexion Alalysis by HOLICs

• T. Futamase,
• Astronomical Institute, Tohoku University, JAPAN
• CollaboratorsY. Okura, K. Umetsu

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• Weak Lensing Flexion
• Flexion Observable- HOLICs
• PSF correction
• Flexion Analysis of Subaru A1689 Data
• Applications
• HSC(Hyper Suprime Camera) for Subaru

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1. Higher-order weak lensing
Linear order
Second order
(((Goldberg Natarajan 2002, Bacon et al. 2005)
Complex representation
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Effects of Convergence, Shear, Flexion
Spin-1
Spin-0
Spin-2
Spin-3
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Where is Flexion useful?
An intermediate regime between WEAK and STRONG
lensing can be well described by shearing and
flexing effects
Arclets lensed images with slight curvatures
quadrupole
skewness
3-fold
Spin-3
Spin-1
Spin-2
Goldberg Natarajan 02, Bacon et al. 2005
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Flexion to Surface Mass Density kS/Scrit
Observable Flexion measures the 1st derivative of
shear
Non-parametric inversion from flexion to mass
density
Bacon et al. 2005
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Shear vs. Flexion
Resolution limit in ordinal (Spin-2) weak
lensing with ground based telescopes (Subaru,
CFHT, etc.)
Ordinal WL is sensitive to structures of 1-10,
which is dominated by clusters of galaxies
Flexion measures the gradient of shear so is
relatively sensitive to small-scale structures
(e.g., galaxies, groups of galaxies) Even
though the higher-order effect is small, at small
scales (r), for large images (L), Flexion signal
might dominate over Shear signal
L image size r distance from the lens
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2. How to measure Flexion-HOLICs(Higher Order
Lensing Image Characteristics)
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HOLICs Moment Method
KSB formalism (Kaiser, Squares, Broadhurst 1995)
Adds in Lensing and
PSF induced response to intrinsic ellipticity
that is randomly oriented
Spin-2
Higher-order generalization of KSB moment method
by Okura, Umetsu, Futamase 2007b
Spin-1
Spin-3
Unbiased estimator for Flexion
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Application to A1689 (Subaru)
Mass Light contours from ShearMagbias data
(Umetsu Broadhurst 07)
15 arcmin (2Mpc/h)
Mass map from Fleixon in a 4x4 region using
ng8 gal/arcmin2 !!! (Okura, Umetsu, Futamase
2007b)
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Mass Map of A1689 from Spin-1 Flexion
Mass reconstruction in the 4x4 core region of
A1689 (z0.18)
E-mode (lensing)
B-mode (noise)
5s
6s
ng8 arcmin-2
0.3FWHM Gaussian
530kpc/h
Okura, Umetsu, Futamase 2007b
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Main Halo and Subhalos
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Results

• First successful cluster mass reconstruction only
  by Flexion incorporating full higher-order PSF
  anisotropy corrections
• Significant detections of cD/group-scale
  substructures at 5-6 sigma levels
• Main density peak of k2.50.45-0.45 is
  consistent with the ACS/Subaru mass model
  (Broadhurst, Takada, Umetsu et al. 05).

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5. Applications
1. Aperture mass using flexion
Apperture mass can be expresed by tangential shear
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Similoarly aperture mass can be exoressed by
Flexions
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Aperture mass using 2pt. Correlation functions
shear
flexions
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2. Spin-2 HOLICs
Degree N and spin number M complex coordinates
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Mass reconstruction using various Spin2-HOLICs
A1689
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Blanck regionN1
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Angular difference
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New possibility to do weak lensing analysis using
HOLICs Not only Flexion(Clusters) but also
(Cosmic) Shear as well
How much we can improve accuracy of mass
reconstruction and power spectrum
measurement(dark energy parameter) are now in
progress
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• Hyper Suprime-Cam

High-z (zlt3) galaxy survey 2000 squire degree
Dark energy observation by Cosmic Shear

• Wide Field of View
• (10 times of SC)
• High Sensitivity( 3 times sensitive than present
  CCD at 1 micron)

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Field of View of HSC
????CCD(8?????16???)
Cosmic shear BAO 2PCF-Power spectrum Neutrino
mass and so on
??
2000??????3?????? Z3?????????????
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