1. Ｗｅａｋ Ｌｅｎｓｉｎｇ Ｆｌｅｘｉｏｎ Ａｌａｌｙｓｉｓ ｂｙ ＨＯＬＩＣｓ
Ｗｅａｋ　Ｌｅｎｓｉｎｇ　 Ｆｌｅｘｉｏｎ　 Ａｌａｌｙｓｉｓ　ｂｙ　ＨＯＬＩＣｓ　
T. Futamase,
Astronomical Institute, Tohoku University, JAPAN
Collaborators:Y. Okura, K. Umetsu

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

3. 1. Higher-order weak lensing
Linear order
Second order
(（（Goldberg & Natarajan 2002, Bacon et al. 2005)
Complex representation

4. Effects of Convergence, Shear, Flexion
Spin-0
Spin-1
Spin-2
Spin-3

5. 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-1
Spin-3
Spin-2
Goldberg & Natarajan 02, Bacon et al. 2005

6. Flexion to Surface Mass Density k=S/Scrit
Observable Flexion measures the 1st derivative of shear
Non-parametric inversion from flexion to mass density
Bacon et al. 2005

7. 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

8. 2. How to measure Flexion-HOLICs (Higher Order Lensing Image Characteristics)
Okura, Umetsu, Futamase, ApJ, 660, 995,(2007)

9. HOLICs Moment Method Spin-2 Spin-1 Spin-3
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

10. Application to A1689 (Subaru)
Mass + Light contours from Shear+Magbias data (Umetsu & Broadhurst 07)
15 arcmin (2Mpc/h)
Mass map from Fleixon in a 4’x4’ region using ng=8 gal/arcmin^2 !!! (Okura, Umetsu, & Futamase 2007b)

11. Mass Map of A1689 from Spin-1 Flexion
Mass reconstruction in the 4’x4’ core region of A1689 (z=0.18)
E-mode (lensing)
B-mode (noise) 5s 6s
ng=8 arcmin^-2
0.’3FWHM Gaussian
530kpc/h
Okura, Umetsu, Futamase 2007b

12. Main Halo and Subhalos

13. 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 k~ is consistent with the ACS/Subaru mass model (Broadhurst, Takada, Umetsu et al. 05).

14. 5. Applications 1. Aperture mass using flexion
Apperture mass can be expresed by tangential shear

15. Similoarly aperture mass can be exoressed by Flexions

16. Aperture mass using 2pt. Correlation functions
shear
flexions

17. 2. Spin-2 HOLICs
Degree N and spin number M complex coordinates

19. Mass reconstruction using various Spin2-HOLICs

20. Blanck region：N1

21. Angular difference

22. 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

23. Hyper Suprime-Cam High-z (z<3) 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)

24. 2PCF-Power spectrum –Neutrino mass and so on
超高感度CCD（8千万画素16億画素）
Field of View of HSC
Cosmic shear
BAO
2PCF-Power spectrum –Neutrino mass
and so on 現状
2000平方度、銀河3億個を観測。
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