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

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

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

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

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

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

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

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

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

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)

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

Main Halo and Subhalos

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~2.5+0.45-0.45 is consistent with the ACS/Subaru mass model (Broadhurst, Takada, Umetsu et al. 05).

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

Similoarly aperture mass can be exoressed by Flexions

Aperture mass using 2pt. Correlation functions shear flexions

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

Mass reconstruction using various Spin2-HOLICs

Blanck region：N1

Angular difference

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

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)

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。 Z～3までの情報を最良画像で取得 24