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Flexion measurement by HOLICs

Flexion measurement by HOLICs. T. Futamase Astronomical Institute, Tohoku University, Sendai, Japan 27 th Jan. 11 @e-Institute, Edinburgh. Collaborator: Yuki. Okura (NAOJ). HOLICs approach to weak lensing. Motivations.

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Flexion measurement by HOLICs

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  1. Flexion measurement by HOLICs T. Futamase Astronomical Institute, Tohoku University, Sendai, Japan 27th Jan. 11 @e-Institute, Edinburgh Collaborator: Yuki. Okura (NAOJ)

  2. HOLICs approach to weak lensing Motivations There are many highly distorted images of faint and distant galaxies which have not used or inaccurately used in the weak lensing analysis How can one make use of these images in the weak lensing analysis? What is the description of these images other than second order moments?

  3. How to find useful combinations of higher order moments Quadruple moments Spin-2 combination Higher-order moments Find combinations having definite spin HOLICs (Higher Order Lensing Characteristics)

  4. Definition of HOLICs Spin-1 Spin-3 Spin-0 We need window function for actual measurement

  5. Relation between Source HOLICs and image HOLICs Source octo-pole moment Lens equation: Flexion Spin-1 Spin-3 First Flexion Second Flexion Relation between source HOLICs and image HOLICs and Flexions

  6. Actually we have to take into account the centroid shift caused by lens mapping Goldberg & Bacon (2005) Spin-2 Spin-4 Spin-1 Spin-3 Spin-5

  7. In the small g limit Where F and G are the reduced Flexions

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

  9. 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 skewness quadrupole 3-fold Spin-3 Spin-1 Spin-2 Goldberg & Natarajan 02, Bacon et al. 2005

  10. 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., groups of galaxies. Substructures in cluster) 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

  11. For the application to the actual observations We need a Window function to measure noisy images Centroid shift Quantity measured w.r.t apparent(observed) center Quantity measured using W’

  12. PSF correction for HOLICs Smearing effect by atmospheric turbulence and imperfect optics is described by PSF(point spread function) We follow KSB The correction is made by using star images which are perfect point sources We need spin-1 and -3 anisotropic kernel q Extra centroid shift is caused by spin-1 PSF anisotropy

  13. Spin-1 PSF Anisotropy Correction: Application to Subaru A1689 data Spin-1 PSF anisotropy from stellar shape moments After Before Okura, Umetsu, Futamase 2007b

  14. Mass map from spin-1 flexion in A1689 (Subaru) Mass + Light contours from Shear+Magbias data (Umetsu & Broadhurst 07) 15 arcmin (2Mpc/h) 530kpc/h Mass map from Fleixon in a 4’x4’ region using ng=8 gal/arcmin^2 (Okura, Umetsu, & Futamase 2007b)

  15. Main Halo and sub halos

  16. Temporary result for A370(Subaru) Ng ~40 arcmin^-2

  17. Flexion signal is only obtained by taking into higher order corrections in g Peaks are detected in S/N~5 ng=19 arcmin^-2

  18. Problems and future • HOLICs is a useful method to measure Flexion and is applied to real cluster date(A1689, A370) • Only first flexion is detected. • HOLICs has a dimension and thus small objects have large intrinsic HOLICs. This means S/N is low for small objects and cannot used for our analysis. • Deep observation does not help much for flexion measurement unlike shear measurement • Accurate shape measurement will be essentially important for flexion (particularly second Flexion) measurement • We may use an appropriate window function for accurate HOLICs measurement (such as elliptical window function for shear measurement)

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