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Introduction to E/B Modes Measurement & High-Order Statistics

This article provides a brief introduction to E/B modes measurement and high-order statistics in cosmic shear analysis, including the top-hat shear variance, shear correlation function, convergence power spectrum, and E/B mode decomposition.

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Introduction to E/B Modes Measurement & High-Order Statistics

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  1. A (very short) introduction to E/B modes Measurement and high order statistics Ludovic Van Waerbeke Department of Physics and Astronomy University of British Columbia

  2. Cosmic Shear two-points Statistics and mass Power Spectrum Top-hat shear variance at scale Qc: Aperture mass (Map) variance at scale Qc: Shear correlation function at separation Q: Convergence (or projected mass) power spectrum:

  3. E and B mode decomposition of the two points statistics Crittenden et al. 2000, Pen et al. 2002:

  4. Top-hat variance, which can be decomposed into E and B modes using Aperture mass variance How to get properly normalised E/B xi and top-hat variance? Use the aperture mass to fix your unknown B mode constant.

  5. Useful formula in Schneider, LVW & Mellier, 2002:

  6. VIRMOS-Descart: high order statistics (LVW, Bernardeau, Mellier, 1999) S3=<K3>/<K2>2 ~40 W-0.8zs-1.3 Convergence PDF Simulated 3x3 degrees reconstructed convergence map Expected W-L constraints

  7. High order statistics: shear 3-pts function (Bernardeau et al. 2003) 3 3 2 1 2 d12 1 Simulated 3x3 degrees shear map 3-pts function pattern

  8. E+B and E-B for the two-points and three-points functions. Dotted line Is TCDM and dashed line is OCDM. Cosmic variance with the OCDM:

  9. Uncorrected star (solid lines) and corrected galaxies (dotted) two and three Points functions.

  10. Aperture mass skewness from three point function integration VIRMOS-Descart CTIO (Pen et al., 2003) (Jarvis et al., 2004)

  11. More to come…soon! Wide CFHTLS Virmos-Descart +DEEP+COSMOS

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