Ludovic Van WaerbekeDepartment of Physics and Astronomy

University of British Columbia

A (very short) introduction to E/B modesMeasurement and high order statistics

2c40 κ34

c

2 )]θ(J[ )( d

πθ

288kkP

k

kM ap

2c10 κ2

c

2 )]θ(J[ )( d

πθ

2γ kkP

k

k

2source0 3D2

0κ F);)(

( Pz d4

9)( z,zz

zD

kkP

L

)θ(J )( d2π

1θ)γ(r)γ(r 00 κr kkPkk

Convergence (or projected mass) power spectrum:

Aperture mass (Map) variance at scale c :

Top-hat shear variance at scale c:

Shear correlation function at separation :

Cosmic Shear two-points Statistics and mass Power Spectrum

ttγγ

rrγγ

Crittenden et al. 2000, Pen et al. 2002:

E and B mode decomposition of the two points statistics

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.

Useful formula in Schneider, LVW & Mellier, 2002:

Simulated 3x3 degrees reconstructed convergenceSimulated 3x3 degrees reconstructed convergence

mapmap

Convergence PDFConvergence PDF

ExpectedExpectedconstraintsconstraints

S3=<K3>/<K2>2

~40 zs-

1.3

VIRMOS-Descart: high order statistics(LVW, Bernardeau, Mellier, 1999)

Simulated 3x3 degrees shearSimulated 3x3 degrees shear

mapmap3-pts function pattern3-pts function pattern

d1212

33

21

High order statistics: shear 3-pts function (Bernardeau et al. 2003)

E+B and E-B for the two-points and three-points functions. Dotted lineIs TCDM and dashed line is OCDM.

Cosmic variance with the OCDM:

Uncorrected star (solid lines) and corrected galaxies (dotted) two and threePoints functions.

(Pen et al., 2003)

Aperture mass skewness from three point function integration

(Jarvis et al., 2004)

CTIOVIRMOS-Descart

+DEEP+COSMOS

More to come…soon!

Virmos-Descart

Wide CFHTLS