Weak Lensing in Cosmology

Halo A. Abdulkhalaq

March 11, 2013

Overview• Introduction• Gravitational lens theory - The deflection angle - Lens equation • Weak lensing - Distortion - Shear• Applications• Summary

Introduction

• Light deflection• Gravitational lensing - strong lensing - Micro lensing - Weak lensing

Gravitational Lens Theory

• Source at distance Ds

• Lensing body (e.g.; Massive galaxies, Galaxy clusters) distance Dd

• α̂ is deflection angle

• Lens Equation β=θ−α(θ)

2cGM4

where

• Lens equation is non-linear• For single source possible several images

)(.DD)(s

ds

Weak Lensing

• Away from centre of galaxies• Jacobi Matrix ≈ Identity • Thus, weak distortions and small

magnifications• Statistical measurement

• Distortion: Shape and Size - described by Jacobi matrix:

gi = /(1-k) is reduced shear - k is convergence; describes size distortion

gggg

12

21

1

1)k1(A

• Shear - shape distortion

- amplitude indicates distortion degree - phase direction of distortion

i221 ei

Applications• Weak lensing mass reconstruction

(MRLens)

Bullet cluster (1E0657-558)

• Dark matter distribution in universe - By estimating convergence K - K; proportional to projected matter

distribution - Can estimate k via shear, which is easier to be

observed - Obtain shear by ellipticity

Summary• Gravitational lensing flourishing field in

cosmology• Weak lensing good observational tool• Measuring shear• Reconstruction of mass distribution • Observing matter distribution• Estimation of dark matter distribution

References • Schneider P. astro-ph/0509252 v1 9 Sep 2005 Weak

Gravitational Lensing (http://arxiv.org/abs/astro-ph/0509252v1)• Kaiser N. 1991. Weak Lensing of distant Galaxies, AA(Canadian

Institute for Theoretical Astrophysics, Toronto, Canada) (http://adsabs.harvard.edu/abs/1992ApJ...388..272K)

• M. Bartelmann and P. Schneider. Weak gravitational lensing. Phys. Rep.,340:291{472, January 2001.

• Bonometto S,. Gorini V and Moschella U, mModern Cosmology. IOP Publishing Ltd 2002

• A. Refregier. Weak Gravitational Lensing by Large-Scale Structure.ARA&A, 41:645{668, 2003.

(http://arxiv.org/abs/astro-ph/0307212v1)• P. Schneider. Detection of (dark) matter concentrations via weak gravitational lensing. MNRAS, 283:837{853, December 1996.