weak lensing presentation
TRANSCRIPT
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Weak Lensing in Cosmology
Halo A. Abdulkhalaq
March 11, 2013
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Overview• Introduction• Gravitational lens theory - The deflection angle - Lens equation • Weak lensing - Distortion - Shear• Applications• Summary
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Introduction
• Light deflection• Gravitational lensing - strong lensing - Micro lensing - Weak lensing
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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
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where
• Lens equation is non-linear• For single source possible several images
)(.DD)(s
ds
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Weak Lensing
• Away from centre of galaxies• Jacobi Matrix ≈ Identity • Thus, weak distortions and small
magnifications• Statistical measurement
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• 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
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• Shear - shape distortion
- amplitude indicates distortion degree - phase direction of distortion
i221 ei
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Applications• Weak lensing mass reconstruction
(MRLens)
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Bullet cluster (1E0657-558)
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• 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
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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
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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.
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(http://arxiv.org/abs/astro-ph/0307212v1)• P. Schneider. Detection of (dark) matter concentrations via weak gravitational lensing. MNRAS, 283:837{853, December 1996.