Weak Lensing Tomography Sarah Bridle University College
London
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3d vs 2d (tomography) Non-Gaussian -> higher order
statistics Low redshift -> dark energy versus
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Weak Lensing Tomography 1.In principle (perfect zs) Hu 1999
astro-ph/9904153 2.Photometric redshifts Csabai et al.
astro-ph/0211080 3.Effect of photometric redshift uncertainties Ma,
Hu & Huterer astro-ph/0506614 4.Intrinsic alignments 5.Shear
calibration
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1. In principle (perfect zs) Qualitative overview Lensing
efficiency and power spectrum Dependence on cosmology Power
spectrum uncertainties Cosmological parameter constraints
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1. In principle (perfect zs) Core reference Hu 1999
astro-ph/9904153 See also Refregier et al astro-ph/0304419 Takada
& Jain astro-ph/0310125
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Cosmic shear two point tomography
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(Hu 1999)
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Lensing efficiency (Hu 1999) Equivalently: g i (z l ) = z l n i
(z s ) D l D ls / D s dz s i.e. g is just the weighted D l D ls / D
s
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Can you sketch g 1 (z) and g 2 (z)? (Hu 1999) g i (z) = z s n i
(z s ) D l D ls / D s dz s
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Lensing efficiency for source plane?
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(Hu 1999)
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Sensitivity in each z bin
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NOT
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(Hu 1999) Why is g for bin 2 higher? A. More structure along
line of sight B. Distances are larger g i (z d ) = z s 1 n i (z s )
D d D ds / D s dz s
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* *
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Lensing power spectrum (Hu 1999)
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Lensing power spectrum Equivalently: P ii (l) = g i (z l ) 2
P(l/D l,z) dD l /D l 2 i.e. matter power spectrum at each z,
weighted by square of lensing efficiency (Hu 1999)
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Measurement uncertainties 1/2 = rms shear (intrinsic + photon
noise) n i = number of galaxies per steradian in bin i (Hu 1999)
Cosmic Variance Observational noise
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(Hu 1999)
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Sensitivity in each z bin
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NOT
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(Hu 1999)
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Dependence on cosmology Refregier et al SNAP3 ?? A. m = 0.35
w=-1 B. m = 0.30 w=-0.7
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Approximate dependence Increase 8 A. P B. P Increase z s A. P
B. P Increase m A. P B. P Increase DE ( K =0) A. P B. P Increase w
A. P B. P Huterer et al
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Effect of increasing w on P Distance to z A. Decreases B.
Increases
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Perlmutter et al.1998 Fainter Further away Decelerating
Accelerating m =1, no DE m =1, DE =0) == ( m = 0.3, DE = 0.7, w DE
=0)
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Perlmutter et al.1998 EdS OR w=0 w=-1 Fainter, further
Brighter, closer
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Effect of increasing w on P Distance to z A. Decreases B.
Increases When decrease distance, lensing effect decreases Dark
energy dominates A. Earlier B. Later
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Effect of increasing w on P Distance to z A. Decreases B.
Increases When decrease distance, lensing decreases Dark energy
dominates A. Earlier B. Later Growth of structure A. Suppressed B.
Increased Lensing A. Increases B. Decreases Net effects: Partial
cancellation decreased sensitivity Distance wins
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Approximate dependence Increase 8 A. P B. P Increase z s A. P
B. P Increase m A. P B. P Increase DE ( K =0) A. P B. P Increase w
A. P B. P Huterer et al
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Approximate dependence Increase 8 A. P B. P Increase z s A. P
B. P Increase m A. P B. P Increase DE ( K =0) A. P B. P Increase w
A. P B. P Huterer et al Note modulus
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Which is more important? Distance or growth? Simpson &
Bridle
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Dependence on cosmology Refregier et al SNAP3 ?? A. m = 0.35
w=-1 B. m = 0.30 w=-0.7
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(Hu 1999)
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See Heavens astro-ph/0304151 for full 3D treatment (~infinite #
bins)
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(Hu 1999)
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Parameter estimation for z~2 (Hu 1999)
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Predict the direction of degeneracy in w versus m plane
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Refregier et al SNAP3
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(Hu 1999)
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Takada & Jain
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(Hu 1999)
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Covariance matrix P 12 is correlated with P 11 and P 22
(ignoring trispectrum contributions) Takada & Jain
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How many redshift bins to use? Ma, Hu & Huterer 5 is enough
Modified from
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Higher order statistics
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Takada & Jain
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Geometric information Jain & Taylor; Kitching et al. Slide
stolen from Tom Kitching
www.astro.dur.ac.uk/Cosmology/SISCO/edin_talks/Kitching.PPT
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Slide stolen from presentation by Andy Taylor
www.shef.ac.uk/physics/idm2004/talks/monday/originals/taylor_andy.ppt
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Slide stolen from presentation by Andy Taylor
www.shef.ac.uk/physics/idm2004/talks/monday/originals/taylor_andy.ppt
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Slide stolen from presentation by Andy Taylor
www.shef.ac.uk/physics/idm2004/talks/monday/originals/taylor_andy.ppt
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Slide stolen from presentation by Andy Taylor
www.shef.ac.uk/physics/idm2004/talks/monday/originals/taylor_andy.ppt
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Some additional tomographic methods Cross-correlation
cosmography Bernstein & Jain astro-ph/0309332 Galaxy-lensing
cross correlation Hu & Jain astro-ph/0312395 Reconstruction of
distance and growth Song; Knox & Song