Sarah Bridle University College London 3d vs 2d tomography NonGaussian gt higher order statistics Low redshift gt dark energy versus Weak Lensing Tomography In principle perfect zs ID: 330610
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Slide1
Weak Lensing Tomography
Sarah Bridle
University College LondonSlide2
3d vs 2d (tomography)
Non-Gaussian -> higher order statistics
Low redshift -> dark energy
versusSlide3
Weak Lensing Tomography
In principle (perfect zs)
Hu 1999
astro-ph/9904153
Photometric redshifts Csabai et al. astro-ph/0211080
Effect of photometric redshift uncertainties
Ma, Hu & Huterer
astro-ph/0506614
Intrinsic alignments
Shear calibrationSlide4
1. In principle (perfect zs)
Qualitative overview
Lensing efficiency and power spectrum
Dependence on cosmologyPower spectrum uncertainties
Cosmological parameter constraintsSlide5
1. In principle (perfect zs)
Core reference
Hu 1999 astro-ph/9904153
See also Refregier et al astro-ph/0304419Takada & Jain astro-ph/0310125Slide6
Cosmic shear two point tomography
Slide7
Cosmic shear two point tomography
Slide8
Cosmic shear two point tomography
qSlide9
Cosmic shear two point tomography
qSlide10
(Hu 1999)Slide11
(Hu 1999)Slide12
Lensing efficiency
(Hu 1999)
Equivalently:
g
i
(z
l
) =
∫
z
l
n
i
(z
s
) D
l
Dls / Ds dzsi.e. g is just the weighted Dl Dls / DsSlide13
Can you sketch g1(z) and g
2
(z)?
(Hu 1999)
g
i
(z) =
∫
z
s
n
i
(z
s
) D
l
D
ls / Ds dzsSlide14
Lensing efficiency for source plane?Slide15Slide16
(Hu 1999)Slide17
Sensitivity in each z binSlide18
NOTSlide19
(Hu 1999)
Why is g for bin 2 higher?
More structure along line of sight
Distances are larger
g
i
(z
d
) =
∫
z
s
1
n
i
(z
s
) D
d Dds / Ds dzsSlide20Slide21
*
*Slide22
Lensing power spectrum
(Hu 1999)Slide23
Lensing power spectrum
Equivalently:
P
ii(l) = ∫
g
i
(z
l
)
2
P(l/D
l
,z) dD
l
/D
l2i.e. matter power spectrum at each z, weighted by square of lensing efficiency(Hu 1999)Slide24
(Hu 1999)Slide25
Measurement uncertainties
<
2int>1/2
= rms shear (intrinsic + photon noise)ni = number of galaxies per steradian in bin i
(Hu 1999)
Cosmic
Variance
Observational
noiseSlide26
(Hu 1999)Slide27
Sensitivity in each z binSlide28
NOTSlide29
(Hu 1999)Slide30
Dependence on cosmology
Refregier et al SNAP3
?
?
A.
m
= 0.35 w=-1
B.
m
= 0.30 w=-0.7Slide31
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 alSlide32
Effect of increasing w on P
Distance to z
A. Decreases B. IncreasesSlide33
Perlmutter et al.1998
Fainter
Further away
Decelerating
Accelerating
m
=1, no DE
(
m
=1,
DE
=0) == (
m
= 0.3,
DE = 0.7, wDE=0)Slide34
Perlmutter et al.1998
EdS OR w=0
w=-1
Fainter, further
Brighter, closerSlide35
Effect of increasing w on P
Distance to z
A. Decreases B. IncreasesWhen decrease distance, lensing effect decreasesDark energy dominates
A. Earlier B. LaterSlide36Slide37Slide38
Effect of increasing w on P
Distance to z
A. Decreases B. IncreasesWhen decrease distance, lensing decreasesDark energy dominates
A. Earlier B. LaterGrowth of structureA. Suppressed B. Increased
Lensing A. Increases B. Decreases
Net effects:
Partial cancellation <-> decreased sensitivity
Distance winsSlide39
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 alSlide40
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
modulusSlide41
Which is more important?Distance or growth?
Simpson & BridleSlide42
Dependence on cosmology
Refregier et al SNAP3
?
?
A.
m
= 0.35 w=-1
B.
m
= 0.30 w=-0.7Slide43
(Hu 1999)Slide44
(Hu 1999)
See Heavens astro-ph/0304151 for full 3D treatment (~infinite # bins)Slide45
(Hu 1999)Slide46
Parameter estimation for z~2
(Hu 1999)Slide47
Predict the direction of degeneracy in w versus
m planeSlide48
Refregier et al SNAP3Slide49
(Hu 1999)Slide50
Takada & JainSlide51
(Hu 1999)Slide52
Covariance matrix
P
12 is correlated with P11 and P
22
(ignoring trispectrum contributions)
Takada & JainSlide53
Takada & JainSlide54
How many redshift bins to use?
Ma, Hu & Huterer
5 is enough
Modified fromSlide55
Higher order statisticsSlide56
Takada & JainSlide57
Takada & JainSlide58
Geometric information
Jain & Taylor; Kitching et al.
Slide stolen from Tom Kitching
www.astro.dur.ac.uk/Cosmology/SISCO/edin_talks/Kitching.
PPT Slide59
Slide stolen from presentation by Andy Taylor
www.shef.ac.uk/physics/idm2004/talks/monday/originals/taylor_andy.ppt
Slide60
Slide stolen from presentation by Andy Taylor
www.shef.ac.uk/physics/idm2004/talks/monday/originals/taylor_andy.ppt
Slide61
Slide stolen from presentation by Andy Taylor
www.shef.ac.uk/physics/idm2004/talks/monday/originals/taylor_andy.ppt
Slide62
Slide stolen from presentation by Andy Taylor
www.shef.ac.uk/physics/idm2004/talks/monday/originals/taylor_andy.ppt
Slide63
Some additional tomographic methods
Cross-correlation cosmography
Bernstein & Jain astro-ph/0309332
Galaxy-lensing cross correlationHu & Jain astro-ph/0312395
Reconstruction of distance and growthSong; Knox & Song