Durham-Edinburgh eXtragalactic Workshop XIV IfA Edinburgh fileDurham-Edinburgh eXtragalactic...
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Durham-Edinburgh eXtragalactic Workshop XIV
IfA Edinburgh
Cosmology withweak-lensing peak counts
Chieh-An Lin
January 8th, 2018
Durham University, UK
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Outline
Motivation Why do we study WL peaks?
Problems How to model WL peaks?
Methodology A stochastic approach
Results Cosmological constraints and others
Perspectives Improvements and new physics
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Motivation
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General relativity
Gravitational lensing
(Source: ALMA)
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Unlensed sources Weak lensing
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Gaussian information
κ map and 2PCF
But the lensing field is highly non-Gaussian
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Weak-lensing peak counts
κ map and peaks 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0Halo mass [log(M/M¯ h
−1)]
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Hal
o nu
mbe
r den
sity
n(logM
) [(M
pc/h)−
3]
Halo mass function
σ8 = 0.76σ8 = 0.82σ8 = 0.88
• Local maxima of the projected mass• Probe the mass function• Constrain cosmology
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Problems
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Dealing with selection function
Projection effects, irregular sampling, noise, ...
Early studiesCount only the true clusters with high S/N(Kruse & Schneider 1999, 2000; Reblinsky et al. 1999)
Recent studiesInclude the selection effect into the model
• Analytical formalism• N -body simulations• Fast stochastic model (this work)
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Difficulties
Analytical models
• Fan et al. (2010) and series; Shirasaki (2017)• Difficult to handle masks and photo-z bias• Difficult to include baryons or intrinsic alignment• Need external covariances
N -body simulations
• Dietrich & Hartlap (2010) and series; Kratochvil et al. (2010) and series
• Very expensive time costs
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Challenges
How to model properly weak-lensing peak counts?
How to resolve the trade off between flexibility and speed?
What cosmological information can we extract from peaks?
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A new model
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Sampled mass
Sample halosfrom a mass function
Assign density profiles,randomize positions
Compute the projectedmass, add noise
Filter maps,create peak catalogues
A stochasticmodel to predict
weak-lensingpeak counts
Lin & Kilbinger (2015a)
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AdvantagesFast
Only few seconds for creating a 25-deg2 field, without MPI or GPU
Flexible
Straightforward to include observational effects and additional features(mask, photo-z bias, IA, baryons, ...)
Full PDF information
Estimate covariances easilyGo beyond the Gaussian likelihood assumption
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AdvantagesFast
Only few seconds for creating a 25-deg2 field, without MPI or GPU
Flexible
Straightforward to include observational effects and additional features(mask, photo-z bias, IA, baryons, ...)
Full PDF information
Estimate covariances easilyGo beyond the Gaussian likelihood assumption
Cosmology with weak-lensing peak counts DEX, Durham — Jan 8th, 2018 14
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AdvantagesFast
Only few seconds for creating a 25-deg2 field, without MPI or GPU
Flexible
Straightforward to include observational effects and additional features(mask, photo-z bias, IA, baryons, ...)
Full PDF information
Estimate covariances easilyGo beyond the Gaussian likelihood assumption
Cosmology with weak-lensing peak counts DEX, Durham — Jan 8th, 2018 14
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AdvantagesFast
Only few seconds for creating a 25-deg2 field, without MPI or GPU
Flexible
Straightforward to include observational effects and additional features(mask, photo-z bias, IA, baryons, ...)
Full PDF information
Estimate covariances easilyGo beyond the Gaussian likelihood assumption
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Validation
We compare the following four cases:
Case 1 — Full N -body runsCase 2 — Replace N -body halos with NFW profiles of the same massCase 3 — Profile replacement and position randomizationCase 4 — Our model
to test two hypotheses:
Comparison 1 & 2 — Ignore unbound matters & halo asphericityComparison 2 & 3 — Absence of the spatial correlationComparison 3 & 4 — Mass function
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Lin & Kilbinger (2015a) Validation
2 3 4 5 6 7S/N ν
10-1
100
101
102
Peak
num
ber d
ensi
ty n
pea
k [d
eg−
2∆ν−
1]
Peak abundance histogram
Noise-only
Full N-body runsN-body: halos→NFWN-body: halos→NFW + random positionOur model
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Results
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Ωm
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
σ8
1.00
2.50
4.005.50
7.00
Ωm-σ8 constraints
abd, cg, confidence1-σ, 68.3%2-σ, 95.4%
abd, svg, confidence1-σ, 68.3%2-σ, 95.4%
abd, svg, confidence1-σ, 68.3%2-σ, 95.4%
Cosmology-dependentcovariance
L = cst + ∆xTC−1∆x
cg = constant covariancesvg = varying covariance
cg svgFoM 46 57
Lin & Kilbinger (2015b)
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+
+
Combined strategy
Separated strategy
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Ωm
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
σ8
Ωm-σ8 constraints
Separated strategy1-σ, 68.3%2-σ, 95.4%
Combined strategy1-σ, 68.3%2-σ, 95.4%
Combined strategy1-σ, 68.3%2-σ, 95.4%
Combined vs separated
The combined mapcreates degeneracy
which elongatesthe contours.
Lin et al. (2016)
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Data from three surveys
Survey Field size Number of Effective density[deg2] galaxies [deg−2]
CFHTLenS 126 6.1 M 10.74KiDS DR1/2 75 2.4 M 5.33DES SV 138 3.3 M 6.65
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0.3
0.8
1.3
σ8
ε= +∞ ε=55.8 ε=50.0 ε=49.2
0.3
0.8
1.3
σ8
ε=48.6 ε=48.2 ε=47.8 ε=47.5
0.1 0.4 0.7Ωm
0.3
0.8
1.3
σ8
ε=47.2
0.1 0.4 0.7Ωm
ε=46.9
PMC ABC posterior evolution
Cosmological constraints
withapproximate Bayesian
computation (ABC)
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0.0 0.2 0.4 0.6 0.8 1.0Ωm
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6σ
8
Ωm-σ8 constraints
PMC ABC1-σ, 68.3%2-σ, 95.4%
PMC ABC1-σ, 68.3%2-σ, 95.4%
Cosmological constraints
Width: ∆Σ8 = 0.13Area: FoM = 5.2
Lin (2016)
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Perspectives
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Improvements
Account forhalo clustering
(Source: HST)
Extend toredshift space distortions
Peacock et al. (2001)
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More physics
Massive neutrinos
(Source: MissMJ@Wikimedia/CC BY 3.0)
Modified gravity
0 1 2 3 4 5 6 7 8S/N ν
100
101
102
103
Peak
num
ber d
ensi
ty n
pea
k [d
eg−
2∆ν−
1]
ΛCDM
f(R), fR0 = 10−4
(Preliminary)
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Summary
• Peaks provide non-Gaussianinformation
• A stochastic model to predict WLpeak counts
• Fast, flexible, full PDF information
• A public code: Camelus@GitHub
Collaborators:
Martin Kilbinger (CEA Saclay)François Lanusse (CMU)Austin Peel (CEA Saclay)Sandrine Pires (CEA Saclay)
References:
[1410.6955][1506.01076][1603.06773][1609.03973]
[1612.02264][1612.04041][1704.00258]http://linc.tw
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Backup slides
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Liu J et al. (2015)
Peaks vs two-point statistics
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Ωm
0.2
0.4
0.6
0.8
1.0
1.2
σ8
DES SV 2-pt non-tomo
DES SV peaks
Kacprzak et al. (2016)
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Approximate Bayesian computation
π
P(π)
πi
prior
ABC posterior
Parameter space
xP(x|πi)
xobs
|x− xobs| ≤ ε
Data space
Distribution of accepted π = prior× green area≈ prior× 2ε× likelihood∝ posterior
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Degeneracy with wde0
0.4
0.6
0.8
1.0
1.2
σ8
Parameter constraintswith likelihood
Starlet, θker =2′, 4′, 8′
1-σ, 68.3%2-σ, 95.4%
Starlet, θker =2′, 4′, 8′
1-σ, 68.3%2-σ, 95.4%
0.1 0.3 0.5 0.7Ωm
-1.8
-1.4
-1.0
-0.6
wde
0
0.4 0.6 0.8 1.0 1.2σ8
Lin et al. (2016)
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Liu X et al. (2016) fR0 constraints
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Liu J et al. (2015)
Other studies
Liu X et al. (2015)
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0.16 0.24 0.32 0.40 0.48Ωm
0.60
0.75
0.90
1.05
1.20
σ8
0.0<S/N<4.0
KiDS-450 2PCFs-tomo S8 =0.745±0.039
Planck15 S8 =0.851±0.024
KiDS-450 SP S8 =0.757+0.054−0.053
Other studies
Martinet et al. (2018)
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