Simulations of Strong Lensing
Nan Li (KICP & ANL)
Collaborators: Salman Habib, Mike Gladders, Katrin Heitmann,Steve Rangel, Tom Peterka, Michael Florian, Lindsey Bleem, etc.
March 19, 2014
Outline
Introduction
Simulations of Strong Lensing
Simulated Lensed Images
Work in Progress
Outline
IntroductionGravitational LensingN-body SimulationSimulations of Strong Lensing
Simulations of Strong Lensing
Simulated Lensed Images
Work in Progress
Gravitational Lensing
• Gravitational lensing is the phenomenon of light deflectingwhen light ray passes through a gravitational potential.
• The occurrence and morphological properties of lensed imagesreflect the properties of the gravitational potential between thesource and the observer.
• Lensing effects can be almost observed on all scales, e.g.,weak lensing ( Mpc), strong lensing ( kpc), micro lensing ( pc).
• Applications: reconstruct mass distribution of lens, detectgalaxies at high redshift, measure the Hubble constant, etc.
Gravitational Lensing
Figure 1 : Illustration of gravitational lensing.
Gravitational Lensing
Figure 2 : Typical observation of strong gravitational lensing.
N-body Simulation
• N-body simulation is a simulation of a dynamical system ofparticles under the influence of gravity.
• In cosmology, it is used to study processes of non-linearstructure formation, e.g., halos and filaments.
The Outer Rim Simulation
Katrin Heitmann
• Vbox = (3h−1Gpc)3.
• Mp = 1.85× 109h−1M�.
• Np = 102403.
• 100 snapshots (10 to 0).
• More than 1000000 clusters.
Simulations of Strong Lensing
• Simulation of gravitational lensing is an effective connectionbetween N-body simulation and Observations.
• Basic steps : 1) estimate density field; 2) calculate deflectionangles; 3) ray-tracing; 4) generate lensed images.
• Comparing the simulated lensed images with the observations,we can study the properties of dark matter particles.
Outline
Introduction
Simulations of Strong LensingEstimate Density FieldCalculate Deflection AnglesPerform Ray-Tracing
Simulated Lensed Images
Work in Progress
Estimate Density Field
• Estimating densities of the halo from N-body simulations is acritical first step for lensing simulations.
• There are several well known methods to estimate density field:Cloud in Cell (CIC), Triangular Shaped Cloud (TSC), SmoothedParticle Hydrodynamics (SPH) ......
• In our work, we use a different way: Delaunay Tessellation FieldEstimator (DTFE). It is fully self-adaptive and more natural thanthe kernel estimators.
Delaunay Tessellation
Compare with Other Methods
−0.2
−0.1
0.0
0.1
0.2
r/r 2
00
SPH CIC
−0.2 −0.1 0.0 0.1 0.2
r/r200
−0.2
−0.1
0.0
0.1
0.2
r/r 2
00
Voronoi
−0.2 −0.1 0.0 0.1 0.2
r/r200
Delaunay
Compare with Other Methods
100 101 102 103
Spatial Frequency
103
104
105
106
107
108
109
1010
1011
1012
Pow
er
Spect
rum
AnalyticSPHCICVoronoiDelaunay
One Example
Steve Rangel
Calculate Deflection Angles
• ~α(~θ) =1
π
∫d2~θ′ κ(~θ′)
~θ − ~θ′
|~θ − ~θ′|2.
• β = θ − α(θ).
Deflection Angles
~̂α(~ξ) =4G
c2
∫d2ξ′Σ(~ξ′)
~ξ − ~ξ′
|~ξ − ~ξ′|2. (1)
κ(~θ) =Σ(Dd
~θ)
Σcrit, Σcrit =
c2
4πG
Ds
DdDds, ~α(~θ) =
Dds
Ds~̂α(Dd
~θ) , (2)
~α(~θ) =1
π
∫d2~θ′ κ(~θ′)
~θ − ~θ′
|~θ − ~θ′|2. (3)
Convergence and Shear
2D projection of 3D Gravitational potential along LOS.
ψ(~θ) =Dds
DdDs
2
c2
∫Φ(Dd
~θ, z)dz (4)
The first order deraviation:
~∇θψ(~θ) =2
c2Dds
Ds
∫~∇⊥Φdz = ~α (5)
The second order deraviation:
κ =1
2(ψ11 + ψ22) , γ =
1
2(ψ11 − ψ22) + i
1
2(ψ12 + ψ12) (6)
Magnificagion
The magnification:
µ =θdωdθ
βdωdβ= ((1− κ)2 − |γ|2)−1 (7)
Or:µ = ((1− ψ11)(1− ψ22)− ψ12ψ21)
−1 (8)
From Lens Plane to Source Plane
6 4 2 0 2 4 66
4
2
0
2
4
6
From Source Plane to Lens Plane
Outline
Introduction
Simulations of Strong Lensing
Simulated Lensed Images
Work in Progress
Monte Carlo Halos
Compare with observations
Figure 3 : Comparing a simulated image with a observed lensed image.
Outline
Introduction
Simulations of Strong Lensing
Simulated Lensed Images
Work in Progress
Work in Progress
1. Our code is ready, we are playing with the sample of the halosfrom The Outer Rim Simulation.
2. Lensing effects on the Gini Coefficient of the backgroundsource galaxies. (HST)
3. Effects of the merging of galaxy clusters on the properties ofarcs. (HST)
4. Prepare to study the statistics of giant lensed arcs in galaxyclusters. (SPT, Gemini).
Work in Progress
1. Our code is ready, we are playing with the sample of the halosfrom The Outer Rim Simulation.
2. Lensing effects on the Gini Coefficient of the backgroundsource galaxies. (HST)
3. Effects of the merging of galaxy clusters on the properties ofarcs. (HST)
4. Prepare to study the statistics of giant lensed arcs in galaxyclusters. (SPT, Gemini).
Gini Coefficient
• The Gini coefficient is ameasure of the inequality oflight distribution. (A/(A+B))
• It reflects some information onproperties of galaxiesstatistically, e.g., type,evolution...
• To measure the GiniCoefficient of the galaxies athigh redshift more accurately.
Lensing Effects on Gini Coefficient
Michael Florian
Work in Progress
1. Our code is ready, we are playing with the sample of the halosfrom The Outer Rim Simulation.
2. Lensing effects on the Gini Coefficient of the backgroundsource galaxies. (HST)
3. Effects of the merging of galaxy clusters on the properties ofarcs. (HST)
4. Prepare to study the statistics of giant lensed arcs in galaxyclusters. (SPT, Gemini).
Cluster Merging and Giant Arcs
Mike Gladders
Cluster Merging and Giant Arcs
Mike Gladders
Work in Progress
1. Our code is ready, we are playing with the sample of the halosfrom The Outer Rim Simulation.
2. Lensing effects on the Gini Coefficient of the backgroundsource galaxies. (HST)
3. Effects of the merging of galaxy clusters on the properties ofarcs. (HST)
4. Prepare to study the statistics of giant lensed arcs in galaxyclusters. (SPT, Gemini).