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).