Combining Weak and Strong Cluster Lensingcont.

July 18, 2008

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 1 / 17

The Method

We combine weak and strong galaxy cluster lensing in thefollowing way:

Reconstruction quantity is the lensing potential ψ

Maximum-likelihood approach

χ2(ψ) = χ2w (ψ) + χ2

s (ψ)

Fully non-parametric

Grid-based

Weak lensing input: ellipticity catalogue

Strong lensing input: critical curve or arc position

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 2 / 17

The Method

We combine weak and strong galaxy cluster lensing in thefollowing way:

Reconstruction quantity is the lensing potential ψ

Maximum-likelihood approach

χ2(ψ) = χ2w (ψ) + χ2

s (ψ)

Fully non-parametric

Grid-based

Weak lensing input: ellipticity catalogue

Strong lensing input: critical curve or arc position

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 2 / 17

The Method

We combine weak and strong galaxy cluster lensing in thefollowing way:

Reconstruction quantity is the lensing potential ψ

Maximum-likelihood approach

χ2(ψ) = χ2w (ψ) + χ2

s (ψ)

Fully non-parametric

Grid-based

Weak lensing input: ellipticity catalogue

Strong lensing input: critical curve or arc position

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 2 / 17

The Method

We combine weak and strong galaxy cluster lensing in thefollowing way:

Reconstruction quantity is the lensing potential ψ

Maximum-likelihood approach

χ2(ψ) = χ2w (ψ) + χ2

s (ψ)

Fully non-parametric

Grid-based

Weak lensing input: ellipticity catalogue

Strong lensing input: critical curve or arc position

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 2 / 17

The Method

We combine weak and strong galaxy cluster lensing in thefollowing way:

Reconstruction quantity is the lensing potential ψ

Maximum-likelihood approach

χ2(ψ) = χ2w (ψ) + χ2

s (ψ)

Fully non-parametric

Grid-based

Weak lensing input: ellipticity catalogue

Strong lensing input: critical curve or arc position

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 2 / 17

The Method

We combine weak and strong galaxy cluster lensing in thefollowing way:

Reconstruction quantity is the lensing potential ψ

Maximum-likelihood approach

χ2(ψ) = χ2w (ψ) + χ2

s (ψ)

Fully non-parametric

Grid-based

Weak lensing input: ellipticity catalogue

Strong lensing input: critical curve or arc position

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 2 / 17

The Method

We combine weak and strong galaxy cluster lensing in thefollowing way:

Reconstruction quantity is the lensing potential ψ

Maximum-likelihood approach

χ2(ψ) = χ2w (ψ) + χ2

s (ψ)

Fully non-parametric

Grid-based

Weak lensing input: ellipticity catalogue

Strong lensing input: critical curve or arc position

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 2 / 17

Weak Lensing

State-of-the-artobservations allow only fora (∼ 10x10) pixelreconstruction grid

Furthermore galaxies arenot distributedhomogeneously over thefield

Solution: Adaptive-averaging-processProblem:Grid points becomecorrelated

χ2w (ψ) =

∑i ,j

(ε− Z (z)γ(ψ)

1− Z (z)κ(ψ)

)i

C−1ij

(ε− Z (z)γ(ψ)

1− Z (z)κ(ψ)

)j

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 3 / 17

Strong Lensing

The exact position of thecritical curve is notobservable

Position of arcs is a verygood approximation forthe location of the criticalcurve

Arc positions are knownwith high accuracy

Using weak lensing gridresolutions would result ininformation loss

χ2s (ψ) =

∑i

|detA(ψ)|2iσ2

i

=∑

i

|(1− Z (z)κ(ψ))2 − |Z (z)γ(ψ)|2|2iσ2

i

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 4 / 17

Cluster Gallery

So far we did reconstructions of:

Purely synthetic simulationsFeed real calculated cluster values into the code togetherwith full critical curve

Realistic simulations by using Massimo’s simulator codeRay-tracing lensing simulation including realistic noise(background galaxy shape, PSF, seeing, foregrounds)

One reconstruction of a real galaxy clusterMS 2137 using VLT and HST images

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 5 / 17

Cluster Gallery

So far we did reconstructions of:

Purely synthetic simulationsFeed real calculated cluster values into the code togetherwith full critical curve

Realistic simulations by using Massimo’s simulator codeRay-tracing lensing simulation including realistic noise(background galaxy shape, PSF, seeing, foregrounds)

One reconstruction of a real galaxy clusterMS 2137 using VLT and HST images

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 5 / 17

Cluster Gallery

So far we did reconstructions of:

Purely synthetic simulationsFeed real calculated cluster values into the code togetherwith full critical curve

Realistic simulations by using Massimo’s simulator codeRay-tracing lensing simulation including realistic noise(background galaxy shape, PSF, seeing, foregrounds)

One reconstruction of a real galaxy clusterMS 2137 using VLT and HST images

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 5 / 17

Cluster Gallery

So far we did reconstructions of:

Purely synthetic simulationsFeed real calculated cluster values into the code togetherwith full critical curve

Realistic simulations by using Massimo’s simulator codeRay-tracing lensing simulation including realistic noise(background galaxy shape, PSF, seeing, foregrounds)

One reconstruction of a real galaxy clusterMS 2137 using VLT and HST images

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 5 / 17

A Synthetic Example

Figure: Fieldsize: 120”x120”; 2000 background galaxies, full criticalcurve

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 6 / 17

A Synthetic Example

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 7 / 17

The only 1D profile-plot I will show!

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 8 / 17

Realistic Simulation

Figure: Fieldsize 400”x400”; 1826background galaxies

Figure: Simulated CCD-imagewith Subaru characteristics

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 9 / 17

Realistic Simulation

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 10 / 17

Realistic Simulations cont. / g1

Name: g1

Fieldsize: 1280”x1280”

Weak lensing: 13797 galaxies

Strong lensing: Full critical curve

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 11 / 17

Realistic Simulations cont. / g51

Name: g51

Fieldsize: 1900”x1900”

Weak lensing: 30839 galaxies

Strong lensing: Full critical curve

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 12 / 17

MS 2137

Figure: Fieldsize 405”x405”; 1500background galaxies, arcsincluded

Figure: HST/WFPC2 image, firstradial arc to be discovered (Fortet al. 1992)

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 13 / 17

MS 2137

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 14 / 17

Outlook (large scale)

Comparison of weak, strong and combinedlensing-reconstructions with Massimo.

Web interface for the lensing simulator andreconstructions of a big simulated cluster sample withPeter and Massimo.

Application to more real data.

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 15 / 17

Outlook (small scale): The ∇,4,∇4-Project

Flexion

Flexion finite differences schemes

Testing their implementation

Flexion χ2(ψ)-function

Fast χ2-minimisation algorithm

Testing its implementation

Reconstructions of synthetic clusters

Realistic simulations including flexion

Multiple image systems

...

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 16 / 17

Outlook (small scale): The ∇,4,∇4-Project

Flexion

Flexion finite differences schemes

Testing their implementation

Flexion χ2(ψ)-function

Fast χ2-minimisation algorithm

Testing its implementation

Reconstructions of synthetic clusters

Realistic simulations including flexion

Multiple image systems

...

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 16 / 17

Outlook (small scale): The ∇,4,∇4-Project

Flexion

Flexion finite differences schemes

Testing their implementation

Flexion χ2(ψ)-function

Fast χ2-minimisation algorithm

Testing its implementation

Reconstructions of synthetic clusters

Realistic simulations including flexion

Multiple image systems

...

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 16 / 17

Outlook (small scale): The ∇,4,∇4-Project

Flexion

Flexion finite differences schemes

Testing their implementation

Flexion χ2(ψ)-function

Fast χ2-minimisation algorithm

Testing its implementation

Reconstructions of synthetic clusters

Realistic simulations including flexion

Multiple image systems

...

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 16 / 17

Outlook (small scale): The ∇,4,∇4-Project

Flexion

Flexion finite differences schemes

Testing their implementation

Flexion χ2(ψ)-function

Fast χ2-minimisation algorithm

Testing its implementation

Reconstructions of synthetic clusters

Realistic simulations including flexion

Multiple image systems

...

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 16 / 17

Outlook (small scale): The ∇,4,∇4-Project

Flexion

Flexion finite differences schemes

Testing their implementation

Flexion χ2(ψ)-function

Fast χ2-minimisation algorithm

Testing its implementation

Reconstructions of synthetic clusters

Realistic simulations including flexion

Multiple image systems

...

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 16 / 17

Outlook (small scale): The ∇,4,∇4-Project

Flexion

Flexion finite differences schemes

Testing their implementation

Flexion χ2(ψ)-function

Fast χ2-minimisation algorithm

Testing its implementation

Reconstructions of synthetic clusters

Realistic simulations including flexion

Multiple image systems

...

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 16 / 17

Outlook (small scale): The ∇,4,∇4-Project

Flexion

Flexion finite differences schemes

Testing their implementation

Flexion χ2(ψ)-function

Fast χ2-minimisation algorithm

Testing its implementation

Reconstructions of synthetic clusters

Realistic simulations including flexion

Multiple image systems

...

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 16 / 17

Outlook (small scale): The ∇,4,∇4-Project

Flexion

Flexion finite differences schemes

Testing their implementation

Flexion χ2(ψ)-function

Fast χ2-minimisation algorithm

Testing its implementation

Reconstructions of synthetic clusters

Realistic simulations including flexion

Multiple image systems

...

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 16 / 17

Have a nice semester break!

Julian Merten (ZAH/ITA) Cluster Mass Reconstruction July 18, 2008 17 / 17