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WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M....

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WSLAP Weak and Strong Lensing Analysis Package Diego 1 , H. Sandvik 2 , P. Prototapas 3 , M. Tegm IFCA (Santander) Max-Planck (Garching) Harvard (Smithsonian) MIT Rencontres de Morion La Thuile, March 200 http://darwin.cfa.harvard.edu/SLAP/
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Page 1: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

WSLAP Weak and Strong Lensing Analysis Package

J.M. Diego1, H. Sandvik2, P. Prototapas3, M. Tegmark4

1 IFCA (Santander)2 Max-Planck (Garching)3 Harvard (Smithsonian)4 MIT Rencontres de Moriond

La Thuile, March 2006

http://darwin.cfa.harvard.edu/SLAP/

Page 2: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

What is this ?Method to find a combined solution of strong and/or weak lensing data.

Uses fast algorithms to invert the problem (a combined solution can be found in few seconds).

Speed also allows to find multiple solutions and to estimate their dispersion.

Non-parametric, i.e. No assumptions about the Mass profile are needed.

Page 3: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

A1689

Page 4: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

Two alternatives.

Parametric vs Non-parametric

Page 5: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

Parametric methods

Big and smooth DM halo containing most of the mass.Many subhalos on top of the galaxies.Each halo contributes with ~ 7 parameters.

Page 6: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

Non-Parametric methods

Starts with regular grid.Each cell contributes with 1 parameter.

Page 7: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

Basics

Lens equation

DLS

DS

DL

DS

DS DLS

DLSDS

Page 8: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

Deflection Angle

M’

M’

4 Gc2DL

’’|2

d’

’’

Approximation.

MDLSDS

Non-Parametric methods

Page 9: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

Weak & strong lensing

dx/dx – dy/dydx/dy = dy/dx

xx+ x

The problemSystem of linear equations with 2Nd equations and (2Ns + Nc) unknowns.

X

yy+ y

Page 10: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

WSLAP : A fast simulation tool.

Fast computation of the kernel .

Use linear algebra to compute theta positions.

Same technique used to calculate the shear distortions.

X

Page 11: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

WSLAP : A fast analysis tool.

Take advantage of algebraic formulation of the problem.

Fast computational techniques allow to find the solution faster (bi-conjugate gradient, SVD, quadratic programming etc).

Cluster from Yago Ascasibar

X

Page 12: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

Finding the solution

Conjugate Gradient

Singular Value Decomposition

Quadratic Programming

R = Xf(X) = RTC-1R = a – bx + (1/2)xAx

UT W VX = (VT W-1 U)

Min [f(X)], X > 0

Weight of the data sets.

Page 13: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

Simulations

SL WL

Page 14: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

Results

Page 15: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

True SL

WL SL + WL

Page 16: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

SL vs WL

SL

WL

SL + WL

Page 17: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

Dispersion of the solution

Page 18: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

Optimal Basis

Compact basis like the Gaussian render better results than for instance power laws or isothermal profiles.

Other more exotic basis can be used as well.

Extended basis like Legendre polynomia perform poorly.

Page 19: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

Application to A1689 (SL only)

Page 20: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

Application to A1689 (SL only)

Page 21: WSLAP Weak and Strong Lensing Analysis Package J.M. Diego 1, H. Sandvik 2, P. Prototapas 3, M. Tegmark 4 1 IFCA (Santander) 2 Max-Planck (Garching) 3 Harvard.

http://darwin.cfa.harvard.edu/SLAP/WSLAP Beta version available at


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