Presentacin de PowerPoint

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WSLAP Weak and Strong Lensing
Analysis Package
http//darwin.cfa.harvard.edu/SLAP/
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
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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.
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A1689
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Two alternatives.
Parametric vs Non-parametric
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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.
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Non-Parametric methods
Starts with regular grid. Each cell contributes
with 1 parameter.
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(No Transcript)
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Non-Parametric methods
Deflection Angle
q-q
a(q) M(q)
4 G
dq
c2DL
q-q2
Approximation.
a(q) l S LM
M(q)
DLS
DS
q - q
q
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Weak strong lensing
qx bx ax
qy by ay
g1 0.5 ( dax/dx day/dy )
g2 dax/dy day/dx
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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.

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WSLAP A fast analysis tool.
Cluster from Yago Ascasibar

Take advantage of algebraic formulation of the
problem. Fast computational techniques allow to
find the solution faster (bi-conjugate gradient,
SVD, quadratic programming etc).
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Finding the solution
Conjugate Gradient
Fast
R Q - GX
f(X) RTC-1R a bx (1/2)xAx
Singular Value Decomposition
Parity
G UT W V
X (VT W-1 U) Q
Quadratic Programming
Mgt0
Min f(X), X gt 0
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Simulations
SL WL

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Results
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True
SL
WL
SL WL
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SL vs WL
SL
SL WL
WL
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Dispersion of the solution
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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.
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Application to A1689 (SL only)
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Application to A1689 (SL only)
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WSLAP Beta version available at
http//darwin.cfa.harvard.edu/SLAP/