Simulating
Gravitational Lensing
1,2
Stefan Hilbert ,
Jan Hartlap1, Robert Smith1, Laura Marian1, ...
l
Argelander-Institut für Astronomie, Universität Bonn, Germany
2
Max-Planck-Institut für Astrophysik, Garching, Germany
Outline
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Introduction
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Results:
●
–
Strong lensing by clusters
–
Weak lensing by LSS: cosmic shear
–
Weak galaxy-galaxy lensing
–
Weak group and cluster lensing
–
Weak lensing of galaxies in clusters
–
Weak lensing mass reconstruction
–
Weak lensing: shear peak statistics
Summary
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Introduction
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●
cosmic structure formation:
–
highly non-linear
–
numerical simulations required
Millennium Simulation (MS):
–
matter structures from galaxy halos to galaxy
clusters and large-scale structure
–
galaxy models with predictions for magnitudes,
colours, etc.
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z=0
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z=0
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Gravitational Lensing
image
source
observer
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Multiple-Lens-Plane Approximation
image
source
observer
slice
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slice
boundary
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Multiple-Lens-Plane Approximation
image
source
observer
slice
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lens plane
slice
boundary
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Multiple-Lens-Plane Approximation
image


source
observer
slice
lens plane
slice
boundary
=(2)-1 ⇒ =
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Gravitational lensing
●
gravitational lensing (GL):
–
–
way to “see” all matter (dark+luminous)
mass distribution
predict
image distortions, etc.
infer
●
use ray-tracing through N-body simulations to:
–
obtain predictions for GL observations
–
study capability of GL to measure mass distribution,
and constrain galaxy physics, cosmology and
fundamental physics
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The Ray-Tracing Algorithm
projection
filling
simulation data

planes
redshift slices
solving for potential

lens planes
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ray-tracing
statistics
lensing maps
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x
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Implementation Details: Box Size
~100 Mpc
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~1 Gpc
~10 Gpc
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Implementation Details: Small Box
zS = 2
~100 Mpc
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only small light cones
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no large-scale modes
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e.g.
Jain, Seljak, & White (2000)
Dietrich & Hartlap (2008)
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Implementation Details: Medium Box
zS = 2
~1 Gpc
●
only small light cones
●
no discontinuity at box boundaries
e.g.
Hilbert, Hartlap, White, & Schneider (2008)
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Implementation Details: Medium Box
●
tilted l.o.s., slices, planes:
➔
large lens planes
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Implementation Details: Large Box
~10 Gpc
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e.g.
Das & Bode (2008)
Teyssier et al. (2009)
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Strong Lensing: Giant Arcs
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Simulations
of Gravitational
Lensing
Abell 2218
(HST image,
Fruchter
et al.)
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Strong Lensing: Giant Arcs
MACSJ0451.9+0006
Horesh et al. (2010)
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Strong Lensing: Giant Arcs
ray-tracing
Horesh et al. (in prep.)
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Strong Lensing: Giant Arcs
Horesh et al. (in prep.)
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Strong Lensing: Giant Arcs
Puchwein & Hilbert (2009)
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Weak lensing
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Simulations
Gravitational
simulation:
S. Colombi,of
IAP
Lensing
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Weak Lensing: Cosmic Shear
foreround
matter
M
background
galaxy image
γ(i)
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θ(ij)
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γ(j)
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Cosmic Shear Power Spectra
from ray-tracing
through MR
zS=2
2π l 2 Pκ(l )
from 3D matter
power spectrum
of MR
from
power spectrum fit
(Smith et al. 2003)
zS=1
Hilbert et al. (2009)
l
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Cosmic Shear in COSMOS
Schrabback et al. (2010)
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Cosmic Shear in COSMOS
Schrabback et al. (2010)
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E/B-mode decomposition
galaxy image
M
E mode shear
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M
B mode shear
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Aperture Mass
Hilbert et al. (2009)
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Weak Halo-Galaxy Lensing
FG galaxy or cluster
BG galaxy
R
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⟨γt(R)⟩ ∝ ΔΣ(R) ⇒ M(R)
γt
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Weak Galaxy-Galaxy Lensing
full ray-tracing
linear approx.
Hilbert et al. (2009)
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Weak Cluster-Galaxy Lensing
Hilbert & White (2010)
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Understanding the Signal
correctly centered
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miscentered
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Cluster Member Galaxies
cluster halo
FG galaxy
BG galaxy
R
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γt
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Cluster Member Galaxies
calibration point
cluster centre
FG galaxy
BG galaxy
γt
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BG galaxy
R
γt
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Cluster Member Galaxies
galaxies binned by subhalo mass
Pastor Mira et al. (in prep.)
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Cluster Member Galaxies
galaxies binned by infall mass and time since infall
Pastor Mira et al. (in prep.)
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Cluster Member Galaxies
galaxies binned by stellar mass and morphology
(LSST)
bulgy
disky
Pastor Mira et al. (in prep.)
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Summary
●
Introduction
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Results (and Problems):
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galaxy lensing (strong and weak):
baryons, substructure, etc.?
–
subhalo profiles from lensing: baryons, etc.?
–
cluster lensing: mass function, baryons?
–
cosmic shear: box size, baryons,
observational artefacts?
–
...
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Thanks
for
Your Attention!
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