Simulating Gravitational Lensing of the CMB

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Simulating Gravitational Lensing of the CMB
Sudeep Das with David Spergel, Paul Bode and
Chris Hirata
Princeton University
June 8, 2007
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Outline

• Why is CMB Lensing interesting?
• Some basics
• Why large sky?
• The simulation
• Results
• Future directions

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Why interesting? Some basics Why
curved sky? Simulation
Future directions
The three Rs of the CMB
Redshift Remoteness Randomness
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
The three Rs of the CMB
A source at a well known Redshift.

• For lensing of the CMB the source redshift is
  accurately known.
• One of the main uncertainties in conventional
  weak lensing studies is the lack of accuracy in
  source redshifts.

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Why interesting? Some basics Why
curved sky? Simulation
Future directions
The three Rs of the CMB
A source which is most Remote.

• CMB can act as a source for lensing by high
  redshift objects.
• Lensing of the CMB by quasars and sub-mm
  galaxies have the potential of telling us about
  the less understood halo properties of these
  objects.

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Why interesting? Some basics Why
curved sky? Simulation
Future directions
The three Rs of the CMB
A source which is Random.

• The hot and cold patches of the CMB are
  featureless. They have no intrinsic shape.
• In conventional weak lensing with galaxies,
  their intrinsic ellipticity is a source of
  systematic noise.

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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Detectable
3.4 ? detection with WMAPNVSS. Smith et al.
arXiv0705.3980v1
With upcoming surveys like ACT, PLANCK, SPT the
effect should be detectable at high significance
in cross correlation with large scale structure
tracers.
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Lensing remaps points

• Typical deflection is non-trivial ( 2.7 arcmin)
  
• Deflections are coherent over few degrees.

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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Lensing smoothes features

• Power from large scales (l60) in the
  deflection field gets aliased into smaller scales
  (l1000) in the CMB.

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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Catching all those modes

• A lot of power from large scale modes in the
  deflection field
• couples to small scale modes in the CMB.

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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Large Scale Structure Simulation
For z lt 4.0
We use a Tree Particle Mesh (TPM) light-cone
simulation. Bode, P., Ostriker, J.P.
2003, ApJS, 145, 1 Lbox 1000 h-1 Mpc N
10243 (mp 6.72 1010Msun /h).
For z gt 4.0

• LSS planes are generated as Gaussian random
  realizations from a theoretical power spectrum.

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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Large Scale Structure Cosmology
The cosmological parameters used are ?b
0.044, ?m 0.216, ?? 0.74, h 0.72, n
s 0.95 and ?8 0.77.
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Large Scale Structure Projection
onto sphere
At each TPM step,
Particles in a z- slice are projected onto the
octant of a HEALpix sphere.
Euler rotated and centroided on the North Pole.
A disc is taken out and the surface mass density
(?) on it saved.
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100 TPM discs are further binned up into 10
planes. Both an effective and a multiple plane
ray tracing are performed.
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Connecting ??? ?????
Multiple Planes
Effective Approximation
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Power Spectrum of ?
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Getting the deflection field ?
The Poisson equation is inverted to get the
lensing potential,
Then the deflection angle, ?r ??is then
calculated as,
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Remapping points
Given the deflection angle field,
rays are propagated using the curved sky
remapping equations,
Lewis, A. Phys. Rev. D71 (2005) 083008
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
The Need to Interpolate
Rays will end up off-centered on subsequent
slices and on the CMB. Both r ? and TCMB have
to be sampled on an irregular grid.
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Non-Isolatitude Spherical Harmonic Transform
(NISHT)
Hirata et al., PRD, 70, 103503, (2004).
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Unlensed CMB Gnomonic Projection
NSIDE4096. 0.856 arcmin.
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Lensed CMB Gnomonic Projection
NSIDE4096. 0.856 arcmin.
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Difference Map Gnomonic Projection
NSIDE4096. 0.856 arcmin.
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Power Spectra
Power Spectra
The theory curves are spectra from CAMB with
mode-coupling due to a tapered polar cap window.
www.camb.info
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Power Spectra
Power Spectra
Structure at zgt4 has a nontrivial contribution to
the lensed signal.
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Utility

• Most of the forthcoming surveys will concentrate
  on the cross- correlation between gravitational
  lensing of the CMB and tracers of large scale.
• The current method provides a natural way to
  simulate such studies.
• The halos can be saved and populated with
  tracers (LRGs, SZ clusters etc.)
• Optical lensing (galaxy shear) studies can be
  simulated with the same LSS and cross correlated
  with the lensed CMB.

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Why interesting? Some basics Why
curved sky? Simulation
Future directions
LRG Maps
In collaboration with Charlie Conroy we are
populating the simulation with LRGs with an HOD
based approach. Conroy et. al, Astrophys. J.
647 (2006) 201-214
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
The Atacama Cosmology Telescope.
Achieved first light on June 8, 2007 pointing at
Jupiter.
ACT will be looking at the SDSS stripe 82 where
we have LRG data.
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Why interesting? Some basics Why
curved sky? Simulation
Future directions
Final Words

• Extension to full sky.
• Internally consistent LRG and SZ maps.
• Shear Maps for the same LSS.
• Use them as training sets for detection
  algorithms.
• Thanks to
• David Spergel (advisor), Paul Bode, Chris Hirata,
  Charlie Conroy.

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Why interesting? Some basics Why
curved sky? Simulation
Future directions
NISHT Errors
In the simulation we sample at 4 times the
Nyquist rate and use a Polynomial of order K10.
1e-2
1e-5
Maximum Error in each Fourier Mode
1e-8
LNyquist/LSampling
Hirata et al., PRD, 70, 103503, (2004).