A search for lensing of CMB in correlation with SDSS

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A search for lensing of CMB in correlation with
SDSS

• Christopher Hirata
• Ohio State
• 2005 January 7

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Weak Lensing

• Gravitational lensing provides a
  model-independent probe of the mass
  inhomogeneities in the universe.
• Lensing studies require a source of photons to be
  lensed
• Several groups have recently detected weak
  lensing of distant galaxies by large-scale
  structure
• The cosmic microwave background represents an
  alternative source.

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Lensing sources for LSSGalaxies vs. CMB

• Advantages of using galaxies- higher
  signal/noise (detections!) available at present-
  no foregrounds- sources at different redshifts ?
  can study evolution of signal strength with
  redshift (tomography)
• Advantages of using CMB- no intrinsic
  alignments- source redshift exactly known (fcn
  of ?mh2, ?bh2, )- random field ? no selection
  biases- most distant screen ? can observe
  longest-wavelength modes of the cosmic density
  field
• Advantage of using both same physics but with
  very different systematics.

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Effect of lensing on CMB

• The CMB is re-mapped by gravitational
  lensingHere ? is the convergence and is a
  projection of the matter density perturbation.
• From the perspective of quadratic estimation
  theory, k is another parameter of the covariance
  matrix ? it can be estimated just like the power
  spectrum!
• w is a symmetric weight matrix. For small k,
  wC-1 is optimal.

convergence estimator
quadratic fcn of temperatures
response matrix
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Estimating the Convergence

• Re-write as
• This expression is in a form that can be computed
  numerically. Hu (2001) Hu Okamoto (2002)
  Hirata Seljak (2002).
• For all-sky data, C-1 and R are trivial spherical
  harmonic convolutions. WMAP is close enough to
  all-sky (just throw out reconstructed map near
  Galactic plane cut).

convergence estimator
quadratic fcn of temperatures (integrated by
parts)
response matrix
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Signal vs. Noise CMB Temperature
WMAP lmax600
Planck lmax1600
anticipated signal
lmax3500
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Signal vs. Noise CMB Polarization
Temperature only
Temp Pol
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Observational search for lensing of CMB

• Because of low S/N per mode, the best chance for
  detecting lensing of CMB in the near future may
  come from cross-correlations with other tracers
  of LSS.
• The ideal tracer will have- low Poisson noise
  (relative to signal)- large solid angle-
  intermediate redshift (probe z of order unity) to
  overlap with lensing window function
• An excellent candidate are photometric luminous
  red galaxies (LRGs) from the Sloan survey.

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CMB Lensing from WMAP

• Recall quadratic estimator. We define the
  lensing vector field v
• WMAP produces 10 CMB maps (K1W4)? 100 v maps
  (quadratic combinations)? We use 56 (ignore
  auto-combinations, K and Ka)
• Filter w peaks at L 350.
• Vector field v has 2 components? longitudinal
  (scalar parity) ? lensing signal? transverse
  (pseudoscalar parity) ? systematics test

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Sloan Digital Sky Survey (SDSS)

• 2.5 m aperture
• 5 colors ugriz
• 6 CCDs per color, 2048x2048, 0.396/pixel
• Integration time 50 sec per color
• Typical seeing 1.5
• Limiting mag i21.3
• 3900 deg2 of imaging data used for this analysis

Image Credit Sloan Digital Sky Survey
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Acknowledgements, etc.

• The work described here is in collaboration
  with? N. Padmanabhan and D. Schlegel (LRGs)? U.
  Seljak (advisor)? the SDSS Collaboration.
• See astro-ph/0406004 (Hirata, Padmanabhan,
  Seljak, Schlegel, and Brinkmann, PRD 70103501)

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LSS Sample

• The main SDSS spectroscopic sample is not deep
  enough (z0.1)
• The quasars are deep enough but have lots of
  Poisson noise
• Various possibilities- all galaxies-
  photometric quasars- photometric luminous red
  galaxies LRGs
• Well-characterized sample constructed for power
  spectrum measurements (approximately) known
  n(z), peaks at z0.5.

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Inversions of LRG redshift distribution Padmanabha
n et al 2004 in prep
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clustering power
Signal-dominated to L300
Poisson noise
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(No Transcript)
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P(ltc2)0.74
Best fit bg 1.811.92
From autopower bg1.800.02
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P(ltc2)0.963
?
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Lensing Map
SCALE
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Lensing Map

• Galactic plane removed
• Only regions within 10 deg of SDSS left unmasked
• Point sources removed

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Power spectrum of v (with pt. src.)
41x41 GHz
41x61
41x94
61x61
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Power spectrum of v (masked pt. src.)
41x41 GHz
41x61
41x94
61x61
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ISW Effect

• Integrated Sachs-Wolfe (ISW) effect
  blue/red-shifting of CMB photons as they pass
  through an evolving gravitational
  potential(assuming no anisotropic stress).
• Competing effects F?0 due to expansion of the
  universe, but grows due to increase in dr/r.
• In linear W1 cosmology, Fconst and there is no
  ISW effect.
• If Wlt1 (open or L cosmology), F?0 and a
  blue-shift is observed in overdense (Flt0)
  regions. Thus we see a positive correlation
  between CMB temperature and density.

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ISW signal
33 GHz
bg 3.931.54
41 GHz
bg 3.741.54
61 GHz
bg 3.831.54
94 GHz
bg 3.931.55

• Used Wm0.3, s80.9, h0.7 templates.
• Compare autopower gives bg 1.800.02.

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Conclusions

• The CMB offers another opportunity to do
  cosmology with weak lensing? complementary to
  lensing with galaxies? no detection yet
  (S/N0.9) but there is potential for (eventually)
  lt1 cosmology at low redshift
• Major challenges? Point sources/secondary
  anisotropies (temperature)? Polarized
  foregrounds? Statistical methods (including
  methods that suppress the foreground contribution)