CrossCorrelating the CMB with the Large Scale Structure of the Universe

1
Cross-Correlating the CMB with the Large Scale
Structure of the Universe

• Niayesh Afshordi
• Princeton University Observatory
• Mar. 16, 2004

2
Collaborators

• Yeong-Shang Loh, Princeton/Colorado
• David N. Spergel (my thesis advisor), Princeton
• Michael A. Strauss, Princeton

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Outline

• Cosmic Microwave Background and WMAP
• Why to cross-correlate? the secondary
  anisotropies
• Cross-power spectrum signal and errors
• Galaxy surveys
• The ISW signal and dark energy
• The thermal SZ signal and X-ray clusters
• Conclusions and Future Prospects

4
Cosmic Microwave Background

• Remnant of the hot early universe
• Isotropic up to 1 part in 105
• Fluctuations
• Primary fluctuations (at LSS), above 0.1 deg (l lt
  1000)
• Linear perturbation theory
• Excellent measure of cosmology and initial
  conditions
• Secondary fluctuations, below 0.1 deg (l gt1000)
  
• (Mostly) non-linear structure formation
• Measures of various phenomena in the mature
  universe

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Wilkinson Microwave Anisotropy Probe (WMAP)-First
Year Data Release
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Why to Cross-Correlate? the Secondary
Anisotropies

• Unlike the primary anisotropies, the secondary
  anisotropies are correlated with tracers of the
  large scale structure in the low-redshift
  universe.
• Integrated Sachs-Wolfe (ISW) effect
• Domination of dark energy/ spatial curvature
• decay of linear gravitational
  potential
• Important at large angles, as it traces the
  potential
• Not observed in the CMB auto-power (at the 3s
  level)!

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Secondary Anisotropies

• Thermal Sunyaev-Zeldovich (SZ) effect
• Scattering of CMB photons off hot electrons
• 
  
• Negative for low and positive for high
  frequencies
• Point Sources
• Contaminate the CMB!

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The Projected Cross-Power Spectrum
Projected galaxy number density
Projected Cross-Power Spectrum
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The Cross-Power Spectrum Signal
A random field, e.g. density, potential

• For a generic secondary effect like
• Limber equation gives

The observable temperature shift due to the
secondary anisotropy
The redshift dependent kernel, depends on the
secondary anisotropy
At most 2-3 for lowest ls
Galaxy comoving density, depends on the sample
3D cross-power spectrum, May depend on redshift
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The Cross-Power Spectrum Error

• For a small cross-correlation signal, the error
  is
• We use the observed auto-powers to estimate the
  error
• Includes the unknown systematics in CMB/galaxy
  survey.
• Monte-Carlo error estimates
• CMB fluctuations are well-understood ? Randomly
  generated CMB skies have the same error
  properties.
• Jack-knife error estimates
• Need many independent patches of sky, not
  possible due to large-angle correlations in the
  CMB

CMB auto-power
Auto-power of projected galaxy distribution
The sky coverage fraction
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Galaxy Surveys

• Galaxies trace the mass density distribution
• Denser samples reduce the Poisson noise and hence
  increase the signal-to-noise at larger ls.
• Larger sky coverage increases the signal-to-noise
  for all ls.
• The angular scale of the cross-correlation signal
  decreases with the survey depth.

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Three parameter fit to the WMAP/2MASS
cross-correlationAfshordi, Loh, Strauss 2003

• Assume WMAP-concordance cosmological model
• Do a simultaneous three parameter fit to 4x3
  cross-power signals, to find
• ISW amplitude (1.5 /- 0.6, in units of the
  expected amplitude), 2.5s
• SZ amplitude, 3.7s
• Radio Point Sources contribution (assuming their
  frequency dependence) , 2.7s

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Different Signals in 2MASSxWMAP

• Deepest magnitude bin
• data best fit model
• ISW SZ
  Point Sources

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Observing ISW in cross-correlationSummary

• Signal comes from llt50 WMAP (1yr) is adequate
• Observed at 2-3? level (2MASS,SDSS,APM,NVSS,HEAO-A
  1)
• Optimal detection 7.5?
• We need 10 million galaxies or 1 million
  clusters in 0ltzlt1.5
• Not the best probe of Dark Energy
• A good probe of Large Scale Physics

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Different Signals in 2MASSxWMAP

• Deepest magnitude bin
• data best fit model
• ISW SZ
  Point Sources

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The Thermal SZ in WMAP/2MASS
ICM temperature- cluster mass relation
Afshordi, Loh, Strauss 2003
Afshordi Cen 2002
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SZ in Cross-CorrelationPoisson vs. Detector
Noise
WMAP 4-yr
WMAP 4-yr 3-yr 2-yr
1-yr

• Bottom line
• SZ has much more to offer!

Afshordi 2004II, in preparation
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Observing SZ in cross-correlationSummary

• Signal comes from small angles ? need higher
  resolution (APEX,SZA,SPT,ACT,Planck )
• Observed at 4? level (2MASS at z0.1)
• Signal is proportional to the number of galaxies
  in 1014 M clusters
• Probes the Thermal History of Intra-Cluster
  Medium at 0ltzlt2

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Conclusions

• Cross-correlating galaxy surveys with the CMB
  gives us invaluable information about the low
  redshift universe.
• Comparing to auto-correlations, the systematic
  errors in cross-correlation, is typically low and
  under control.
• A survey with 10 million galaxies within 0ltzlt1
  yields a near optimal ISW detection at 5?, and
  looks at physics at the largest physical scales.
• For WMAP x 2MASS cross-correlation, we see
• ISW signal at the 2.5s level, consistent with
  LCDM prediction.
• Thermal SZ, at the 3.7s level, consistent with
  X-ray clusters (2yr data, S/N goes up to 6s).
• SZ has much more to offer.

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Future Prospects

• Find the best statistics to cross-correlate with
  the SZ signal
• Constraints on the halo model based on the
  cross-correlation signal
• Cross-correlate
• 2MASS color-selected galaxies
• complete SDSS
• Pan-STARRs/LSST
• With
• WMAP 2-year data
• Next generation of CMB experiments
  (SPT/ACT/Planck)

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ISW in Cross-Correlation Coverage in redshift
and multipole space

• WMAP is adequate for any ISW detection in
  cross-correlation

Afshordi 2004
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ISW in Cross-Correlation Poisson Limited Surveys

• Bottom line
• We need 10 million galaxies or
• 1 million clusters in 0ltzlt1.5 to get
• most of the ISW signal

Afshordi 2004
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ISW effect and Dark Energy
Spergel et al. 2003

• ISW effect
• Not the best probe of Dark Energy
• A good probe of Large Scale Physics

SDSS 2dF
Perfect ISW, zlt 3
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The Thermal SZ and Point Source Signals in
2MASS/ WMAP

• Thermal SZ model
• WMAP concordance cosmology
• Peacock and Dodds non-linear power spectrum
• Constant galaxy bias
• Constant pressure bias, normalized to the cluster
  mass-temperature relation
• where 1ltQlt2 from X-ray observations
• Sheth Tormen mass function
• We use the frequency dependence to distinguish
  the Point Source and SZ signals.

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Scale-dependent bias and variable gas fraction

• Scale-dependent bias increases the theoretical
  prediction for SZ
• Variable gas fraction decreases the theoretical
  prediction for SZ
• Q 1.46
  /- 0.38

Bryan 2000
Adiabatic Simulation Courtesy of P. Zhang