Teppei%20OKUMURA%20(Nagoya%20University,%20Japan)

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Anisotropic Correlation Function of Large-Scale
Galaxy Distribution from the SDSS LRG Sample
OQSCM _at_ Imperial College London Mar. 29, 2007

• Teppei OKUMURA (Nagoya University, Japan)
• Takahiko Matsubara1, Daniel Eisenstein2,
• Issha Kayo1, Chiaki Hikage1, Alex Szalay3,
• SDSS Collaboration
• 1Nagoya, 2Arizona, 3Johns Hopkins

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What we did
Motivation

• Cosmological parameters are constrained with high
  precision.
• However, to understand the properties of dark
  energy (cosmological constant? time evolution?
  spatial clustering??), we need both more accurate
  observations and analyses.

• We calculated an Anisotropic Correlation
  Function, ?(s?,s//), from SDSS LRG sample,
  focusing on anisotropy of baryon acoustic
  oscillations.
• We then constrained cosmological parameters, Om,
  Ob, h, and w, by comparing it with a
  corresponding theoretical model.

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Baryon Acoustic Oscillations in LSS
s2?(s)

• Correlation Function
• Eisenstein et al.(2005)
• Power Spectrum
• Cole et al. (2005)
• Tegmark et al.(2006)
• Percival et al.(2007a,b)
• Padmanabhan et al. (2007)

Eisenstein et al.(2005)
Sound Horizon scale at decoupling
kP(k)
Our analysis can be complementary to the previous
analyses above.
Tegmark et al.(2006)
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Cosmological Information in the Redshift-Space
Correlation Function
fbOb/Om

• 1. Mass Power Spectrum in Comoving Space
• Omh, Ob/Om, (h)

Omh
real space
redshift space

• 2. Dynamical Redshift Distortion
• ß Om0.6/b
• (for Kaisers effect)

non-linear
linear
? H(z)

• 3. Geometrical Distortion
• Om, O?, w

? z/DA(z)
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Cosmological Information in the Redshift-Space
Correlation Function
fbOb/Om

• 1. Mass Power Spectrum in Comoving Space
• Omh, Ob/Om, (h)

Omh
real space
redshift space

• 2. Dynamical Redshift Distortion
• ß Om0.6/b
• (for Kaisers effect)

non-linear
To include all of these information, we calculate
a correlation function as two variables,
?(s?,s//), from the SDSS LRGs.
linear
? H(z)

• 3. Geometrical Distortion
• Om, O?, w

? z/DA(z)
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Anisotropic Correlation Function of LRGs
Baryon Ridges Correspond to the 1D Baryon
Peak scale detected by Eisenstein et al.
?lt0 ??0
Angle average!
(left)Analytical Formulae (Matsubara 2004)
(right)SDSS LRG Correlation Function
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Anisotropic Correlation Function of LRGs
Baryon Ridges Correspond to the 1D Baryon
Peak scale detected by Eisenstein et al.

• Dynamical distortion is due to the peculiar
  velocity of galaxies

(left)Analytical Formulae (Matsubara 2004)
(right)SDSS LRG Correlation Function
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Anisotropic Correlation Function of LRGs
Baryon Ridges Correspond to the 1D Baryon
Peak scale detected by Eisenstein et al.

• Geometrical distortion can be also measured when
  deviation of ridges from the ideal sphere in
  comoving space is detected.
  (Alcock-Paczynski)

(left)Analytical Formulae (Matsubara 2004)
(right)SDSS LRG Correlation Function
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The Covariance Matrix for the Measured
Correlation Function

• Much more realizations than the degrees of
  freedom of the binned data points are needed,
  2000 realizations.
• Possible Methods for Mock Catalogs and Covariance
• Jackknife resampling
• The easiest way, but it is unsure whether this
  can provide a reliable of estimator of the cosmic
  variance.
• N-body Simulations
• A robust and reliable way, but it is too
  expensive.
• 2LPT code (Crocce, Pueblas Scoccimarro 2006)
  Biased selection of galaxies
  with weighting of ? ebd
• We use in this work

m
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Correlation Functions Measured from Our Mocks

• The averaged correlation function measured from
  our mocks match the one of LRGs well as for ?(s)

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Correlation Functions Measured from Our Mocks

• The averaged correlation function measured from
  our mocks match the one of LRGs well as for ?(s)

We generate 2,500 mock catalogs to construct the
covariance matrix.
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Results(1) Fundamental Parameters

• We consider 5D Parameter Space

40ltslt200Mpc/h
60ltslt150Mpc/h
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Results(2) Dark Energy Parameters

• (Extended) Alcock-Paczynski

WMAP3
WMAP3SN Ia
Our results
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Future Works Toward Precision Cosmology

• Covariance Matrix
• For more accurate covariance, we should run a
  huge number of N-body simulations with
  independent initial conditions.
• Nonlinear regions (? 4060 Mpc/h)
• Also contain abundant cosmological information.
  However we have discarded all of them in this
  analysis. In addition, the baryonic signature is
  affected by nonlinearity. We should estimate
  non-linear corrections somehow. (e.g. using
  N-body simulation or higher-order perturbations)

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Summary

• We have calculated the correlation function of
  SDSS LRGs as a function of 2-variables,
  ?(s?,s//),
• and have estimated cosmological parameters using
  only the data of linear-scale regions.
• We have obtained the consistent results with the
  previous LRG works.
• This method can be useful in probing Dark Energy
  (like Seo Eisenstein 2003, Hu Haiman 2003,
  and Glazebrook Blake 2005), when a future deep
  redshift survey such as WFMOS (Wide-Field
  Multi-Object Spectrograph) gets available.

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AppendixCorrelation Function in Redshift Space

• General Formulae of Correlation Function in
  Redshift Space derived from a Linear Perturbation
  Theory (Matsubara 2000 2004)