Anisotropic Correlation Function of Large-Scale Galaxy Distribution from the SDSS LRG Sample

1. Anisotropic Correlation Function of Large-Scale Galaxy Distribution from the SDSS LRG Sample OQSCM @ 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

2. We calculated an Anisotropic Correlation Function, ξ(s⊥,s//), from SDSS LRG sample, focusing on anisotropy of baryon acoustic oscillations. We then constrained cosmological parameters, Ωm, Ωb, h, and w, by comparing it with a corresponding theoretical model. 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. Motivation What we did

3. Baryon Acoustic Oscillations in LSS s2ξ(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)

4. Cosmological Information in the Redshift-Space Correlation Function fb=Ωb/Ωm • 1. Mass Power Spectrum in Comoving Space • Ωmh, Ωb/Ωm, (h) Ωmh • 2. Dynamical Redshift Distortion • β= Ωm0.6/b (for Kaiser’s effect) real space redshift space non-linear linear ∝ H(z) • 3. Geometrical Distortion • Ωm, ΩΛ, w ∝ z/DA(z)

5. Cosmological Information in the Redshift-Space Correlation Function fb=Ωb/Ωm • 1. Mass Power Spectrum in Comoving Space • Ωmh, Ωb/Ωm, (h) Ωmh • 2. Dynamical Redshift Distortion • β= Ωm0.6/b (for Kaiser’s effect) real space redshift space non-linear To include all of these information, we calculate a correlation function as two variables, ξ(s⊥,s//), from the SDSS LRGs. linear ∝ H(z) • 3. Geometrical Distortion • Ωm, ΩΛ, w ∝ z/DA(z)

6. Anisotropic Correlation Function of LRGs Baryon Ridges Correspond to the 1D Baryon Peak scale detected by Eisenstein et al. ξ＜0 ξ≧0 Angle average! (left)Analytical Formulae (Matsubara 2004) (right)SDSS LRG Correlation Function

7. 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

8. 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

9. 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 ∝ebδ • We use in this work m

10. s2ξ(s) LRG 2LPT + biased selection Correlation Functions Measured from Our Mocks • The averaged correlation function measured from our mocks match the one of LRGs well as for ξ(s)

11. and ξ(s⊥,s//) 2LPT + bias LRG Correlation Functions Measured from Our Mocks • The averaged correlation function measured from our mocks match the one of LRGs well as for ξ(s) We generate 2,500 mock catalogs to construct the covariance matrix.

12. Results(1): Fundamental Parameters • We consider 5D Parameter Space 40<s<200Mpc/h 60<s<150Mpc/h

13. Results(2) : Dark Energy Parameters WMAP3 • (Extended) Alcock-Paczynski WMAP3+SN Ia Our results

14. 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(≦ 40~60 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)

15. Summary • We have calculated the correlation function of SDSS LRGs as a function of 2-variables, ξ(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.

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