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Progress in mapping the large scale structure of the Universe

Progress in mapping the large scale structure of the Universe. Saleem Zaroubi Max-Planck-Institut für Astrophysik Garching, Germany. Introduction. Density contrast is defined as d= (r-r 0 )/r 0 Peculiar velocity is defined as deviation from Hubble expansion:.

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Progress in mapping the large scale structure of the Universe

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  1. Progress in mapping the large scale structure of the Universe Saleem Zaroubi Max-Planck-Institut für Astrophysik Garching, Germany

  2. Introduction Density contrast is defined asd= (r-r0)/r0 Peculiar velocity is defined as deviation from Hubble expansion: In linear regime GI gives a simple relation between density and velocity:

  3. Large Scale Structure Probes Galaxy Redshift Surveys: Reconstruction ofd, v, Fof galaxies (biased) Power Spectrum b=W0.6/b from redshift distortions (Kaiser 87)

  4. Results From 2dF (Percival et al. 01 & Peacock et al 01)

  5. Large Scale Structure Probes Galaxy Redshift Surveys: Reconstruction ofd, v, Fof galaxies (biased) Power Spectrum b=W0.6/b from redshift distortions (Kaiser 87) Peculiar Velocity Catalogs: Bulk Flow within a volume (Vb) Reconstruction ofW0.6 d, v, F Power Spectrum, ... Comparison of both givesb=W0.6/b

  6. Large Scale Structure Probes • Abundance evolution with z • Cluster Surveys (e.g., REFLEX) • Cosmic Shear Results consistent with (very) low W • Power Spectrum, e.g., Croft et al. 2001: slight disagreement with standard LCDM • Fluctuations in the Equation of State (Schaye et al. 00,Theuns & Zaroubi 01, …: find Temp. jump at z~3.1 Galaxy-Clusters Weak Grav. Lensing The Lyman- Forest: QSOs, Radio Sources, XRB, CMB!!, ….

  7. Peculiar Velocity Data Sets Mark3 (Willick et al. 1996): TF and Dn-s for ~3000 (spiral & elliptical) galaxies grouped to ~1200 objects. ENEAR (da Costa et al. 99): Dn-s for ~2000 early type galaxies grouped to ~750 SFI (Haynes et al. 1998): TF for ~2000 spiral galaxies grouped to ~1200

  8. Asterix Obelix Tortuous Convulvulus Dogmatix

  9. The Bulk Flow Statistic The bulk flow vector Vb is the mean velocity vector within a given volume. Convergence to null velocity at large radii!! The points show the Vb from Mark3 Data (Willick et al. 97) as calculated by Dekel 96

  10. A direct estimation of this vector is given by minimizing the following c2Statistic: uiis the measured radial velocity, wiis some weighting, is a unit radius vector Bulk Flow Measurements Bulk Flow From ENEAR Uniform Weighting ____________________________________ Sample N |Vb| l b R<2000 km/s 77 442±97 310±16 21±10 R<4000 km/s 324 147±62 306±18 9±14 R<6000 km/s 656 220±42 304±16 25±11 da Costa et al. 2000

  11. Bulk Flow Measurements Courteau et al. (93) Bulk flow of 300km/s at 6000km/s Giovanelli et al. (98; SFI) No bulk flow at 6000km/s (~130 km/s) da Costa et al. (00;ENEAR) Bulk flow of 220km/s at 6,000km/s Lauer & Postman (94) Bulk flow of 600 km/s at 15,000km/s Riess et al. (96) SNIa are at rest (relative to CMB) Saglia et al. (98; EFAR) No bulk flow at 10,000 km/s Hudson et al.(99; SMAC) Bulk flow of 600km/s at 15,000 km/s in a different direction from LP Willick (99; LP10K) Bulk flow of 600km/s at 15,000km/s in a different direction from LP Dale et al. (99; EFAR) No bulk flow to 20,000km/s Tonry et al. (00; SBF) Bulk Flow of 400km/s at 2000km/s Vb from PSCz consistent with CDM (Branchini et al. 99)

  12. The Value of b Bias can be nonlinear, non-local, stochastic, etc. Here we assume linearity galaxy = b dark matter v-v & d-d comparisons yield the value ofb. Where,=0.6/b

  13. Branchini et al. (2001) have derived  from comaring the measured peculiar velocities from the SFI catalog with the PV derived from the IRAS-PSCz Redshift Catalog using theVELMOD method (Willick et al. 97)

  14. ‘Green Function’ For the Density & Velocity Fields POTENT (Bertschinger & Dekel 89), Wiener filter (Zaroubi et al. 99),UMV estimator (Zaroubi et al. 2001)

  15. Testing the method · The original density field smoothed with Gaussian filter on 9 Mpc/h (upper left). · Reconstruction from error free "data"(upper right). · Reconstruction from data with error (lower left). · Error estimates from Monte-Carlo.

  16. - scatter plot. v-v scatter plot

  17. b from Vel.-Vel. Comparison Likelihood contours for the value of b from v-v analysis v-v scatter plot b = 0.510.08

  18. UMV SG Plane reconstruction of the real Secat; with G12. PSCz G12 SG plane density (Branchini et al. 99) bfrom density-density Comparison

  19. The Preferred value of b is 0.580.1. Symbol size is inverse proportional to error in reconstructed density

  20. The Value ofb Density-Density Comparison (dgalaxyvs. Ñ×v) POTENT (Sigad et al. 98) Mark III vs. IRAS 1.2Jy b = 0.89 ± 0.12 UMV(Zaroubi et al. 2001) SEcat vs. PSCzb = 0.58 ± 0.1 Velocity-velocity Comparison Velmod (Willick et al. 97, 98) Mark III vs. IRAS 1.2Jy b = 0.50 ± 007 (Branchini et al. 2001) SFI vs. PSCz b = 0.42 ± 0.07 ITF (Davis et al. 96) Mark III vs. IRAS 1.2Jy b = ? (da Costa et al. 98) SFI vs. IRAS 1.2Jyb = 0.6 ± 0.1 (Nusser et al. 2000) ENEAR vs. IRAS b = 0.55 ± 0.1 UMV (Zaroubi et al. 2001) SEcat vs. PSCz b = 0.51 ± 0.08 Redshift survey based measurements yield b » 0.4-0.6

  21. Power spectrum analysis Bias free power spectrum (1.2P(k)) Velocities are more `linear' than densities Likelihood analysis assumes Gaussian distribution for the radial velocities and their errors: Where the data is given by:di = ui + i The correlation matrix is given by:

  22. PS models and Results 1- COBE normalized CDM Power spectra (Bennet et al. 96) 2- G-shape model free of COBE normalization (Efstathiou et al. 92) ENEAR (Zaroubi et al. 2001)

  23. Power Spectra from ENEAR, SFI & Mark3 galaxy peculiar velocity catalogs.

  24. Summary of PS results Too High!!! For COBE normalized flat LCDM & H0=65 km s-1Mpc-1 one gets the following estimates for W: m=0.560.14 Mark3 (Zaroubi et al. 97) m=0.520.10 SFI (Freudling et al. 99) m=0.660.143 ENEAR (Zaroubi et al. 01) Possible Explanations: Non-Gaussianity, Nonlinearity wrong PS or/and Error Model

  25. Principal Component Analysis (PCA) Hoffman & Zaroubi (2000) Good model should yield a Goodness of fit of order one: Solve the eigen-modes equation: Express the velocities in the new coordinate system: Normal independent variables:

  26. Cumulative c2 of ranked modes and their probability (Mark3 & SFI) Silbermann et al. 2001: addition of non-linear component to the correlation function improves but doesn’t solve Our models appear not to be compatible with the data!!! Silberman et al. 2001 claim that accounting for nonlinearity reduce the problems!!

  27. Conclusions Bulk Flow Results within 8000 km/s are generally consistent with each other and with LCDM predictions. At larger scales the results are still not conclusive!! from v-v and-comparison yield a consistent result of~0.4-0.6 Power spectrum analysis still yields relatively higher amplitudes however the discrepancy could be attributed to non-linear structures and possibly correlated noise properties ignored in the analysis

  28. Future Redshift catalogs: 2dF, SDSS Peculiar Velocity SDSS 6dF SNfactory Warpfire NFP Kinetic SZ effect (Planck) ... • Matter Distribution at high redshifts: • Clusters of galaxies (imaging, SZ, ...) • Lyman-a forest • ...

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