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Cosmology and the Shape of Large-Scale Structure

Explore the significance of cluster shape in cosmology, its impact on structure evolution, and powerful tools for analysis. Discover how cluster ellipticity and alignment offer insights into the universe's formation and evolution.

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Cosmology and the Shape of Large-Scale Structure

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  1. Cosmology and the Shape of Large-Scale Structure Neta A. Bahcall Princeton University

  2. What is the Shape of Large-Scale Structure? [Clusters, Superclusters] Why important?  What is the Universe like?  Formation & Evolution of Structure  Proper Use of Clusters  Cosmology

  3. Topics  The Shape of Clusters  Alignment of Cluster Pairs  Evolution of Shape & Alignment New Tool in Cosmology:  Cluster Ellipticity  Superclusters: Filaments or Pancakes?

  4. Hot Gas in Clusters(X-rays;SZ)

  5. Clusters and Cosmology  Mass-to-Light Function  M/L x Lo  m = 0.2+-0.05  Cluster Abundance and Evolution  ncl(z)  m = 0.2 +- 0.05 8 = 0.9 +- 0.1  Baryon Fraction: b/m = 0.18  m = 0.23 +- 0.05  Mass ~ Light

  6. Shape Impact Clusters typically assumed spherical Impact of Non-Sphericity: • Selection Bias (in lensing; optical; X-ray; SZ) ‘pointed’ clusters affect Rcl, Vcl, Mcl, ncl(>threshold) • Impacts Ho from Clusters(X-Rays + SZ) (Ho too low if ‘pointed’ clusters prefered)  Other • New Tool for Cosmology, Structure Formation

  7. Cluster Shape • Large-Scale Simulations of LCDM [15003 Mpc3; m= 0.27; Dark-Matter; 1.2E11 Mo/p] • 106 Clusters[M180 > 2E13 h-1 Mo] z = 0 to 3 Determine Cluster Best-Fit Ellipse (2nd-moment of particles) (Iij = XiXj ) a1 > a2 > a3   = 1 - a2/a1  E2D = 1 - a22D/a12D (projected)  <E> ~ 0.3 - 0.5

  8. Cluster Ellipticity Distribution(Hopkins, Bahcall, Bode 2005) Ncl Z=0.03 Z=0.34 Z=0.71 Z=1.08 Z=1.70 Z=2.52 Ellipticity 0 0.5 1 0.5 1

  9. Evolution of Cluster Ellipticity<E> versus Redshift and Mass 0.6 <E> 0.5 0.4 0.3 2 3 1 0 Redshift

  10. Mean Cluster EllipticityEcl versus z, R, M FOF 1.5 1.0 0.5 (Evans &Bridle ’09) (Hoekstra etal ’04)

  11. Clusters Shape  Large Ellipticities: <E> ~ 0.3 - 0.5 a2/a1 ~ 0.5 - 0.7  <E> increases with Mcl, Rcl, z  <E> = 0.33 + 0.05z  <E> ~ 0.3 at z ~ 0 ~0.5 at z ~ 3

  12. Cosmology • Ωm: Mass-Density of Universe (Ωm = m/critical)  8: Amplitude of Mass Fluctuations (on 8 Mpc scale)  8Ωm0.6~ 0.35 +- 0.05 (From observed cluster abundance) 8 ~ 0.9 Ωm ~ 0.2 0.7 0.3 0.6 0.4 Amplitude 8 Not well determined

  13. Cluster Abundance and Evolution  Powerful method to determine mand 8 8 = Amplitude of mass fluctuations (initial ‘seeds’) • ncl (z~0) 8m0.6~ 0.35 • ncl (hi z)Breaks degeneracy  m= 0.2 +- 0.05 and 8 = 0.9 +- 0.1  • 8(galaxies)(obs) ~ 0.9 • If Mass ~ Light (on large scale)  8(m) ~ 0.9

  14. Cluster Mass-Function(SDSS)(Bahcall, Dong, et al ‘03)Best-fit MF: m=0.2 and 8=0.9 Fit: m=0.2 8=0.9

  15. Ωm -  (Clusters MF)

  16. m - 8 constraints from SDSS cluster MF[Bahcall etal ‘03 Rozo etal ’09] m=0.2, 8=0.9

  17. Cluster Abundance Evolution  8(Bahcall & Bode ‘03) 8

  18. Cosmological Constraints (Bahcall & Bode)(from Low and Hi redshift cluster abundance)  - m Low z Hi z WMAP5

  19. Cluster Ellipticity  (Ho, Bahcall, Bode ‘06)

  20. Alignment of Clusters(Hopkins, Bahcall, Bode 05) Alignment Z=0-0.5 Z=0.5-1 Z=1.5-2 Z=1-1.5 Z=2-2.5 Z=2.5-3 1 10 100 Cluster pair separation (Mpc)

  21. Alignments in Filaments(Hopkins, Bahcall, Bode ‘05) Overdensity In Filament Cluster Alignment

  22. Cluster Alignment Function(Hopkins, Bahcall, Bode ‘05)  Alignment of Clusters to ~100 Mpc • Alignment increases with cluster Mass • Alignment increases with Redshift • Alignment happens alongFilaments  Clusters start highly elliptical and aligned; both decrease with time!  Predictions can be tested against observations

  23. Superclusters (SDSS)

  24. Large-Scale Structure; Superclusters

  25. Superclusters • Filaments? ‘Pancakes’?Properties? • Defined: Clusters of Clusters • Select using F.O.F. of Clusters (= Percolation) • Function of Percolation Length L b = L/rcc ~ 0.15 - 0.5; L ~ 3 - 10 Mpc, z ~ 0, Mcl > 1.75E13 Mo • Use LCDM Simulations

  26. Superclusters Map(Wray, Bahcall, Bode, etal ‘06)

  27. Superclusters Size Distribution ncl Size (Radius in Mpc) 100 1 10

  28. Superclusters Axis-Ratio:a2/a1(Wray, Bahcall, Bode etal) Nsc 0 1 Axis-Ratio: a2/a1

  29. Superclusters Axis-Ratio:a3/a1 Axis Ratio a3/a1

  30. Filaments or Pancakes?(Wray, Bahcall, Bode, etal ‘06) 1 1D - Filaments 3D - Spherical a3/a2 Triaxial 2D - Pancakes 0 a2/a1 0 1 0.6

  31. Conclusions Superclusters • Supeclusters are Triaxial > More so at ealier times • Size: reaching ~200h-1 Mpc • Shape: <a2/a1> ~ 0.6, <a3/a1> ~ 0.1-0.2 e.g., ~ 100 x 60 x 10-20 Mpc(z ~ 0)  Nearing ‘Pancakes’ at z ~ 0

  32. Conclusions Clusters • Clusters are Triaxial > More so at earlier times • <Ecl> ~ 0.3 to 0.5(z ~ 0 to 3) • Strong Cluster Alignment to ~100 Mpc • Alignment and Ellipticity increase with z  New ToolinCosmology: <Ecl>  8, m

  33. Cluster Ellipticity (z)(Ho, Bahcall, Bode 07)

  34. Supercluster Axis-Ratio:a3/a2 Axis-Ratio: a3/a2

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