2. 7 March 2006Leiden1 Sergei Shandarin University of Kansas Lawrence CITA Toronto 1/1-7/15, 2006

3. 7 March 2006Leiden2 Outline Introduction: Cosmological model. What is Cosmic Web? Gravitational Instability: Zel’dovich approximation,Adhesion Approximation Morphological Statistics for LSS Percolation. Genus. Minkowski Functionals. Shapefinders Summary and remaining questions

4. 7 March 2006Leiden3 History of the Universe = =

5. 7 March 2006Leiden4 CMB: Power and Anisotropy Spectra COBE

6. 7 March 2006Leiden5 Wilkinson MAP: Full sky map (resolution ~10 arcmin)

7. 7 March 2006Leiden6 CMB power spectrum Percival 2006

8. 7 March 2006Leiden7 APM

9. 7 March 2006Leiden8 2dFGRS

10. 7 March 2006Leiden9 SDSS Gott III etal. astro-ph/0310571

11. 7 March 2006Leiden10 Power spectrum from galaxy surveys wavelength

12. 7 March 2006Leiden11 Cosmological Parameters = === =

13. 7 March 2006Leiden12 Marinoni et al 2005

14. 7 March 2006Leiden13 Cosmic Web: first hints Observations Simulations Gregory & Thompson 1978 Klypin & Shandarin 1983 3D N-body Simulation Shandarin 1975 2D Zel’dovich Approximation

15. 7 March 2006Leiden14

16. 7 March 2006Leiden15 Changing Variables

17. 7 March 2006Leiden16

18. 7 March 2006Leiden17 Zel’dovich Approximation (2D) N-body simulations (2D) versus

19. 7 March 2006Leiden18 Adhesion Approximation Burgers’ equation Graphical solution in 1D Fig. from Williams, Heavens, Peacock, Shandarin, 1991 Gurbatov, Saichev, Shandarin 1985, 1987 Parabola

20. 7 March 2006Leiden19 Evolution in 1D x Fig. from Sahni, Sathyaprakash Shandarin 1994

21. 7 March 2006Leiden20 Graphical solution in 2D Fig from Kofman, Pogosyan, Shandarin 1990 Paraboloid in 2D and 3D Initial (i.e. linear) potential

22. 7 March 2006Leiden21 Evolution in 2D Fig. from Sahni, Sathyaprakash, Shandarin 1994

23. 7 March 2006Leiden22 Comparison of Adhesion Approximatin with N-body Simulation in 2D (tessellation) Kofman, Pogosyan, Shandarin, Melott 1994

24. 7 March 2006Leiden23 Adhesion Approximation: mock redsift survey Weinberg & Gunn 1990 Jones 1999: Adhesion model for two component system

25. 7 March 2006Leiden24 What kind of tessellation is this? Peaks of the initial potential

26. 7 March 2006Leiden25 Morphological Statistics for Cosmic Web (Cosmic Foam?)

27. 7 March 2006Leiden26

28. 7 March 2006Leiden27 Filling Factor of overdense regions DM density must be smoothed!

29. 7 March 2006Leiden28 Lorenson & Cline 1987; Sheth, Sahni, Shandarin, Sathyaprakash 2004

30. 7 March 2006Leiden29 Superclusters in LCDM simulation (VIRGO consortium) by SURFGEN Sheth, Sahni, Shandarin, Sathyaprakash 2003, MN 343, 22; astro-ph/0210136 Percolating i.e. largest supercluster

31. 7 March 2006Leiden30 VOIDS Shandarin et al. 2004, MNRAS,

32. 7 March 2006Leiden31 Approximation of voids by ellipsoids: uniform void has the same inertia tensor as the uniform ellipsoid Shandarin, Feldman, Heitmann, Habib 2006

33. 7 March 2006Leiden32 Minkowski Functionals Introduction to cosmology: Mecke, Buchert & Wagner 1994

34. 7 March 2006Leiden33 Set of Morphological Parameters

35. 7 March 2006Leiden34 Sizes and Shapes Sahni, Sathyaprakash & Shandarin 1998 For each supercluster or void Convex boundaries !

36. 7 March 2006Leiden35 Toy Example: Triaxial Torus Sahni, Sathyaprakash & Shandarin 1998

37. 7 March 2006Leiden36 Superclusters vs.. Voids Red: super clusters = overdense Blue: voids = underdense dashed: the largest object solid: all but the largest Solid: 90% Dashed: 10% Superclusters by mass Voids by volume Shandarin, Sheth, Sahni 2004

38. 7 March 2006Leiden37 Superclusters vs. Voids Red: super clusters = overdense Blue: voids = underdense dashed: the largest object solid: all but the largest Solid: 90% Dashed: 10% Superclusters by mass Voids by volume

39. 7 March 2006Leiden38 Percolation thresholds Blue: mass estimator Red: volume estimator Green: area estimator Magenta: curvature estimator Superclusters Voids Gauss

40. 7 March 2006Leiden39 Superclusters vs. Voids Mass Volume Density Length Breadth Thickness Planarity Filamentarity LCDM

41. 7 March 2006Leiden40 Correlation with mass (SC) or volume (V) log(Length) Breadth Thickness Planarity Filamentarity Genus (SC) log(Genus) (V) Green: at percolation Red: just before percolation Blue: just after percolation Solid lines mark the radius of sphere having same volume as the object.

42. 7 March 2006Leiden41 SDSS mock catalog Cole et al. 1998 Volume limited catalog J. Sheth 2003

43. 7 March 2006Leiden42 Top curves TCDM Bottom curves LCDM Cumulative probability functions J. Sheth 2003

44. 7 March 2006Leiden43 Summary and questions LCDM: density field in real space seen with resolution 5/h Mpc displays filaments but no isolated pancakes have been detected so far! Smoothing? Web has both characteristics: filamentary network and bubble structure (at different density thresholds !) At percolation: number of superclusters/voids, volume, mass and other parameters of the largest supercluster/void rapidly change (phase transition) but genus curve shows no features/ peculiarites. Percolation and genus are different (independent?) characteristics of the web. Morphological parameters (L,B,T, P,F) can discriminate models. EC ~ Genus --> Betti numbers? Voids have complex substructure. Isolated structures are possible along with tunnels. Voids have more complex topology than superclusters. Voids: G~50; superclusters: G~a few Adhesion model approximates the structure as a tessellation (Not Voronoi) Cosmic foam!? How to find the skeleton from galaxy distribution? Voronoi diagrams?

45. 7 March 2006Leiden44

46. 7 March 2006Leiden45 Genus vs. Percolation Genus as a function of Filling Factor PERCOLATION Ratio Genus of the Largest Genus of Exc. Set Red: Superclusters Blue: Voids Green: Gaussian

47. 7 March 2006Leiden46 At percolation number of superclusters/voids and volume, mass and other parameters of the largest supercluster/void rapidly change but (global) genus curve shows no peculiarity