2. 06/29/06Bernard's Cosmic Stories1 Sergei Shandarin University of Kansas Lawrence Statistic of Cosmic Web

3. 06/29/06Bernard's Cosmic Stories2 “… understanding of what is taking place or has taken place at an early time, is relevant…” Bernard Jones

4. 06/29/06Bernard's Cosmic Stories3 Plan Introduction: What is Cosmic Web? Field statistics v.s. Object statistics Dynamical model Minkowski functionals Scales of LSS structure in Lambda CDM cosmology How many scales of nonlinearity? Substructure in voids Summary

5. 06/29/06Bernard's Cosmic Stories4 1971 Peebles A&A 11, 377 Rotation of Galaxies and the Gravitational Instability Picture Method: Direct Summation N particles: 90 Initial conditions coordinates: Poisson velocities: v=Hr(1-0.05) 30 internal v=Hr(1+0.025) 60 external Boundary cond: No particles at R>R_0

6. 06/29/06Bernard's Cosmic Stories5 1978 Peebles A&A 68, 345 Stability of a Hierarchical Clustering in the Distribution Of Galaxies Method: Direct Summation N particles: 256 Initial conditions coordinates: Soneira, Peebles’ model velocities: virial for each subclump Boundary cond: Empty space (*) Two types of particles (m=1, m=0)

7. 06/29/06Bernard's Cosmic Stories6 1979 Efstathiou, Jones MNRAS, 186,133 The Rotation of Galaxies: Numerical investigation Of the Tidal Torque Theory Method: Direct Summation (Aarseth’ code) N particles: 1000 Initial conditions coordinates: Poisson 10 inner particles m=10 990 particles m=1 velocities: v=Hr Boundary cond: No particles at R>R_0

8. 06/29/06Bernard's Cosmic Stories7 1979 Aarseth, Gott III, Ed Turner ApJ, 228, 664 N-body Simulations of Galaxy Clustering. I. Initial Conditions and Galaxy Collapse Time Method: Direct Summation (Aarseth’s code) N particles: 4000 Initial conditions coordinates: On average 8 particles are randomly placed on random 125 rods This mimics P = k^(-1) spectrum velocities: v=Hr Boundary cond: reflection on the sphere Z=14.2 Z=0

9. 06/29/06Bernard's Cosmic Stories8 1980 Doroshkevich, Kotok, Novikov, Polyudov, Shandarin, Sigov MNRAS, 192, 321 Two-dimensional Simulations of the Gravitaional System Dynamics and Formation of the Large-Scale Structure of the Universe Initial conditions: Growing mode, Zel’dovich approximation

10. 06/29/06Bernard's Cosmic Stories9 1981 Efstathiou, Eastwood MNRAS, 194, 503 On the Clustering of Particles in an Expanding Universe Method: P^3M N grid: 32^3 N particles: 20000 or less Initial conditions (i) Poisson (Om=1, 0.15) (ii) cells distribution (Om=1) Boundary cond: Periodic

11. 06/29/06Bernard's Cosmic Stories10 1983 Klypin, Shandarin, MNRAS, 204, 891 Three-dimensional Numerical Model of the Formation of Large-Scale Structure in the Universe Method: PM=CIC N grid: 32^3 N particles: 32^3 Initial conditions: Growing mode, Zel’dovich approximation Boundary cond: Periodic First time reported at the Erici workshop organized by Bernard in 1981

12. 06/29/06Bernard's Cosmic Stories11 Cosmic Web: first hints Observations Simulations Gregory & Thompson 1978 Klypin & Shandarin 1981 3D N-body Simulation Shandarin 1975 2D Zel’dovich Approximation

13. 06/29/06Bernard's Cosmic Stories12 1985 Efstathiou, Davis, Frenk, White ApJS, 57, 241 Numerical Techniques for Large Cosmological N-body Simulations Methods: PM, P^3M Initial conditions: Growing mode, Zel’dovich approximation A separate section is devoted to the description of generating initial conditions (IV. SETTING UP INITIAL CONDITIONS” pp 248-250). Quote: Boundary cond: Periodic Test of accuracy: comparison with 1D (ref to Klypin and Shand.)

14. 06/29/06Bernard's Cosmic Stories13 Lick catalogue

15. 06/29/06Bernard's Cosmic Stories14

16. 06/29/06Bernard's Cosmic Stories15 Soneira & Peebles 1978 Both distributions have similar 1-point, 2-point, 3-point, and 4-point correlation functions Lick catalog vs simulated

17. 06/29/06Bernard's Cosmic Stories16 Einasto, Klypin, Saar, Shandarin 1984 Redshift catalog H.Rood, J.Huchra

18. 06/29/06Bernard's Cosmic Stories17 Field statistics v.s. ‘object’ statistics

19. 06/29/06Bernard's Cosmic Stories18 Sensitivity to morphology (i.e. to shapes, geometry, topology, …) Type of statistic Sensitivity to morphology Examples of statistics sensitive to morphology : *Percolation (Shandarin 1983) Minimal spanning tree (Barrow, Bhavsar & Sonda 1985) *Global Genus (Gott, Melott, Dickinson 1986) Voronoi tessellation (Van de Weygaert 1991) *Minkowski Functionals (Mecke, Buchert & Wagner 1994) Skeleton length (Novikov, Colombi & Dore 2003) Various void statistics (Aikio, Colberg, El-Ad, Hoyle, Kaufman, Mahonen, Piran, Ryden, Vogeley, …) Inversion technique (Plionis, Ragone, Basilakos 2006) “cataract” “blind” 3-point, 4-point functions 1-point and 2-point functions

20. 06/29/06Bernard's Cosmic Stories19

21. 06/29/06Bernard's Cosmic Stories20 SDSS slice

22. 06/29/06Bernard's Cosmic Stories21 Millennium simulation Springel et al. 2004

23. 06/29/06Bernard's Cosmic Stories22 Dynamical model * Nonlinear scale R_nl ~1/k_nl * Small scales r < R_nl : hierarchical clustering * Large scale r > R_nl : linear model * Large scale r > R_nl : Zel’dovich approximation OR

24. Zel’dovich Approximation (1970) in comoving coordinates potential perturbations Density are eigen values of is a symmetric tensor Density becomes

25. 06/29/06Bernard's Cosmic Stories24 ZA: Examples of typical errors/mistakes * ZA is a kinematic model and thus does not take into account gravity * ZA can be used only in Hot Dark Matter model ( initial spectrum must have sharp cutoff on small scales)

26. 06/29/06Bernard's Cosmic Stories25 ZA v.s. Eulerian linear model N-body Truncated Linear ZA Truncated ZA Linear Coles et al 1993

27. 06/29/06Bernard's Cosmic Stories26 ZA v.s. Eulerian linear model N-body Truncated Linear ZATruncated ZA Linear Coles et al 1993

28. 06/29/06Bernard's Cosmic Stories27 Dynamical model k_nl = 4 k_c = 4 k_c = 32 k_c = 256

29. 06/29/06Bernard's Cosmic Stories28 Dynamical model P ~ k^(-2) P ~ k^0 P ~ k^2

30. 06/29/06Bernard's Cosmic Stories29 Little, Weinberg, Park 1991Melott, Shandarin 1993

31. 06/29/06Bernard's Cosmic Stories30 Dynamical model and archetypical structures Zel’dovich approximation describes well the structures in the quazilinear regime and therefore the archetypical structures are pancakes, filaments and clumps. The morphological technique is aimed to dettect and measure such structures.

32. 06/29/06Bernard's Cosmic Stories31 Superclusters and voids are defined as the regions enclosed by isodensity surface = excursion set regions * Interface surface is build by SURFGEN algorithm, using linear interpolation * The density of a supercluster is higher than the density of the boundary surface. The density of a void is lower than the density of the boundary surface. * The boundary surface may consist of any number of disjointed pieces. * Each piece of the boundary surface must be closed. * Boundary surface of SUPERCLUSTERS and VOIDS cut by volume boundary are closed by corresponding parts of the volume boundary

33. 06/29/06Bernard's Cosmic Stories32

34. 06/29/06Bernard's Cosmic Stories33 Superclusters in LCDM simulation (VIRGO consortium) by SURFGEN Sheth, Sahni, Shandarin, Sathyaprakash 2003, MN 343, 22 Percolating i.e. largest supercluster

35. 06/29/06Bernard's Cosmic Stories34 Superclusters vs.. Voids Red: super clusters = overdense Blue: voids = underdense dashed: the largest object solid: all but the largest Solid: 90% of mass/volume Dashed: 10% of mass/volume Superclusters by mass Voids by volume

36. 06/29/06Bernard's Cosmic Stories35 SUPERCLUSTERS and VOIDS should be studied before percolation in the corresponding phase occurs. Individual SUPERCLUSTERS should be studied at the density contrasts corresponding to filling factors Individual VOIDS should be studied at density contrasts corresponding to filling factors CAUTION: The above parameters depend on smoothing scale and filter Decreasing smoothing scale i.e. better resolution results in growth of the critical density contrast for SUPERCLUSTERS but decrease critical Filling Factor decrease critical density contrast for VOIDS but increase the critical Filling Factor There are practically only two very complex structures in between: infinite supercluster and void.

37. 06/29/06Bernard's Cosmic Stories36 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

38. 06/29/06Bernard's Cosmic Stories37 Minkowski Functionals Mecke, Buchert & Wagner 1994

39. 06/29/06Bernard's Cosmic Stories38 Set of Morphological Parameters

40. 06/29/06Bernard's Cosmic Stories39 Percolation thresholds are easy to detect Blue: mass estimator Red: volume estimator Green: area estimator Magenta: curvature estimator Superclusters Voids Gauss

41. 06/29/06Bernard's Cosmic Stories40 Sizes and Shapes Sahni, Sathyaprakash & Shandarin 1998 For each supercluster or void Basilakos,Plionis,Yepes,Gottlober,Turchaninov 2005

42. 06/29/06Bernard's Cosmic Stories41 Toy Example: Triaxial Torus For all Genus = - 1 ! red points

43. 06/29/06Bernard's Cosmic Stories42 Superclusters vs Voids log(Length) Breadth Thickness LCDM Median (+/-) 25% Top 25% Shandarin, Sheth, Sahni 2004

44. 06/29/06Bernard's Cosmic Stories43 Are there olther “scales of nonlinearity”? Fry, Melott, Shandarin 1993

45. 06/29/06Bernard's Cosmic Stories44 Superclusters vs. Voids LCDM Median (+/-)25% Top 25%

46. 06/29/06Bernard's Cosmic Stories45 Correlation with mass (SC) or volume (V) log(Length) Breadth Thickness Planarity Filamentarity Genus log(Genus) Green: at percolation Red: just before percolation Blue: just after percolation Solid lines mark the radius of sphere having same volume as the object. SC V

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

48. 06/29/06Bernard's Cosmic Stories47 More examples of voids in the density destribution in LCDM

49. 06/29/06Bernard's Cosmic Stories48 SDSS mock catalog Cole et al. 1998 Volume limited catalog J. Sheth 2004

50. 06/29/06Bernard's Cosmic Stories49 J. Sheth 2004

51. 06/29/06Bernard's Cosmic Stories50 Summary LCDM: density field in real space seen with resolution 5/h Mpc displays filaments but no isolated pancakes have been detected. 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/peculiarities. Percolation and genus are different (independent?) characteristics of the web. Morphological parameters (L,B,T, P,F) can discriminate models. Voids defined as closed regions in underdense excursion set are different from common-view voids. Why? 1) different definition, 2) uniform 5 Mpc smoothing, 3) DM distribution 4) real space Voids have complex substructure. Isolated clumps may present along with filaments. Voids have more complex topology than superclusters. Voids: G ~ 50; superclusters: G ~ a few