Sergei Shandarin. University of Kansas 11/19/04 1

Transcription

1 Sergei Shandarin University of Kansas 11/19/04 1

2 Plan Introduction: Cosmic Web Non-morphological statistics N-point functions. Morphology of LSS Percolation. Genus. Minkowski Functionals. Shapefinders Lambda CDM cosmology Supercluster Void network Collaborators: J. Sheth, V. Sahni, Sathyaprakash Summary 11/19/04 2

3 Cosmic Web: first hints Observations Gregory & Thompson 1978 Simulations Shandarin D Zel dovich Approximation 11/19/04 Klypin & Shandarin D N-body Simulation 3

4 =uuruuruuuruuruuuururruuuur nini is initial Zel dovich position of a fluid Approximatin element (Zel'dovich ) is position 1970) of) a fluid elemen 11/19/04 4

5 SDSS Tegmark et al astro-ph/ /19/04 5

6 -3 1start3 0CDM CDM /19/04 6

7 Soneira & Peebles 1978 Both distributions have similar 1-point, 2-point, 3-point, and 4-point correlation functions 11/19/04 7

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9 Einasto, Klypin, Saar, Shandarin 1984 Redshift catalog H.Rood, J.Huchra 11/19/04 9

10 Density fields vs. Pointwise distributions Linear (quasilinear) theory Real and mock galaxy catalogs N-body simulations *Superclusters vs.. voids* Smoothing with some window (Gaussian, top-hat, CIC), SPH, Wavelets, DTFE) Quasi Poisson process 11/19/04 10

11 Examples of multiscale stuctures in 2D N-body simulations 11/19/04 11

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13 LCRS Bharadwaj, Sahni, Sathyaprakash, & Shandarin 2000, ApJ, 528, 21 central part of the slice n specifies the level of coarse graining FF = Filling Factor =Fraction of Area in Black 11/19/04 13

14 SUPERCLUSTERS and VOIDS are defined as the regions enclosed by isodensity surface. 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 parts of the volume boundary 11/19/04 14

15 Filling Factor of overdense regions 23/ Smoothing 11/19/04 15

16 Superclusters in LCDM simulation (VIRGO consortium) by SURFGEN Percolating i.e. largest supercluster Sheth, Sahni, Shandarin, Sathyaprakash 2003, MNRAS, 343, 22 11/19/04 16

17 VOIDS Shandarin et al. 2004, MNRAS, 11/19/04 17

18 Approximation of a void by the inertia tensor ellipsoid 11/19/04 18

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20 V Por = V VE min V max b a E = 1 c + b = 2 for perfect fit by ellipsoid for a sphere 11/19/04 20

21 15sLhMpc = 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 11/19/04 21

22 SUPERCLUSTERS and VOIDS should be studied before percolation in the corresponding phase occurs. 1.8δ Individual SUPERCLUSTERS should be studied at the density contrasts 0.07CFF corresponding to filling factors Individual VOIDS should be studied 0.22VFF at density contrasts corresponding to filling factors 0.5δ There are practically only two very complex structures in between: infinite supercluster and void. CAUTION: The above parameters depend on smoothing: with decreasing smoothing scale i.e. better resolution critical density contrast for SUPERCLUSTERS will increase while critical Filling Factor will decrease the critical density contrast for VOIDS will decrease while the critical Filling Factor will increase 11/19/04 22

23 Superclusters vs. Voids 15sLhMpc = Red: super clusters = overdense dashed: the largest object solid: all but the largest Blue: voids = underdense Solid: 90% Dashed: 10% Superclusters by mass Voids by volume VC FFFF for SC for V VC FFFF for SC for V 11/19/04 23

24 Plotting morphological CFF characteristics of SUPERCLUSTERS as a function of while morphological vff characteristics of VOIDS as a function of allows direct comparison of SUPERCLUSTERS and VOIDS 1CVFFFF+= 11/19/04 24

25 Genus vs. Percolation Red: Superclusters Blue: Voids Green: Gaussian Genus as a function of Filling Factor PERCOLATION Ratio Genus of the Largest Genus of Exc. Set 11/19/04 25

26 At percolation number of superclusters/voids and volume, mass and other parameters of the largest supercluster/void rapidly change but genus curve shows no peculiarity 11/19/04 26

27 Minkowski Functionals 12Surface Area: 111Integrated MeanVolume : Mecke, Buchert & Wagner /19/04 27

28 Percolation thresholds 1.8δ= Gauss Blue: mass estimator Red: volume estimator Green: area estimator Magenta: curvature estimator Gauss 0.5δ= Superclusters Voids 11/19/04 28

29 Set of Morphological Parameters Partial Minkowski Functionals vo MFs of percolating supercluster or void, Global MFs:,, iiiivvaaccg 11/19/04 29

30 Sizes and Shapes Sphere: C4T=B=L=R For each supercluster or void Sphere: P=F=0B - TPlanari Sahni, Sathyaprakash & Shandarin 1998 Convex boundaries! 11/19/04 30

31 Toy Example: Triaxial Torus Sahni, Sathyaprakash & Shandarin /19/04 31

32 LCDM Superclusters vs.. Voids Mass Volume Density log(length) Breadth Thickness Median 25%± Planarity Filamentarity 11/19/04 32

33 LCDM Superclusters vs. Voids Mass Volume Density Length Breadth Thickness Top 25% Planarity Filamentarity 11/19/04 33

34 Correlation with mass (SC) or volume (V) Genus Green: at percolation Red: just before percolation Blue: just after percolation Planarity Filamentarity log(length) Breadth Thickness log(genus) Solid lines mark the radius of sphere having same volume as the object. 11/19/04 34

35 For both SUPERCLUSTERS and VOIDS Length > R, while Breadth < R and Thickness < R. Where R is radius of sphere having same volume as SUPERCLUSTER or VOID Difference increases with growth of mass of SUPERCLUSTERS and volume of VOIDS 11/19/04 35

36 SDSS mock catalog Cole et al Volume limited catalog J. Sheth Smoothing scalef 11/19/04 36

37 Cumulative probability functions Top curves TCDM Bottom curves LCDM 11/19/04 37

38 Top curves TCDM Cumulative probability functions Bottom curves LCDM 11/19/04 38

39 Galaxy Morphology 11/19/04 39

40 Ellipticity Rahman & Shandarin 2004 Ellipticals (e>0.2) Spirals (in optics) 11/19/04 40

41 Orientation Ellipticals (e>0.2) Spirals (in optics) 11/19/04 41

42 Summary Real space studies are interesting especially if we know cosmological model (parameters, initial spectrum ) 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/ peculiarites. 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 excurtion 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 structures are possible along with tunnels. Voids have more complex topology than superclusters. Voids: G~50; superclusters: G~a few 11/19/04 42