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Quantitaive Morphology of the Cosmic Web. Sergei Shandarin. University of Kansas Lawrence. Outline. Introduction: What is Cosmic Web? Physics of structure formation Field statistics vs. Object statistics Shapes of superclusters and voids, percolation, genus Minkowski functionals

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## Sergei Shandarin

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**Quantitaive Morphology**of the Cosmic Web SergeiShandarin University of Kansas Lawrence IPAM**Outline**• Introduction: What is Cosmic Web? • Physics of structure formation • Field statistics vs. Object statistics • Shapes of superclusters and voids, percolation, genus • Minkowski functionals • Role of phases • Summary IPAM**N-BODY SIMULATIONS (Efstathiou, Eastwood 1981)**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 IPAM**Cosmic Web: first hints**Observations Theory N-body simulation Gregory & Thompson 1978 Shandarin 1975 2D; Zel’dovich Approximation Klypin & Shandarin 1981, 1983 3D, N-body Simulation, HDM IPAM**Observations**IPAM**Sloan Digital Sky Survey (SDSS)**2d projection of 3D galaxy distribution in the wedge region. The Earth is at the center; the radius of the circle is about 2,500 million light years. Each dot represents a galaxy. The galaxy number density field is highly non-Gaussian. The visual impression suggests that many galaxies are concentrated into filaments. Present time Gott III et al. 2003 IPAM**N-body: Millennium simulation**Springel et al. 2004 IPAM**Wilkinson Microwave Anisotropy Probe**Full sky map (resolution ~10 arcmin) IPAM**Dynamical model**IPAM**The Zel’dovich Approximation (1970)**The Zel’dovich approximation describes anisotropic collapse**ZA vs. Linear model**Truncation means that in the initial conditions P(k) is set to zero at k > k_nl Truncated Linear Linear N-body ZA Truncated ZA IPAM**Dynamical model and archetypical structures**Zel’dovich approximation describes well the structures in the quazilinear regime and predicts the archetypical structures: * pancakes, * filaments, * clumps. (Arnol’d, Shandarin, Zel’dovich 1982) The morphological statistics has a goal to identify and quantify these structures. IPAM**N-body simulations**in four cosmological models IPAM**Sensitivity to morphology (i.e. to shapes, geometry,**topology, …) Type of statistic Sensitivity to morphology “blind” 1-point and 2-point functions “cataract” 3-point, 4-point functions Examples of statistics sensitive to morphology : *Percolation (Shandarin 1983) Minimal spanning tree (Barrow, Bhavsar & Sonda 1985) *GlobalGenus (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) IPAM**Superclusters and voids**are defined as the regions enclosed by isodensity surfaces = 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 IPAM**Examples of superclusters in LCDM simulation**(VIRGO consortium) by SURFGEN Percolating i.e. largest supercluster Sheth, Sahni, Sh, Sathyaprakash 2003, MN 343, 22 IPAM**Shandarin et al. 2004, MNRAS,**Examples of VOIDS Fitting voids by ellipsoids Shandarin,Feldman,Heitmann,Habib 2006, MNRAS IPAM**Percolation**Gaussian fields Non-linear evolution P = 1/k^2 SC P = k^4 Voids Gauss Conspicuous connectedness of the web in LCDM cosmology has two causes: 1) initial spectrum has considerable power at k<k_nl 2) nonlinear dynamics IPAM**Superclusters vs. Voids**Red: super clusters = overdense Blue: voids = underdense Solid: 90% of mass/volume Dashed: 10% of mass/volume Superclusters by mass Voids by volume dashed: the largest object solid: all but the largest IPAM**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 IPAM**SUPERCLUSTERS and VOIDS should be studied before percolation**in the corresponding phase occurs. IndividualSUPERCLUSTERS should be studied at the density contrasts Individual VOIDS should be studied at the density contrasts There are only two very complex structures in between: infinite supercluster and void. 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 IPAM**MinkowskiFunctionals**Mecke, Buchert & Wagner 1994 IPAM**Sizes and Shapes**For each supercluster or void Sahni, Sathyaprakash & Shandarin 1998 Basilakos,Plionis,Yepes,Gottlober,Turchaninov 2005 IPAM**N-body: Millennium simulation**Springel et al. 2004 IPAM**LCDM**Superclusters vs Voids Top 25% Median (+/-) 25% log(Length) (radius) Breadth Thickness Shandarin, Sheth, Sahni 2004 IPAM**LCDM**Superclusters vs. Voids Top 25% Median (+/-)25% IPAM**Correlation with mass (SC)**or volume (V) SC Genus Green: at percolation Red: just before percolation Blue: just after percolation Planarity Filamentarity log(Length) Breadth Thickness V log(Genus) Solid lines mark the radius of sphere having same volume as the object. IPAM**Nonlinear evolution:**IPAM**Are there other “scales of nonlinearity”?**Ryden, Gramann (1991) showed that phases become significantly different from the initial values on the scale of average displacement. Fry, Melott, Shandarin 1993: scaling of 3-point functions with d_rms x This scale can be computed from the initial power spectrum (Shandarin 1993) t_0 n = -1 is critical IPAM**Swap of amplitudes and phases**Courtesy of P. Coles Globe WMAP Phases Phases Amplitudes WMAP phases Globe amplitudes Globe phases WMAP amplitudes IPAM**Summary**In the LCDM model there are at least 2 scales of nonlinearity: thickness ~ breadth ~ 1/k_nl< d_rms ~ length of filaments 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 global genus curve shows no features or peculiarities. Percolation and genus are different (independent?) characteristics of the web. Morphological parameters (L,B,T, P,F) can discriminate models. Voids have more complex topology than superclusters. Voids: G ~ 50; superclusters: G ~ a few Phases are very important for patterns, but it’s not known how they are related to patterns IPAM

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