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Statistic of Cosmic Web. Sergei Shandarin. University of Kansas Lawrence. “… understanding of what is taking place or has taken place at an early time, is relevant…” Bernard Jones. Plan. Introduction: What is Cosmic Web?

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## Sergei Shandarin

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**Statistic of Cosmic Web**SergeiShandarin University of Kansas Lawrence Bernard's Cosmic Stories**“… understanding of what is taking place**or has taken place at an early time, is relevant…” Bernard Jones Bernard's Cosmic Stories**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 Bernard's Cosmic Stories**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 Bernard's Cosmic Stories**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) 1978 Peebles A&A 68, 345 Stability of a Hierarchical Clustering in the Distribution Of Galaxies Bernard's Cosmic Stories**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 Bernard's Cosmic Stories**1979 Aarseth, Gott III, Ed Turner**ApJ, 228, 664 N-body Simulations of Galaxy Clustering. I. Initial Conditions and Galaxy Collapse Time Z=14.2 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=0 Bernard's Cosmic Stories**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 Bernard's Cosmic Stories**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 Bernard's Cosmic Stories**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 Bernard's Cosmic Stories**Cosmic Web: first hintsObservations**Simulations Shandarin 1975 2D Zel’dovich Approximation Gregory & Thompson 1978 Klypin & Shandarin 1981 3D N-body Simulation Bernard's Cosmic Stories**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.) Bernard's Cosmic Stories**Lick catalogue**Bernard's Cosmic Stories**Both distributions have similar**1-point, 2-point, 3-point, and 4-point correlation functions Lick catalogvs simulated Bernard's Cosmic Stories Soneira & Peebles 1978**Einasto,**Klypin, Saar, Shandarin 1984 Redshift catalog H.Rood, J.Huchra Bernard's Cosmic Stories**Field statistics v.s. ‘object’ statistics**Bernard's Cosmic Stories**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) Bernard's Cosmic Stories**SDSS**slice Bernard's Cosmic Stories**Millennium simulation**Springel et al. 2004 Bernard's Cosmic Stories**Dynamical model*** Nonlinear scale R_nl ~1/k_nl * Small scales r < R_nl : hierarchical clustering * Large scale r > R_nl : linear model OR * Large scale r > R_nl : Zel’dovich approximation Bernard's Cosmic Stories**Zel’dovich Approximation (1970)**in comoving coordinates Density potential perturbations is a symmetric tensor Density becomes are eigen values of**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) Bernard's Cosmic Stories**ZA v.s. Eulerian linear model**Coles et al 1993 Linear N-body Truncated Linear Truncated ZA ZA Bernard's Cosmic Stories**ZA v.s. Eulerian linear model**Coles et al 1993 Truncated Linear Linear N-body ZA Truncated ZA Bernard's Cosmic Stories**Dynamical model**k_nl = 4 k_c = 4 k_c = 256 k_c = 32 Bernard's Cosmic Stories**Dynamical model**P ~ k^(-2) P ~ k^0 P ~ k^2 Bernard's Cosmic Stories**Little, Weinberg, Park 1991**Melott, Shandarin 1993 Bernard's Cosmic Stories**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. Bernard's Cosmic Stories**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 Bernard's Cosmic Stories**Superclusters in LCDM simulation (VIRGO consortium)**by SURFGEN Percolating i.e. largest supercluster Sheth, Sahni, Shandarin, Sathyaprakash 2003, MN 343, 22 Bernard's Cosmic Stories**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 Bernard's Cosmic Stories**SUPERCLUSTERS and VOIDS should be studied before percolation**in the corresponding phase occurs. IndividualSUPERCLUSTERS should be studied at the density contrasts corresponding to filling factors Individual VOIDS should be studied at density contrasts corresponding to filling factors There are practically 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 Bernard's Cosmic Stories**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 Bernard's Cosmic Stories**MinkowskiFunctionals**Mecke, Buchert & Wagner 1994 Bernard's Cosmic Stories**Set of Morphological Parameters**Bernard's Cosmic Stories**Percolation thresholds**are easy to detect Blue: mass estimator Red: volume estimator Green: area estimator Magenta: curvature estimator Gauss Gauss Superclusters Voids Bernard's Cosmic Stories**Sizes and Shapes**For each supercluster or void Sahni, Sathyaprakash & Shandarin 1998 Basilakos,Plionis,Yepes,Gottlober,Turchaninov 2005 Bernard's Cosmic Stories**Toy Example: Triaxial Torus**For all Genus = - 1 ! red points Bernard's Cosmic Stories**LCDM**Superclusters vs Voids Top 25% Median (+/-) 25% log(Length) Breadth Thickness Shandarin, Sheth, Sahni 2004 Bernard's Cosmic Stories**Are there olther “scales of nonlinearity”?**Fry, Melott, Shandarin 1993 Bernard's Cosmic Stories**LCDM**Superclusters vs. Voids Top 25% Median (+/-)25% Bernard's Cosmic Stories**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. Bernard's Cosmic Stories**Approximation of voids by ellipsoids:**uniform void has the same inertia tensor as the uniform ellipsoid Shandarin, Feldman, Heitmann, Habib 2006**More examples of voids in the density destribution in LCDM**Bernard's Cosmic Stories**SDSS mock catalog**Cole et al. 1998 Volume limited catalog J. Sheth 2004 Bernard's Cosmic Stories**J. Sheth 2004**Bernard's Cosmic Stories**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 Bernard's Cosmic Stories

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