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Dynamics & Multiscale Morphology Cosmic Web

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  1. Dynamics & Multiscale Morphology Cosmic Web Rien van de Weygaert 3rd KIAS Workshop, Oct 27-28, Seoul, 2008

  2. Collaboration & References: Pablo Araya-Melo Miguel Aragon-Calvo Erwin Platen Emilio Romano-Diaz Willem Schaap Bernard Jones GertVegter (comp. geometry & topology)

  3. Foams in Nature

  4. Foams in Nature • The largest complex pattern found in nature is Megaparsec Scale: • the Cosmic Web • manifestation of the gravitational origin, emergence and growth of ALL structure in the cosmos …

  5. The Cosmic Web Stochastic Spatial Pattern of  Clusters,  Filaments &  Walls around  Voids in which matter, (DM, gas, gal’s) has agglomerated

  6. The Cosmic Web Significance:  Manifestation mildly nonlinear clustering: Transition stage between linear phase and fully collapsed/virialized objects  Weblike configurations contain cosmological information: e.g. Void shapes & alignments (recent study J. Lee 2007)  Cosmic environment within which to understand the formation of galaxies.

  7. Web Analysis • Translate discrete galaxy/particle distribution into continuous density field/image: - DTFE: Delaunay Tessellation Field Estimator • (Post)processing: - filtering/smoothing image - identifying clusters (peaks in image) - identifying filaments/walls: * MMF & spine (Morse theory) - tracing void regions: * watershed transform (Morse theory) - topological aspects * alpha shapes

  8. The Cosmic Web • Web Discretely Sampled: • By far, most information on the • Cosmic Web concerns • discrete samples: • observational: • Galaxy Distribution • theoretical: • N-body simulation particles

  9. Power of Tessellations

  10. Multiscale MorphologyFilter filament MMF dissection of cosmic web into sheets, filaments, clusters … cluster sheet

  11. Spine of the Cosmic Web: Morse complex & search for singularities

  12. Watershed Void Identification

  13. Alpha Shapes Alpha Shape of cosmological simulation left to right: alpha value increases. LSS Topology

  14. Cosmic WebEvolution &Dynamics

  15. Dynamical Evolution Cosmic Web

  16. Dynamical Evolution Cosmic Web ● hierarchical structure formation ● anisotropic collapse ● void formation: asymmetry overdense vs. underdense

  17. Anisotropic Collapse ●Gravitational Instability: - any small initial deviation from sphericity of a collapsing cloud gets magnified - gravitational collapse proceeds along sequence: ● collapse along smallest axis planar geometry wall ● collapse medium axis elongated filament ● full 3-D collapse clump halo  clump/halo virialization cosmic object (courtesy: A. Kravtsov).

  18. Formative agent of the Cosmic Web: Tidal strain induced my the Megaparsec Matter Distribution: - anisotropic collapse of structures - connection clusters-filaments: clusters main agent for stretching filaments

  19. Ellipsoidal Collapse short axis medium axis spherical long axis Self-gravity  Internal tidal shear (due to shape)  External tidal shear

  20. Cosmic Web & Clusters Perseus Cluster (A426)

  21. Tidal Constraints: Example: elongated filamentary feature Constrained Field:

  22. Cosmic Web Theory: Specification Cluster Node Locations & Orientation: Outline Cosmic Web •  Spatial structure of Cosmic Web structure present in primordial density field. •  Geometry of primordial field mainly filamentary (not Zel’dovich sheets), by sheer of statistics Gaussian field. • Filaments defined by tidal field imposed by cluster patches. • Incremental improvement of cosmic web spatial outline by inserting more and more clusters Bond & Myers 1996 Bond et al. 1996

  23. Cosmic Web Theory : Specification Cluster Node Locations & Orientation: Outline Cosmic Web Bond & Myers 1996 Bond et al. 1996

  24. Cosmic Web Theory : Specification Cluster Node Locations & Orientation: Outline Cosmic Web •  Spatial structure of Cosmic Web structure present in primordial density field. •  Geometry of primordial field mainly filamentary (not Zel’dovich sheets), by sheer of statistics Gaussian field. • Filaments defined by tidal field imposed by cluster patches. • Incremental improvement of cosmic web spatial outline by inserting more and more clusters Bond et al. 1996

  25. Multiscale Nature Anisotropic Collapse • Structure arises over • a vast range of scales • Small scales: • fully collapsed objects • - Very large scales: • still linear (& Gaussian) • Medium Mpc scales: • weblike features • Two analytical formalisms: • statistical Press-Sch. •  dynamical PeakPatch

  26. Hierarchical Pattern Formation

  27. Hierarchical Void Evolution: • “Local” Excursion Set Approach •  Two-barrier description: • - void merger • - void collapse •  Peaked Void Size Distribution Void Merging Void Collapse

  28. Galaxy/Halo&Web Environment

  29. Halo Shape Alignments Halo & Galaxy Environmental Influences Halo Shape Alignment evolution Filaments: Haloes elongated along filament Walls: Haloes elongated within plane wall (major axis in wall) Orientation weakens in time Effect stronger for low-mass haloes

  30. Spinning the Galaxies

  31. Spinning the Galaxies Spinning Up a collapsing protogalaxy by Tidal Torque

  32. Spinning the Galaxies Connection Galaxy Spin Cosmic Web Spinning the Galaxies: Tidal Forces that also Shape Cosmic Web

  33. Cosmic Web: Environmental Impact Halo & Galaxy Formation: Environmental influences • Environmental dependence strongest wrt. Alignments: - halo shape - halo spin direction  To be understood from the crucial role of tidal forces in shaping the Cosmic Web

  34. Cosmic Web: Environmental Impact Halo & Galaxy Formation: Environmental influences  Environmental dependence on the halo spin distribution To a large extent influenced by presence of unbound particles Halo Spin distribution in clusters, filaments & sheets

  35. Halo Spin Alignments

  36. Halo Spin Alignments Halo & Galaxy Environmental Influences Halo Spin Alignment evolution Filaments: High-mass haloes: always perpendicular Low-mass haloes: starting perpendicular, they evolve to parallel Walls: High & Low-mass: always in plane of wall

  37. Filament-Galaxy alignment SDSS DR5

  38. Filament-Galaxy alignment SDSS DR5 Jones et al. 2008 (in prep.) edge-on galaxies

  39. Cosmic WebAnalysis

  40. Exploiting the Adaptive Nature of Voronoi/Delaunay Tessellations Natural Neighbour Interpolation Discrete Point/Galaxy Distribution Continuous Field (Sibson 1980, 1981; Watson 1992)

  41. Point Sample Continuous Field Aspects: ● Anisotropy of Structural Features ● Hierarchical Infrastructure ● Voids, cq. empty regions ● Inhomogeneous Sampling

  42. Dual Tessellations Voronoi Delaunay Voronoi Vertices: Centers Circumscribing Spheres 4 nuclei Delaunay Tetrahedron

  43. Delaunay Tessellation Delaunay Tetrahedron: Set of 4 nuclei, circumscribing sphere not containing any other nuclei Space-Covering Complete Set Delaunay Tetrahedra: Delaunay Tessellation Voronoi Tessellation & Delaunay Tessellation: Duals Delaunay Tetrahedra: Natural Multidimensional Interpolation Volume

  44. NN-neighbour Interpolation Kernel