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The ORIGAMI
Cosmic Web
Bridget Falck Institute of Cosmology and Gravitation
University of Portsmouth, UK
Some Notes
• “ORIGAMI: Delineating Halos using Phase Space Folds” – Falck, Neyrinck, & Szalay 2012, ApJ, 754, 126,
arXiv:1201.2353
• ORIGAMI finds halo, filament, wall, and void particles, not grid cells
• Terminology: – Halos ≠ Knots = Clusters
– Walls = Sheets
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ORIGAMI: Finding folds in phase-space
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The ORIGAMI method
• ORIGAMI finds shell-crossing by looking for particles out of order with respect to their original configuration
• Halo particles have undergone shell-crossing along 3 orthogonal axes, filaments along 2, walls 1, and voids 0
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In this 1D example,
particles flow toward an
initial overdensity at the
origin, eventually creating
a fold in phase-space
Halo
Filament
Wall
Void
Halo
Filament
Wall
Void
Void
Wall
Filament
Halo
Halo
Filament
Wall
Void
Halo
Filament
Wall
Void
Particle Density from Voronoi/Delaunay Tessellation
• Use the dual Voronoi/Delaunay tessellation field estimator to get scale-independent density for each particle – Schaap & van de Weygaert 2009,
and see Pandey et al. 2013
• Instead of depending on scale, distributions of both VTFE density and ORIGAMI morphology depend on the simulation resolution
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Delaunay tessellation
connects particles,
Voronoi tessellation
surrounds particles
Particle Density by ORIGAMI Morphology
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void
filament
wall
halo
1283
100 Mpc/h
Increasing the simulation resolution results in a higher fraction of halo particles as smaller structures become detectable
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void
filament
wall
halo
2563
100 Mpc/h
Increasing the simulation resolution results in a higher fraction of halo particles as smaller structures become detectable
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void
filament
wall
halo
5123
100 Mpc/h
Halo
Filament
Wall
Void
1283
200 Mpc
Halo
Filament
Wall
Void
2563
200 Mpc
5123
200 Mpc
Halo
Filament
Wall
Void
128 256 512
100
200
Halo Filament Wall Void
Converting from particles to grid
• Select morphology with maximum number of particles in the grid cell
• If there are zero particles, cell is void (obvi.)
• If there is a “tie,” i.e. Nmax = Nvoid = Nwall, assign lowest morphology (void < wall < filament < halo) to the cell – This was surprisingly important for the lowest resolution
simulations – lots of ties!
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128 256 512
100
200
Halo Filament Wall Void
The percent of halo particles increases with simulation resolution,
and percent of void particles decreases
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Grid mass fractions similar, but more halo grids and lower
filament and wall grid mass fractions
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Particle volume fractions change less with simulation resolution
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Grid volume fractions more variable than particle volume fractions
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Grouping Particles into Halos/Voids
• Collect particles into individual structures in order to: – Calculate halo mass function, void
volume function, etc.
– Relate to observations of halos (galaxies) and voids (lack of galaxies)
• Delaunay tessellation provides a set of nearby neighbors and a density estimate for every particle
• Density criterion is required to prevent over-connected halos and percolating voids (more on this later)
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Delaunay tessellation
connects particles,
Voronoi tessellation
surrounds particles
Halo Comparison to FOF
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• Mass functions similar; ORIGAMI halos larger
• Size difference due to definition of halo edge
• FOF may miss some collapsed particles (Anderhalden & Diemand 2011)
• (See also Knebe et al. 2011: Halo-Finder Comparison Project)
Comparison to SO Spherical Overdensity halos
ORIGAMI morphology
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Halo Environment
• ORIGAMI: use number of connected halos and morphology of connected particles on the Delaunay tessellation – If connected to > 2 halos, M=3 (cluster), otherwise
choose M with maximum fraction of neighbors
• FOF halos in the comparison project: use web environment of the cell the halo is in – This means all halos that dominate their 2 Mpc/h cell are
counted as in a “knot,” unfortunately
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Halo Environment ORIGAMI Halos FOF Halos
= Clusters = Filaments = Walls = Voids
Mass Functions
ORIGAMI – neighbor particles FOF – grid cell
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Void Regions General Relativity
Chameleon f(R) Gravity
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Percolation
• Connecting all ORIGAMI void particles results in a largest void that percolates, i.e. fills the simulation volume
• Thus walls and filaments, defined by shell-crossing, do not split up the universe into isolated voids: single-stream regions percolate
• The set of all multi-stream regions (non-void particles) also creates a percolating structure
• Instead of density (Shandarin et al. 2004, 2010) or a cosmic web parameter (Forero-Romero et al. 2009), ORIGAMI percolation depends on simulation resolution
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Volume & Mass fraction of largest void with respect to total void
particles depend on resolution, but vary slowly
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Multi-stream regions also percolate, and volume/mass fractions
vary more rapidly with resolution
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Halos may percolate in high resolution simulations
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Summary/Conclusion
• ORIGAMI identifies structures by looking for folds in phase space – (Falck, Neyrinck, & Szalay
2012, ApJ, arXiv:1201.2353)
• Each particle identified as halo, filament, wall, or void
• Single-stream regions (voids) percolate
• Interesting applications to modified gravity simulations – stay tuned
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