Eric Gjerde, origamitessellations.com

ORIGAMI:Structure finding with phase-

space foldsMark NeyrinckJohns Hopkins University

Some collaborators:Bridget Falck, Miguel Aragón-Calvo, Guilhem Lavaux, Alex

SzalayJohns Hopkins University

Outline- The Universe as Origami

- Lagrangian coordinates: perhaps underappreciated for simulation analysis

- Finding stream-crossings/caustics: a parameter-free morphology classifier

- Stretching/contraction of the “origami sheet” in position space also useful for halo finding

Mark Neyrinck, JHU

Spherical collapse in phase space

(e.g. Bertschinger 1985)

Mark Neyrinck, JHU

A simulation in phase space: a 2D simulation

slice

Mark Neyrinck, JHU

xvx

y

xz

y

- 1d: particle in a halo if its order wrt any another particle is swapped compared to the original Lagrangian ordering - 3d: particle in a halo if this condition holds along 3 orthogonal axes (2 axes=filament, 1 axis=wall, 0 axes=void)- Need some diagonal axes as well- Finds places where streams have crossed

Order-ReversIng Gravity, Apprehended Mangling Indices

ORIGAMI

Mark Neyrinck, JHU

200 Mpc/h simulation, 0.8 Mpc/h cells

δinitial

log(1+δfinal)

(measured using Voronoi tessellation)

plotted on Lagrangian grid

200 Mpc/h simulation:

# axes along which particle has crossed another particle

(on Lagrangian grid)

blue: 0 (void)cyan: 1 (sheet)yellow: 2 (filament)red: 3 (halo)

Morphology of particles, showing Eulerian position.

A 200 Mpc/h simulation: final-conditions morphology of particles, showing Eulerian position.

Lines between initial, final positions, colored according to morphology.

Fraction of dark matter in various structures.

a

walls+filaments+haloes

walls+filaments

walls

How to group halo particles once they’re identified?

- Eulerian: group adjacent particles in Voronoi tessellation(Lagrangian grouping better?)- Halo mass function(Knebe et al, Halo-finder comparison):

Mark Neyrinck, JHU

How much does the origami sheet stretch?

- Look at spatial part, ∇L⋅ψ. Lagrangian displacement ψ = xf - xi. ∇L⋅ψ ~ -δL.- ∇L⋅ψ = -3: halo formation, where ∇L⋅xf = 0.

Mark Neyrinck, JHU

Duality between structures inEulerian, Lagrangian coordinates

Mark Neyrinck, JHU

- Blobs become “points” (haloes)

- Discs between blobs become filaments

- Haloes look like voids in Lagrangian space!

- Duality in Kofman et al. 1991, adhesion approx.

Filaments often stretched out.

- Could allow access to smaller-scale initial fluctuations than naively you would think?

Eric Gjerde, origamitessellations.com

- An interesting method to detect structures, independent of density

Origami

Mark Neyrinck, JHU