Various Mostly Lagrangian Things

Various Mostly Lagrangian Things

Mark NeyrinckMark NeyrinckJohns Hopkins UniversityJohns Hopkins University

Collaborators: Bridget Falck, Collaborators: Bridget Falck, Miguel Aragón-Calvo, Xin Wang, Miguel Aragón-Calvo, Xin Wang,

Donghui Jeong, Alex SzalayDonghui Jeong, Alex Szalay

Tracing the Cosmic Web, Leiden, Tracing the Cosmic Web, Leiden, Feb 2014Feb 2014

Mark Neyrinck, JHU

OutlineOutline

• Comparison in Lagrangian spaceComparison in Lagrangian space• Halo spins in an origami modelHalo spins in an origami model• Lagrangian substructuresLagrangian substructures• Incorporating rotation into a velocity-Incorporating rotation into a velocity-field classificationfield classification• Halo bias deeply into voids with the Halo bias deeply into voids with the MIPMIP

Mark Neyrinck, JHU

Information, printed on the spatial “sheet,” tells it where to fold and form

structures.

200 Mpc/h

Why “folding?” In phase space ...

Why “folding?” In phase space ...

(e.g. analytical result in Bertschinger 1985)

Mark Neyrinck, JHU

N-body cosmological simulation in phase space:

a 2D slice

N-body cosmological simulation in phase space:

a 2D slice

Mark Neyrinck, JHU

x

vxy

xz

y

Eric Gjerde, origamitessellations.com

Rough analogy to origami: initially flat (vanishing bulk velocity) 3D sheet folds

in 6D phase space.

Rough analogy to origami: initially flat (vanishing bulk velocity) 3D sheet folds

in 6D phase space.- The powerful Lagrangian picture of structure formation: follow mass elements. Particles are vertices on a moving mesh.

- Eulerian morphologies classified by Arnol’d, Shandarin & Zel’dovich (1982)

- See also Shandarin et al (2012), Abel et al. (2012) …

(Neyrinck 2012; Falck, Neyrinck & Szalay 2012)

The Universe’s crease patternThe Universe’s crease pattern

Crease pattern before folding

After folding

Mark Neyrinck, JHU

Web comparison in Lagrangian coordinates

Warming up: Lagrangian → Eulerian → Lagrangian for ORIGAMI

Mark Neyrinck, JHU

Web comparison in Lagrangian coordinates

ORIGAMI

Mark Neyrinck, JHU

Web comparison in Lagrangian coordinates

Forero & Romero

Mark Neyrinck, JHU

Web comparison in Lagrangian coordinates

Nuza, Khalatyan & Kitaura

Mark Neyrinck, JHU

Web comparison in Lagrangian coordinates

NEXUS+

Flat-origami approximation implications:

Flat-origami approximation implications:

- # of filaments per halo in 2D: generically 3, unless very special initial conditions are present.

- # of filaments per halo in 3D: generically 4. Unless halo formation generally happens in a wall

•Assumptions: no stretching, minimal #folds to form structures

Flat-origami approximation implications:

Flat-origami approximation implications:

Galaxy spins?

•To minimize # streams, haloes connected by filaments have alternating spins

•Are streams minimized in Nature? Probably not, but interesting to test.

•A void surrounded by haloes will therefore have an even # haloes — before mergers

Chirality correlations

Connect to TTT (tidal torque theory): haloes spun up by misaligned tidal tensor, inertia tensor. Expect local correlations between tidal field, but what about the inertia tensor of a collapsing object?

- Observational evidence for chiral correlations at small separation (… Pen, Lee & Seljak 2000, Slosar et al. 2009, Jiminez et al. 2010)

ORIGAMI halo spins in a 2D simulationORIGAMI halo spins in a 2D simulation

Galaxy spins?

•To minimize # streams, haloes connected by filaments have alternating spins

•A void surrounded by haloes will therefore have an even # haloes

Mark Neyrinck, JHU

Lagrangian slice:initial densities

Mark Neyrinck, JHU

Lagrangian slice:VTFE* log-densities

*Voronoi Tesselation Field Estimator (Schaap & van de Weygaert 2000)

Mark Neyrinck, JHU

Lagrangian slice:LTFE* log-densities

Halo cores fairly good-looking!

*Lagrangian Tesselation Field Estimator (Abel, Hahn & Kahler 2012, Shandarin, Habib & Heitmann 2012)

Mark Neyrinck, JHU

Lagrangian slice:ORIGAMI morphology

node

filament

sheet

void

LTFE in Lagrangian Space — evolution with time

LTFE in Lagrangian Space — evolution with time

Mark Neyrinck, JHU

“Time spent as a filament/structure” map

Morphologies with rotational invariants of velocity gradient tensor

Slides from Xin Wang

SN-SN-SN (halo)

UN-UN-UN (void)

SN-S-S (filament)

UN-S-S (wall)

1Mpc/h Gaussian filter, using CMPC 512 data

SFS SFCUFS UFC

both potential & rotational flow

Slides from Xin Wang

Stacked rotational flow

from MIP simulationSlides from Xin Wang

Halo bias deeply into voids without stochasticity/discreteness with Miguel’s MIP simulations

Mark Neyrinck, JHU

MN, Aragon-Calvo, Jeong & Wang 2013,

arXiv:1309.6641

Comparison of:

Halo-density field

with

Halo-density field predicted from the matter fieldMark Neyrinck, JHU

Not much environmental dependence beyond the density by eye!

“Conclusion”

Visualization of the

displacement field

Mark Neyrinck, JHU