various mostly lagrangian things
DESCRIPTION
Various Mostly Lagrangian Things. Mark Neyrinck Johns Hopkins University Collaborators: Bridget Falck, Miguel Aragón-Calvo, Xin Wang, Donghui Jeong, Alex Szalay Tracing the Cosmic Web, Leiden, Feb 2014. Outline Comparison in Lagrangian space Halo spins in an origami model - PowerPoint PPT PresentationTRANSCRIPT
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