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Various Mostly Lagrangian Things

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

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Various Mostly Lagrangian Things

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  1. 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

  2. Outline • Comparison in Lagrangian space • Halo spins in an origami model • Lagrangian substructures • Incorporating rotation into a velocity-field classification • Halo bias deeply into voids with the MIP • Mark Neyrinck, JHU

  3. Information, printed on the spatial “sheet,” tells it where to fold and form structures. 200 Mpc/h • Mark Neyrinck, JHU

  4. (e.g. analytical result in Bertschinger 1985) Why “folding?” In phase space ... • Mark Neyrinck, JHU

  5. N-body cosmological simulation in phase space: a 2D slice vx x y z x y • Mark Neyrinck, JHU

  6. 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) … Eric Gjerde, origamitessellations.com

  7. The Universe’s crease pattern Crease pattern before folding After folding • (Neyrinck 2012; Falck, Neyrinck & Szalay 2012)

  8. Web comparison in Lagrangian coordinates Warming up: Lagrangian → Eulerian → Lagrangian for ORIGAMI • Mark Neyrinck, JHU

  9. Web comparison in Lagrangian coordinates ORIGAMI • Mark Neyrinck, JHU

  10. Web comparison in Lagrangian coordinates Forero & Romero • Mark Neyrinck, JHU

  11. Web comparison in Lagrangian coordinates Nuza, Khalatyan & Kitaura • Mark Neyrinck, JHU

  12. Web comparison in Lagrangian coordinates NEXUS+ • Mark Neyrinck, JHU

  13. Flat-origami approximation implications: • Assumptions: no stretching, minimal #folds to form structures - # 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

  14. 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

  15. 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)

  16. ORIGAMI 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

  17. Lagrangian slice: initial densities • Mark Neyrinck, JHU

  18. Lagrangian slice: VTFE* log-densities *Voronoi Tesselation Field Estimator (Schaap & van de Weygaert 2000) • Mark Neyrinck, JHU

  19. 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

  20. Lagrangian slice: ORIGAMI morphology node filament sheet void • Mark Neyrinck, JHU

  21. LTFE in Lagrangian Space — evolution with time

  22. “Time spent as a filament/structure” map • Mark Neyrinck, JHU

  23. Morphologies with rotational invariants of velocity gradient tensor Slides from Xin Wang

  24. both potential & rotational flow SN-SN-SN (halo) UN-UN-UN (void) SN-S-S (filament) UN-S-S (wall) SFS UFS SFC UFC Slides from Xin Wang 1Mpc/h Gaussian filter, using CMPC 512 data

  25. Slides from Xin Wang Stacked rotational flow from MIP simulation

  26. Halo bias deeply into voids without stochasticity/discreteness with Miguel’s MIP simulations MN, Aragon-Calvo, Jeong & Wang 2013, arXiv:1309.6641 • Mark Neyrinck, JHU

  27. Not much environmental dependence beyond the density by eye! Comparison of:Halo-density field withHalo-density field predicted from the matter field • Mark Neyrinck, JHU

  28. “Conclusion” Visualization of the displacement field • Mark Neyrinck, JHU

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