Cosmological N-Body Simulation - Topology of Large scale Structure

1. Cosmological N-Body Simulation- Topology of Large scale Structure CCP 2006. 8. 29 Changbom Park with Juhan Kim (Korea Institute for Advanced Study) & J. R. Gott (Princeton), J. Dubinski (CITA)

2. History of Universe

3. Theme: Origin & Formation Mechanism of Cosmic Structures 1. Want to know Origin – primordial density fluctuations from inflation Formation Mechanism – galaxies form at peaks in density field smoothed over galactic scale? 2. Time is ripe Large redshift surveys of galaxies  High precision measurements of 1. Relations among internal physical properties 2. Relations between internal properties and spatial & temporal environments

4. CfA1986 SDSS2006

5. h-1Mpc SDSS galaxies (Park et al. 2005, ApJ, 633, 11)

6. Effects ofNL Gravitational Evolution, Biasing, & Redshift Space Distortionon galaxy clustering & properties Cosmological N-Body Simulation For PRECISION COMPARISONbetween cosmological models with observations

7. Cosmological N-Body Simulation Requirement for galaxy formation study 1. Several times larger than largest survey >> 1000 h-1Mpc : for LSS formation + galaxy formation, velocity field * SDSS[2006] ~ 500 h-1Mpc * Hubble Depth S.[2015] ~ 2000 h-1Mpc 2. Should resolve objects with <<1011 h-1Msun (~ M*+2) : mean separation < 0.2 h-1Mpc  currently 0.2~2000Mpc Number of particles > 50003~ 100003 will do! (100~1000 billion =10~100* current maximum)

8. Cosmological N-Body Simulation Progresses • ~ 104 CPUs • > 1010 particles Log N=0.2(Y-1970)+2

9. TreePM Code1 About Code 1. Long range (r>4 pixels, PM) + Short range(PM+Tree) G-forces 2. Tree generation in each slab & in each cube of 43 pixels 3. Min. # of particles for tree generation – Direct P2 if #(cube) < Ntree 4. Memory : ~3 x [16] x words per particle * 16 per particle: index2, position3, velocity3, acceleration3, mass1, softening length, computational work measurement, pointer * factor ~3 for memory imbalance * Buffer zone particles

10. TreePM Gravitational Force Tree + PM PM Gaussian Smoothed RG=0.9 pixels PM Force

11. TreePM Code2 Advantages 1. O(N log N) Tree operations for short range force – unlike P3M 2. Periodic boundary condition solved by PM – unlike Tree 3. No need to build a global tree – force correction only out to 4 pixels 4. Local Trees  Parallelizable by domain decomposition (time) & disposable local trees keeping trees in 8x8xnz pixels (memory)

12. Parallelization 1. PM part 2. Tree part : Domain slabs of equal thickness : Domain slabs of equal # of tree force interactions & Buffer zone particles

13. TreePM Code3 5. Accuracy : ~ 0.5% RMS error in acceleration for θ=1 6. Performance

14. CPU time per step 10243 particles Regular backup & Pre-halo finding calculation

15. Load balance 10243 particles # of particles in domain slabs / homogeneous distribution

16. ΛCDM Simulations(Kim & Park 2004. 7) TreePM code GOTPM (Dubinski, Kim, Park 2003) 20483 mesh (initial condition) 20483 CDM particles 1024 & 5632 h-1Mpc size boxes 50 & 275 h-1kpc force resolutions * Using IBM SP3 at KISTI, 128 CPUs, 900 Gbytes, FOR PRECISION COMPARISON between cosmological models & real universe

17. Growth of Structures from initial Density Fluctuations 11.8b 13.7b t=0 7.7b

19. Dark Halo Identification (Kim& Park 2006: ΛCDM1024 h-1Mpc) Physically Self-Bound Halos Halo centers - local density peaks Binding E wrt local halo centers Tidal radii of subhalos wrt bigger halos Halos with >=53 particles (5x1011 M⊙)

20. PSB HalosVSOthers

23. Topology study 1. Gaussianity of the linear (primordial) density field predicted by simple inflationary scenarios 2. Topology of galaxy distribution at NL scales sensitive to cosmological parameters & to galaxy formation mechanism 3. Direct Intuitive meaning Large ScalesSmall Scales Primordial Gaussianity Galaxy Formation Cosmological Parameters

24. Genus– A Measure of Topology • Definition G = # of holes - # of isolated regions in iso-density contour surfaces = 1/4π·∫S κ dA (Gauss-Bonnet Theorem) [ex. G(sphere)=-1, G(torus)=0, ] : 2 holes – 1 body = +1 • Gaussian Field Genus/unit volume g(ν) = A (1-ν2) exp(- ν2/2) where ν=(ρ- ρb)/ ρbσ & A=1/(2π)2 <k2/3>3/2 if P(k)~kn, A RG3 =[8√2π2]-1 *[(n+3)/3]3/2

25. Clusters Bubbles HDM • Non-Gaussian Field (Toy models) (Weinberg, Gott & Melott 1987)

26. Non-Gaussianity: Genus-related statistics 1. Shift parameter :  2. Asymmetry parameters :AC, AV 3. Amplitude drop : RAAobs/APS RA  AC Av

27. Biased Formation of Galaxies L-dependence of 1 & 2 point distribution, but also topology ! (Park et al. 2005)

28. Topology of LSS can be explained by GF models? LCDM1024 Matter field can’t ! void splitting void percolation Merger  Halo formation (Park, Kim et al. 2005)

29. Probably yes! Topology of LSS can be explained by GF models? (Park et al. 2005) ~1 & Little evolution at low z HOD model for VL : sample Mr<-19.5 Direction of evolution ! <Nsat> = (M/M1)α for M>Mmin where logMmin=11.76, log M1=13.15, α=1.13 Mergers of halos AV < 1 !

30. Comparison of topology: SDSS vs CDM SDSS & 6 h-1Mpc scale; Kim+Park(o) & Springel(x)

31. Future of Cosmological N-Body Simulation 1. Useful for cosmology & galaxy formation study (until star formation can be properly simulated by radiative hydro-codes) 2. Need to reach # of particles >> 50003~ 100003 (10~100 current maximum) Dynamic range for other studies * Internal properties & environment: 1kpc ~ 100 Mpc * Galactic structure & star formation : 0.1pc ~ 100kpc