1. Study of Proto-clusters by Cosmological Simulation Tamon SUWA, Asao HABE (Hokkaido Univ.) Kohji YOSHIKAWA (Tokyo Univ.)

2. Plan of the presentation Introduction Structure formation in the universe Recent observation of proto-clusters Numerical method Results Overdensity of halo and mass at z=5 Large scale structure at z=5 Summary

3. hot plasma Neutral hydrogen formation The present Big bang z ～ 1000 Cosmic microwave background Galaxy formation z=0 The beginning z<10 1.Introduction Big bang and Expansion of the universe

4. Cosmic microwave background WMAP observation of CMB tell us many cosmological information (Spergel et al. 2003). Flat universe Content of the Universe 73% dark energy 23% cold dark matter 3% baryon Hubble constant:H 0 =73km /s /Mpc Age of the universe: 13.7 Gyr There exists small density fluctuation

5. The initial density fluctuation of Cold Dark Matter Assuming CDM model, spectrum of initial density fluctuation can be obtained analytically. Amplitude of fluctuation is large for small scale. Small scale structures are formed earlier than large ones.

6. CDM model and hierarchical structure formation Under the CDM model, hierarchical structure formation is expected. Small structures are formed earlier Large structures are made from small ones

7. Recent observations of proto- clusters Recent observations of Lyα emitters (LAEs) with Subaru, VLT, etc., show candidates of proto-clusters. Shimasaku et al. 2003 Ouchi et al. 2005 z=4.9 z=5.7

8. Questions Such proto-clusters are naturally expected or not in CDM universe? How LAEs are formed in high-z universe? What is reliable indicator to characterize proto-clusters? Is number density of LAEs really suitable?

9. Our study We investigate cluster formation at high-z universe in CDM universe by cosmological simulation. We compare our numerical results with observations. Simulation box is large enough to realize many clusters.

10. 2. Numerical method (N-body/SPH Simulation) Particle-Particle-Particle-Mesh (P 3 M) and Smoothed Particle Hydrodynamics (SPH) method Size of box: (214 Mpc) 3 (1pc = 3.26 lyr; periodic boundary) 256 3 ( ～ 17 million) particles of dark matter and the same number of gas Mass of a particle: 2.15×10 10 M O for DM 2.08×10 9 M O for gas Softening length: 80kpc

11. Cosmological Parameters Density parameter, W 0 = 0.3 Hubble constant, H 0 = 70km/s/Mpc Baryon density,  b = 0.015h -1 Cosmological constant, 0 = 0.7 Amplitude of initial fluctuation,  8 = 1.0

12. Initial (z=35) distribution of dark matter particles Mpc Colour indicate density of matter

13. Dark matter distribution at z=5 Mpc

14. Dark matter distribution at z=0

15. Mpc Distribution of dark matter and galaxy clusters at z=0 White circles indicate clusters of galaxies.

16. Proto-cluster regions We find 61 clusters (>10 14 M O ) at z=0. We identify dark matter and gas particles belong to clusters at z=0 and trace back to high-z. The regions which include the particles are defined “proto-cluster regions”. z=0 present z=5 past cluster Trace back to high-z Proto-cluster

17. Example of cluster z=0 z=5 ～ 5Mpc ～ 40Mpc(comoving)

18. Dark halos in proto-clusters We investigate dark halos of which masses are >10 12 M O as galaxies at high-z. We compare results of our numerical simulation and observed LAEs distributions. Dark halos (M>10 12 M O )

19. ３． Results Mass overdensity (δ mass ) and halo overdensity (δ halo ) of proto-cluster regions δ halo at high-z and the largest dark halo at z=0 in the same regions Large scale structure at high-z universe

20. Indicators of proto-cluster regions We use following indicators: Halo overdensity: Mass overdensity: We obtain halo and mass overdensity for proto-clusters and random selected fields. Smoothing scale is 25Mpc (comoving unit; typical scale of proto-clusters).

21. Correlation map of δ halo and δ mass at z=5 δ mass δ halo red :proto-cluster regions green: random selected regions blue: random selected regions which overlapped with proto- clusters No bias Natural bias 0.6 -0.20 0 2 8 6 4

22. Bias parameter The ratio δ halo /δ mass is called bias parameter b. No bias: b=1 Analytical prediction (natural bias): b ～ 2 (for 10 12 M O at z=5) For large δ mass, esp. proto-cluster, b is larger than natural bias. In proto-cluster region, galaxies form earlier than analytical prediction. Numerical simulation is necessary to obtain this result because of its non-linearity.

23. There exist field regions which has large δ halo What is the reliable threshold of δ halo ? We calculate δ halo in random selected regions at z=5 ⇒ find the largest dark halo in that region at z=0 δ halo at high-z and the largest dark halo at z=0 in the same regions Calculate δ halo Is there rich cluster? Z=5Z=0

24. Pickup many (25Mpc) 3 regions in simulation box For each region, we obtain δ halo at z=5 mass of the largest dark halo at z=0 We check whether the halo is rich cluster or not. Calculate δ halo Is there rich cluster? Z=5Z=0 δ halo at high-z and the largest dark halo at z=0 in the same regions (2)

25. δ halo at high-z and rich cluster (M>10 14 M O ) at z=0 Fraction of regions which include rich cluster at z=0 δ halo @z=5

26. Large scale structure at z=5 depth 0-40Mpc Filamentary structure Void like structure

27. Large scale structure at z=5 Large filamentary structure of dark halos ～ several ten Mpc scale are formed at z=5. Observation of LAEs at z=5.7 by Ouchi et al. (2005) also show large scale structure. 200×200×40 Mpc 3 This suggest that LAEs are in massive dark halos (M>10 12 M O ). Ouchi et al. 2005

28. Summary We do P 3 MSPH simulation in order to investigate property of proto-clusters and large scale structures Large box size:(214Mpc) 3 Large # of particles: 17 million×2(DM & SPH) δ halo,δ mass of proto-clusters at z=5 Large bias for large δ mass (esp. proto-cluster) δ halo at z=5 and rich cluster at z=0 80% of regions contain galaxy cluster if δ halo >3 at z=5. Large filamentary structure in high-z universe