Study of Proto-clusters by Cosmological Simulation

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

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:H0=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 structuresare 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 cosmologicalsimulation. • We compare our numericalresults with observations. • Simulation box is large enough to realize many clusters.

10. 2. Numerical method(N-body/SPH Simulation) • Particle-Particle-Particle-Mesh (P3M) and Smoothed Particle Hydrodynamics (SPH) method • Size of box: (214 Mpc)3(1pc = 3.26 lyr; periodic boundary) • 2563 (～17 million) particles of dark matter and the same number of gas • Mass of a particle: • 2.15×1010MOfor DM • 2.08×109MO for gas • Softening length: 80kpc

11. Cosmological Parameters • Density parameter, W0 = 0.3 • Hubble constant, H0= 70km/s/Mpc • Baryon density, b = 0.015h-1 • Cosmological constant, 0 = 0.7 • Amplitude of initial fluctuation, 8 = 1.0

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

13. Mpc Dark matter distribution at z=5 Mpc

14. Mpc Dark matter distribution at z=0 Mpc

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

16. Proto-cluster regions • We find 61 clusters (>1014MO) 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=5 past z=0 present Trace back to high-z Proto-cluster cluster

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

18. Dark halos (M>1012MO) Dark halos in proto-clusters • We investigate dark halos of which masses are >1012MO as galaxies at high-z. • We compare results of our numerical simulation and observed LAEs distributions.

19. ３．Results • Mass overdensity (δmass) and halo overdensity (δhalo) of proto-cluster regions • δhalo 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. Natural bias No bias Correlation map of δhalo and δmass at z=5 red :proto-cluster regions green: random selected regions blue: random selected regions which overlapped with proto-clusters 8 6 δhalo 4 2 0 0.6 δmass -0.2 0

22. Bias parameter • The ratio δhalo/δmass is called bias parameter b. • No bias: b=1 • Analytical prediction (natural bias): b～2 (for 1012MO at z=5) • For large δmass, 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. Is there rich cluster? Calculate δhalo Z=5 Z=0 δhalo at high-z and the largest dark halo at z=0 in the same regions • There exist field regions which has large δhalo • What is the reliable threshold of δhalo? • We calculate δhalo in random selected regions at z=5⇒find the largest dark halo in that region at z=0

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

25. δhalo at high-z and rich cluster (M>1014MO) at z=0 Fraction of regions which include rich cluster at z=0 δhalo@z=5

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

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 Mpc3 • This suggest that LAEs are in massive dark halos (M>1012MO). Ouchi et al. 2005

28. Summary • We do P3MSPH 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) • δhalo,δmass of proto-clusters at z=5 • Large bias for large δmass (esp. proto-cluster) • δhalo at z=5 and rich cluster at z=0 • 80% of regions contain galaxy cluster if δhalo >3 at z=5. • Large filamentary structure in high-z universe