Study of Proto-clusters by Cosmological

Simulation

Tamon SUWA, Asao HABE (Hokkaido Univ.)

Kohji YOSHIKAWA (Tokyo Univ.)

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

hot plasma

Neutral hydrogen formation

The present

Big bang

z～ 1000

Cosmic microwave background

Galaxy formation

z=0

The beginning

z<10

1. IntroductionBig bang and Expansion of the universe

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

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.

CDM model and hierarchical structure formation

Under the CDM model, hierarchical structure formation is expected.Small structures are formed earlierLarge structures are made from small ones

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

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 prot

o-clusters? Is number density of LAEs really suitable?

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.

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: 2.15×1010MO for DM 2.08×109MO for gas

Softening length: 80kpc

Cosmological Parameters

Density parameter, 0 = 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

Initial (z=35) distribution of dark matter particles

Mpc

Mp

c

Colour indicate density of matter

Dark matter distribution at z=5

Mpc

Mp

c

Mpc

Mp

c

Dark matter distribution at z=0

Mpc

Mp

c

Distribution of dark matter and galaxy clusters at z=0

White circles indicate clusters of galaxies.

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=0present

z=5past

cluster

Trace back to high-z

Proto-cluster

Example of cluster z=0

z=5～ 5Mpc

～ 40Mpc(comoving)

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.

Dark halos (M>1012MO)

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

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).

BG

1proto clus

ha

ter

lo

n

n

BG

BG BG

1 proto clumas

sters

Correlation map of δhalo and δma

ss at z=5

δmass

δ ha

lo

red :proto-cluster regionsgreen: random selected regionsblue: random selected regions which overlapped with proto-clusters

No bias

Natural bias

0.6-0.2 0

02

86

4

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 ana

lytical prediction. Numerical simulation is necessary to obtain this resul

t because of its non-linearity.

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⇒

δhalo at high-z and the largest dark halo at z=0 in the same regions

Calculate δhaloIs there rich cluster?

Z=5 Z=0

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.

Calculate δhaloIs there rich cluster?

Z=5 Z=0

δhalo at high-z and the largest dark halo at z=0 in the same regions (2)

δhalo at high-z and rich cluster (M>1014MO) at z=0

Fra

ctio

n of

reg

ions

whi

ch

incl

ude

rich

clus

ter

at z

=0

δhalo@z=5

Large scale structure at z=5

depth0-40Mpc

Filamentary structure

Void like structure

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

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