Study of Protoclusters by Cosmological Simulation

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Study of Proto-clusters by Cosmological
Simulation

• Tamon SUWA, Asao HABE (Hokkaido Univ.)
• Kohji YOSHIKAWA (Tokyo Univ.)

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Plan of the presentation

• Introduction
• Structure formation in the universe
• Recent observation of proto-clusters
• Numerical method
• Results
• Overdensity of halo and mass at z5
• Large scale structure at z5
• Summary

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• IntroductionBig bang and Expansion of the
  universe

Neutral hydrogen formation
hot plasma
Big bang
Cosmic microwave background
Galaxy formation
zlt10
z1000
z0
The present
The beginning
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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 constantH073km /s /Mpc
• Age of the universe 13.7 Gyr
• There exists small density fluctuation

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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.

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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

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Recent observations of proto-clusters

• Recent observations of Lya emitters (LAEs) with
  Subaru, VLT, etc., show candidates of
  proto-clusters.
• Shimasaku et al. 2003
• Ouchi et al. 2005

z4.9
z5.7
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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?

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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.

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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
• 2.151010MO for DM
• 2.08109MO for gas
• Softening length 80kpc

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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

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Mpc
Initial (z35) distribution of dark matter
particles
Colour indicate density of matter
Mpc
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Mpc
Dark matter distribution at z5
Mpc
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Mpc
Dark matter distribution at z0
Mpc
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Mpc
Distribution of dark matter and galaxy clusters
at z0 White circles indicate clusters of
galaxies.
Mpc
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Proto-cluster regions

• We find 61 clusters (gt1014MO) at z0.
• We identify dark matter and gas particles belong
  to clusters at z0 and trace back to high-z.
• The regions which include the particles are
  defined proto-cluster regions.

z5 past
z0 present
Trace back to high-z
Proto-cluster
cluster
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Example of cluster
z0
5Mpc
z5
40Mpc(comoving)
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Dark halos in proto-clusters

• We investigate dark halos of which masses are
  gt1012MO as galaxies at high-z.
• We compare results of our numerical simulation
  and observed LAEs distributions.

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3.Results

• Mass overdensity (dmass) and halo overdensity
  (dhalo) of proto-cluster regions
• dhalo at high-z and the largest dark halo at z0
  in the same regions
• Large scale structure at high-z universe

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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).

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Correlation map of dhalo and dmass at z5
red proto-cluster regions green random selected
regions blue random selected regions which
overlapped with proto-clusters
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dhalo
4
2
0
0.6
dmass
-0.2
0
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Bias parameter

• The ratio dhalo/dmass is called bias parameter b.
• No bias b1
• Analytical prediction (natural bias) b2 (for
  1012MO at z5)
• For large dmass, 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.

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dhalo at high-z and the largest dark halo at z0
in the same regions

• There exist field regions which has large dhalo
• What is the reliable threshold of dhalo?
• We calculate dhalo in random selected regions at
  z5?find the largest dark halo in that region at
  z0

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dhalo at high-z and the largest dark halo at z0
in the same regions (2)

• Pickup many (25Mpc)3 regions in simulation box
• For each region, we obtain
• dhalo at z5
• mass of the largest dark halo at z0
• We check whether the halo is rich cluster or not.

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dhalo at high-z and rich cluster (Mgt1014MO) at z0
Fraction of regions which include rich cluster at
z0
dhalo_at_z5
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Large scale structure at z5
depth 0-40Mpc
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Large scale structure at z5

• Large filamentary structure of dark halos
  several ten Mpc scale are formed at z5.
• Observation of LAEs at z5.7 by Ouchi et al.
  (2005) also show large scale structure.
• 20020040 Mpc3
• This suggest that LAEs are in massive dark
  halos (Mgt1012MO).

Ouchi et al. 2005
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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 million2(DM SPH)
• dhalo,dmass of proto-clusters at z5
• Large bias for large dmass (esp. proto-cluster)
• dhalo at z5 and rich cluster at z0
• 80 of regions contain galaxy cluster if dhalo gt3
  at z5.
• Large filamentary structure in high-z universe