Heating of Cluster Cores by Acoustic Waves

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Heating of Cluster Cores by Acoustic Waves

• Yutaka Fujita (Nat. Astron. Obs., Japan)
• Takeru Ken Suzuki (Kyoto U., Japan)

2
Heating of Cluster Cores

• Two popular heating sources
• Thermal Conduction
• Theoretically predicted conductivity rates are
  not high enough to balance radiation losses
• AGN
• A poor correlation between radio flux of the
  central galaxy and the temperature decrement of
  the cooling flow
• Is it about time to consider another heating
  source?

3
Substructures in a Cluster
N-body simulation

• Dark matter distribution in a cluster
• Many substructures
• Moving with the velocity of ?1000 km s-1

Fukushige Makino (2001)
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Turbulence in Intracluster Medium (ICM)
Velocity distribution in ICM (simulation)

• Substructure Motion in a cluster produces
  turbulence in the ICM
• Internal velocities of the ICM
• 20-30 of the sound speed even when a cluster is
  relatively relaxed

Nagai et al. (2003)
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Acoustic Waves

• Turbulence produces acoustic waves
• These waves, having a finite (not infinitesimal)
  amplitude, eventually form shocks to shape
  sawtooth waves (N-waves)
• Directly heat the surrounding ICM by dissipation
  of their wave energy

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Acoustic Waves in ICM
Waves
Cluster

• We investigate waves propagating inward
• They may heat cluster cores (Pringle 1989).

Turbulence
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Models

• Assumptions
• Spherical symmetry
• Time-independent
• Waves are generated far from the center of a
  cluster
• Heating by waves
• The heating model for the solar corona based on
  the weak shock theory (Suzuki 2002 Stein
  Schwartz 1972)
• Combined with heating by thermal conduction

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In Case of the Solar Corona
Suzuki (2002)

• The waves are excited by granule motions of
  surface convection

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Equations 1

• Equation of continuity
• Equation of momentum conservation
• Fw energy flux by waves
• ?w wave amplitude normalized by sound velocity
  (??v / cs)

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Equations 2

• Energy equation
• Fw energy flux by waves
• Fc energy flux by thermal conduction
• Wave evolution
• ?w wave amplitude normalized by sound speed
  (??v / cs)
• ? wave period

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Comparison with Observations

• We compare the results with the observations of
  two clusters
• A1795
• Thermal conduction alone can heat the cluster
  core if fc 0.2 (Zakamska Narayan 2003).
• fc the ratio of the actual thermal conductivity
  to the Spitzer conductivity.
• We will show that even if fc 210-3, waves can
  heat the cluster core.
• Ser 159-03
• Thermal conduction cannot transfer enough energy
  even if fc 1 (Zakamska Narayan 2003).
• We will show that even if fc 0.2, waves can
  heat the cluster core.

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Results 1

• Temperature and density profiles
• Observations
• A1795
• Ettori et al. (2002), Tamura et al. (2001)
• Ser159-03
• Kaastra et al. (2001)

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Results 2

• Wave amplitude normalized by sound velocity (?w)
• At the cluster centers, ?w increases.
• The ratio of heat flux by waves to that by
  thermal conduction (Fwfc / Fc)
• Waves transfer much more energy than thermal
  conduction.

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Turbulence at the Cluster Center

• Waves grow at the cluster center
• If waves coming from different directions collide
  each other, they may produce strong turbulence at
  the cluster center.
• Optical observations
• Warm rapidly moving gas at cluster centers (v
  ?300 km s-1)
• Evidence of turbulence?

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Summary

• We showed that acoustic waves generated by
  turbulent motion in ICM might effectively heat
  the central region of a cluster.
• We assumed that the turbulence is generated by
  substructure motion in a cluster.
• Our model can reproduce observed density and
  temperature profiles.
• Waves can transfer more energy from outer region
  of a cluster than thermal conduction alone.