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Heating of Cluster Cores by Acoustic Waves. Yutaka Fujita (Nat. Astron. Obs., Japan) Takeru Ken Suzuki (Kyoto U., Japan). Heating of Cluster Cores. Two popular heating sources Thermal Conduction Theoretically predicted conductivity rates are not high enough to balance radiation losses AGN

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heating of cluster cores by acoustic waves

Heating of Cluster Cores by Acoustic Waves

Yutaka Fujita (Nat. Astron. Obs., Japan)

Takeru Ken Suzuki (Kyoto U., Japan)

heating of cluster cores
Heating ofCluster 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?
substructures in a cluster
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)

turbulence in intracluster medium icm
Turbulence in Intracluster Medium (ICM)

Velocity distribution in ICM (simulation)

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

Nagai et al. (2003)

acoustic waves
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
acoustic waves in icm
Acoustic Waves in ICM

Waves

Cluster

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

Turbulence

models
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 theweak shock theory (Suzuki 2002; Stein & Schwartz 1972)
    • Combined with heating by thermal conduction
in case of the solar corona
In Case of the Solar Corona

Suzuki (2002)

  • The waves are excited by granule motions of surface convection
equations 1
Equations 1
  • Equation of continuity
  • Equation of momentum conservation
      • Fw: energy flux by waves
      • w: wave amplitude normalized by sound velocity (v / cs)
equations 2
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
comparison with observations
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 = 2×10-3,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.
results 1
Results 1
  • Temperature and density profiles
  • Observations
    • A1795
      • Ettori et al. (2002), Tamura et al. (2001)
    • Ser159-03
      • Kaastra et al. (2001)
results 2
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.
turbulence at the cluster center
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?
summary
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.