MHD Turbulence and Cosmic Ray Reacceleration in...
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Andrey BeresnyakLos Alamos Fellow, T2
2nd ICM workshop, Michigan, 2011
MHD Turbulence and Cosmic RayReacceleration in Galaxy Clusters
Collaborators: Hao Xu (UCSD), Hui Li (LANL),Reinhard Schickeiser (RuhrUniversität)
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Brown & Rudnick, 2011
Diffuse radio halos...
Bonafede et al 2010, Brunetti 2011
...are observed, but assuming electrons are secondary,are incompatible with not observed gamma-ray emission!
Morphology also suggests a different origin for electrons.
The problem with electrons is that they constantly lose energy due to synchrotron and inverse Compton, and need to be produced at a high rate. What if they are not produced but re-accelerated by turbulence (see, e.g. Brunetti & Lazarian 2011)?
Why electrons are more energetic than we expect?
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Simulated clusters
From Xu et al 2010: z=30÷1, standard ΛCDM, B injected by AGN
On applicability of MHD vs plasma:
Free energy budget of plasma –
Estimates of the mesoscale are plenty, e.g. Lazarian & Beresnyak (2006)
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Nonlinear Small-Scale Dynamo
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MHD scale
hydrodynamiccascade
MHDcascade
Nonlinear Small-Scale Dynamo
Zeroth Law of Dynamo: Beresnyak, PRL 108, 035002 (2012)
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Compressible MHD turbulence• SubAlfvenic on small scales (mean B field dominates)• Four basic modes: Alfven, slow, fast, entropy
Inertia: fluid,Restoring force: Lorentz
Inertia: fluid,Restoring force: Lorentz+pressure
Inertia: fluid,Restoring force: pressure
Alfven
fast
slow
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Compressible MHD turbulence• SubAlfvenic on small scales (B
0 dominates!)
• Four basic modes: Alfven, slow, fast, entropy
B
k
A
f
s
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Anisotropy of MHD Turbulence
Structure function
Beresnyak & Lazarian (2009)
calculated with respect to the local magnetic fieldYou do not need to have a mean field B
0
Isotropicallydriven MHD turbulence
0.01
0.10
GSanisotropy
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Particle scattering: Alfven and slow modes are inefficient
from Beresnyak et al 2011
Bottom line: you have to measure mode amplitudes to understand CR scattering
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Mode decomposition, previous work
Cho & Lazarian (2003): relies on a global mean field
Wavelets? Impossible to use wavelets directly: k-space is too discrete
k=0,1,2,4,8... Kowal & Lazarian (2010)
Does a Fourier transform of each wavelet -- slow!
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Mode decomposition
Beresnyak, 2011
• Doesn't rely on a global mean field• Relies on a 3-point structure function• ...• FAST!
Direct structure function method
slow fast
Alfven
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1. Introduce local measurement with structure functions
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2. Measure turbulent dissipation rate
lifetime
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3. Decompose into modes
Alfven slow fast
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4. Measure a fraction of the dissipation rate pertaining to the fast mode
A model in Cho & Lazarian (2003) predicts fast mode amplitude fraction
for subsonic case. This is much smallerthan that we observe
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What is the nature of electron acceleration?
Flux of particles through momentum space
Is this what's really happening?
Flux of energy through momentum space:
Should be smaller than the dissipation rate!
cut-off due to losses
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What is the nature of electron acceleration?
Flux of energy through momentum space:
Should be smaller than the dissipation rate!
In the energy range important for ~1 GHz radio, electron spectrum is concave due to combination of secondary electrons plus synchrotron cutoff of reaccelerated electrons
secondary electrons
reaccelerated electrons
synchrotron/inverse Compton cutoff
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• Diffuse radio halos is an important diagnostic of clusters
• Electron acceleration is required to explain diffuse radio halos
• The key to study in-situ turbulent acceleration is MHD modes
• We use an efficient and simple method to extract modes from any MHD simulation (without mean field, inhomogeneous, etc)
• We obtained fast mode fraction which is much larger than was predicted earlier. We think this is because ICM turbulence is driven by mergers, compressible transsonic motions.
• A limit, imposed by the energy flux constraint of the fast mode turbulence leads to a steeper spectrum, which has an cutoff at lower energies for electrons and could explain soft radio spectra.
Summary