interstellar turbulence: theory, implications and consequences
DESCRIPTION
Interstellar Turbulence: Theory, Implications and Consequences. Alex Lazarian ( Astronomy, Physics and CMSO ). Collaboration : H. Yan, A. Beresnyak, J. Cho, G. Kowal, A. Chepurnov , E. Vishniac, G. Eyink, P. Desiati, G. Brunetti …. Theme 2. - PowerPoint PPT PresentationTRANSCRIPT
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Interstellar Turbulence: Theory, Implications and Consequences
Alex Lazarian (Astronomy, Physics and CMSO)Alex Lazarian (Astronomy, Physics and CMSO)Collaboration: H. Yan, A. Beresnyak, J. Cho, G. Kowal, A. Chepurnov , E. Vishniac, G. Eyink, P. Desiati, G. Brunetti …Collaboration: H. Yan, A. Beresnyak, J. Cho, G. Kowal, A. Chepurnov , E. Vishniac, G. Eyink, P. Desiati, G. Brunetti …
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Theme 2. Propagation and Acceleration of Cosmic Rays in Turbulent
Magnetic Fields
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Icecube measurement 2010
M. Duldig 2006
Highly isotropic
MHD turbulence theory induces changes on our understanding of CRs propagation and stochastic acceleration
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Scattering and second order Fermi acceleration of cosmic rays by MHD turbulence
Perpendicular diffusion of cosmic rays
Acceleation of cosmic rays by shocks in turbulent media
Points of Part 2:
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Scattering and second order Fermi acceleration of cosmic rays by MHD turbulence
Perpendicular diffusion of cosmic rays
Acceleation of cosmic rays by shocks in turbulent media
Points of Part 2:
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In case of small angle scattering, Fokker-Planck equation can be used to describe the particles’ evolution:
Cosmic Rays Magnetized medium
S : Sources and sinks of particles2nd term on rhs: diffusion in phase space specified by Fokker -Planck coefficients Dxy
Cosmic rays interact with magnetic turbulence
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Correct diffusion coefficients are the key to the success of such an approach
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Turbulence induces second order Fermi process
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Magnetic “clouds”
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Resonance and Transit Time Damping (TTD) are examples of 2nd order Fermi process
BBrL
n=1
n=0
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Diffusion in the fluctuating EM fields
Collisionless Fokker-Planck equationBoltzmann-Vlasov eq
B, v<<B0, V (at the scale of resonance)
Fokker-Planck coefficients: D≈ 2/t, Dpp ≈ p2/t are the fundermental parameters we need. Those are determined by properties of turbulence!
For TTD and gyroresonance, , scsc//acac≈ Dpp / p2D ≈ (VA/v)2
Turbulence properties determine the diffusion and acceleration
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~
~~Propagation
StochasticAcceleration
•The diffusion coeffecients are determined by the statistical properties of turbulence
The diffusion coefficients define characteristics of particle propagation and acceleration
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Gyroresonance(n = ± 1, ± 2 …),Which states that the MHD wave frequency (Doppler shifted) is a multiple of gyrofrequency of particles (v|| is particle speed parallel to B).
So,
BBrL
Gyroresonance scattering depends on the properties of turbulence
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scattering efficiency is reduced
lperp<< l|| ~ rL
2. “steep spectrum”
steeper than Kolmogorov!Less energy on resonant
scaleeddiesB
l||
l⊥
1. “random walk”
B 2rL
Alfenic turbulence injected at large scales is inefficient for cosmic ray scattering/acceleration
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Alternative solution is needed for CR scattering (Yan & Lazarian 02,04 Brunetti & Lazarian 0,).
Scat
terin
g fre
quen
cy
(Kolmogorov)
Alfven modes
Big difference!!!
Kinetic energy
(Chandran 2000)
Total path length is ~ 104 crossings at
GeV from the primary to
secondary ratio.
Inefficiency of cosmic ray scattering by Alfvenic turbulence is obvious and contradicts to what we know about cosmic rays
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modesmodes momodes
Depends ondamping
Fast modes are identified as the dominate source for CR scattering (Yan & Lazarian 2002, 2004).
fast modes
plot w. linear scale
Scat
terin
g fre
quen
cy
Kinetic energy
Fast modes efficiently scatter cosmic rays solving problems mentioned earlier
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Viscous damping (Braginskii 1965)
Collisionless damping (Ginzburg 1961, Foote & Kulsrud
1979)
Damping increases with plasma Pgas/Pmag and the angle between
k and B.
Damping is for fast modes is usually defined for laminar fluids and is not applicable to turbulent environments
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direction changes during cascade
Randomization of local B: field line wandering by shearing via Alfven modes: dB/B ≈ (V/L)1/2 tk
1/2
Randomization of wave vector k: dk/k ≈ (kL)-1/4 V/Vph
B
k
Lazarian,
Vishniac & Cho 2004
Field line wandering
To calculate fast mode damping one should take into account wandering of magnetic field lines induced by Alfvenic turbulence
Magnetic field wandering induced by Alfvenic turbulence was described in Lazarian & Vishniac 1999
Yan & Lazarian 2004
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Flat dependence of mean free path can occur due to collisionless damping.
CR Transport in ISM
Mean
fre
e p
ath
(p
c)
Kinetic energy
haloWIMText
from Bieber et al 1994
Palmer consensusPalmer consensus
Modeling that accounts for damping of fast modes agrees with observations
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• Alfvenic turbulence is inefficient for scattering if it is generated on large scales.
• Fast modes dominate scattering, but damping of them is necessary to account for.
• Calculation of fast mode damping requires accounting for field wandering by Alfvenic turbulence.
• Scattering depends on the environment and plasma beta.
• Actual turbulence and acceleration in collisionless environments may be more complex
Take home message 8:
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Scattering and second order Fermi acceleration of cosmic rays by MHD turbulence
Perpendicular diffusion of cosmic rays
Acceleation of cosmic rays by shocks in turbulent media
Points of Part 2:
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Perpendicular transport is due to Perpendicular transport is due to turbulent B fieldturbulent B field
Perpendicular transport is due to Perpendicular transport is due to turbulent B fieldturbulent B field
Dominated by field line wandering.
BB00
– Particle trajectory— Magnetic field
Intensive studies: e.g., Jokipii & Parker 1969, Forman 74,
Urch 77, Bieber & Matthaeus 97, Giacolone & Jokipii 99, Matthaeus et al
03, Shalchi et al. 04
What if we use the tested model of turbulence?What if we use the tested model of turbulence?
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Perpendicular Perpendicular transporttransport
Perpendicular Perpendicular transporttransport
MA< 1, CRs free stream over distance L, thus D⊥ =R2 /∆t= Lv|| MA
4
Whether and to what degree CRs Whether and to what degree CRs diffusion is suppressed depends on diffusion is suppressed depends on Alfven Mach number, i.e MAlfven Mach number, i.e MAA= V= Vinjinj/V/VAA..
Lazarian & Vishniac 1999, Lazarian 2006, Yan & Lazarian 2008
Earlier works suggested MA2 dependence
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Predicted MA4 suppression is
observed in simulations!Predicted MA
4 suppression is observed in simulations!
Differs from M2 dependence in classical works, e.g. in Jokipii & Parker 69, Matthaeus et al 03.
Xu & Yan 2013
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Is Subdiffusion (∆x ~ ∝tIs Subdiffusion (∆x ~ ∝taa, a<1) typical?, a<1) typical?Is Subdiffusion (∆x ~ ∝tIs Subdiffusion (∆x ~ ∝taa, a<1) typical?, a<1) typical?
Subdiffusion (or compound diffusion, Getmantsev 62, Lingenfelter et al 71, Fisk et al. 73, Webb et al 06) was observed in near-slab turbulence, which can occur on small scales due to instability.
What about large scale turbulence?
Example: diffusion of a dye on a ropea) A rope allowing retracing, ∆t =lrope
2 /Db) A rope limiting retracing within
pieces lrope /n, ∆t =lrope2 /nD
Diffusion is slow if particles retrace their trajectories.
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Is there subdiffusion (∆xIs there subdiffusion (∆x22∝∆t∝∆taa, a<1) ?, a<1) ?Is there subdiffusion (∆xIs there subdiffusion (∆x22∝∆t∝∆taa, a<1) ?, a<1) ?
Subdiffusion (or compound diffusion, Getmantsev 62, Lingenfelter et al 71, Fisk et al. 73, Webb et al 06) was observed in near-slab turbulence, which can occur on small scales due to instability.
Diffusion is slow only if particles retrace their trajectories.
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In turbulence, CRs’ trajactory become independent when field lines are seperated by the smallest eddy size , l⊥,min. The separation between field lines grows exponentially, provides LRR =|||,min log(l⊥,min /rL)
Subdiffusion only occurs below LRR. Beyond LRR, normal diffusion applies.
ll,min,min
–– Particle trajectoryParticle trajectory—— Magnetic fieldMagnetic field
Subdiffusion does not happen in realistic astrophysical turbulence
Lazarian 06, Yan & Lazarian 08
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General Normal Diffusion is observed in simulations!
General Normal Diffusion is observed in simulations!
Cross field transport in 3D turbulence is in general a normal diffusion!
incompressible turbulence
Beresnyak et al. (2011)
compressible turbulence (Xu & Yan 2013 )
∝ t∝ t
rL /L
0.001
0.01
rL /L
0.001
0.01
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Perpendicular propagation is superdiffusive on scales less than the injection scale
Lazarian, Vishniac & Cho 2004
Magnetic field separation follows the law y2_x3 (Richarson law), x<Linj
x
Xu & Yan 2013
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• Alfvenic Perpendicular diffusion scales as MA4,
not MA2
• Subdiffusion does not happen
• Superdiffusion takes place on scales smaller than the injection scale
Take home message 9:
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Scattering and second order Fermi acceleration of cosmic rays by MHD turbulence
Perpendicular diffusion of cosmic rays
Acceleation of cosmic rays by shocks in turbulent media
Points of Part 2:
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Acceleration in shocks requires scattering of particles back from the upstream region.
Downstream Upstream
Magnetic turbulence generated by shock
Magnetic fluctuations generated by streaming
Point 5. Turbulence alters processes of Cosmic Ray acceleration in shocks
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Chandra
In postshock region damping of magnetic turbulence explains X-ray observations of young SNRs
Alfvenic turbulence decays in one eddy turnover time (Cho & Lazarian 02), which results in magnetic structures behind the shock being transient and generating filaments of a thickness of 1016-1017cm (Pohl, Yan &
Lazarian 05).
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B
vA
shock
Streaming instability in the preshock region is a textbook solution for returning the particles to shock region
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shock
1. Streaming instability is suppressed in the presence of external turbulence (Yan & Lazarian 02, Farmer & Goldreich 04, Beresnyak & Lazarian 08).
2. Non-linear stage of streaming instability is inefficient (Diamond & Malkov 07).
Streaming instability is inefficient for producing large field in the preshock region
B
Beresnyak & Lazarian 08
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BjCR
shock
Bell (2004) proposed a solution based on the current instability
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Precursor forms in front of the shock and it gets turbulent as precursor interacts with gas density fluctuation
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MHD scale
hydrodynamiccascade
Turbulence efficiently generates magnetic fields as shown by Cho et al. 2010
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The model allows to calculate the parameters of magnetic field
Beresnyak, Jones & Lazarian 2010
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BjCR
current instability
Take home message 9: Magnetic field generated by precursor -- density fluctuations interaction might be larger than the arising from Bell’s instability