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 …

Theme 2. Propagation and Acceleration of Cosmic Rays in Turbulent

Magnetic Fields

Icecube measurement 2010

M. Duldig 2006

Highly isotropic

MHD turbulence theory induces changes on our understanding of CRs propagation and stochastic acceleration

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:

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:

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

Correct diffusion coefficients are the key to the success of such an approach

Turbulence induces second order Fermi process

QuickTime™ and a decompressor

are needed to see this picture.

Magnetic “clouds”

QuickTime™ and a decompressor

are needed to see this picture.

Resonance and Transit Time Damping (TTD) are examples of 2nd order Fermi process

BBrL

n=1

n=0

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

~

~~Propagation

StochasticAcceleration

•The diffusion coeffecients are determined by the statistical properties of turbulence

The diffusion coefficients define characteristics of particle propagation and acceleration

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

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

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

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

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

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

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

• 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:

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:

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?

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

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

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.

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.

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

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

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

• 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:

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:

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

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).

B

vA

shock

Streaming instability in the preshock region is a textbook solution for returning the particles to shock region

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

BjCR

shock

Bell (2004) proposed a solution based on the current instability

Precursor forms in front of the shock and it gets turbulent as precursor interacts with gas density fluctuation

MHD scale

hydrodynamiccascade

Turbulence efficiently generates magnetic fields as shown by Cho et al. 2010

The model allows to calculate the parameters of magnetic field

Beresnyak, Jones & Lazarian 2010

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