Cosmic Ray (CR) Cosmic Ray (CR) transport in MHD transport in MHD

turbulenceturbulence

Cosmic Ray (CR) Cosmic Ray (CR) transport in MHD transport in MHD

turbulenceturbulence Huirong Yan

Kavli Institute of Astronomy & Astrophysics, Peking U

OutlineOutlineDiscovery of CRs and importance of the studies of transport processes.

Basic formalism and interaction mechnism.

Cosmic Ray (CR) scattering by numerically tested models of turbulence.

Turbulence generation and particle confinement at shocks

Instabilities and Back-reaction of CRs (small scale)

Implications for various astrophysical problems

Insight into Gamma Ray Burst

What are Cosmic rays?

What are Cosmic rays?

Cosmic rays: energetic charged particles from space.

Observational distribution of CRS

Observational distribution of CRS

Icecube measurement

M. Duldig 2006

Highly isotropic

Importance of CR propagationImportance of CR propagationImportance of CR propagationImportance of CR propagation

CMB synchrotron foreground

Diffuse ɣ ray emissionDiffuse ɣ ray emission

diffuse Galactic 511 keV radiation

Identification of dark matter

Importance of CR acceleration: Importance of CR acceleration: Fermi IIFermi II

Importance of CR acceleration: Importance of CR acceleration: Fermi IIFermi II

Magnetic “clouds”

Stochastic Acceleration:

Fermi (49)

Gamma ray burstGamma ray burst

Solar FlareSolar Flare

Importance to Fermi I accelerationImportance to Fermi I accelerationImportance to Fermi I accelerationImportance to Fermi I acceleration

Pre-shock Post-shockPre-shock Post-shockregionregion regionregion

Shock frontShock front

Shock Acceleration

Turbulencegenerated by shock

Turbulence generated

by streaming

Tycho’s remanentTycho’s remanentKrymsky 77, Axford et al 77, Bell Krymsky 77, Axford et al 77, Bell

78, Blandford & Ostriker 78, 78, Blandford & Ostriker 78, Drury 83Drury 83

Diffusion of CRs

More data are available for model fitting

More data are available for model fitting

Big simulation itself is not adequate

Big simulation itself is not adequate

big numerical simulations fit results due to the existence of "knobs" of free parameters (see, e.g., http://galprop.stanford.edu/).

Self-consistent picture can be only achieved on the basis of theory with solid theoretical foundations and numerically tested.

Basic equationsBasic equationsBasic equationsBasic equations

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

Fokker Planck (FP)diffusion coeffcients

Fokker Planck (FP)diffusion coeffcients

FP coefficients can be used to FP coefficients can be used to find transport and acclerationfind transport and accleration

propertiesproperties

FP coefficients can be used to FP coefficients can be used to find transport and acclerationfind transport and accleration

propertiesproperties

~

~~Propagation

StochasticAcceleration

Dμμ δB,

Dpp δΕδ

•Where do δB, δ come from? MHD turbulence! •The diffusion coeffecients are primarily determined by the statistical properties of turbulence

Resonance mechanismResonance mechanismResonance mechanismResonance mechanism

Gyroresonanceω- k||v|| = nΩ(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, k||,res~ Ω/v = 1/rL

BBrL

large scale perturbation , adiabatic invariant

small scale averaged out

large scale perturbation , adiabatic invariant

small scale averaged out

Transit Time Damping (TTD)Transit Time Damping (TTD)Transit Time Damping (TTD)Transit Time Damping (TTD)

Transit time damping (TTD)

Compressibility of B field required!

no resonant scale All scales contribute

Scattering due to TTD

Landau resonance condition: k||v|| vA = ωk v|| cosθ

μvA/ vcosθ

mirror effect is a result of adiabatic invariant!

small amplitude needs comoving

mirror effect is a result of adiabatic invariant!

small amplitude needs comoving

Betatron Acceleration by CompressibleTurbulence

Traditionally, Betatron acceleration was only considered behind shocks. Turbulence, however, can also compress the magnetic field and therefore accelerate dust through the induced electric field (Berger et al 1958; Kulrud & Pearce 1971; Cho & Lazarian 2006; Yan 2009).

particle orbit

Turbulence is ubiquitous!

Turbulence is ubiquitous!

Extended Big Power Law

Armstrong et al. (1995), Chepurnov & Lazarian (2009)

Supernovae blow interstellar "bubbles"

turbulent LMC

•Re VL/ν 1010 >> 1

ν rLvth, vth < V, rL<< L

Models of MHD turbulence

Models of MHD turbulence

Ad hoc turbulence models

Tested models of MHD turbulence 1. Alfven and slow modes: Goldreich-Sridhar 95 scaling 2. Fast modes: isotropic, similar to accoustic turbulence

Slab model: Only MHD modes propagating along the magnetic

field are counted. Kolmogorov turbulence: isotropic, with 1D spectrum E(k)~k-5/3

Alf

ven

and

slow

A

lfve

n an

d sl

ow

mod

es (

GS

95)

mod

es (

GS

95)

fast

mod

es

fast

mod

es

BB

Numerically tested models for Numerically tested models for MHD turbulenceMHD turbulence

Numerically tested models for Numerically tested models for MHD turbulenceMHD turbulence

Alfven slow

fast

~k~k--5/35/3 ~k~k--5/35/3

~k~k-3/2-3/2

Equal velocity correlation contour (Cho & Lazarian 02, Kowal & Lazarian 2010)

anisotropic eddies

scattering efficiency is reduced

l⊥ << l|| ~ rL

2. “steep spectrum”

E(k ⊥ )~ k ⊥ -5/3, k ⊥ ~ L1/3k||3/2

E(k||) ~ k||-2

steeper than Kolmogorov!Less energy on resonant

scaleeddiesB

l||

l⊥

1. “random walk”

B

Contrary to common belief: Contrary to common belief: Scattering in Alfvenic turbulence is Scattering in Alfvenic turbulence is

negligible!negligible!

Contrary to common belief: Contrary to common belief: Scattering in Alfvenic turbulence is Scattering in Alfvenic turbulence is

negligible!negligible!

2rL

The often adopted Alfven modes are useless. Alternative solution is needed for CR scattering (Yan & Lazarian 02,04)?

Sca

tter

ing

freq

uenc

y

(Kolmogorov)

Alfven modes

Big difference!!!

Alvenic turbuelence cannot scatter Alvenic turbuelence cannot scatter cosmic rays!cosmic rays!

Alvenic turbuelence cannot scatter Alvenic turbuelence cannot scatter cosmic rays!cosmic rays!

Kinetic energy

? Remarkable

isotropy δ~6x10-4 and long age 10 7

yrs

? Remarkable

isotropy δ~6x10-4 and long age 10 7

yrs

(Chandran 2000)

Total path length is ~ 104 crossings at

GeV from the primary to

secondary ratio.

fast modes are dominant!fast modes are dominant!fast modes are dominant!fast modes are dominant!

modesmodes momodesDepends ondamping

dam damping

Fast modes are identified as the dominate source for CR scattering (Yan & Lazarian 2002, 2004)!

fast modes

plot w. linear scale

Sca

tter

ing

freq

uenc

y

Kinetic energy

Linear damping of fast waves

Linear damping of fast waves

Viscous damping (Braginskii 1965)

Collisionless damping (Ginzburg 1961, Foote & Kulsrud

1979)

Increase with plasma βPgas/Pmag and the angle θ between k and B.

damping in turbulent mediumdamping in turbulent mediumdamping in turbulent mediumdamping in turbulent medium

complication: finite randomization of θ 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

θ

Lazarian, Vishniac & Cho

2004

Field line wandering

Field line wandering is necessary to account for!Field line wandering is necessary to account for!

Observed secondary elements Observed secondary elements supports scattering by fast supports scattering by fast

modes!modes!

Observed secondary elements Observed secondary elements supports scattering by fast supports scattering by fast

modes!modes!

Scattering by fast modes

k cL

1au

1pc

With randomization

Anisotropy of fast modes arising from Anisotropy of fast modes arising from dampingdamping

Anisotropy of fast modes arising from Anisotropy of fast modes arising from dampingdamping

Cutoff scale in different media

Wave pitch angle

ISM phases

Wave pitch angle

Damping depends on medium.

Anisotropic damping results in quasi-slab geometry.

Field line wandering should be accounted for.

halo

WIM

Yan & Lazarian (2008)

With randomization

Solar corona

Petrosian , Yan, & Lazarian (2006)

Application to stellar wind

Application to stellar wind

heating by collisionless damping is dominant in rotating stars (Suzuki, Yan, Lazarian, & Casseneli 2005).

B

Comparison w. test particle simulation

Comparison w. test particle simulation

a realistic fluctuatating B fields from numerical simulations

– Particle trajectory— Magnetic field

Results of Monte-Carlo simulationsResults of Monte-Carlo simulations

Particle scattering in incompressible turbulence

Dμμ/Ω~r (TTD)

Dμμ/Ω~r2.5

(gyroresonance)

— gyration frequency,L — outer scale of turbulence.

(obtained from quality-controlled particle tracer, Beresnyak, Yan & Lazarian 2010)

μ=0.5

CR Transport varies from place CR Transport varies from place to place!to place!

CR Transport varies from place CR Transport varies from place to place!to place!

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

Detailed study of solar flare Detailed study of solar flare acceleration must include damping, acceleration must include damping,

nonlinear effectsnonlinear effects

Detailed study of solar flare Detailed study of solar flare acceleration must include damping, acceleration must include damping,

nonlinear effectsnonlinear effects

TTD Acceleration by fast modes is an important mechanism

to generate energetic electrons in Solar flares (Yan,

Lazarian & Petrosian 2008).

Com

pari

son o

f ra

tes

Kinetic energy

Loss

Escape

Acceleration

With randomization

Solar corona

Petrosian , Yan, & Lazarian (2006) Loss

Wave pitch angle

Idea of fast modes takes over in other

fields

Idea of fast modes takes over in other

fields

Brunetti & Lazarian (2007)

Dust dynamics is dominated by MHD turbulence!

Grains can reach supersonic speed due to acceleration by turbulence and this results in more efficient shattering and adsorption of heavy elements (Yan & Lazarian 2003, Yan 2009).

velo

city

of

charg

ed g

rain

s

Grain size

1km/s!1km/s!

What are the implications for dust dynamics?

Extinction curve varies according to local Conditions of turbulence (Hirachita & Yan 2009).

Extinction curveEvolving grain size distribution in turbulence

50 Myr100 Myr

50 Myr100 Myr

initial

Interaction w. small scale waves: Interaction w. small scale waves: Streaming instabilityStreaming instability

Interaction w. small scale waves: Interaction w. small scale waves: Streaming instabilityStreaming instability

Acceleration in shocks requires scattering of particles back from the upstream region.

Downstream Upstream

Turbulencegenerated by shock

Turbulence generated by streaming

Streaming cosmic rays result in formation of perturbation that scatters cosmic rays back and increases perturbation. This is streaming instability that can return cosmic rays back to shock and may prevent their fast leak out of the Galaxy.

Streaming instability is Streaming instability is suppressed in background suppressed in background

turbulence!turbulence!

Streaming instability is Streaming instability is suppressed in background suppressed in background

turbulence!turbulence!

• In turbulent medium, wave-turbulence interaction damps waves (Yan & Lazarian 2002, 2004, Farmer &

Goldreich 2004, Beresnyak & Lazarian 2008).

BB

Streaming instability of CRs is suppressed

(Cont.)

Streaming instability of CRs is suppressed

(Cont.)

2. Calculations for weak case (δB<B):With background compressible turbulence (Yan & Lazarian 2004):

Εmax ≈ 1.5 10-9 [np-1(VA/V)0.5(LcΩ/V2)0.5]1/1.1E0

This gives Εmax ≈ 20GeV for HIM.

Similar estimate was obtained with background Alfvenic

turbulence (Farmer & Goldreich 2004).

1. MHD turbulence can suppress streaming instability (Yan & Lazarian 2002).

Alternative for upstream tubulence?

Alternative for upstream tubulence?

Beresnyak, Jones & Lazaian (2009)

Implication: Magnetically limited X-ray Implication: Magnetically limited X-ray filaments in young SNRsfilaments in young SNRs

Implication: Magnetically limited X-ray Implication: Magnetically limited X-ray filaments in young SNRsfilaments in young SNRs

Strong magnetic field produced by streaming instability at upstream of the shock, may be damped by turbulence at downstream, generating filaments of a thickness of 1016-1017cm ( Pohl, Yan & Lazarian 2005).

Chandra

Feedback of CRs on MHD turbulence

Feedback of CRs on MHD turbulence

Slab modes with

Lazarian & Beresnyak 2006 , Yan & Lazarian 2011

Wave Growth is limited by Nonlinear Suppression!

Wave Growth is limited by Nonlinear Suppression!

Turbulence compression

Scattering by instability generated slab wave

A

β≝ Pgas/Pmag < 1, fast modes (isotropic cascade +anisotropic damping )β > 1 slow modes (GS95)

Scattering by growing wavesScattering by growing waves

Anisotropy cannot reach δv/vA, the predicted value earlier, and the actual growth is slower and smaller amplitude due to nonlinear suppression (Yan &Lazarian 2011).

By balancing it with the rate of increase due to turbulence compression , we can get

Bottle-neck of growth due to energy constraint:

Simple estimates:

domains for different regimes of CR scattering

domains for different regimes of CR scattering

Damped by background turbulence

λfb

cutoff due to linear damping

SummarySummarySummarySummary

Changes in the MHD turbulence paradigm necessitates revision of CR theories. Changes in the MHD turbulence paradigm necessitates revision of CR theories.

Compressible fast modes dominates CR transport through direct scattering. CR transport therefore Compressible fast modes dominates CR transport through direct scattering. CR transport therefore varies from place to place.varies from place to place.

Slab waves are naturally generated in compressible turbulence by the gyroresonance instability, Slab waves are naturally generated in compressible turbulence by the gyroresonance instability, which dominates the scattering of low energy CRs (<100GeV).which dominates the scattering of low energy CRs (<100GeV).

Instabilities are subjected to damping by background turbulence.Instabilities are subjected to damping by background turbulence.

Implications are wide from solar flares to cluster of galaxies. Implications are wide from solar flares to cluster of galaxies.

For perpendicular transport:For perpendicular transport:

Perpendicular transportPerpendicular transport

Future perspectiveFuture perspectiveFuture perspectiveFuture perspective

etc…etc…

Full numerical testingin incompressible andcompressible medium

Revisit shockacceleration

Knee andstreaminginstability

Clarificationof modeling

synchrotronforeground

CR transport in Galaxyaccounting for turbulence

damping in different phases

diffuse gammaray emission

Modeling CR transportin cluster

Stochastic accelerationin solar flare, GRB

radio halo

Applicability

Fermi

Acceleration in solar flares,Acceleration in solar flares,GRBS, and radio halosGRBS, and radio halos

Acceleration in solar flares,Acceleration in solar flares,GRBS, and radio halosGRBS, and radio halos

modeling CR transport in clustersmodeling CR transport in clustersGRBS, and radio halosGRBS, and radio halos

modeling CR transport in clustersmodeling CR transport in clustersGRBS, and radio halosGRBS, and radio halos

revisit shock revisit shock acceleration acceleration revisit shock revisit shock acceleration acceleration

ApplicabilityApplicabilityGRBS, and radio halosGRBS, and radio halos

ApplicabilityApplicabilityGRBS, and radio halosGRBS, and radio halos

diffusediffuse gamma ray gamma ray emissionemission

diffusediffuse gamma ray gamma ray emissionemission

synchrotron synchrotron foregroundforeground emissionemission

synchrotron synchrotron foregroundforeground emissionemission

CR transport in Galaxy due to CR transport in Galaxy due to compressible modescompressible modes

CR transport in Galaxy due to CR transport in Galaxy due to compressible modescompressible modes

Full numerical testing in Full numerical testing in incompressible and incompressible and

compressible mediumcompressible mediumGRBS, and radio halosGRBS, and radio halos

Full numerical testing in Full numerical testing in incompressible and incompressible and

compressible mediumcompressible mediumGRBS, and radio halosGRBS, and radio halos

Clarification of modelingClarification of modelingClarification of modelingClarification of modeling

knee and knee and streaming streaming instabilityinstability

knee and knee and streaming streaming instabilityinstability

Quasilinear theory is not adequateQuasilinear theory is not adequateQuasilinear theory is not adequateQuasilinear theory is not adequate

Long standing problem: 90 degree scattering Kres= Ω/v||→∞, the scale is below the dissipation scale of turbulence No scattering at 90o? λ|| →∞?!

A key assumption in Quasilinear

theory:

guiding center is unperturbed

Z0=vμt

Nonlinear theory:

In reality, the guiding center is perturbed, especially on large

scales,

z=(vμ Δv||)t.

Nonlinear broadening of Nonlinear broadening of resonance solves the 90resonance solves the 90oo problem! problem!

Nonlinear broadening of Nonlinear broadening of resonance solves the 90resonance solves the 90oo problem! problem!

• On large scale, unperturbed orbit assumption in QLT fails due to conservation of adiabatic invariant v⊥

2/B (Volk 75).

Pitch angle cosine

Broadened resonance

varying v⊥ varying v||

-∆ vμtv|| t v|| t∆

Test particle simulation

Scattering due to transit time damping (TTD, cf. Schlickeiser &

Miller 1998)

QLT NLT

Yan & Lazarian (2008)