MHD turbulence:MHD turbulence:Consequencies and Consequencies and

Techniques to studyTechniques to study

Huirong YanHuirong Yan

Supervisor: Alex LazarianSupervisor: Alex Lazarian

University of Wisconsin-MadisonPredoctoral work in Stanford (04-05)

Directions of ResearchDirections of Research

• Cosmic Ray (CR) transport and acceleration (Yan & Lazarian 2002 Physical Review Letters, Yan & Lazarian 2004 ApJ Lazarian, Cho & Yan 2003 review, Recent Res. Dev. Astrophys. Cho, Lazarian & Yan 2002 review, ASP)

• Interstellar dust dynamics and their implications (Yan, Lazarian & Draine 2004 ApJ, Yan & Lazarian 2003 ApJ, Lazarian & Yan 2002 ApJ, Lazarian & Yan 2004 review, ASP, Yan & Lazarian 2004 Texas Symposium)

•Polarimetric study of interstellar and circumstellar magnetic fields by atomic alignment (Yan & Lazarian submitted to ApJ, Yan & Lazarian 2004 Polarimetry Symposium, Lazarian & Yan 2005 review)

•Solar physics and others Yan, Petrosian & Lazarian 2005 submitted, Suzuki, Yan, Lazarian & Cassenelli 2005 submitted, Pohl, Yan & Lazarian 2005 ApJL, Lazarian, Petrosian, Yan & Cho 2003 review)

Directions of Research (cont.)Directions of Research (cont.)

Cosmic ray Scattering Cosmic ray Scattering •Propagation Isotropy

Light elements: Li, Be, B, etcLong age

Post-shock Pre-shockregion region

1st order Fermi 2nd order Fermi

•Acceleration

Shock frontMagnetic “clouds”

• Where does B come from? MHD turbulence!

• Re ~VL/ ~1010 >> 1

~ rLvth, vth < V, rL<< L

Cosmic Rays interstellar medium

EM perturbations, E, (local CR frame)

Interstellar medium is magnetized and turbulent!

Cosmic ray physics is a general problem (ISM, ray burst, solar flares). Here we are concentrated on ISM.

Cosmic ray transportCosmic ray transport

Diffusion in the fluctuating EM fields

Collisionless Fokker-Planck equationBoltzmann-Vlasov eq

B<<B0 (at the scale of scattering)

Fokker-Planck coefficients: D, Dp, Dpp are the fundermentalparameters we need! They are primarily determined by the statistical properties of MHD turbulence!

How do we study the scattering?How do we study the scattering?

Examples of MHD modes (Pmag > Pgas)

Alfven mode (v=VA cos)

incompressible;restoring force=mag. tension

k

B

slow mode (v=cs cos)

fast mode (v=VA)restoring force = Pmag + Pgas

Bk

B

restoring force = |Pmag-Pgas|

Models of MHD turbulenceModels of MHD turbulence

• Earlier models Slab model: Only MHD modes propagating along the magnetic field are counted.

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

• Realistic MHD turbulence (Cho & Lazarian 2002, 2003)

1. Alfven and slow modes: Goldreich-Sridhar 95 scaling

2. Fast modes: isotropic, similar to accoustic turbulence

Anisotropy of MHD modes

Alfven and slow modes Alfven and slow modes fast modes fast modes E

qual

vel

ocity

cor

rela

tion

Equ

al v

eloc

ity c

orre

latio

n c

onto

urco

ntou

r

BB

Resonant scattering

Gyroresonance: - k||v|| = n(n = ± 1, ± 2 …),

Which states that the MHD wave frequency (Doppler shifted)

is a multiple of gyrofrequency of particles (v is particle speed).

So, k||,res~ /v = 1/rL

Resonance mechanismResonance mechanism

BB

Scattering by Alfvenic turbulence

Scattering by Alfvenic turbulence

Alfven modes do not contribute to particle scattering if energy is injected from large scale!

2rL

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 in resonant scale

eddieseddiesBB

ll||||

ll

1. “random walk”

B

Alfven modes are inefficient. Fast modes dominateCR scattering in spite of damping (Yan & Lazarian 2002).

Scattering by MHD turbulence Scattering by MHD turbulence S

catt

erin

g fr

eque

ncy

(Kolmogorov)

Alfven modesAlfven modes

Big difference!!!Big difference!!!

Fast modesFast modes

Depends on dampingDepends on damping

Damping of fast modesDamping of fast modes

Viscous damping

Collisionless damping

Ion-neutral damping

increase with both plasma and the

angle between k and B.

Cutoff wave number kc :

defined as the scales on which damping rate is equal to

cascading rate

k-1

= (kc vk)2 = (kc L)1/2 V2/Vph .

complication: randomization of during cascade

Randomization of wave vector k:

dk/k ≈ (kL)-1/4 V/Vph

Randomization of local B: field line wandering by shearing via Alfven modes:

dB/B ≈ (V/L)1/2 tk1/2 = (kL)-1/4 (Vph /V)1/2

Anisotropic Damping of fast modes

Anisotropic Damping of fast modes

Anisotropic damping results in redistribution of fast mode energy (slab geometry).

kk

BB

Damping depends on the angle

Damping of fast modes in various media

Damping of fast modes in various media

Cutoff scale in different media

Log 1

0(k

c)

Left: cutoff wave number kc in interstellar medium vs. Yan & Lazarian 2004)

1au

1pc

ISM phasesISM phases

With randomization

Without randomization

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

Transit time damping (TTD)

Compressibility required!

Landau resonance condition: k||v|| Vph = k v|| cos

kk

i) no resonant scale;i) no resonant scale;ii) ii) kk

broadened broadened

Landau resonance.Landau resonance.

(i) gyroresonance with fast modes is dominant;(ii) scattering rate varies with medium and

depends on plasma

What are the scattering rates for different ISM phases?

What are the scattering rates for different ISM phases?

(Yan & Lazarian 2004)

(iii) near 90o transit time damping (TTD) should be taken into account. Use of function entails error.(iv) in high and patially ionized media where gyroresonance doesn’t exist due to severe damping, TTD is dominant.

What are the scattering rates for different ISM phases? (Cont.)

What are the scattering rates for different ISM phases? (Cont.)

(Yan & Lazarian 2004)

Streaming instability of CRStreaming instability of CR

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

Post-shock Pre-shockregion region

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 of CR (Cont.)

Streaming instability of CR (Cont.)

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

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

This gives max ≈ 20GeV for HIM.

This is similar to the estimate obtained with background Alfvenic

turbulence (Farmer & Goldreich 2004).

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

3. Strong case (e.g. shocks):Magnetic field itself can be amplified through inverse cascade.

As a result, B > B0, the growth rate becomes higher in this case.

And the streaming instability operates till higher energies (Yan

& Lazarian 2004): max ≈ (a(LeB0)0.5U3/(m0.5V2c2))1/(0.5+a)E0,

where is the ratio of the pressure of CRs at the shock and the upstream momentum flux entering the shock front, U is the shock front speed, a-4 is the spectrum index of CRs at the shock front. This gives max ≈ 2 107 (t/kyr)-9/4 for HIM.Shock acceleration should be revised.Cosmic Ray confinement in galaxies should be revised.

Streaming instability of CR (Cont.)

Streaming instability of CR (Cont.)

Applications to stellar physics

Applications to stellar physics

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

B

Acceleration by fast modes is an important mechanism to generatehigh energy particles in Solar flares (Yan, Petrosian & Lazarian 2005);

Thermal damping of turbulence in solar flares

Thermal damping of turbulence in solar flares

Dam

pi n

cu

t off

sca

le o

f f a

st m

odes

The angle between k and B

From Suzuki, Yan, Lazarian, From Suzuki, Yan, Lazarian, Cassenelli (2005)Cassenelli (2005)

Ti m

esc

al s

e f

or

casc

ad

e

ad

n li n

ear

ddam

pi n

g

Wave number

Nonthermal damping of turbulence in solar flares

Nonthermal damping of turbulence in solar flares

Nonthermal damping (cont.)Nonthermal damping (cont.)D

am

pi n

cu

t off

sca

le o

f f a

st m

odes

The angle between k and B Transit time damping with nonthermal particle can dominate damping of fast modes with large pitch angles

Nothermal damping (Cont.)Nothermal damping (Cont.)

Damping by gyroresonance is subdominant.

Ti m

esc

al s

e f

or

casc

ad

e

ad

n li n

ear

ddam

pi n

g

Wave number

Acceleration of dust grainsAcceleration of dust grains

ewmechanism:Gyroresonance (Yan & Lazarian 2003)

• The dynamics of turbulence ought to be taken into account, resulting in resonance broadening.

Grain velocities in various media were calculated in Grain velocities in various media were calculated in Yan, Lazarian & Draine (2004)Yan, Lazarian & Draine (2004)

1km/s!1km/s!

Shattering and coagulation thresholds

Shattering and coagulation thresholds• Acceleration by turbulence is most effcient• Grains get supersonic• Grains may get aligned• Turbulence mixing of grains is efficient• Correlation between turbu- lence and grain size

Toy model:Definition: Atomic Alignment is defined here as differential occupation of the fine or hyperfine sublevels of the ground state. Atomic alignment is induced by anisotropic radiation.

Species to align: virtually most atoms with fine or hyperfine structures. (optical and UV lines)

Atomic alignment (work in progress)

Atomic alignment (work in progress)

Requirement for Requirement for alignmentalignment::

Requirement for Requirement for alignmentalignment::

• Can unpolarized light induce alignment?

Yes, magnetic substates with opposite “MF” will be symmetrically populated, but alignment will be present.

• Major requirement: anisotropic radiation (usual for astrophysics)

• Has atomic alignment been observed?

In laboratory Na alignment has been studied in relation to maser research (Brossel et al 1952, Hawkins 1955).

• Why hyperfine structure (if exists) is important?

Hyperfine interaction causes substantial precession of J about F before spontaneous emission occurs (Walkup 1982). Presence of nuclear moment splits the ground level and allows alignment in the ground state.

NaI

NV AlIII HI NI OII

58925898

12391243

18551863

912-1216

865-1201

834

OI CrII CII OIV CI OIII

911-1302

2060 1336 790 1115-1661

834

Examples of alignable species (Yan & Lazarian 2005)

L–Larmor frequency

R-photon arrival rate

A-Einstein coefficient

Range of applicablity:Range of applicablity:

Role of magnetic fieldRole of magnetic field

Magnetic field causes precession of atoms and therefore changes the alignment of atoms caused by radiation.

M=2M=2

M=1M=1

M=0M=0

M=-1M=-1M=-2M=-2

zz

BB

FF

radiationradiation

atomsatomsAngular momentum

Quantum Electrodynamics calculations

Quantum Electrodynamics calculations

Main object: density tensor: Main object: density tensor: kkqq

22: dipole moment: dipole moment44: quardripole moment: quardripole moment

They can be obtained from statistical equilibrium They can be obtained from statistical equilibrium equation of the upper state and ground state of an atom.equation of the upper state and ground state of an atom.

Quantum Electrodynamics calculations (Cont.)

Quantum Electrodynamics calculations (Cont.)

Theoretical and observational frame

Theoretical and observational frame

(B)(B)

Left: Radiation geometry and the polarization vectors; Right: Transformation from observational frame to theoretical frame by two successive rotations specified by Euler angles (B, )

Differential population of ground state

Differential population of ground state

The density tensor components 2,4 of ground state of Cr II line 6S5/2 6P7/2; left: without multiplet effect, only the transition between the two levels are counted; right: with multiplet effect.

rr rr

The observed polarization depends on both line of sight and the direction of incident light. Polarization vs. the direction of incident light for fixed line of sight =90o and =0o.

Polarization of emission linesPolarization of emission linesPolarization of emission linesPolarization of emission lines

polar anglepolar angleazimuthal angleazimuthal angle

rr rr

pp

Application: magnetic fields in Application: magnetic fields in the wake of a cometthe wake of a comet

Application: magnetic fields in Application: magnetic fields in the wake of a cometthe wake of a comet(a)

(a) Resonance scattering of solar light by sodium tail from comet;

z

y x

(b)

v

(b) MHD simulations of comet’s wake;

(c) Polarization caused by sodium aligned in the comet wake.

(c)

y (rcomet)

E1

• Sensitive to smaller scale fluctuations.

• 3D information of magnetic field can be

obtained from atomic alignment.

• Provide independent test to grain alignment

theory.

In comparison with dust alignment:In comparison with dust alignment:In comparison with dust alignment:In comparison with dust alignment:

Summary of the most important results for PhD work

Summary of the most important results for PhD work

• Fast MHD modes are identified as the major scattering agent for Galactic cosmic rays. Scattering of cosmic rays depends on the medium . • Streaming instability is partially suppressed by turbulence.• Results are applied to solar physics.

• Gyroresonance is identified as a new acceleration mechanism, which can drive grains to supersonic velocities. This can have implications in various topics, including grain alignment, grain mixing and CR abundance, etc.

• Atomic alignment is identified as a new tool to study 3D geometry of interstellar and circumstellar magnetic fields.

agnetic field study

Cosmic ray transport

Dust dynamicsDust dynamics