cosmic ray (cr) transport in mhd turbulence huirong yan kavli institute of astronomy &...
Post on 20-Dec-2015
216 views
TRANSCRIPT
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)