MHD turbulence Consequencies and Techniques to study Huirong
MHD turbulence: Consequencies and Techniques to study Huirong Yan Supervisor: Alex Lazarian University of Wisconsin-Madison Predoctoral work in Stanford (04 -05)
Directions of Research • Cosmic Ray (CR) transport and acceleration (Yan & Lazarian 2002 Physical Review Letters, Yan & Lazarian 2004 Ap. J 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 Ap. J, Yan & Lazarian 2003 Ap. J, Lazarian & Yan 2002 Ap. J, Lazarian & Yan 2004 review, ASP, Yan & Lazarian 2004 Texas Symposium)
Directions of Research (cont. ) • Polarimetric study of interstellar and circumstellar magnetic fields by atomic alignment (Yan & Lazarian submitted to Ap. J, 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 Ap. JL, Lazarian, Petrosian, Yan & Cho 2003 review)
Cosmic ray Scattering • Propagation Isotropy Light elements: Li, Be, B, etc Long age • Acceleration 1 st order Fermi Shock front Post-shock region Pre-shock region 2 nd order Fermi Magnetic “clouds”
Cosmic ray transport Cosmic ray physics is a general problem (ISM, g ray burst, solar flares). Here we are concentrated on ISM. Cosmic Rays interstellar medium EM perturbations, d. E, d. B (local CR frame) • Where does d. B come from? MHD turbulence! • Re ~VL/n ~1010 >> 1 n ~ r. Lvth, vth < V, r. L<< L Interstellar medium is magnetized and turbulent!
How do we study the scattering? Diffusion in the fluctuating EM fields Collisionless Boltzmann-Vlasov eq Fokker-Planck equation d. B<<B 0 (at the scale of scattering) Fokker-Planck coefficients: Dmm, Dmp, Dpp are the fundermental parameters we need! They are primarily determined by the statistical properties of MHD turbulence!
Examples of MHD modes (Pmag > Pgas) B Alfven mode (v=V cosq) A k incompressible; restoring force=mag. tension B slow mode (v=cs cosq) restoring force = |Pmag-Pgas| B k fast mode (v=VA) restoring force = Pmag + Pgas
Models of MHD turbulence • Earlier models Slab model: Only MHD modes propagating along the magnetic field are counted. Kolmogorov turbulence: isotropic, with 1 D 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 Equal velocity correlation contour Alfven and slow modes B fast modes
Resonance mechanism Resonant scattering Gyroresonance: w - k||v|| = n. W, (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~ W/v = 1/r. L B
Scattering by Alfvenic turbulence 1. “random walk” 2 r. L B l ^ << l|| ~ r. L l|| eddies l^ 2. “steep spectrum” E(k^)~ k^-5/3, k^~ L 1/3 k||3/2 E(k||) ~ k||-2 steeper than Kolmogorov! Less energy in resonant B scale scattering efficiency is reduced Alfven modes do not contribute to particle scattering if energy is injected from large scale!
Scattering frequency Scattering by MHD turbulence Alfven modes (Kolmogorov) Big difference!!! Fast modes Depends on damping Alfven modes are inefficient. Fast modes dominate CR scattering in spite of damping (Yan & Lazarian 2002).
Damping of fast modes Viscous damping Collisionless damping increase with both plasma b and the angle q between k and B. Ion-neutral damping Cutoff wave number kc : defined as the scales on which damping rate is equal to cascading rate tk-1 = w-1(kc vk)2 = (kc L)1/2 V 2/Vph.
Anisotropic Damping of fast modes Damping depends on the angle q § complication: randomization of q during cascade Randomization of wave vector k: dk/k ≈ (k. L)-1/4 V/Vph k q B Randomization of local B: field line wandering by shearing via Alfven modes: d. B/B ≈ (V/L)1/2 tk 1/2 = (k. L)-1/4 (Vph /V)1/2 Anisotropic damping results in redistribution of fast mode energy (slab geometry).
Damping of fast modes in various media Cutoff scale in different media Log 10(kc) 1 au 1 pc ISM phases Without randomization With randomization q Left: cutoff wave number kc in interstellar medium vs. q (Yan & Lazarian 2004)
Transit Time Damping (TTD) Transit time damping (TTD) Landau resonance condition: w k||v|| Vph = w/k v|| cosq Compressibility required! i) no resonant scale; ii) w tk-1 broadened Landau resonance. k
What are the scattering rates for different ISM phases? (Yan & Lazarian 2004) (i) gyroresonance with fast modes is dominant; (ii) scattering rate varies with medium and depends on plasma b;
What are the scattering rates for different ISM phases? (Cont. ) (Yan & Lazarian 2004) (iii) near 90 o transit time damping (TTD) should be taken into account. Use of d function entails error. (iv) in high b and patially ionized media where gyroresonance doesn’t exist due to severe damping, TTD is dominant.
Streaming instability of CR Acceleration in shocks requires scattering of particles ba the upstream region. Post-shock region Turbulence generated by shock Pre-shock region 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. ) 1. MHD turbulence can suppress streaming 2. instability (Yan & Lazarian 2002). 2. Calculations for weak case (d. B<B): With background compressible turbulence (Yan & Lazarian 2004): Emax ≈ 1. 5 10 -9 [np-1(VA/V)0. 5(Lc. W 0/V 2)0. 5]1/1. 1 E 0 This gives Emax ≈ 20 Ge. V for HIM. This is similar to the estimate obtained with background Alfvenic turbulence (Farmer & Goldreich 2004).
Streaming instability of CR (Cont. ) 3. Strong case (e. g. shocks): Magnetic field itself can be amplified through inverse cascade. As a result, d. B > B 0, the growth rate becomes higher in this case. And the streaming instability operates till higher energies (Yan & Lazarian 2004): Emax ≈ (ae(Le. B 0)0. 5 U 3/(m 0. 5 V 2 c 2))1/(0. 5+a)E 0, where e 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 gmax ≈ 2 107 (t/kyr)-9/4 for HIM. Shock acceleration should be revised. Cosmic Ray confinement in galaxies should be revised.
Applications to stellar physics Acceleration by fast modes is an important mechanism to generate high energy particles in Solar flares (Yan, Petrosian & Lazarian 2005); B heating by collisionless damping is dominant in rotating stars (Suzuki, Yan, Lazarian, & Casseneli 2005).
Dampin cutoff scale of fast modes Thermal damping of turbulence in solar flares From Suzuki, Yan, Lazarian, Cassenelli (2005) The angle between k and B
Timescalse for cascade adn linear ddamping Nonthermal damping of turbulence in solar flares Wave number
Dampin cutoff scale of fast modes Nonthermal damping (cont. ) The angle between k and B Transit time damping with nonthermal particle can dominate damping of fast modes with large pitch angles
Timescalse for cascade adn linear ddamping Nothermal damping (Cont. ) Wave number Damping by gyroresonance is subdominant.
Acceleration of dust grains New mechanism: Gyroresonance (Yan & Lazarian 2003) • The dynamics of turbulence ought to be taken into account, resulting in resonance broadening. 1 km/s! Grain velocities in various media were calculated in Yan, Lazarian & Draine (2004)
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 turbulence and grain size
Atomic alignment (work in progress) 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) Toy model:
Requirement for alignment: • Major requirement: anisotropic radiation (usual for astrophysics) • Can unpolarized light induce alignment? Yes, magnetic substates with opposite “MF” will be symmetrically populated, but alignment will be present. • 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. • Has atomic alignment been observed? In laboratory Na alignment has been studied in relation to maser research (Brossel et al 1952, Hawkins 1955).
Range of applicablity: w. L–Larmor frequency R-photon arrival rate A-Einstein coefficient Na. I NV Al. III HI NI OII 5892 1239 1855 912 - 865 - 83 5898 1243 1863 1216 1201 4 OI Cr. II CII OIV 911 - 2060 1336 790 CI OII I 1115 83 Examples of alignable species (Yan & Lazarian 2005)
Role of magnetic field z atoms M=2 M=1 Angular momentum radiation Magnetic field causes precession of atoms and therefore changes the alignment of atoms caused by radiation. M=0 M=-1 M=-2 B F q
Quantum Electrodynamics calculations Main object: density tensor: rkq r 2: dipole moment r 4: quardripole moment They can be obtained from statistical equilibrium equation of the upper state and ground state of an atom.
Quantum Electrodynamics calculations (Cont. )
Theoretical and observational frame (B) Left: Radiation geometry and the polarization vectors; Right: Transformation from observational frame to theoretical frame by two successive rotations specified by Euler angles (f. B, b)
r 2, 4 Differential population of ground state qr qr The density tensor components r 2, 4 of ground state of Cr II line 6 S 5/2 6 P 7/2; left: without multiplet effect, only the transition between the two levels are counted; right: with multiplet effect.
Polarization of emission lines q: polar angle f: azimuthal angle p qr fr 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 q=90 o and f=0 o.
Application: magnetic fields in the wake of a comet (a) (b) v E 1 (a) Resonance scattering of solar light by sodium tail from comet; (c) (b) MHD simulations of comet’s wake; (c) Polarization caused by sodium aligned in the comet wake. y (r )
In comparison with dust alignment: • 3 D information of magnetic field can be obtained from atomic alignment. • Provide independent test to grain alignment theory. • Sensitive to smaller scale fluctuations.
Summary of the most important results for Ph. D work Cosmic ray transport • 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. Dust dynamics • 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. Magnetic field study • Atomic alignment is identified as a new tool to study 3 D geometry of interstellar and circumstellar magnetic fields.
- Slides: 40