1. 27 i 2012AronsFest1 Anisotropic Plasma Astrophysics Roger Blandford Paul Simeon Yajie Yuan KIPAC Stanford

2. 27 i 2012AronsFest2 Describing Cosmic Plasma Fluid description –P, , v, B… –Magneto Fluid Dynamics Flux-freezing, conservation of mass, momentum, energy P ~    isotropic! –Relativistic flows –Electromagnetic Flows Kinetic description –f(p,x,t), E, B… –Collisionless plasmas Vlasov equation for f –Nonthermal distributions –Transport effects –Ultrarelativistic plasmas Need a hybrid approach to tackle contemporary problem

3. Anisotropic MHD MHD commonly developed and computed assuming isotropic pressure Collisionless plasmas are observed and expected to be anisotropic How and when can we discuss this at the fluid level using a pressure tensor? Interesting and possibly different when dominant pressure (and current) is due to ultrarelativistic particles while the flow is locally non-relativistic Dissipation due to radiation not collisions or plasma instabilities Diffusive Shock Acceleration – SNR, clusters… –Pinches - PWN, jets… 27 i 2012AronsFest3

4. 27 i 2012AronsFest4 Particle Acceleration   V ~  I ~ V / Z 0 Z 0 ~100  P ~ V I ~ V 2 /Z 0 Unipolar Induction Stochastic Acceleration U c  E/E ~ +/-u/c ln(E) ~ u/c (Rt) 1/2

5. 27 i 2012AronsFest5 Cahill Dedication, Caltech GeV TeV PeV EeV ZeV Cosmic Rays protons protons?? heavies?

6. 27 i 2012AronsFest6 Cahill Dedication, Caltech GeV TeV PeV EeV ZeV Cosmic Rays solar system active galactic nuclei ?? supernova remnants pulsars?

7. 27 i 2012AronsFest7 Supernova remnants. Chandra Crab Nebula Cassiopeia A X-ray Radio Cosmic rays SN1006 X-ray SN1006 Cas ATycho W44

8. 27 i 2012AronsFest Particle acceleration in SNR ~ 100TeV gamma rays – ~0.3 PeV cosmic rays –Hadronic and leptonic (Fermi) Variable X-rays –100 TeV electrons –~ 1 mG magnetic field Shocks also amplify magnetic field –Details controversial SN1006 Cas A Tycho Perseus Cluster 8

9. Ultra High Energy Cosmic Rays Zevatrons? –Top down exotica GZK cutoff EM channel not seen and hard to avoid –Massive BH in AGN (~30-50 Mpc) AGN may be too weak Acceleration must be remote from BH –Gamma-Ray Bursts Stellar BH or millisecond magnetar? Too distant? Too much radiation? –Cluster Shocks (Norman,Ryu,Bohringer…) High Mach accretion shocks Hard to accelerate p to ZeV energy Heavy elements may be predicted e.g. Fe; range ~ 10 Mpc? Composition controversial Analysis should be aided by LHC 27 i 2012AronsFest9

10. Entropy Matters S gas =1.5 ln[(T/T rec )(n/n rec ) -2/3 ]k (relative to recombination) –Much more in CMB Shocks create gas entropy –  S[M]=1.5ln[(5M 2 /4-1/4)(1/4+3/4M 2 ) 5/3 ]k Before reionization –Weak shocks M ~ 1-3 –  S < k During reionization (z~10) –Ionization entropy –Moderate shocks M ~1-20 –  S <3k After reionization –May need  S as large as 10k –Would imply M~100 e.g. V~1000, s~10 km s -1 27 i 2012AronsFest10 r Simionescu et al Perseus M Recent strong evidence for presence of high M accretion shocks around clusters 16 15 14 13 17 18 S gas /k

11. (100 Mpc/h) 2 2D slice pancake filament Shocks in Structure Formation Simulations LxLx  gas T MsMs 27 i 2012AronsFest11 LCDM simulation with 1024 3 cells, computational box: (100h -1 Mpc) 3, TVD: grid-based Eulerian hydro code (Ryu et al 2003) cluster Simulations exhibit high M shocks

12. GeV  -rays from Clusters of Galaxies Active Galactic Nuclei Primordial cosmic rays Dark Matter Annihilation Upper limits are interesting! Keith Bechtol 27 i 201212AronsFest Han et al 2012

13. UHECR at accretion shocks?? Accretion shocks Invisible v~500-1000 km/s? R ~ 3-10Mpc B ~ 3 x 10 20 V/v R ~10  G! However, SNR generate phenomenal fields OK if UHECR is Fe Counter-evolutionary tendency 27 i 2012AronsFest13 Norman Ryu Bohringer…

14. Collisionless Shocks 27 i 2012AronsFest14 Explain intensity and spectrum of Galactic cosmic rays Scatter off magnetic waves

15. 27 i 2012AronsFest15 Too good to be true! Diffusion: CR create their own magnetic irregularities ahead of shock through instability if >a –Instability likely to become nonlinear - Bohm limit –What happens in practice? –Parallel vs perpendicular diffusion? Cosmic rays are not test particles –Include in Rankine-Hugoniot conditions –u=u(x) –Include magnetic stress too? Acceleration controlled by injection –Cosmic rays are part of the shock What happens when v ~ u? –Relativistic shocks Energy cutoff? –E < euBR ~ PeV for mG magnetic field

16. 27 i 2012AronsFest16 Particle Transport Alfven waves scatter cosmic rays – ~ (B/  B) 2 r L Bohm? –D ~ c /3 Parallel vs perpendicular –L ~ D/u > 100r L ~ 100 E PeV B  G -1 Z -1 pc R SNR < 10pc –Highest energy cosmic rays stream furthest ahead of shock L ~ E ? –“Magnetic Bootstrap” Firehose and other instabilities P(E) /  u 2 GeV TeV PeV 0.1 Shock X X P(E) /  u 2 E E GeV TeV PeV Cosmic Ray Pressure dominates Magnetic and Gas Pressure far ahead of Shock

17. 27 i 201217 Magnetic Bootstrap Assume: –Cosmic rays accelerated by DSA at shock front to ~PeV energy –P CR ~ 0.1  u 2 E 9 -0.2 –Magnetic field amplified upstream > r L –Dynamical effects on background small Wave turbulence maintained at Bohm level mainly by Firehose modes –Also mirror, gyroresonant, Bell-Lucek –Transport by field line modeling –“Uniform” field is turbulent field created by higher energy upstream Cosmic rays with energy ~ E max stream away from the shock –Firehose dominates if u > (a ISM c) 1/2 (P CR /  u 2 ) -1/4 ~1000 km s -1 Fermi observations are instructive! RB Funk 2007 AronsFest

18. 27 i 201218 Magnetic Bootlaces How can a small magnetic pressure mediate the interaction between two particle “fluids”? th CR mag X P X j AronsFest

19. 27 i 2012AronsFest19 Cygnus A 3C31 3C75 Extragalactic Jets Pictor A M87 NGC 326 3C273 PictorA

20. 27 i 2012AronsFest20 McKinney Tschekhoskoy RB 2012

21. Crab Nebula 27 i 2012AronsFest21

22. Flaring behavior 27 i 2012AronsFest22 April 2011 Buehler et al Singular events or power spectrum? No variation seen in other bands Power~10 29 W

23. Spectrum of “Flare” 27 i 2012AronsFest23 Electron synchrotron radiation: E~PeV,  ~10 9 ; B~100nT synchrotron spectrum

24. Where does the variation originate ? Long term variation of nebula likely due to changes in magnetic field Peak power is ~ 3 percent of nebular power Flare energy equals that stared in a region of size L~ 20B -7 1/2 lt d ~ 2B -7 1/2 arcsec We want to learn where and how nature accelerates particles to high energy Not the Pulsar –No correlation with rotation frequency Wind shocks when momentum flux equals nebular pressure Wind, Shock, Jet, Torus are all possibilities 1 lt hr = 3 mas Larmor radius= 60  9 B -7 -1 mas 27 i 201224AronsFest W S J T P =10,000mas

25. Pinch? Resistance in line current –Current carried by high energy particles –Resistance due to radiation reaction –Pairs undergo poloidal gyrations which radiate in all directions –Relativistic drift along direction of current Jet!! –Compose current from orbits self- consistently –Illustration of Poynting’s theorem! –Variation intrinsic due to instability 27 i 2012AronsFest25 j BB r X E

26. MHD with Pressure Tensor 27 i 2012AronsFest26 Linear Perturbations etc Double Adiabatic Ansatz (CGL) First invariant has validity but second is questionable in real plasmas (Kulsrud…). However something like this may be a reasonable approximation for some problems including those of current interest etc

27. 27 i 2012AronsFest27 Friedrich Diagrams V  (  )

28. 27 i 2012AronsFest28 Firehose (and mirror) instabilities

29. Conjectures Relativistic CR ahead of nonrelativistic shock wave behave like a highly anisotropic fluid with an equation of state and this dictates the growth of magnetic field Firehose dominates, resonant, Bell, Weibel… Cosmic ray acceleration kinetics can be solved self-consistently in this background 27 i 2012AronsFest29

30. Particle drifts and current 27 i 2012AronsFest30 Normal approach is to analyze particle orbits and deduce currents Can also start from static equilibrium and understand what is happening Curvature perpendicular magnetization gradient ExB Parallel current contains a part that is magnetization drift Also a part that is resistive – collisional/radiative

31. Conjectures Unipolar inductor potential differences maintained into jets and nebulae Pinches (relatively) stabilized by flow, expansion… Highest energy particles with largest gyro radii carry current and dissipate resistively through radiation Steady and explosive instability generic leading to in situ acceleration and emission 27 i 2012AronsFest31

32. Summary Major challenges to particle acceleration from Crab, blazar flares UHECR… Hybrid – fluid/kinetic problems Currents may be carried by highest energy particles and dissipation can be primarily radiative May be possible to gain insight at fluid level using anisotropic RMHD Drift currents etc can emerge from MHD rather than vice versa Particle trajectories must still be solved in this background 27 i 2012AronsFest32