1. Mikhail Medvedev (KU) Marc Kamionkowski (Caltech) Luis Silva (IST, Portugal) Z-90, IKI, Moscow, Russia December 21, 2004

2. The fact : Magnetic fields in clusters do exist (but only upper limits on fields in IGM)  Faraday rotation  Synchrotron emission  radio halos  relic radio sources  radio emission from shocks Direct evidence Indirect evidence  Long life-time of sharp temperature gradients  cold fronts  temperature inhomogeneity

3. Faraday rotation (Ensslin et al 2003) (Vogt, Ensslin 2003)

4. Faraday rotation maps (Taylor et al 2002)(Ensslin, Vogt, Pfrommer, 2003) Hydra A PKS1246-410

5. Cold fronts (Vikhlinin, Markevich, Murray, ApJL, 2000) B ~ 10 microgauss

6. Cluster shocks X-rays T Surface brightness + shock model (Markevich et al 2002) Detection of synchrotron emission from shocks is not 100% solid yet

7. How do the fields get there? primordialproduced in citu Fields are advected with accreting gas from the inter-cluster medium and amplified by compression  Battery  Radiation pressure  Early universe Fields are generated inside a cluster a fast process. Needs energy source:  Shocks  Turbulence  Temperature gradient  AGNs Typically B 2 < nT by ~2 orders of magnitude Fine tuning (why “<“ ?), “magnetically arrested flow” Natural: energy conservation, “equipartition”

8. Incomplete list of models   Biermann battery (Biermann ’50)   Harrison mechanism (Harrison ’70)    dynamo [stretch-twist-fold] (Parker ’71)  galactic dynamo [  -dynamo] (Lesch, et al ’88)  QCD phase transition (Quashnock, Loeb, Spergel ’89)   turbulent amplification [kinetic dynamo] (Kulsrud, Andersom ’92)  seed fields from inflation (Ratra ’92)  string cosmology (Gasperini, Giovannini, Veneziano, 95)  first order phase transitions (Sigl, Olinto, Jedamzik ’97)  cosmological models with textures (Sicotte ’97)  supernova explosions [B.batt. + shocks] (Miranda, Opher, Opher ’98)  gravitomagnetic plasma battery [B.batt. + Kerr BH] (Khanna ’98)  reionization [Biermann batt.] (Gnedin, Ferrara, Zweibel ’00)  quasar outflows (Firlanetto,Loeb ’01)  primordial helical seeds (Sigl ’02)   two-stream instability at shocks (Medvedev, Silva, Kamionkowski, in prep.)

9. Biermann battery Induction equation + Ohm’s law with pressure gradient  T T  n n electron average transport (-current)

10. Reionization Two scenarios: nHnH B z=4 n T (Gnedin, et al 2000)

11. Harrison mechanism Spherical region of radius r uniformly rotating and expanding matter:  r 3 = const  r 5 = const   r 4 = const     r 5 = const radiation: … particle density … … angular momentum … Radiation dominated universe: Thompson scattering couples radiation to electrons, but not protons  protons ~  r -2 and  elecrtons ~    r -1  current

12. Stretch-twist-fold dynamo 4. Reconnect field lines 2J  1. Stretch the loop 2. Twist the loop 3. Fold the loop B JJ

13.  -dynamo advection dissipation (reconnection) dynamo action Angular velocity of a cloud Mean-free-path of turbulent clouds Generation of magnetic flux (Lesch, et al 1988)

14. Turbulent amplification B0B0 B(t)>B 0 V(x) Sheared flow stretches the field lines  amplification of the field  no magnetic flux is generated saturation B sat,gal ~ 10 -5 gauss Kolmogorov turb.

15. In brief… Biermann battery B~10 -18 Needs:  T    Harrison effect B~10 -16 Needs: primordial rotation before recombination Dynamo B~10 -5 (sub-equipartition) Needs: rotation or helical turbulence: (v   v)  0 Turbulent amplification B~10 -5 (sub-equipartition) Problem: field is amplified the most at small scale Needs: seed field of B~10 -12 (many e-foldings over cluster lifetime) Other: inflation, strings, textures, phase transitions,… ?

16. Let’s go back… The first principles approach

17. Cosmological shocks (Kang, et al, ApJ, 2003) 3D cosmological simulations: hydrodynamic gas + dark matter Inter- and Intra-cluster shocks

18. Conditions at a shock Anisotropic distribution of particles (counter-propagating streams) at the shock front p e-e- shock IGM vv v ||

19. … and a precursor Particles with energies >> thermal = cosmic rays CR form a similar counter-stream, but in some extended region in the upstream direction ICM CR

20. Cold fronts (Nagai, Kravtsov 2003) X-rays T Chandra would see it as

21. Conditions at a cold front f=f 0 +  f,  f ~ v   T Constraints:   f  =0 [continuity]  v 2  f  =0 [energy balance]  v  f  =0 [zero current]  v  v 2 f  < 0 [negative heat flux] q ~ -  T  T T (Okabe & Hattori, ApJ, 2003) Anisotropic distribution

22. General remarks  An anisotropic particle distribution is always unstable: “counter-streaming” or Weibel instability  The instability generates magnetic fields, one always need to make sure that there is no a faster instability, which can isotropize particle distribution on a shorter time-scale!

23. General description Anisotropy:   >   characteristic energies (e.g., T) in the directions parallel and perpendicular to the shock propagation direction (or  T) Introduce: plasma frequency anisotropy parameter A=(   -   )/  ~ ( M -1)/( M +1) Growth rate Field scale Field strength  v/c)  p  1/k  c/  p     ~ (   -   )  efficiency (from simulations)

24. How are the fields produced at shocks? The mechanism of the instability

25. Two-stream (Weibel) instability x y z J J … current filamentation … B e v x B … B - field produced …  c   pp ~ 10 10 cm  (v/c)  pp ~ 10 3 n -1/2 -4 sec (Medvedev & Loeb, 1999, ApJ) Produced magnetic field: * sub-equipartition * small-scale (<<Larmor)

26. ISM ejecta  cloud 3D PIC simulations: -electron-positron pairs -relativistic -10 9 particles

27. Astrophysical shocks. Setup u

28. The shock structure (Frederiksen, et al., 2003) Electron currents Proton currents Field spectrum (color) Field amplitude (lines)

29. Evolution of B-field scale B-field scale grows exponentially downstream, where  B ~ constant k ~ t / c (Frederiksen, et al., 2003)

30. Magnetic field generation Steady state is achieved – a shock has been formed BB EE E || B || Linear instability, B ~ exp (  p t) Saturation,  B ~ 0.1 Nonlinear regime,  B ~ constant Field is predominantly transverse,   >> B || (Silva, et al., 2003)

31. Particle “thermalization” Particles are randomized over pitch angle by the produced small-scale magnetic fields => “Thermalization” => Instability quenches forward and reverse shocks (Silva, et al., 2003)

32. How long will the produced fields live? The long-term dynamics of the instability Fields must populate cosmologically large volumes

33. Nonlinear evolution of fields After N ~ few, v=dx/dt ~ c … filament coalescence instability … Magnetic field scale grows linearly,  ~ c t x y z size ~ separation ~ R 0 B 0 = 2I 0 /cR 0, dF = c -1 I 0 dl x B 0 d 2 x/dt 2 ~ I 0 2 / (c 2 mnR 0 2 x) Coalescence: I N ~ I 0 2 N, R N ~ R 0 2 N/2 … 2D gas of filaments … current I 0  N ~ R N /c

34. Simulations… Electron-positron simulations Electron-proton simulations m p /m e = 1860 B-field E-field B-field E-field

35. Evolution of B  Electron-positron simulations Electron-proton simulations m p /m e = 1860

36. The evolution of B Log ( B ) Log(t) e - e + medium e - e + p medium e - p medium B ~ t 0.8 As the spatial scale grows “super-diffusively”, the standard (diffusive) dissipation quenches

37. Field dissipation Diffusive dissipation: Field scaling: Solution: Log B Log t  <1/2 sub-diffusion  =1/2  >1/2 no dissipation  =0 diffusion Weibel fields,  ~0.8

38. An important remark The growth of B is NOT an MHD inverse cascade! It is a deeply KINETIC regime,  Larmor  B At (much) later times, when  Larmor << B, the field turbulent evolution is described by the standard MHD INVERSE CASCADE.

39. Particle acceleration… Preliminary results

40. Parallel momentum. Ejecta Forward shock  Reverse shock  (Silva, et al., 2003)

41. Parallel momentum. ICM (Silva, et al., 2003)

42. Particle acceleration. Ejecta Particle distribution evolves with time: low-energy slope (Silva, et al., 2003) Initial particle distribution p~-7 p~-4 p~-2  =-(p+1)/2    p>=-1

43. Particle acceleration. ICM Power-law segment with index ~ 2.2 continuously expands (Silva, et al., 2003) Initial particle distribution

44. Magnetic field at shocks  Magnetic field is generated at shocks  No decay on a time-scale much larger than  p  Can populate a large volume downstream  Field strength:  Sub-equpartition,    thermal x (efficiency ~ 10 -3 … 10 –4 ) that is B ICM ~ 10 -7...-8 gauss  Field geometry:  Random, but mostly in the plane of a shock  “Inverse cascades” from the sub-Larmor scale  Provides pitch angle scattering  effective collisions  MHD can be used in the shock dynamics studies

45. Schlickeiser & Shukla, 2003 Their analysis indicates that the instability operates when u > v th,e, where the thermal velocities [e.g., that of the electrons, v th,e ] are referred to the post-shock plasma. Since v th,e ~ (m p /m e ) 1/2 c s, they obtain the condition, M = (u/c s ) > (m p /m e ) 1/2 ~ 43 However, in the derivation, they assume This is a BAD approximation for the post-shock plasma, because Coulomb collisions are too rare and cannot equilibrate the temperatures at the shock, >> shock thickness Correct condition is: v th,e ~ v th,p. Re-doing the analysis, we get M > 1