Mikhail Medvedev (KU) Marc Kamionkowski (Caltech) Luis Silva (IST, Portugal) Z-90, IKI, Moscow, Russia December 21, 2004 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 Faraday rotation (Ensslin et al 2003) (Vogt, Ensslin 2003) Faraday rotation maps (Taylor et al 2002)(Ensslin, Vogt, Pfrommer, 2003) Hydra A PKS Cold fronts (Vikhlinin, Markevich, Murray, ApJL, 2000) B ~ 10 microgauss Cluster shocks X-rays T Surface brightness + shock model (Markevich et al 2002) Detection of synchrotron emission from shocks is not 100% solid yet 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 B 0 V(x) Sheared flow stretches the field lines amplification of the field no magnetic flux is generated saturation B sat,gal ~ gauss Kolmogorov turb. In brief Biermann battery B~ Needs: T Harrison effect B~ 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~ (many e-foldings over cluster lifetime) Other: inflation, strings, textures, phase transitions, ? Lets go back The first principles approach Cosmological shocks (Kang, et al, ApJ, 2003) 3D cosmological simulations: hydrodynamic gas + dark matter Inter- and Intra-cluster shocks Conditions at a shock Anisotropic distribution of particles (counter-propagating streams) at the shock front p e-e- shock IGM vv v || 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 Cold fronts (Nagai, Kravtsov 2003) X-rays T Chandra would see it as 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 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! 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) How are the fields produced at shocks? The mechanism of the instability Two-stream (Weibel) instability x y z J J current filamentation B e v x B B - field produced c pp ~ cm (v/c) pp ~ 10 3 n -1/2 -4 sec (Medvedev & Loeb, 1999, ApJ) Produced magnetic field: * sub-equipartition * small-scale ( B || (Silva, et al., 2003) 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) How long will the produced fields live? The long-term dynamics of the instability Fields must populate cosmologically large volumes 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 Simulations Electron-positron simulations Electron-proton simulations m p /m e = 1860 B-field E-field B-field E-field Evolution of B Electron-positron simulations Electron-proton simulations m p /m e = 1860 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 Field dissipation Diffusive dissipation: Field scaling: Solution: Log B Log t 1/2 no dissipation =0 diffusion Weibel fields, ~0.8 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 =-1 Particle acceleration. ICM Power-law segment with index ~ 2.2 continuously expands (Silva, et al., 2003) Initial particle distribution 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 4 ) that is B ICM ~ 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 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