Making Large Scale Magnetic Fields Steve Cowley UK Atomic Energy Authority and Imperial College

For Russell at 85

Why bother? Russell Kulsrud Academic Genealogy Jeremiah Ostriker Bengt Strongren Subrahmanyan Chandrasekhar Arthur Stanley EddingtonRalph Fowler Isaac Newton?

Why bother? Russell Kulsrud Begat 1965 Thomas J. Birmingham (w/J. Dawson) 1970 Robert L. Dewar 1971 Catherine Cesarsky (not 1 st advisor) 1974 Russell S. Johnston 1975 Scott Tremaine (not 1 st advisor) 1977 Ellen Zweibel (not 1 st advisor) 1978 Edward Allen Adler Adilnawaz B.S. Hassam 1982 Carl Goran Schultz 1985 Steven C. Cowley Darwin D.-M. Ho 1986 Carl Richard DeVore 1991 Steven W, Anderson 1995 Armando Howard 1996 Victoria Dormand 1997 Benjamin D.G. Chandran 1998 Dmitri A. Uzdensky 2000 Gianmarco Felice 2001 Alexander Schekochihin 2001 Leonid Malyshkin 2001 Troy Carter 2010 Yansong Wang Amitava Bhattacharjee Chris Hegna Eric Held John James SIX GENERATIONS!

When was the first significant field? Before, during or after structure? Top down or bottom up? Is field made/amplified at small scale then “cascaded” to large scale or does it just grow at large scale? Is the seed relevant? Does subsequent amplification and processing by turbulence wash out any relic? SKA -- Understanding cosmic magnetism Magnetogenesis. On the Origin of Cosmic Magnetic Fields Russell Kulsrud and Ellen Zweibel Reports on Progress in Physics, Volume 71, Issue 4, pp (2008).

“The author will attempt to describe one of the more important of these plasma-astrophysical problems, and discuss why its resolution is so important to astrophysics. This significant example is fast, magnetic reconnection. Another significant example is the large-magnetic-Reynolds number magnetohydrodynamics (MHD) dynamo.” Kulsrud 1994 Maxwell prize address Both problems are unfinished. Maxwell Prize.

M51 Spiral galaxy M 51 with magnetic field data. Credit: MPIfR Bonn Rosse’s M51 Sketch in 1845

Cluster Turbulence The Coma Cluster: pressure map [Schuecker et al. 2004, A&A 426, 387] L ~ 10 2 …10 3 kpc U ~ 10 2 …10 3 km/s (subsonic) L/U ~ 10 8 …10 9 yr Mergers AGNs Wakes

Cluster MHD Turbulence Turbulence scale is around here TURBULENCE Coma cluster [Schuecker et al. 2004, A&A 426, 387] MAGNETIC FIELDS Hydra A Cluster [Vogt & Enßlin 2005, A&A 434, 67] Magnetic Reynolds #, Rm ~ Magnetic Reynolds #, Rm ~

Many Questions 1.Seed Field: making the first field.. Particle physics, Weibel instability, stars. -- typical assumption SEED few times gauss 2.How fast can field be amplified -- just magnetic energy. Small-scale-dynamo. SSD -- mean -- structured flow – what structure? Helicity, sheared flow,..? 2.What is the structure of the Saturated field ? few times gauss -- folds, plasmoids, Alfven waves, -- 2 / 3.Universality – do the transport properties of the medium matter. -- P M the magnetic Prandtl number (viscosity/resistivity) -- plasma versus rock, neutrals, cosmic rays -- 4.Instability: -- Providing the stirring flow – MRI, convection etc. Large scale? -- Small scale instability – plasma instability – firehose, mirror, heat flow etc.

Cluster Turbulence Scales and Times forcing 1/L 102 kpc k ~ Re 3/4 /L 10 kpc 1/ mfp ~ Re/LM 1…10 kpc M=U/v thi Mach No. Viscous Turnover time 1/  0 ~ Re –1/2 L/U ~ 10 7 …10 8 yr Kinetic energy k-5/3 kk  ~ Pm 1/2 k ~1000 km [Schekochihin et al., ApJ 612, 276 (2004)] Turnover time L/U ~ 10 9 yr TOO SLOW MAGNETO-FLUID PHYSICS | PLASMA PHYSICS

ICM is Magnetised forcing 1/Lk 1/ mfp Turnover time 1/  0 ~ Re –1/2 L/U ~ 10 7 …10 8 yr Magnetic energy Kinetic energy k -5/3 kkk l SSD Smaller is quicker Seed could be small scale, Stars: Rees Plasma Instabilities; Medvedev

ICM is Magnetised forcing 1/Lk 1/ mfp Turnover time 1/  0 ~ Re –1/2 L/U ~ 10 7 …10 8 yr Magnetic energy Kinetic energy k -5/3 kkk SSD k 3/2 Batchellor 1950 Saffman 1963 Kazantsev 1968 Menaguzzi and Poquet 1963 Chandran 1997, Schekochihin …… Kulsrud and Anderson 1992 Homogeneous dynamo

Bending and Stretching. Weak B Strong B BendStretch Compress Curvature and |B| anti-correlated.

Amplification without generating smaller scales. BendStretch Compress Compress in the direction along which B doesn’t change. Only some of the random motions do this.

Folded Structure Visualised [see Schekochihin et al. 2004, ApJ 612, 276; Schekochihin & Cowley, astro-ph/ for an account of theory and simulations] Fold thickness is resistive scale k  ~ k  Fold length is size of stretching eddy k || ~ k.

Intermediate Nonlinear Growth forcing k -5/3 k0k0 Kinetic energy kks(t)ks(t) Define stretching scale l s (t) : [Schekochihin et al. 2002, NJP 4, 84] k  ~ Pm 1/2 k k ~ Re 3/4 k 0

Saturation forcing k0k0 k  ~ Re –1/2 k 0 k ~ Re 3/4 k 0 Kinetic energy k Magnetic energy saturates 10 9 years Nonlinear growth/selective decay/fold elongation continue until l s ~ l 0  B 2  ~  u 2  and l  ~ Rm –1/2 l 0 [Schekochihin et al. 2002, NJP 4, 84] ? How do we destroy the small scale field? Unwinding?

Current Sheets Go Unstable? [Alexey Iskakov] |u||u||B||B| Pm = 50, Re ~ 300 Reconnection of folds Alfven waves forming cascade? Goldreich-Sridhar

Unwinding – what is the viscosity in the field? Plasma Turbulence: 1995 Santa Barbara Conservation of adiabatic invariant If the motion is magnetized (when larmor Radius is smaller than turbulent scale): Even at low field – if we double field we double perpendicular energy.

Magnetized Viscosity --Anisotropic Pressure Anisotropic pressure tensor in magnetized plasma. Because of fast motion around the field the tensor must be of the form: DEFINITION OF PRESSURE TENSOR. Chew, Goldberger and Low 1956 – Kulsrud 1963 Varenna notes.

Magnetized Viscosity. B Collisionless particle motion restricted to being close to field line and conserving . Compressing Field Collisionless. Relaxed by Collisions. P

Collisionless Micro-Instability. What does it do to the macroscopic behaviour.

Firehose. Parallel pressure forces squeeze tube out. Rosenbluth 1956 Southwood and Kivelson 1993 P || Tighter bend grows faster. Unstable when Growth rate at negligible B VERY FAST

Marginal Instability 0.1

MORE COLLISIONS? – mode scatters particles. effective collision rate FOLD FIELD TO ENFORCE HOW DO WE ENFORCE MARGINAL INSTABILITY? Sharma, Hammett and Quataert 2006 Schekochihin and Cowley 2006 Reduces viscosity – creates smaller velocity scales Schekochihin,Cowley, Kulsrud, Rosin, Heineman PRL 2006

MORE COLLISIONS? – mode scatters particles. effective collision rate FOLD FIELD TO ENFORCE Explosive Growth Sharma, Hammett and Quataert 2006 Schekochihin and Cowley 2006

So where are we? There is time for plenty of field growth. The seed field is probably not visible in the data. I still don’t understand how the field structure forms – and what it is. Russell we aren’t finished