Making Large Scale Magnetic Fields Steve Cowley UK

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

For Russell at 85

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

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 De. Vore 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 Why bother? Russell Kulsrud Amitava Bhattacharjee Chris Hegna Eric Held John James SIX GENERATIONS!

Magnetogenesis. On the Origin of Cosmic Magnetic Fields Russell Kulsrud and Ellen Zweibel Reports on Progress in Physics, Volume 71, Issue 4, pp. 046901 (2008). • 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

Maxwell Prize. • “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.

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

Cluster Turbulence • Mergers • AGNs • Wakes L ~ 102… 103 kpc U ~ 102… 103 km/s (subsonic) L/U ~ 108… 109 yr The Coma Cluster: pressure map [Schuecker et al. 2004, A&A 426, 387]

Cluster MHD Turbulence TURBULENCE Coma cluster [Schuecker et al. 2004, A&A 426, 387] • Magnetic Reynolds #, Rm ~ 1029. MAGNETIC FIELDS Hydra A Cluster [Vogt & Enßlin 2005, A&A 434, 67] Turbulence scale is around here

Many Questions 1. Seed Field: making the first field. . Particle physics, Weibel instability, stars. -- typical assumption SEED few times 10 -10 gauss 2. How fast can field be amplified -- <B 2> just magnetic energy. Small-scale-dynamo. SSD -- mean <B> -- structured flow – what structure? Helicity, sheared flow, . . ? 2. What is the structure of the Saturated field? few times 10 -6 gauss -- folds, plasmoids, Alfven waves, -- <B>2/<B 2> • Universality – do the transport properties of the medium matter. -- PM the magnetic Prandtl number (viscosity/resistivity) -- plasma versus rock, neutrals, cosmic rays -- 2. 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 Kinetic energy k-5/3 Viscous Turnover time 1/ 0 ~ Re– 1/2 L/U ~ 107… 108 yr forcing MAGNETO-FLUID PHYSICS | PLASMA PHYSICS 1/L 102 kpc k ~ Re 3/4/L 10 kpc Turnover time L/U ~ 109 yr TOO SLOW 1/ mfp ~ Re/LM 1… 10 kpc M=U/vthi Mach No. [Schekochihin et al. , Ap. J 612, 276 (2004)] k ~ Pm 1/2 k ~1000 km k

ICM is Magnetised Kinetic energy k-5/3 Turnover time 1/ 0 ~ Re– 1/2 L/U ~ 107… 108 yr SSD forcing 1/L Magnetic energy k 1/ mfp k l k Smaller is quicker Seed could be small scale, Stars: Rees Plasma Instabilities; Medvedev

ICM is Magnetised Kinetic energy k-5/3 Turnover time 1/ 0 ~ Re– 1/2 L/U ~ 107… 108 yr k 3/2 forcing 1/L k Kulsrud and Anderson 1992 SSD Magnetic energy 1/ mfp Batchellor 1950 Saffman 1963 Homogeneous dynamo Kazantsev 1968 Menaguzzi and Poquet 1963 Chandran 1997, Schekochihin …… k k

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

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

Folded Structure Visualised [see Schekochihin et al. 2004, Ap. J 612, 276; Schekochihin & Cowley, astro-ph/0507686 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 Kinetic energy k-5/3 forcing k 0 ks(t) k ~ Re 3/4 k 0 k ~ Pm 1/2 k Define stretching scale ls(t) : [Schekochihin et al. 2002, NJP 4, 84] k

Saturation Kinetic energy ? Magnetic energy saturates 109 years How do we destroy the small scale field? Unwinding? forcing k 0 k ~ Re 3/4 k 0 k ~ Re– 1/2 k 0 Nonlinear growth/selective decay/fold elongation continue until ls ~ l 0 B 2 ~ u 2 and l ~ Rm– 1/2 l 0 [Schekochihin et al. 2002, NJP 4, 84] k

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

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

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

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

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

Marginal Instability 0. 1

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

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

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