Galactic Dynamos and ISM Turbulence. Steve Cowley,UCLA/ Imperial College Alex Schekochihin, Imperial Jim McWilliams, UCLA Greg Hammett, Princeton Greg Howes, UCLA/Imperial Russell Kulsrud, Princeton Ben Chandran, Univ. Iowa Jason Maron, Iowa/Rochester Sam Taylor, Imperial

Outline Galactic Dynamos; can they work? What can we do to improve our knowledge of this kind of dynamo? Experiments? Theory? Can we understand anything if we dont solve everything.Galactic Dynamos; can they work? What can we do to improve our knowledge of this kind of dynamo? Experiments? Theory? Can we understand anything if we dont solve everything. ISM turbulence issues. Experiments? Theory.ISM turbulence issues. Experiments? Theory.

Field in M51. Polarization of 6cm emission. Indicates direction of B field. Large scale coherent Field. Beck 2000

Theorists Milky Way Vertical Field in Center B ~1mG Horizontal Field in Disc B ~ 3 G Supernova explosion. Scale Eddy turnover time Scale Rotation time VG2108years LG41020m 0107years l031018m V

Observed Density Fluctuations -- Small Scale Turbulence. A spectrum of density fluctuations is inferred from various radio scattering observations. It has the classic k -5/3 spectrum from above the mean free path to gyro-radius scales. This is more than a whole talk in itself.A spectrum of density fluctuations is inferred from various radio scattering observations. It has the classic k -5/3 spectrum from above the mean free path to gyro-radius scales. This is more than a whole talk in itself. It is believed to be evidence of an MHD turbulent cascade. Goldreich, Shridhar, Maron, Vishniac, Lithwick, Lazarian,Boldyrev, ……. Etc.It is believed to be evidence of an MHD turbulent cascade. Goldreich, Shridhar, Maron, Vishniac, Lithwick, Lazarian,Boldyrev, ……. Etc.

Galactic Dynamo -- The Usual Mechanism - Almost Coriolis Twist Parker 1956 R ()R

The Usual Mechanism - Almost Parker 1956 Rotation Rate ()

Velocity Spectrum -- with no B field k V k 2 l m Viscous scale 10 5 years Viscous eddy Turnover. Smaller eddies turnover faster. k 5/3 Helical part of spectrum 1 L G 1 l 0 1 l Kolmogorov 1941.

The Large Prandtl Number Case: Galaxies, Clusters etc. Magnetic Prandtl number = Pr = = in the ISM. THIS IS VERY DIFFERENT FROM THE SUN AND EARTH WHERE Pr << 1.Magnetic Prandtl number = Pr = = in the ISM. THIS IS VERY DIFFERENT FROM THE SUN AND EARTH WHERE Pr << 1. On the turnover time of the viscous eddies the seed field grows. The field develops structure below the viscous scale down to the resistive scale l = Pr -1/2 lOn the turnover time of the viscous eddies the seed field grows. The field develops structure below the viscous scale down to the resistive scale l = Pr -1/2 l l

Stage 1. Small Scale Dynamo V k 2 1 L G 1 l 0 1 l D 1 l R Resistive scale Is very small- l R 10 6 m B(k,t) 2 k 3/2 t 1/2 exp 5(lnk) 2 4t 3t 4

Large Pr Dynamo: Numerical. Schekochihin, SCC, McWilliams, Maron.

Energy spectra Simulation and Theory

Stage 2. The First Inverse Cascade? V k 2 k B 2 Perhaps an approach to equipartition? I like to think of untangling the small scales and building the large scale field. 1 L G 1 l 0 1 l D 1 l R

No Numerical evidence for equipartition. No Goldrich-Sridhar. Stirring scale still folding Field lines. Alfven waves on folded field lines? Folded field lines - small scale energy.

Folded Field saturated state.

Stage 3. The Inverse Cascade? 1 L G 1 l 0 1 l D 1 l R V k 2 B 2

Helicity Will Save Us? Coriolis TwistR ()R

Helicity Will Save Us?

Can the Helical Dynamo work when = and Helicity is small? One assumption is yes -- it is common to use the - dynamo equations for the disk even though there is no kinematic regime for the helical galactic dynamo.One assumption is yes -- it is common to use the - dynamo equations for the disk even though there is no kinematic regime for the helical galactic dynamo. One old assumption was that the homogeneous turbulence acts like a turbulent resistivity on and. It doesnt of course at high Pr.One old assumption was that the homogeneous turbulence acts like a turbulent resistivity on and. It doesnt of course at high Pr. Jason Maron and Eric Blackman looked at this in a homogeneous box and got growth -- the resolution was unavoidably low and Pr 1.Jason Maron and Eric Blackman looked at this in a homogeneous box and got growth -- the resolution was unavoidably low and Pr 1. This is a significant question. I expect the dynamo to be suppressed but ??This is a significant question. I expect the dynamo to be suppressed but ??

Better simulations? Need geometry -- Greg Howes is doing disc simulations. Buoyancy, shear. Galactic MRI?Need geometry -- Greg Howes is doing disc simulations. Buoyancy, shear. Galactic MRI? Extra physics: Ambipolar drift, tensor viscosity.Extra physics: Ambipolar drift, tensor viscosity. Inhomogeneous ISM, clouds etc.Inhomogeneous ISM, clouds etc. RESOLUTION.RESOLUTION. I would be progress just to get the homogeneous isotropic Pr»1dynamo and steady state field sorted out. (the MHD Kolmogorov problem)I would be progress just to get the homogeneous isotropic Pr»1dynamo and steady state field sorted out. (the MHD Kolmogorov problem)

Sodium experiments? Pr<1 small scale dynamo may not exist -- see Schekochihin submitted to PRL (see XXX). For sodium Pr Pr<1 small scale dynamo may not exist -- see Schekochihin submitted to PRL (see XXX). For sodium Pr Only the helical dynamo.Only the helical dynamo. Relevant for the sun and geodynamo.Relevant for the sun and geodynamo. Could try to increase sodium viscosity to reduce Re. (temperature control fillings etc.)Could try to increase sodium viscosity to reduce Re. (temperature control fillings etc.)

Plasma Pr>1 Dynamo experiments? Is the RFP dynamo relevant -- perhaps it is for sustainment.Is the RFP dynamo relevant -- perhaps it is for sustainment. It would be nice to have a flow driven plasma dynamo experiment.It would be nice to have a flow driven plasma dynamo experiment. I dont have a clue how to do that.I dont have a clue how to do that.