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Galactic Dynamos and ISM Turbulence.

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.

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Galactic Dynamos and ISM Turbulence.

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  1. 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

  2. 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 don’t solve everything. • ISM turbulence issues. Experiments? Theory.

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

  4. L » 4 ´ 10 20 m G t » 2 ´ 10 8 years l » 3 ´ 10 18 m G 0 t » 10 7 years 0 Theorist’s Milky Way Vertical Field in Center B ~1mG Horizontal Field in Disc B ~ 3G V V Scale Rotation time Supernova explosion. Scale Eddy turnover time

  5. 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. • It is believed to be evidence of an MHD turbulent cascade. Goldreich, Shridhar, Maron, Vishniac, Lithwick, Lazarian,Boldyrev, ……. Etc.

  6. w R ( w + d w ) R Galactic Dynamo -- The Usual Mechanism - Almost Parker 1956 Coriolis Twist

  7. ( w + d w ) The Usual Mechanism - Almost Parker 1956 Rotation Rate w Rotation Rate

  8. 5 t = 10 years  Velocity Spectrum -- with no Bfield Kolmogorov 1941. 2 V 14 l 5 10 m ´ = k  Viscous scale - 5 / 3 k Viscous eddy Turnover. Helical part of spectrum Smaller eddies turnover faster. k 1 1 1 L l l G 0 

  9. The Large Prandtl Number Case: Galaxies, Clusters etc. • Magnetic Prandtl number = Pr =  = 1012 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 l l 

  10. Stage 1. Small Scale Dynamo æ k 5 (ln k ) 3 g t ö 3 / 2 2 ç 2 B ( k , t ) = exp - + 2 V è ø 1 / 2 t 4 g t 4 k Resistive scale Is very small- 6 l » 10 m R 1 1 1 1 L l l l G 0 D R

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

  12. Energy spectra Simulation and Theory

  13. 2 V k 2 B 1 1 1 1 L l l l G 0 D R Stage 2. The First Inverse Cascade? Perhaps an approach to equipartition? I like to think of untangling the small scales and building the large scale field. k

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

  15. Folded Field saturated state.

  16. 2 V k 2 B 1 1 1 1 L l l l G 0 D R Stage 3. The Inverse Cascade?

  17. w R ( w + d w ) R Helicity Will Save Us? Coriolis Twist

  18. Helicity Will Save Us?

  19. Can the Helical Dynamo work when <B2> = <v2> 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 old assumption was that the homogeneous turbulence acts like a turbulent resistivity on <B> and <B2>. It doesn’t 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. • This is a significant question. I expect the dynamo to be suppressed but ??

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

  21. Sodium experiments? • Pr<1 small scale dynamo may not exist -- see Schekochihin submitted to PRL (see XXX). For sodium Pr ≈ 10-4. • Only the helical dynamo. • Relevant for the sun and geodynamo. • Could try to increase sodium viscosity to reduce Re. (temperature control fillings etc.)

  22. Plasma Pr>1 Dynamo experiments? • Is the RFP dynamo relevant -- perhaps it is for sustainment. • It would be nice to have a flow driven plasma dynamo experiment. • I don’t have a clue how to do that.

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