Galactic Dynamos and ISM Galactic Dynamos and ISM Turbulence. Turbulence. Steve Cowley,UCLA/ Imperial Steve Cowley,UCLA/ Imperial College College Alex Schekochihin, Imperial Alex Schekochihin, Imperial Jim McWilliams, UCLA Jim McWilliams, UCLA Greg Hammett, Princeton Greg Hammett, Princeton Greg Howes, UCLA/Imperial Greg Howes, UCLA/Imperial Russell Kulsrud, Princeton Russell Kulsrud, Princeton Ben Chandran, Univ. Iowa Ben Chandran, Univ. Iowa Jason Maron, Iowa/Rochester Jason Maron, Iowa/Rochester Sam Taylor, Imperial Sam Taylor, Imperial
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Galactic Dynamos and ISM Turbulence. Steve Cowley,UCLA/ Imperial College Alex Schekochihin, Imperial Jim McWilliams, UCLA Greg Hammett, Princeton Greg.
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Galactic Dynamos and ISM Galactic Dynamos and ISM Turbulence.Turbulence.
• Galactic Dynamos; can they work? What can we Galactic Dynamos; can they work? What can we do to improve our knowledge of this kind of do to improve our knowledge of this kind of dynamo? Experiments? Theory? dynamo? Experiments? Theory? Can we Can we understand anything if we don’t solve everything.understand anything if we don’t solve everything.
• ISM turbulence issues. Experiments? Theory.ISM turbulence issues. Experiments? Theory.
Field in M51.Field in M51.
Polarization of 6cm emission. Indicates direction of B field.
Large scale coherentField.
Beck 2000
Theorist’s Milky WayTheorist’s Milky WayVertical Field in Center B ~1mG
Horizontal Field in Disc B ~ 3G
Supernova explosion.Supernova explosion.
ScaleScaleEddy turnover timeEddy turnover time
ScaleScaleRotation timeRotation time
V
GG 221010 88 yearsyearsLLGG 44 1010 2020 mm
001010 77 yearsyears
ll003310101818 mm
V
Observed Density Fluctuations -- Observed Density Fluctuations -- Small Scale Turbulence.Small Scale Turbulence.
• A spectrum of density fluctuations is A spectrum of density fluctuations is inferred from various radio scattering inferred from various radio scattering observations. It has the classic kobservations. It has the classic k-5/3-5/3 spectrum from above the mean free path to spectrum from above the mean free path to gyro-radius scales. This is more than a gyro-radius scales. This is more than a whole talk in itself.whole talk in itself.
• It is believed to be evidence of an MHD It is believed to be evidence of an MHD turbulent cascade. turbulent cascade. Goldreich, Shridhar, Maron, Vishniac, Goldreich, Shridhar, Maron, Vishniac, Lithwick, Lazarian,Boldyrev, ……. Etc.Lithwick, Lazarian,Boldyrev, ……. Etc.
Galactic Dynamo -- The Usual Galactic Dynamo -- The Usual Mechanism - AlmostMechanism - Almost
Velocity Spectrum -- with no BVelocity Spectrum -- with no B fieldfield
k
Vk
2
l 51014
m
Viscous scale 10
5years
Viscous eddy Turnover.
Smaller eddies turnover faster.
k5/ 3
Helical part of spectrum
1
LG
1l0
1l
Kolmogorov 1941.
The Large Prandtl Number Case: Galaxies, The Large Prandtl Number Case: Galaxies, Clusters etc.Clusters etc.
• Magnetic Prandtl numberMagnetic Prandtl number = Pr = = Pr = = 10 = 1012 12 in in the ISM. the ISM. THIS IS VERY DIFFERENT FROM THIS IS VERY DIFFERENT FROM THE SUN AND EARTH WHERE Pr << 1.THE SUN AND EARTH WHERE Pr << 1.
• On the turnover time of the viscous eddies the On the turnover time of the viscous eddies the “seed field” grows. The field develops structure “seed field” grows. The field develops structure below the viscous scale down to the resistive scale below the viscous scale down to the resistive scale ll= Pr = Pr -1/2 -1/2 ll
l
Stage 1. Small Scale DynamoStage 1. Small Scale Dynamo
Vk
2
1
LG
1l0
1lD
1
lR
Resistive scaleIs very small-
lR 106m
BB(( kk,, tt )) 22 kk 33 // 22
tt11 // 22 expexp 55(ln(ln kk ))22
44tt
33tt
44
Large Pr Dynamo: Numerical.Large Pr Dynamo: Numerical.Schekochihin, SCC, McWilliams, Maron.
Energy spectra Simulation and TheoryEnergy spectra Simulation and Theory
Stage 2. The First Inverse Cascade?Stage 2. The First Inverse Cascade?
Vk
2
kB2 Perhaps an approach
to equipartition? I like tothink of untangling the small scales and building the large scale field.
1
LG
1l0
1lD
1
lR
No Numerical evidence for No Numerical evidence for equipartition. No Goldrich-Sridhar.equipartition. No Goldrich-Sridhar.
Stirring scalestill folding Field lines.
Alfven waveson folded field lines?
Folded fieldlines - smallscale energy.
Folded Field saturated state.Folded Field saturated state.
Stage 3. The Inverse Cascade?Stage 3. The Inverse Cascade?
1
LG
1l0
1lD
1
lR
Vk
2
B2
Helicity Will Save Us?Helicity Will Save Us?
Coriolis Twist
RR
(( )) RR
Helicity Will Save Us?Helicity Will Save Us?
Can the Helical Dynamo work when Can the Helical Dynamo work when <B<B22> = <v> = <v22> and Helicity is small?> and Helicity is small?
• One assumption is yes -- it is common to use the One assumption is yes -- it is common to use the -- dynamo equations for the disk even though there is no dynamo equations for the disk even though there is no kinematic regime for the helical galactic dynamo.kinematic regime for the helical galactic dynamo.
• One old assumption was that the homogeneous turbulence One old assumption was that the homogeneous turbulence acts like a turbulent resistivity on <B> and <Bacts like a turbulent resistivity on <B> and <B22>. It doesn’t >. It doesn’t of course at high Pr.of course at high Pr.
• Jason Maron and Eric Blackman looked at this in a Jason Maron and Eric Blackman looked at this in a homogeneous box and got growth -- the resolution was homogeneous box and got growth -- the resolution was unavoidably low and Pr ≈ 1.unavoidably low and Pr ≈ 1.
• This is a significant question. I expect the dynamo to be This is a significant question. I expect the dynamo to be suppressed but ??suppressed but ??
Better simulations?Better simulations?
• Need geometry -- Greg Howes is doing disc Need geometry -- Greg Howes is doing disc simulations. Buoyancy, shear. Galactic MRI?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 I would be progress just to get the homogeneous
isotropic Pr»1dynamo and steady state field sorted isotropic Pr»1dynamo and steady state field sorted out. (the MHD Kolmogorov problem)out. (the MHD Kolmogorov problem)
Sodium experiments?Sodium experiments?
• Pr<1 small scale dynamo may not exist -- Pr<1 small scale dynamo may not exist -- see Schekochihin submitted to PRL (see see Schekochihin submitted to PRL (see XXX). For sodium Pr ≈ 10XXX). For sodium Pr ≈ 10-4-4..
• 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 Could try to increase sodium viscosity to
reduce Re. (temperature control fillings reduce Re. (temperature control fillings etc.)etc.)
Plasma Pr>1 Dynamo experiments?Plasma Pr>1 Dynamo experiments?
• Is the RFP dynamo relevant -- perhaps it is Is the RFP dynamo relevant -- perhaps it is for sustainment.for sustainment.
• It would be nice to have a flow driven It would be nice to have a flow driven plasma dynamo experiment.plasma dynamo experiment.
• I don’t have a clue how to do that.I don’t have a clue how to do that.