Magnetogenesis in Clusters

1
Magneto-genesis in Clusters?

• Alex Schekochihin, Cambridge.
• Steve Cowley, UCLA Imperial.
• Jim McWilliams, UCLA.
• Alexei Iskakov, UCLA.
• Russell Kulsrud, Princeton.
• Greg Hammett, Princeton.
• Prateek Sharma, Princeton.
• Eliot Quataert, Berkeley.
• Bill Dorland, Maryland.
• Ben Chandran, Iowa.
• Jason Maron, AMNH.

M51.
2
Where does the large scale magnetic field in the
universe come from?

• Primordial origin - before structure.
• Fermi 1950
• During structure formation.
• Kulsrud, Schekochihin, SCC.
• Made in galaxies by dynamo ejected
• into IGM.
• Parker.
• Made in discs or stars by dynamo
• ejected in jets.
• Rees, Kronberg,

4 basic possibilities
3
Galaxy Cluster Parameters

• Size l01-3Mpc.
• Turbulent Flow u0?Cs. Perhaps from mergers.
• T1-10 keV.
• n10-2-10-3cm-3.
• l0/u0 109years.
• Reynolds , Re 102 - 103.
• Magnetic Reynolds , Rm 1029.
• B 1 - 10?G.
• Similarity to most proto-galactic plasmas.

APPLICATION OF IDEAS FROM SPACE PLASMAS.
4
Key Question.

• Can magnetic fields be amplified from seed fields
  of lt 10-18G
• by the turbulence in clusters to the size and
  spectrum seen
• in observations?

Subsidiary Questions.
2. What is the small scale structure of the
magnetic field and is this universal in MHD? 3.
How do the collisionless scales affect the
dynamics? 4. How does the field structure affect
the transport properties, Heat transport,
effective viscosity, mixing, etc.?
5
Velocity Spectrum
Kolmogorov 1941.
2
V
Observed Schuecker et. Al. 2004.
k
-
5
/
3
k
Smaller eddies turnover faster.
k
1
l
?
6
Oberved Magnetic Spectrum
Vogt and Emsslin 2003.
2
Seems to cut off at about the mean free path
- ?mfp 1-10kpc. Not at Resistive Scale l?
107cm.
V
k
Bk
-
5
/
3
k
k
1
_
1
??
?mfp
l
?
7
Incompressible MHD.
Viscosity
F a random force
Resistivity
Computations in a box.
8
The Large Prandtl Number Case Galaxies,
Clusters, Hot Discs.

• Magnetic Prandtl number Pr ??? 1026.
• 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
?
9
Large Pr Dynamo Numerical.
Schekochihin, SCC, McWilliams, Maron Ap. J. 2004.
10
Kinematic Stage - Intermittent Folded Structure.
Grayscale is B.
11
Less intermittent, but still Folded saturated
state.
12
Amplification by stretching.
Small box of plasma
We can think of a little bit of the field line
being stretched by the flow. To preserve volume
some other direction must compress making field
lines get closer together. Lines align with
stretching direction.
13
Bending and Stretching.
Bend
Stretch
Curvature and B anti-correlated.
Compress
14
Amplification without generating smaller scales.
Bend
Stretch
Compress in the direction along which B doesnt
change. Only some of the random motions do this.
Compress
15
Saturated Energy Spectra Simulation and Theory

• Fit using same parameters
• for all Pr.
• If Pr becomes very large
• M(k) k0.23.
• Magnetic field small scale
• dominated. DOWN TO
• RESISTIVE SCALE.
• NOT LIKE THE
• OBSERVATIONS.

16
No Numerical evidence for equipartition.
Stirring scale still folding Field lines.
Folded field lines - small scale energy.
Alfven waves on folded field lines?
Mean Field, Alfven waves Maron and Goldreich.
17
Magnetized Viscosity --Anisotropic Pressure
DEFINITION OF PRESSURE TENSOR.
Anisotropic pressure tensor in magnetized plasma.
Because of fast motion around the field the
tensor must be of the form
18
Magnetized Viscosity - Magnetic pumping.
B Bb
Collisionless particle motion restricted to being
close to field line and conserving ?.
In an increasing field v? increases but not v.
Makes P?gtP. Collisions relax this trying to
re-establish isotropy. Thus
Compressing Field
? Is the collision rate. (of ions)
19
Incompressible Braginski MHD.
This viscosity does not damp alfven waves and
therefore allows velocities below the viscous
cutoff. Can these velocities unwind the small
scale field? Kulsrud, Cowley, Gruzinov and
Sudan, 1996. Malyshkin and Kulsrud 2002.
20
Firehose Instability.
Look at instabilities that are smaller scale than
the field and growing faster than the stretching
rate. We take a constant unperturbed stretching
and B0. LINEARIZATION.
For Alfven wave Polarization.
Field still frozen to the plasma.
Unstable if
Parallel pressure forces squeeze tube out.
Rosenbluth 1956 Southwood and Kivelson 1993
P
P
21
Stretching and compressing
Stretched at the turnover rate of the viscous
eddies.
Using Braginskiis Expression we get P-P?
Re-1/2P
Field increasing Plt P? Mirror mode Unstable.
Field decreasing PgtP? Firehose Unstable.
22
More Firehose.
Unstable when B2lt energy in viscous scale eddies
(roughly for Blt5?G). Obviously in early stages
of dynamo. Since
Growth at small scales is very fast.
Collisionless theory gives same growth formula
down to
where
Tighter bend grows faster.
23
Scales
?
EV
EB ?
k
Ion Larmor Radius Scale _at_ B 1?G 105km.
Mean-Free Path. ?mfp l0Re-11-10kpc
Viscous Scale l? l0Re-3/4 10 - 30 kpc
l0 1-3Mpc
Resistive Scale l0Rm-1/2 104km
l0 /u0109 years
l?/ u?108 years
24
Enhanced Scattering.
The effect of the firehose and mirror
instabilities may be to scatter the particles
making an effective mean free path of order ?i
Viscosity decreased vthi ?mfp ? vthi ?i
Large Re.
Has the interesting effect of increasing the
initial field growth because it increases the
eddy turnover rate of the viscous eddies.
Very small scale field
25
What was this talk about? Conclusions?

• Growth of B in clusters is easy. Small scale
  amplification is very rapid.
• Magnetic structure is still not understood.
• Plasma physics issues that are familiar in the
  space context are critical.