Post on 04-Jan-2016
Dynamo theory and Dynamo theory and magneto-rotational instabilitymagneto-rotational instability
Axel Brandenburg (Nordita)
seedfield
primordial (decay)
diagnostic interest (CMB)
AGN outflows MRI driven
galacticLS dynamo
helicity losses
2
The primordial alternative:The primordial alternative:Decay of field Decay of field growth of scale growth of scale
• Starting point: EW phase transition t=10-10 s, B=1024 G
• Horizon scale very short: ~ 3 cm
• With cosmological expansion: ~ 1 AU
• Can field grow to larger scales?
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Inverse cascade of magnetic helicityInverse cascade of magnetic helicity
kqp EEE |||||| kqp HHH and
||2 pp HpE ||2 qq HqE Initial components fully helical: and
||||||2|||| qpkkqp HHkHkEHqHp
),max(||||
||||qp
HH
HqHpk
qp
qp
argument due to Frisch et al. (1975)
k is forcedto the left
4
3-D simulations3-D simulations
Initial slope E~k4
Christensson et al.(2001, PRE 64, 056405)
helical vsnonhelical
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Helical decay law:Helical decay law:Biskamp & MBiskamp & Müüller (1999)ller (1999)
constELH
LELU // 2/33 tE d/d
HELEtE //d/d 2/52/3 3/2 tE
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Revised helical decay lawRevised helical decay law
HkH H22
sI tHE 22/1/||
H not exactly constant
rHH ttkk 00 /Assume power law
H follows power law iff r=1/2; thenstH 2
2diff
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20 / HHH tktks
M. Christensson, M. Hindmarsh, A. Brandenburg: 2005, AN 326, 393M. Christensson, M. Hindmarsh, A. Brandenburg: 2005, AN 326, 393
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All length scales scale similarlyAll length scales scale similarlyintegral scalehel. scale|H|/M
M/|C|
HHttR /)( EEttQ /)(
should be s should be ½+2s
stE 22/1 m/25 Rs
ss is correction is correctionfor finite Rfor finite Rmm
s
R Q
1/Rm
seedfield
primordial (decay)
diagnostic interest (CMB)
AGN outflows MRI driven
galacticLS dynamo
helicity losses
weak by comparison
Accretion discsCorona heated by MRIOutflow (+also magn tower)
9
Alfven and slow magnetosonic wavesAlfven and slow magnetosonic wavescoupled to rotation and shearcoupled to rotation and shear
xyzy
xzx
yzxx
xzyx
bquBb
uBb
bBuqu
bBuu
'0
'0
'0
'0
2
2
0222 22A
2A
22A
24 qq
kvAA
Vertical field B0
Dispersion relation
Alfven frequency:
qrr )(
effect ofrotation,
effect ofshear: q
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March 23, 1965: Gemini 3March 23, 1965: Gemini 3Gus Grissom & John Young: docking with Agena space craft
jiii Kr
GM
i
rrrr 3
22K
22A 2 q
232 p
Space craft experiment
MRI (Balbus & Hawley 1991)
Tidal disruption of a starAnalogies:
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Nonlinear shearing sheet simulationsNonlinear shearing sheet simulationsDynamo makes its own turbulence
5123 resolution
divergentspectrum
12
Vertical stratificationVertical stratification
Brandenburg et al. (1996)
const turb ss cHc
HczHc ss )(turb z-dependence of
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Heating near disc boundaryHeating near disc boundary
Turner (2004)
radp
radp
gasp
2
2...J
u
t
Tcv
022 / Bu
weak z-dependence of energy density
0/ BJ where
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Alternative: Magnetisation from quasars?Alternative: Magnetisation from quasars?
10,000 galaxies for 1 Gyr, 1044 erg/s each
G182
tV
cMN
F
FB sw
kin
poyntrms
Similar figure also for outflows from protostellar disc
B. von Rekowski, A. Brandenburg, W. Dobler,B. von Rekowski, A. Brandenburg, W. Dobler,
A. Shukurov, 2003 A. Shukurov, 2003 A&A A&A 398398, , 825-844825-844
Poynting flux
205.0 scM
seedfield
primordial (decay)
diagnostic interest (CMB)
AGN outflows MRI driven
galacticLS dynamo
helicity losses
weak by comparison
Dynamo saturationRm dependent??Helicity losses essential
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Close boxClose box, no shear, no shear: resistively limited saturation: resistively limited saturation
Significant fieldalready after
kinematicgrowth phase
followed byslow resistive
adjustment
0 bjBJ
0 baBA
0221 f
bB kk
021211 f
bB kkBlackman & Brandenburg (2002, ApJ 579, 397)
Brandenburg & SubramanianPhys. Rep. (2005, 417, 1-209)
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Connection with Connection with effect: effect: writhe with writhe with internalinternal twist as by-product twist as by-product
clockwise tilt(right handed)
left handedinternal twist
Yousef & BrandenburgA&A 407, 7 (2003)
031 / bjuω both for thermal/magnetic
buoyancy
Helicity fluxes in the presence of shearHelicity fluxes in the presence of shear
geometryhere relevantto the sun
Mean field withno helicity, e.g.
Mean field:azimuthalaverage
...
JWB t
Rogachevskii & Kleeorin (2003)
UW
kjikji BBu 4 ,C F
Vishniac & Cho (2001, ApJ 550, 752)Subramanian & Brandenburg (2004, PRL 93, 20500)
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ConclusionsConclusions
• Primordial: B2~t-1/2 (if fully helical), not B2~t-2/3 • Outflows: via MRI-heated corona• Dynamo: j.b saturation
– even for WxJ effect– (only shear, no stratification)
• Helical outflows necessary• Possible for shear flow
1046 Mx2/cycle(for the sun)