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?

3

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

5

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

6

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

20

20 / HHH tktks

M. Christensson, M. Hindmarsh, A. Brandenburg: 2005, AN 326, 393M. Christensson, M. Hindmarsh, A. Brandenburg: 2005, AN 326, 393

7

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

10

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:

11

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

13

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

14

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

16

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)

17

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)

19

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)