Magnetic dynamo over different Magnetic dynamo over different astrophysical scalesastrophysical scales

Axel Brandenburg & Fabio Del Sordo (Nordita)with contributions from many others

seedfield

primordial (decay)

diagnostic interest (CMB)

AGN outflows MRI driven SS dynamo

galacticLS dynamo

helicity losses

2

Early-Universe B-field may have Early-Universe B-field may have been helical: 3-D decay simulationsbeen helical: 3-D decay simulations

Initial slope E~k4

Christensson et al.(2001, PRE 64, 056405)

helical vsnonhelical

cosmological scale: ~3 cm

3

Proposed helical decay lawProposed helical decay law

HkH H22

sI tHE 22/1/||

H not exactly constant

rHH ttkk 00 /Assume power law, not const

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

4

Many astrophysical sources of Many astrophysical sources of turbulence are potentialturbulence are potential

No dynamo action in nearly potential flows (at least not so far)

and t are also small

Examples: EW phase transition bubbles, SN explosions

f

5

Nearly potential flowsNearly potential flows

ln22

2

Sωωuω

BBuB

t

t

neither nor B is produced, unless …M

ee & B

randenburg (2006, MN

RA

S 370, 415)

6

Baroclinic and battery termsBaroclinic and battery terms

G10 s10

/

1/

19115

p

22

22

B

me

pt

pt

Bω

ωωuω

ωωuω

B

BBB

pp 21Analogy between and B eqns

even with baroclinicity

Kulsrud et al. (1996) relevance to oblique cosmological shocks

degreeof ionisation

7

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

8

To maintain equipartition-strength fieldsTo maintain equipartition-strength fields need dynamos: need dynamos: small-scale vs large-scalesmall-scale vs large-scale

B-scale larger than U-scale

B-scale smaller than U-scale

Wavenumber=1/scale

energy

injectionscale

9

Small-scale vs large-scale dynamoSmall-scale vs large-scale dynamo

10

Growth rate, applied to galaxyGrowth rate, applied to galaxy

=2x10-9 yr-1

urms=10 km/skf=2/70 pc=0.1 pc-1

urmskf=10-6 s-1

Re=109

=3x10-2 yr-1 (very fast)

)dynamo (

)dynamo ( 2

22

k

kk

t

t

Amplication factors: exp(t)=104 for 5 Gr

11

Kick-start the GBF with strong BKick-start the GBF with strong B

Forced turbulence with shearand strong initial field at k=6

12

Weaker initial fieldWeaker initial field

Kazantsev slope,exponential growth

13

Reach full saturation: need helicity fluxesReach full saturation: need helicity fluxes evidence from different simulations evidence from different simulations

Convective dynamo in a boxwith shear and rotation

Käpylä, Korpi, Brandenburg(2008, A&A 491, 353)

Only weak field if box is closed

Forced turbulence in domain with solar-like shear

Brandenburg (2005, ApJ 625, 539)

3-D simulations, no mean-field modeling

14

Saturation phase: here for convectionSaturation phase: here for convection

Käpylä et al (2008,A&A 491, 353)

with rotation without rotation

15

It can take some time…It can take some time…

1

f

rms1t

1

ff

12

31

31

1t

k

k

u

U

k

UC

k

k

kkC

CCD

u

uω

Rm

=121, B

y , 5123

LS dynamo not always excited

16

ConclusionConclusion

70 pc 10 pc

factor 500

slope 3/2

factor10,000