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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