Magnetic field generation Magnetic field generation on long time scaleson long time scales

Axel Brandenburg (Nordita/Stockholm)

Kemel+12Kemel+12 Ilonidis+11Ilonidis+11 Brandenburg+11Brandenburg+11Warnecke+11Warnecke+11KKäpylääpylä+12+12

2

White light image ofyesterday

3

Tips of icebergs:Magnetic flux concentrations in magnetogram!

The thin flux tube paradigm

4

Caligari et al. (1995) Charbonneau & Dikpati (1999)

5

Standard dynamo waveStandard dynamo wave

Differential rotation(faster inside) Cyclonic convection;

Buoyant flux tubesEquatorward

migration

New loop

-effect

6

Alternative proposal:Alternative proposal:Conveyor belt modelConveyor belt model

Dikpati et al. (2006)

7

Simulations of the solar dynamo?Simulations of the solar dynamo?

• Tremendous stratification– Not only density, also scale height change

• Near-surface shear layer (NSSL) not resolved• Contours of cylindrical, not spoke-like• (i) Rm dependence (catastrophic quenching)

– Field is bi-helical: to confirm for solar wind

• (ii) Location: bottom of CZ or distributed– Shaped by NSSL (Brandenburg 2005, ApJ 625, 539)– Formation of active regions near surface

Brun, Brown, Browning, Miesch, ToomreBrun, Brown, Browning, Miesch, Toomre

8Brown et al. (2011)ASH code: anelastic

spherical harmonics

9

• Cycle now common!

• Activity from bottom of CZ

• but at high latitudes

Ghizaru, Ghizaru, Charbonneau, Charbonneau,

Racine, …Racine, …

Racine et al. (2011)

PencilPencilcodecode

• Started in Sept. 2001 with Wolfgang Dobler• High order (6th order in space, 3rd order in time)• Cache & memory efficient• MPI, can run PacxMPI (across countries!)• Maintained/developed by ~80 people (SVN)• Automatic validation (over night or any time)• 0.0013 s/pt/step at 10243 , 2048 procs• http://pencil-code.googlecode.com

• Isotropic turbulence– MHD, passive scl, CR

• Stratified layers– Convection, radiation

• Shearing box– MRI, dust, interstellar– Self-gravity

• Sphere embedded in box– Fully convective stars– geodynamo

• Other applications– Chemistry, combustion– Spherical coordinates

11

Dynamo wave from simulations Kap

yla et al (2012)

Type of Type of dynamo?dynamo?

12

• Use phase relation

• Closer to 2 dynamo

• Wrong for dyn.

Mitra et al. (2010)

Oscillatory 2 dynamo

13

Remaining aspectsRemaining aspects

(i) Bi-helical fields inverse cascade

(ii) Solar wind also bi-helical field

(iii) Formation of active regions at solar surface

(i) Dynamo produces bi-helical field(i) Dynamo produces bi-helical field

BAdkkH )(

Magnetic helicity spectrum

031 / bjuω

Pouquet, Frisch, & Leorat (1976)

15

Helicity fluxes to alleviate Helicity fluxes to alleviate catastrophic quenchingcatastrophic quenching

Bra

nden

burg

(20

05, A

pJ)

1046 Mx2/cycle

FBJBA 2d

d

t

Magnetic helicity fluxMagnetic helicity flux

• EMF and resistive terms still dominant

• Fluxes import at large Rm ~ 1000

• Rm based on kf

• Smaller by 2

16

m22d

dF BJBBA ε

t

f22d

dF bjBba ε

t

Magnetic helicity fluxMagnetic helicity flux

• EMF and resistive terms still dominant

• Fluxes import at large Rm ~ 1000

• Rm based on kf

• Smaller by 2

17

m22d

dF BJBBA ε

t

f22d

dF bjBba ε

t

Gauge-invariant in steady state!

Del Sordo, Guerrero, Brandenburg (2013, MNRAS 429, 1686)

18

This is how it looks like…This is how it looks like…Coronal mass ejections from helical structures

Gibson et al. (2002)

19

(ii) Helicity from solar wind(ii) Helicity from solar wind

)()( xBxBM jiij

)(

)()(

kHki

kEkkkM

kijk

jiijij

)()( xBxBM jiij

)()()( rxxr jiij BBM

Matthaeus et al. (1982) Measure correlation function

In Fourier space, calculatemagnetic energy and helicity spectra

Should be done with Ulysses data away from equatorial plane

20

Measuring 1-D correlation tensorMeasuring 1-D correlation tensor

tuRR R 0Taylor hypothesis:

RRNRTR kkBkBkH /)()(~

Im4)( *

21

Bi-helical fields from UlyssesBi-helical fields from Ulysses

• Taylor hypothesis• Broad k bins• Southern latitude

with opposite sign• Small/large distances• Positive H at large k• Break point with

distance to larger k

22

ComparisonComparison

• Field in solar wind is clearly bi-helical

• ...but not as naively expected

• Need to compare with direct and mean-field simulations

• Recap of dynamo bi-helical fields

Helicity LS SS

Dynamo + -

Solar wind - +

23

Dynamos with exterior Dynamos with exterior CMEs? CMEs?W

arnecke, B

randen

burg, Mitra (2011, A

&A

, 534, A11)

24Strong fluctuations, but positive in north

War

nec

ke, B

rand

enbu

rg, M

itra

(20

11, A

&A

, in

pre

ss)

Shell dynamos with ~CMEsShell dynamos with ~CMEs

To carry negative flux: need positive gradientTo carry negative flux: need positive gradient

f2f

m2m

22d

d

22d

d

FBJB

FBJB

t

t

t

h

t

h

Brandenburg, Candelaresi, Chatterjee(2009, MNRAS 398, 1414)

Sign reversal makes sense!

26

(iii) How deep are sunspots rooted?(iii) How deep are sunspots rooted?

• Solar activity may not be so deeply rooted• The dynamo may be a distributed one• Near-surface shear important

Hindm

an et al. (2009, ApJ)

27

Two alternative sunspot originsTwo alternative sunspot origins

Theories for shallow spots:Theories for shallow spots:

(i) Collapse by suppression(i) Collapse by suppressionof turbulent heat fluxof turbulent heat flux

(ii) Negative pressure effects(ii) Negative pressure effectsfrom <from <uuiiuujj> vs > vs BBiiBBjj

Kosovichev et al. (2000)

Kosovichev et al. (2000)

28

Negative effective magnetic pressure instability

• Gas+turb. press equil.

• B increases

• Turb. press. Decreases

• Net effect?

Self-assembly of a magnetic spot• Minimalistic model• 2 ingredients:

– Stratification & turbulence

• Extensions– Coupled to dynamo– Compete with rotation– Radiation/ionization

29

Imposed vs. self-assembly• Appearance of sunspot

when coupled to radiation

• Can be result of self-assembly when ~1000 G field below surface

30Stein & Nordlund (2012)

Rempel et al. (2009)

31

ConclusionsConclusions• Interest in predicting solar activity

• Cyclonic convection ( helicity)

• Near surface shear migratory dynamo

• Bi-helical fields, inverse cascade

• Solar wind also bi-helical field, but reversed

• Formation of active regions and sunspots by negative effective magnetic pressure inst.