Magnetic field generation on long time scales Axel Brandenburg (Nordita/Stockholm) Kemel+12 Ilonidis+11Brandenburg+11Warnecke+11 Käpylä+12

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White light image of yesterday 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 wave Differential rotation (faster inside) Cyclonic convection; Buoyant flux tubes Equatorward migration New loop    - effect

6 Alternative proposal: Conveyor belt model Dikpati et al. (2006)

7 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, Toomre 8 Brown et al. (2011) ASH code: anelastic spherical harmonics

9 Cycle now common! Activity from bottom of CZ but at high latitudes Ghizaru, Charbonneau, Racine, … Racine et al. (2011)

Pencil code Started in Sept with Wolfgang Dobler High order (6 th order in space, 3 rd 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)  s/pt/step at , 2048 procs 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 Kapyla et al (2012)

Type of dynamo? 12 Use phase relation Closer to  2 dynamo Wrong for  dyn. Mitra et al. (2010) Oscillatory  2 dynamo

13 Remaining 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 Magnetic helicity spectrum Pouquet, Frisch, & Leorat (1976)

15 Helicity fluxes to alleviate catastrophic quenching Brandenburg (2005, ApJ) Mx 2 /cycle

Magnetic helicity flux EMF and resistive terms still dominant Fluxes import at large Rm ~ 1000 Rm based on k f Smaller by 2  16

Magnetic helicity flux EMF and resistive terms still dominant Fluxes import at large Rm ~ 1000 Rm based on k f Smaller by 2  17 Gauge-invariant in steady state! Del Sordo, Guerrero, Brandenburg (2013, MNRAS 429, 1686)

18 This is how it looks like… Coronal mass ejections from helical structures Gibson et al. (2002)

19 (ii) Helicity from solar wind Matthaeus et al. (1982) Measure correlation function In Fourier space, calculate magnetic energy and helicity spectra  Should be done with Ulysses data away from equatorial plane

20 Measuring 1-D correlation tensor Taylor hypothesis:

21 Bi-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 Comparison 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 HelicityLSSS Dynamo +- Solar wind -+

23 Dynamos with exterior  CMEs? Warnecke, Brandenburg, Mitra (2011, A&A, 534, A11)

24 Strong fluctuations, but positive in north Warnecke, Brandenburg, Mitra (2011, A&A, in press) Shell dynamos with ~CMEs

To carry negative flux: need positive gradient Brandenburg, Candelaresi, Chatterjee (2009, MNRAS 398, 1414) Sign reversal makes sense!

26 (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 Hindman et al. (2009, ApJ)

27 Two alternative sunspot origins Theories for shallow spots: (i) Collapse by suppression of turbulent heat flux (ii) Negative pressure effects from vs B i B j 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 30 Stein & Nordlund (2012) Rempel et al. (2009)

31 Conclusions 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.