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Magnetic field generation on long time scales

Magnetic field generation on long time scales. Axel Brandenburg (Nordita/Stockholm). Kemel+12. K äpylä +12. Ilonidis+11. Warnecke+11. Brandenburg+11. White light image of yesterday. Tips of icebergs: Magnetic flux concentrations in magnetogram !. The thin flux tube paradigm.

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Magnetic field generation on long time scales

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

  2. White light image ofyesterday Tips of icebergs: Magnetic flux concentrations in magnetogram!

  3. The thin flux tube paradigm Caligari et al. (1995) Charbonneau & Dikpati (1999)

  4. Standard dynamo wave New loop Differential rotation (faster inside) Cyclonic convection; Buoyant flux tubes Equatorward migration  a-effect

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

  6. Simulations of the solar dynamo? • Tremendous stratification • Not only density, also scale height change • Near-surface shear layer (NSSL) not resolved • Contours of W 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

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

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

  9. Pencilcode • 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 ms/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

  10. Dynamo wave from simulations Kapyla et al (2012)

  11. Type of dynamo? • Use phase relation • Closer to a2 dynamo • Wrong for aW dyn. Oscillatory a2 dynamo Mitra et al. (2010)

  12. Remaining aspects • Bi-helical fields  inverse cascade • Solar wind also bi-helical field • Formation of active regions at solar surface

  13. (i) Dynamo produces bi-helical field Magnetic helicity spectrum Pouquet, Frisch, & Leorat (1976)

  14. Helicity fluxes to alleviate catastrophic quenching Brandenburg (2005, ApJ) 1046Mx2/cycle

  15. Magnetic helicity flux • EMF and resistive terms still dominant • Fluxes import at large Rm ~ 1000 • Rm based on kf • Smaller by 2p

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

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

  18. (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

  19. Measuring 1-D correlation tensor Taylor hypothesis:

  20. 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

  21. 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

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

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

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

  25. (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)

  26. Two alternative sunspot origins Kosovichev et al. (2000) Theories for shallow spots: (i) Collapse by suppression of turbulent heat flux (ii) Negative pressure effects from <uiuj> vs BiBj

  27. Negative effective magnetic pressure instability • Gas+turb. press equil. • B increases • Turb. press. Decreases • Net effect?

  28. 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 Rempel et al. (2009) Stein & Nordlund (2012)

  30. 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.

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