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This is how it looks like…

This article investigates the solar dynamo and its spots, exploring the differences between solar and stellar dynamos and the theory and observations of magnetic helicity and flux emergence. The simulations of the solar dynamo and the formation of active regions near the surface are also discussed.

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This is how it looks like…

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  1. The solar dynamo and its spots This is how it looks like… Solar & stellar dynamos: differences? Magnetic helicity: theory & observations Flux emergence  sunspots Axel Brandenburg (Nordita, Stockholm)

  2. 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

  3. ASH code simulations ASH code: anelastic spherical harmonics Brown et al. (2011)

  4. EULAGcode • Cycle now common! • Activity from bottom of CZ • but at high latitudes Racine et al. (2011)

  5. Pencil Code simulations (x5 solar) Käpylaä et al (2012)

  6. Dynamo regimes? inactive Brandenburg, Saar, Turpin (1998, ApJL) active Karak et al. (2015, A&A, in press)

  7. Quenching models Tobias (1996, MNRAS) Karak et al. (2015, A&A, in press)

  8. Global models suggest • Distributed dynamo action • Surface field from upper layers • Mostly cylindrical W-contours (cf Jörn’s talk) Other aspects of dynamos: rotation & stratification • Bi-helical fields  inverse cascade • Solar wind also bi-helical field • Formation of active regions at solar surface

  9. Dynamos produce bi-helical fields Magnetic helicity spectrum Southern hemisphere Pouquet, Frisch, & Leorat (1976)

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

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

  12. 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)

  13. Lessons from dynamo theory • Helicity • Not just a measure of complexity • Critically important in dynamos • To confirm observationally • Opposite signs at different scales • Opposite signs in different hemispheres

  14. Northern/southern hemispheres north equator south Cyclones: Down: faster Up: slower g W g W

  15. Helicity from solar wind: in situ 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

  16. Measure 2-point correlation tensor u1 u2 Taylor hypothesis:

  17. 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 Brandenburg, Subramanian, Balogh, & Goldstein (2011, ApJ 734, 9)

  18. Latitudinal scaling and trend • Antisymmetric about equator • Decline toward minum LS: + SS: -

  19. Comparison Southern hemisphere • 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 for southern hemisphere

  20. Shell dynamos with ~CMEs Warnecke, Brandenburg, Mitra (2011, A&A, 534, A11) SS: - Strong fluctuations, but positive in north

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

  22. Similar method for solar surface Zhang, Brandenburg, & Sokoloff (2014, ApJ 784, L45)

  23. E

  24. Results& realizability 30,000 G2Mm/(2 6Mm 70,000 G2)=0.04 • Isotropy • Positive hel. • Expected for south 30,000 G2Mm x (200Mm)2 = 1043 Mx2/100Mm cf. Manolis’ talk

  25. Radio observations of coronal fields? Stokes Q and U parameters slope=RM Intrinsic polarized emission from B Brandenburg & Stepanov (2014, ApJ 786, 91) Cancellation condition Helical field w/ positive helicity

  26. Galactic  solar sectors • RM synthesis: measure magnetic helicity • Need line of sight component: edge-on galaxy • Expect polarized intensity only in 2 quadrants • 2 characteristic peaks:  eclipsing binaries?? . x x .

  27. Flux emergence in global simulations Nelson, Brown, Brun, Miesch, Toomre (2014)

  28. AR & sunspots • Rising flux tubes? • Hierachical convection? • Self-organization as part of the dynamo g.B  u.B g.W u.w  A.B

  29. Sunspot decay

  30. Self-assembly of a magnetic spot • Minimalistic model • 2 ingredients: • Stratification & turbulence • Extensions • Coupled to dynamo • Compete with rotation • Radiation/ionization

  31. A possible mechanism ReM here based on forcing k Here 15 eddies per box scale ReM=70 means 70x15x2p=7000 based on box scale Brandenburg et al (2011,ApJ 740, L50) Breakdown of quasi-linear theory

  32. Negative effective magnetic pressure instability Kleeorin, Rogachevskii, Ruzmaikin (1989, 1990) • Gas+turbulent+magnetic pressure; in pressure equil. • B increases  turbulence is suppressed •  turbulent pressure decreases • Net effect?

  33. Setup • 3-D box, size (2p)3, isothermal MHD • Random, nonhelical forcing at kf/k1=5, 15 or 30 • Stratified in z, r~exp(-z/H), H=1, Dr=535 • Periodic in x and y • stress-free, perfect conductor in z • Weak imposed field B0 in y • Run for long times: what happens? • Turnover time tto=(urmskf)-1, turb diff ttd=(htk12)-1 • Is longer by factor 3(kf/k1)2 = 3 152 = 675 • Average By over y and Dt=80tto

  34. Basic mechanism Anelastic: descending structure  compression B amplifies B amplifies Growth rate

  35. Sunspot formation that sucks Mean-field simulation: Neg pressure parameterized Typical downflow speeds Ma=0.2…0.3 Brandenbur et al (2014)

  36. Or, instead, cascade/transfer? Finite cross helicity: Analogy with A.B? cross helicity production: Stratification + B-field Rudiger et al (2011)

  37. Bi-polar regions in simulations with corona Warnecke et al. (2013, ApJL 777, L37)

  38. Coronal loops? Warnecke et al. (2013, ApJL 777, L37)

  39. First dynamo-generated bi-polar regions Mitra et al. (2014, arXiv)

  40. Still negative effective magnetic pressure?Or something new? Mitra et al. (2014, arXiv)

  41. Global models Jabbari et al. (2015, arXiv)

  42. New aspects in mean-field concept Ohm’s law Theory and simulations: a effect and turbulent diffusivity Turbulent viscosity and other effects in momentum equation

  43. Next meeting www.nordita.org/sunspots

  44. Conclusions • No evidence for deeply rooted spots • Local confinement of spots required •  negative effective magnetic pressure instability? Other effects? • Further concentration from downflow • Application to star spots: big ones

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