1. Sunspots: the interface between dynamos and the theory of stellar atmospheres Axel Brandenburg (Nordita/Stockholm) 70 yr Guenther

2. 2 Solar dynamo: what’s missing? “We must know, what we don’t know” alpha effect? Turbulent diffusion? Mitra et al. (2010)

3. Importance of nonlocality?

4. Early hydro nonlocality

5. When is nonlocality important

6. How to deal with it? Rheinhardtalet al. (2014)

7. Some new type of inverse cascade/transfer?

8. Could stratification be a missing link? Could stratification be a missing link? 8 Finite cross helicity: Analogy with A.B? cross helicity production: Stratification + B-field Brandenburg et al (2014)

9. Self-assembly of a magnetic spot Minimalistic model 2 ingredients: –Stratification & turbulence Extensions –Coupled to dynamo –Compete with rotation –Radiation/ionization 9

10. Sunspots simulated realistically Appearance of sunspot when coupled to radiation and confined by imposed inflows 10 Rempel et al. (2009)Swedish Solar 1-m Telescope

11. Sunspot decay 11

12. Examples of self-assembly Can be result of self-assembly when ~1000 G field below surface 12 Stein & Nordlund (2012)

13. Turbulent sunspot origins?

14. 14 A possible mechanism Breakdown of quasi-linear theory Re M here based on forcing k Here 15 eddies per box scale Re M =70 means 70x15x2  =7000 based on box scale Brandenburg et al (2011,ApJ 740, L50)

15. 15 Negative effective magnetic pressure instability Gas+turbulent+magnetic pressure; in pressure equil. B increases  turbulence is suppressed  turbulent pressure decreases Net effect? Kleeorin, Rogachevskii, Ruzmaikin (1989, 1990)

16. 16 Setup 3-D box, size (2  ) 3, isothermal MHD Random, nonhelical forcing at k f /k 1 =5, 15 or 30 Stratified in z,  ~exp(-z/H), H=1,  =535 Periodic in x and y stress-free, perfect conductor in z Weak imposed field B 0 in y Run for long times: what happens? Turnover time  to =(u rms k f ) -1, turb diff  td =(  t k 1 2 ) -1 Is longer by factor 3(k f /k 1 ) 2 = 3 15 2 = 675 Average B y over y and  t=80  to

17. 17 Basic mechanism Anelastic: descending structure  compression B amplifies Growth rate

18. 18 Much stronger with vertical fields Gas+turb. press equil. B increases Turb. press. Decreases Net effect?

19. Or, instead, cascade/transfer? 19 Finite cross helicity: Analogy with A.B? cross helicity production: Stratification + B-field Rudiger et al (2011)

20. Sunspot formation that sucks 20 Typical downflow speeds Ma=0.2…0.3 Mean-field simulation: Neg pressure parameterized Brandenbur et al (2014)

21. Bi-polar regions in simulations with corona 21 Warnecke et al. (2013, ApJL 777, L37)

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

23. First dynamo-generated bi-polar regions 23 Mitra et al. (2014, arXiv)

24. Still negative effective magnetic pressure? Or something new? 24 Mitra et al. (2014, arXiv)

25. Parker’s early work on the subject 25 Equatorward migration

26. Need for hydraulics 26 Near-surface concentration   deeply roted tubes

27. Sunspots from downdrafts 27

28. Clustered sunspots 28 “spontaneous”   “instability” Parker (1981)

29. Flux emergence 29 Later times 70h, 105h, 140h Rempel & Cheung (2014) Early times 24h, 28h, 32h  Updraft during emergence,  Downdraft during spot formation

30. Move to the bottom of CZ

31. The thin flux tube paradigm 31 Caligari et al. (1995)Charbonneau & Dikpati (1999)

32. 32 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

33. 33 Earlier results for low Rm Rädler (1974) computed magnetic suppression (for other reasons) Rüdiger (1974)  works only for Pm < 8 Rüdiger et al. (1986) Maxwell tension formally negative for Rm > 1, but invalid Rüdiger et al. (2011, arXiv), no negative effective magnetic pressure for Rm < 1. Kleeorin et a. (1989, 1990, 1996), Kleeorin & Rogachevskii (1994, 2007)

34. 34 Fit formula and Rm dependence

35. Suction with/without ionization

36. Fixed/variable ionization

37. Suction in action Temperature profils

38. Nonstandard convection? 38

39. 39 Conclusions No evidence for deeply rooted spots Local confinement of spots required Anticipated by Parker (1978, 1979)  negative effective magnetic pressure instability? Other effects? Further concentration from downflow