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Sunspots: the interface between dynamos and the theory of stellar atmospheres

Sunspots: the interface between dynamos and the theory of stellar atmospheres. Axel Brandenburg (Nordita/Stockholm). 70 yr Guenther. Solar dynamo: what’s missing?. “We must know, what we don’t know” alpha effect? Turbulent diffusion?. Mitra et al. (2010). Importance of nonlocality ?.

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Sunspots: the interface between dynamos and the theory of stellar atmospheres

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

  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? Brandenburg et al (2014) cross helicity production: Stratification + B-field Finite cross helicity: Analogy with A.B?

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

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

  11. Sunspot decay

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

  13. Turbulent sunspot origins?

  14. 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

  15. 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?

  16. 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

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

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

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

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

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

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

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

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

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

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

  27. Sunspots from downdrafts

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

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

  30. Move to the bottom of CZ

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

  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. 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. Fit formula and Rm dependence

  35. Suction with/without ionization

  36. Fixed/variable ionization

  37. Suction in action Temperature profils

  38. Nonstandard convection?

  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

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