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Sunspots: the interface between dynamos and the theory of stellar atmospheres Axel Brandenburg (Nordita/Stockholm) 70 yr Guenther
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2 Solar dynamo: what’s missing? “We must know, what we don’t know” alpha effect? Turbulent diffusion? Mitra et al. (2010)
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Importance of nonlocality?
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Early hydro nonlocality
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When is nonlocality important
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How to deal with it? Rheinhardtalet al. (2014)
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Some new type of inverse cascade/transfer?
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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)
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Self-assembly of a magnetic spot Minimalistic model 2 ingredients: –Stratification & turbulence Extensions –Coupled to dynamo –Compete with rotation –Radiation/ionization 9
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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
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Sunspot decay 11
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Examples of self-assembly Can be result of self-assembly when ~1000 G field below surface 12 Stein & Nordlund (2012)
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Turbulent sunspot origins?
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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)
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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)
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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
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17 Basic mechanism Anelastic: descending structure compression B amplifies Growth rate
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18 Much stronger with vertical fields Gas+turb. press equil. B increases Turb. press. Decreases Net effect?
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Or, instead, cascade/transfer? 19 Finite cross helicity: Analogy with A.B? cross helicity production: Stratification + B-field Rudiger et al (2011)
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Sunspot formation that sucks 20 Typical downflow speeds Ma=0.2…0.3 Mean-field simulation: Neg pressure parameterized Brandenbur et al (2014)
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Bi-polar regions in simulations with corona 21 Warnecke et al. (2013, ApJL 777, L37)
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Coronal loops? Warnecke et al. (2013, ApJL 777, L37)
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First dynamo-generated bi-polar regions 23 Mitra et al. (2014, arXiv)
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Still negative effective magnetic pressure? Or something new? 24 Mitra et al. (2014, arXiv)
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Parker’s early work on the subject 25 Equatorward migration
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Need for hydraulics 26 Near-surface concentration deeply roted tubes
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Sunspots from downdrafts 27
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Clustered sunspots 28 “spontaneous” “instability” Parker (1981)
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Flux emergence 29 Later times 70h, 105h, 140h Rempel & Cheung (2014) Early times 24h, 28h, 32h Updraft during emergence, Downdraft during spot formation
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Move to the bottom of CZ
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The thin flux tube paradigm 31 Caligari et al. (1995)Charbonneau & Dikpati (1999)
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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
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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)
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34 Fit formula and Rm dependence
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Suction with/without ionization
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Fixed/variable ionization
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Suction in action Temperature profils
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Nonstandard convection? 38
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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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