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

2 Simulations of the solar dynamo? Tremendous stratification –Not only density, also scale height change Near-surface shear layer (NSSL) not resolved Contours of  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

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

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

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

6 Dynamo regimes? Brandenburg, Saar, Turpin (1998, ApJL) inactive 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 (a)Distributed dynamo action (b)Surface field from upper layers (c)Mostly cylindrical W -contours (cf Jörn’s talk) (i)Bi-helical fields  inverse cascade (ii)Solar wind also bi-helical field (iii)Formation of active regions at solar surface Other aspects of dynamos: rotation & stratification

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

10 Helicity fluxes to alleviate catastrophic quenching Brandenburg (2005, ApJ) Mx 2 /cycle

Magnetic helicity flux EMF and resistive terms still dominant Fluxes import at large Rm ~ 1000 Rm based on k f Smaller by 2  11

Magnetic helicity flux EMF and resistive terms still dominant Fluxes import at large Rm ~ 1000 Rm based on k f Smaller by 2  12 Gauge-invariant in steady state! 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

Northern/southern hemispheres Cyclones: Down: faster Up: slower north south g  g  equator

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 Taylor hypothesis: u1u1 u2u2

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 1.Antisymmetric about equator 2.Decline toward minum LS: + SS: -

19 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 HelicityLSSS Dynamo -+ Solar wind +- Southern hemisphere for southern hemisphere

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

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

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

E 23

Results & realizability 24 Isotropy Positive hel. Expected for south 30,000 G 2 Mm/(2 6Mm 70,000 G 2 )= ,000 G 2 Mm x (200Mm) 2 = Mx 2 /100Mm cf. Manolis’ talk

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

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.   u.   A.B

Sunspot decay 29

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

31 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)

32 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)

33 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 = = 675 Average B y over y and  t=80  to

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

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

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

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

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

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

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

Global models 41 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

Next meeting

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