1 This is how it looks like… Magnetic helicity at the solar surface and in the solar wind Axel Brandenburg (Nordita, Stockholm) Properties of magn helicity Lessons from dynamo theory What do we see in solar wind? What we can see at solar surface? How about solar corona?

2 Magnetic helicity measures linkage of flux Therefore the unit is Maxwell squared

3 Other fun examples Relevance: Slows down decay Growth at large scales Large-scale dynamos (Candelaresi and Brandenburg (2011)) Trefoil knot H=3  2

4 Decaying helical fields Tevzadze, Kisslinger, Brandenburg, Kahniashvili (2012, ApJ,) (i) Transfer to Large scales (ii) slow-down of decay

5

Dynamos produce bi-helical fields Magnetic helicity spectrum Pouquet, Frisch, & Leorat (1976) Southern hemisphere g.   u.   a.b

Self-inflicted twist: feedback & CMEs N-shaped (north) S-shaped (south) (the whole loop corresponds to CME) Blackman & Brandenburg (2003) =coronal mass ejection

Magnetic helicity flux EMF and resistive terms still dominant Fluxes import at large Rm ~ 1000 Rm based on k f Smaller by 2  8

Magnetic helicity flux EMF and resistive terms still dominant Fluxes import at large Rm ~ 1000 Rm based on k f Smaller by 2  9 Gauge-invariant in steady state! Del Sordo, Guerrero, Brandenburg (2013, MNRAS 429, 1686)

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

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

12 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

13 (i) 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

14 Measure 2-point correlation tensor Taylor hypothesis: u1u1 u2u2

15 Ulysses: scaling with distance * Fairly isotropic * Falls off faster than R -2 * Need to compensate before R averaging Power similar to US consumption Energy density similar to ISM Vector helium magnetometer 2 sec resolution 10 pT sensitivity (0.1  G)

16 Noisy helicity from Ulysses Taylor hypothesis Roundish spectra Southern latitude with opposite sign Positive H at large k Brandenburg, Subramanian, Balogh, & Goldstein (2011, ApJ 734, 9)

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 1 AU -1 ~ 1  Hz

18 Latitudinal scaling and trend 1.Antisymmetric about equator 2.Decline toward minum

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

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)

Only works if RM > 0 and k > 0 But difficult/impossible to recover F(  ) Peak determined by single parameter (Burn 1966) Positivity: Brandenburg & Stepanov (2014, ApJ 786, 91)

Expect bi-helical fields Magnetic helicity conserved Inverse cascade produces small-scale waste! Opposite sign of helicity (or k) 27 Blackman & Brandenburg (2003)

28 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.

29 Magnetic  cross helicity Large-scale structures from stratified turbulence? Application to sunspots? g.B  u.B g.   u.   A.B

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

Conclusions Magnetic helicity –Essential for dynamo –Expect bi-helical Solar wind: yes, but reversed! Galaxies: yes, in theory Brandenburg & Stepanov (2014, ApJ 786, 91)