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Catastrophic a -quenching alleviated by helicity flux and shear

Catastrophic a -quenching alleviated by helicity flux and shear. Axel Brandenburg ( Nordita, Copenhagen ) Christer Sandin ( Uppsala ) Collaborators: Eric G Blackman ( Rochester ), Kandu Subramanian ( IUCAA, Pune ), Petri K äpylä ( Oulu ). Theoretical framework: aW model. Cycle frequency.

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Catastrophic a -quenching alleviated by helicity flux and shear

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  1. Catastrophic a-quenching alleviated by helicity flux and shear Axel Brandenburg (Nordita, Copenhagen) Christer Sandin (Uppsala) Collaborators: Eric G Blackman (Rochester), Kandu Subramanian (IUCAA, Pune), Petri Käpylä (Oulu)

  2. Theoretical framework: aW model • Cycle frequency • Migration direction  meridional circulation Migration away from equator Penalty to pay for a Pouquet, Frisch, Leorat (1976) (in practice anisotropic)

  3. Internal twist as feedback on a (Pouquet, Frisch, Leorat 1976) How can this be used in practice? Need a closure for <j.b> Brandenburg: helicity flux and shear

  4. Example of bi-helical structure Yousef & Brandenburg (2003, A&A) Brandenburg: helicity flux and shear

  5. Tilt  pol. field regeneration Blackman & Brandenburg (2003, ApJ) standard dynamo picture  internal twist as dynamo feedback N-shaped (north) S-shaped (south)

  6. Sigmoidal filaments (from S. Gibson)

  7. Examples ofhelical structures Brandenburg: helicity flux and shear

  8. History of a quenching “catastrophic” a quenching Rm –dependent (Vainshtein & Cattaneo 1972, Gruzinov & Diamond 1994-96) “conventional” a quenching e.g., a~B-3, independent of Rm (Moffatt 1972, Rüdiger 1973) periodic box simulations: saturation at super-equipartition, but after resistive time (Brandenburg 2001) open domains: removal of magnetic waste by helicity flux (Blackman & Field 2000, Kleeorin et al 2000-2003) Dynamical quenching Kleeorin & Ruzmaikin (1982)

  9. Current helicity flux • Advantage over magnetic helicity • <j.b> is what enters a effect • Can define helicity density Rm also in the numerator Brandenburg: helicity flux and shear

  10. Full time evolution Significant field already after kinematic growth phase followed by slow resistive adjustment Brandenburg: helicity flux and shear

  11. Helical MHD turbulence • Helically forced turbulence (cyclonic events) • Small & large scale field grows exponentially • Past saturation: slow evolution  Explained by magnetic helicity equation Brandenburg: helicity flux and shear

  12. Large scale vs small scale losses Diffusive large scale losses:  lower saturation level (Brandenburg & Dobler 2001) Periodic box with LL losses Small scale losses (artificial)  higher saturation level  still slow time scale Numerical experiment: remove field for k>4 every 1-3 turnover times (Brandenburg et al. 2002)

  13. Significance of shear • a transport of helicity in k-space • Shear  transport of helicity in x-space • Mediating helicity escape ( plasmoids) • Mediating turbulent helicity flux Expression for current helicity flux: (first order smoothing, tau approximation) Schnack et al. Vishniac & Cho (2001, ApJ) Expected to be finite on when there is shear Arlt & Brandenburg (2001, A&A)

  14. Simulating solar-like differential rotation • Still helically forced turbulence • Shear driven by a friction term • Normal field boundary condition Brandenburg: helicity flux and shear

  15. Impose toroidal field  measure a previously: Brandenburg: helicity flux and shear

  16. Helicity fluxes at large and small scales Negative current helicity: net production in northern hemisphere Brandenburg: helicity flux and shear

  17. Helical turbulence with shearand diffusive model corona By field at periphery of box Brandenburg: helicity flux and shear

  18. Conclusions • Connection between a-effect and helicity flux • a-effect produces LS (~300Mm) magnetic helicity (+ north, - south)  SS magnetic helicity as “waste” • Surface losses: observed component from SS (< 30Mm) (- north, + south), about 1046 Mx2/cycle • a at least 30 times larger with open boundary conditions Presence of shear important • Currently: include low plasma beta exterior Brandenburg: helicity flux and shear

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