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Critical issues to get right about stellar dynamos

Critical issues to get right about stellar dynamos. Small scale dynamo and LES Pm=0.1 or less (to elim. SS dyn) Magn. Helicity transport and loss. Axel Brandenburg (Nordita, Copenhagen). Shukurov et al. (2006, A&A 448 , L33) Schekochihin et al. (2005, ApJ 625, L115)

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Critical issues to get right about stellar dynamos

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  1. Critical issues to get right about stellar dynamos • Small scale dynamo and LES • Pm=0.1 or less (to elim. SS dyn) • Magn. Helicity transport and loss Axel Brandenburg (Nordita, Copenhagen) Shukurov et al. (2006, A&A 448, L33) Schekochihin et al. (2005, ApJ 625, L115) Brandenburg & Subramanian (2005, Phys. Rep., 417, 1) Brandenburg (2001, ApJ 550, 824; and 2005, ApJ 625, 539)

  2. Long way to go: what to expect? • Turbulent inertial range somewhere • Departures from k -5/3 • k -0.1 correction • Bottleneck effect • Screw-up from MHD nonlocality? • EM(k) and EK(k) parallel or even overlapping? • Or peak of EM(k) at resistive scales? • Does small scale dynamo work for Pm<<1 and Rm>>1? • How is large scale dynamo affected by small scales? • Implications for catastrophic a-quenching

  3. Hyperviscous, Smagorinsky, normal height of bottleneck increased with hyper Haugen & Brandenburg (Phys. Fluids, astro-ph/041266) onset of bottleneck at same position CS=0.20 Inertial range unaffected by artificial diffusion

  4. Allow for B: small scale dynamo action non-helically forced turbulence PrM=n/h=1 PrM=n/h=50

  5. Peaked at small scales? k+3/2 Kazantsev spectrum, even for Pm=1 During saturation peak moves to smaller k. PrM=n/h=1 Can we expect inertial range at (much) larger resolution? PrM=n/h=50

  6. Looks like k-3/2 at 10243 Spectra not on top of each other??  Different from case with imposed field! Still not large enough?!

  7. Help from LES and theory  converging spectra at large k ?? Can be reproduced with prediction by Müller & Grappin (2005, PRL) : |EM(k)-EK(k)| ~ k-7/3 EM(k)+EK(k) ~ k-5/3

  8. Maybe no small scale “surface” dynamo? Small PrM=n/h: stars and discs around NSs and YSOs Schekochihin Haugen Brandenburg et al (2005) k Here: non-helically forced turbulence When should we think of extrapolating to the sun? Implications for global models (w/strong SS field)

  9. Large scale dynamos • Dynamo number for a2 dynamo • May Ca and/or CaCw not big enough • Catastrophic quenching • Suppression of lagrangian chaos? • Suffocation from small scale magnetic helicity? • Applies also to Babcock-Leighton • Most likely solution: magnetic helicity fluxes

  10. Penalty from a effect: writhe with internal twist as by-product a effect produces helical field W clockwise tilt (right handed)  left handed internal twist both for thermal/magnetic buoyancy

  11. Slow saturation Brandenburg (2001, ApJ 550, 824) • Excellent fit formula • Microscopic diffusivity

  12. Slow-down explained by magnetic helicity conservation molecular value!!

  13. Helical dynamo saturation with hyperdiffusivity for ordinary hyperdiffusion ratio 53=125 instead of 5 PRL 88, 055003

  14. Scale separation: inverse cascade Position of the peak compatible with Decomposition in terms of Chandrasekhar-Kendall-Waleffe functions No inverse cascade in kinematic regime LS field: force-free Beltrami

  15. Periodic box, no shear: resistively limited saturation Brandenburg & Subramanian Phys. Rep. (2005, 417, 1-209) Significant field already after kinematic growth phase followed by slow resistive adjustment Blackman & Brandenburg (2002, ApJ 579, 397)

  16. Boundaries instead of periodic Brandenburg & Subramanian (2005, AN 326, 400)

  17. Revised nonlinear dynamo theory(originally due to Kleeorin & Ruzmaikin 1982) Two-scale assumption Dynamical quenching Kleeorin & Ruzmaikin (1982) ( selective decay) Steady limit  algebraic quenching:

  18. General formula with current helicity flux • Advantage over magnetic helicity • <j.b> is what enters a effect • Can define helicity density Rm also in the numerator

  19. 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 550, 752) Subramanian & Brandenburg (2004, PRL 93, 20500) Expected to be finite on when there is shear Arlt & Brandenburg (2001, A&A 380, 359)

  20. Helicity fluxes at large and small scales Negative current helicity: net production in northern hemisphere 1046 Mx2/cycle Brandenburg & Sandin (2004, A&A 427, 13) Helicity fluxes from shear: Vishniac & Cho (2001, ApJ 550, 752) Subramanian & Brandenburg (2004, PRL 93, 20500)

  21. Forced LS dynamo with no stratification azimuthally averaged no helicity, e.g. Rogachevskii & Kleeorin (2003, 2004) geometry here relevant to the sun neg helicity (northern hem.)

  22. Examples ofhelical structures

  23. Mean field model with advective flux Shukurov et al. (2006, A&A 448, L33)

  24. Saturation behavior with advective flux Shukurov et al. (2006, A&A 448, L33)

  25. Conclusions • LES & DNS  EM(k) and EK(k) overlap (?) • SS dynamo may not work in the sun • Only LS dynamo, if excited • and if CMEs etc. 1046 Mx2/cycle

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