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Dynamo theory and magneto-rotational instability

Dynamo theory and magneto-rotational instability. diagnostic interest (CMB). primordial (decay). seed field. Axel Brandenburg (Nordita). AGN outflows MRI driven. galactic LS dynamo. helicity losses. The primordial alternative: Decay of field  growth of scale.

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Dynamo theory and magneto-rotational instability

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  1. Dynamo theory and magneto-rotational instability diagnostic interest (CMB) primordial (decay) seed field Axel Brandenburg (Nordita) AGN outflows MRI driven galactic LS dynamo helicity losses

  2. The primordial alternative:Decay of field  growth of scale • Starting point: EW phase transition t=10-10 s, B=1024 G • Horizon scale very short: ~ 3 cm • With cosmological expansion: ~ 1 AU • Can field grow to larger scales?

  3. Inverse cascade of magnetic helicity argument due to Frisch et al. (1975) and Initial components fully helical: and  k is forced to the left

  4. 3-D simulations helical vs nonhelical Initial slope E~k4 Christensson et al. (2001, PRE 64, 056405)

  5. Helical decay law:Biskamp & Müller (1999)

  6. Revised helical decay law M. Christensson, M. Hindmarsh, A. Brandenburg: 2005, AN 326, 393 H not exactly constant Assume power law H follows power law iff r=1/2; then

  7. All length scales scale similarly integral scale hel. scale |H|/M M/|C| s is correction for finite Rm R Q 1/Rm s should be s should be ½+2s

  8. diagnostic interest (CMB) primordial (decay)  weak by comparison seed field AGN outflows MRI driven galactic LS dynamo helicity losses • Accretion discs • Corona heated by MRI • Outflow (+also magn tower)

  9. Alfven and slow magnetosonic wavescoupled to rotation and shear Vertical field B0 Alfven frequency: Dispersion relation effect of rotation, W effect of shear: q slow magnetosonic

  10. March 23, 1965: Gemini 3 Gus Grissom & John Young: docking with Agena space craft Analogies: Tidal disruption of a star Space craft experiment MRI (Balbus & Hawley 1991)

  11. Nonlinear shearing sheet simulations Dynamo makes its own turbulence divergent spectrum 5123 resolution

  12. Vertical stratification Brandenburg et al. (1996) z-dependence of

  13. Heating near disc boundary weak z-dependence of energy density where Turner (2004)

  14. Alternative: Magnetisation from quasars? Poynting flux 10,000 galaxies for 1 Gyr, 1044 erg/s each Similar figure also for outflows from protostellar disc B. von Rekowski, A. Brandenburg, W. Dobler, A. Shukurov, 2003 A&A 398, 825-844

  15. diagnostic interest (CMB) primordial (decay)  weak by comparison seed field AGN outflows MRI driven galactic LS dynamo helicity losses • Dynamo saturation • Rm dependent?? • Helicity losses essential

  16. Close 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)

  17. Connection with a effect: writhe with internal twist as by-product clockwise tilt (right handed) W  left handed internal twist Yousef & Brandenburg A&A 407, 7 (2003) both for thermal/magnetic buoyancy

  18. Helicity fluxes in the presence of shear Mean field: azimuthal average geometry here relevant to the sun Mean field with no helicity, e.g. Vishniac & Cho (2001, ApJ 550, 752) Subramanian & Brandenburg (2004, PRL 93, 20500) Rogachevskii & Kleeorin (2003)

  19. Conclusions • Primordial: B2~t-1/2 (if fully helical), not B2~t-2/3 • Outflows: via MRI-heated corona • Dynamo: j.b saturation • even for WxJ effect • (only shear, no stratification) • Helical outflows necessary • Possible for shearflow 1046 Mx2/cycle (for the sun)

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