Dynamo theory and magneto-rotational instability Axel Brandenburg (Nordita) seed field primordial (decay) diagnostic interest (CMB) 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= s, B=10 24 G Horizon scale very short: ~ 3 cm With cosmological expansion: ~ 1 AU Can field grow to larger scales?

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

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

5 Helical decay law: Biskamp & Müller (1999)

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

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

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

9 Alfven and slow magnetosonic waves coupled to rotation and shear Vertical field B 0 Dispersion relation Alfven frequency: slow magnetosonic effect of rotation,  effect of shear: q

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

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

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

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

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

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

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

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

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

19 Conclusions Primordial: B 2 ~t -1/2 (if fully helical), not B 2 ~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 shear flow Mx 2 /cycle (for the sun)