Astrophysical Magnetism Axel Brandenburg (Nordita, Stockholm)

2 Similar physics on different scales Galaxies: radius 10 kpc (=3x10 20 m), 2-20 m G Galaxy cluster: radius 1 Mpc (=3x10 22 m), m G Sun: radius 700 Mm (=7x10 8 m), G Earth: radius 60 Mm (=6x10 8 m), 0.5 G

3 Importance of solar interior

4 Large scale coherence Active regions, bi-polarity systematic east-west orientation opposite in the south

5 Solar cycle Longitudinally averaged radial field Spatio-temporal coherence –22 yr cycle, equatorward migration Poleward branch or poleward drift? butterfly diagram

6

7 Karlsruhe dynamo experiment (1999)

8 Cadarache experiment (2007)

9 Dynamos: kinetic  magnetic energy thermal energy kinetic energy magnetic energy Nuclear fusion surface radiation viscous heat Ohmic heat

10 Faraday dynamo But we want to make it self-exciting, without wires, and without producing a short circuit!

11 MHD equations (i)

12 MHD equations (ii) Momentum and continuity eqns (usual form)

13 Vector potential B=curlA, advantage: divB=0 J=curlB=curl(curlA) =curl2A Not a disadvantage: consider Alfven waves B-formulation A-formulation 2 nd der once is better than 1 st der twice!

14 Comparison of A and B methods

15 Kolmogorov spectrum nonlinearity constant flux  cm 2 /s 3    k E(k)E(k)E(k)E(k)  cm 3 /s 2  a=2/3, b=  5/3

16 Hyperviscous, Smagorinsky, normal Inertial range unaffected by artificial diffusion Haugen & Brandenburg (PRE, astro-ph/ ) height of bottleneck increased onset of bottleneck at same position

17 Small-scale vs large-scale dynamos B-scale larger than U-scale B-scale smaller than U-scale Wavenumber =1/scale energy injection scale

18 Small scale and large scale dynamos non-helically forced turbulence helically forced turbulence Scale separation :== There is room on scales Larger than the eddy scale

19 Dynamo in kinematic stage – no large-scale field? Fully helical turbulence, periodic box, resistive time scale!

20  -effect dynamos (large scale) Differential rotation (prehelioseism: faster inside) Cyclonic convection; Buoyant flux tubes Equatorward migration New loop    - effect ?need meridional circulation

21 Revised theory for  -effect 1 st aspect: replace triple correlation by quadradatic 2 nd aspect: do not neglect triple correlation 3 rd aspect: calculate rather than Similar in spirit to tau approx in EDQNM  (Heisenberg 1948, Vainshtein & Kitchatinov 1983, Kleeorin & Rogachevskii 1990, Blackman & Field 2002, Rädler, Kleeorin, & Rogachevskii 2003)

22 Implications of tau approximation 1.MTA does not a priori break down at large R m. (Strong fluctuations of b are possible!) 2.Extra time derivative of emf 3.  hyperbolic eqn, oscillatory behavior possible!  is not correlation time, but relaxation time with

23 Kinetic and magnetic contributions

24  2 -effect calculation

25 Connection with  effect: writhe with internal twist as by-product  clockwise tilt (right handed)  left handed internal twist both for thermal/magnetic buoyancy  effect produces helical field

26 Paradigm shifts i)1980: magnetic buoyancy (Spiegel & Weiss)  overshoot layer dynamos ii)1985: helioseismology: d W /dr > 0  dynamo dilema, flux transport dynamos iii)1992: catastrophic a -quenching a~ Rm - 1 (Vainshtein & Cattaneo)  Parker’s interface dynamo  Backcock-Leighton mechanism

(i) Is magnetic buoyancy a problem? Stratified dynamo simulation in 1990 Expected strong buoyancy losses, but no: downward pumping Tobias et al. (2001)

(ii) Before helioseismology Angular velocity (at 4 o latitude): –very young spots: 473 nHz –oldest spots: 462 nHz –Surface plasma: 452 nHz Conclusion back then: –Sun spins faster in deaper convection zone –Solar dynamo works with d  /dr<0: equatorward migr Yoshimura (1975) Thompson et al. (1975) Brandenburg et al. (1992)

29 Near-surface shear layer: spots rooted at r/R=0.95? Benevolenskaya, Hoeksema, Kosovichev, Scherrer (1999) Pulkkinen & Tuominen (1998)  =  AZ  =(180/  ) (1.5x10 7 ) (2  ) =360 x 0.15 = 54 degrees!

30 (iii) Problems with mean-field theory? Catastrophic quenching? –  ~ R m -1,  t ~ R m -1 –Field strength vanishingly small? Something wrong with simulations –so let’s ignore the problem Possible reasons: –Suppression of lagrangian chaos? –Suffocation from small scale magnetic helicity?

31 Revisit paradigm shifts i)1980: magnetic buoyancy  counteracted by pumping ii)1985: helioseismology: d W /dr > 0  negative gradient in near-surface shear layer iii)1992: catastrophic a -quenching  overcome by helicity fluxes  in the Sun: by coronal mass ejections

32 Upcoming dynamo effort in Stockholm Soon hiring: 4 students4 students 4 post-docs4 post-docs 1 assistant professor1 assistant professor Long-term visitorsLong-term visitors

Pencil Code Started in Sept with Wolfgang Dobler High order (6 th order in space, 3 rd order in time) Cache & memory efficient MPI, can run PacxMPI (across countries!) Maintained/developed by ~20 people (SVN) Automatic validation (over night or any time) Max resolution so far , 256 procs Isotropic turbulence – –MHD, passive scl, CR Stratified layers – –Convection, radiation Shearing box – –MRI, dust, interstellar – –Self-gravity Sphere embedded in box – –Fully convective stars – –geodynamo Other applications – –Homochirality – –Spherical coordinates

34 Increase in # of auto tests

35 Evolution of code size

36 Simulations showing large-scale fields Helical turbulence (B y ) Helical shear flow turb. Convection with shear Magneto-rotational Inst. Käpyla et al (2008)

37 Convection with shear and W Käpylä et al (2008) with rotationwithout rotation

38 How do they work? Interlocked poloidal and toroidal fields

39 Magnetic helicity

40 How do they work? a effect Produce interlocked field at large scale (of positive helicity, say) … by generating interlocked small-scale field of opposite helicity

41 Effect of helicity Brandenburg (2005, ApJ) Mx 2 /cycle

42 Conclusion 11 yr cycle Dyamo (SS vs LS) Problems –  -quenching – slow saturation Solution –Modern  -effect theory –j.b contribution –Magnetic helicity fluxes Location of dynamo –Distrubtion, shaped by –near-surface shear Mx 2 /cycle