Astrophysical Magnetism Axel Brandenburg Nordita Stockholm Similar physics
Astrophysical Magnetism Axel Brandenburg (Nordita, Stockholm)
Similar physics on different scales Earth: radius 60 Mm (=6 x 108 m), 0. 5 G Sun: radius 700 Mm (=7 x 108 m), 20 -2000 G Galaxies: radius 10 kpc (=3 x 1020 m), 2 -20 m. G Galaxy cluster: radius 1 Mpc (=3 x 1022 m), 0. 1 -1 m. G 2
Importance of solar interior 3
Large scale coherence Active regions, bi-polarity systematic east-west orientation opposite in the south 4
Solar cycle • Longitudinally averaged radial field • Spatio-temporal coherence – 22 yr cycle, equatorward migration butterfly diagram Poleward branch or poleward drift? 5
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Karlsruhe dynamo experiment (1999) 7
Cadarache experiment (2007) 8
Dynamos: kinetic magnetic energy surface radiation thermal energy viscous heat Ohmic heat kinetic energy magnetic energy Nuclear fusion 9
Faraday dynamo But we want to make it self-exciting, without wires, and without producing a short circuit! 10
MHD equations (i) 11
MHD equations (ii) Momentum and continuity eqns (usual form) 12
Vector potential • B=curl. A, advantage: div. B=0 • J=curl. B=curl(curl. A) =curl 2 A • Not a disadvantage: consider Alfven waves B-formulation A-formulation 2 nd der once is better than 1 st der twice! 13
Comparison of A and B methods 14
Kolmogorov spectrum nonlinearity constant flux e [cm 2/s 3] [cm 3/s 2] E (k ) e e k a=2/3, b= -5/3 15
Haugen & Brandenburg (PRE, astro-ph/0402301) Hyperviscous, Smagorinsky, normal height of bottleneck increased onset of bottleneck at same position Inertial range unaffected by artificial diffusion 16
Small-scale vs large-scale dynamos energy injection scale Wavenumber =1/scale B-scale smaller than U-scale B-scale larger than U-scale 17
Small scale and large scale dynamos non-helically forced turbulence Scale separation : == There is room on scales Larger than the eddy scale 18
Dynamo in kinematic stage – no large-scale field? Fully helical turbulence, periodic box, resistive time scale! 19
a-effect dynamos (large scale) New loop Differential rotation (prehelioseism: faster inside) ? need meridional circulation Cyclonic convection; Buoyant flux tubes a-effect Equatorward migration 20
Revised theory for a-effect 1 st aspect: replace triple correlation by quadradatic Similar in spirit to tau approx in EDQNM 2 nd aspect: do not neglect triple correlation 3 rd aspect: calculate rather than (Heisenberg 1948, Vainshtein & Kitchatinov 1983, Kleeorin & Rogachevskii 1990, Blackman & Field 2002, Rädler, Kleeorin, & Rogachevskii 2003) 21
Implications of tau approximation 1. MTA does not a priori break down at large Rm. (Strong fluctuations of b are possible!) 2. Extra time derivative of emf with 3. hyperbolic eqn, oscillatory behavior possible! 4. t is not correlation time, but relaxation time 22
Kinetic and magnetic contributions 23
2 a -effect calculation 24
Connection with 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 25
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 26
(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 n. Hz – oldest spots: 462 n. Hz – Surface plasma: 452 n. Hz • Conclusion back then: – Sun spins faster in deaper convection zone – Solar dynamo works with d. W/dr<0: equatorward migr Yoshimura (1975) Thompson et al. (1975) Brandenburg et al. (1992)
Near-surface shear layer: spots rooted at r/R=0. 95? Benevolenskaya, Hoeksema, Kosovichev, Scherrer (1999) Pulkkinen & Tuominen (1998) Df=t. AZDW=(180/p) (1. 5 x 107) (2 p 10 -8) =360 x 0. 15 = 54 degrees! 29
(iii) Problems with mean-field theory? • Catastrophic quenching? – a ~ Rm-1, ht ~ Rm-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? 30
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 31
Upcoming dynamo effort in Stockholm Soon hiring: • • 4 students 4 post-docs 1 assistant professor Long-term visitors 32
Pencil Code • • Started in Sept. 2001 with Wolfgang Dobler High order (6 th order in space, 3 rd order in time) Cache & memory efficient MPI, can run Pacx. MPI (across countries!) Maintained/developed by ~20 people (SVN) Automatic validation (over night or any time) Max resolution so far 10243 , 256 procs • Isotropic turbulence – • Stratified layers – • MRI, dust, interstellar Self-gravity Sphere embedded in box – – • Convection, radiation Shearing box – – • MHD, passive scl, CR Fully convective stars geodynamo Other applications – – Homochirality Spherical coordinates
Increase in # of auto tests 34
Evolution of code size 35
Simulations showing large-scale fields Helical turbulence (By) Käpyla et al (2008) Convection with shear Helical shear flow turb. Magneto-rotational Inst. 36
Convection with shear and W Käpylä et al (2008) with rotation without rotation 37
How do they work? Interlocked poloidal and toroidal fields 38
Magnetic helicity 39
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 40
Brandenburg (2005, Ap. J) Effect of helicity 1046 Mx 2/cycle 41
• 11 yr cycle • Dyamo (SS vs LS) • Problems Conclusion – a-quenching – slow saturation • Solution – Modern a-effect theory – j. b contribution – Magnetic helicity fluxes • Location of dynamo – Distrubtion, shaped by – near-surface shear 1046 Mx 2/cycle 42
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