1 / 42

Astrophysical Magnetism

Explore the similarities between physics on different scales, from Earth to the Sun, galaxies, and galaxy clusters. Understand the importance of solar interior and the dynamics of active regions and the solar cycle. Investigate the self-excitation of dynamos and the MHD equations. Learn about the implications of the a-effect and the connection with the w-effect. Discover paradigm shifts in magnetic buoyancy and the challenges in mean-field theory. Join the upcoming dynamo effort in Stockholm.

donjones
Download Presentation

Astrophysical Magnetism

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Astrophysical Magnetism Axel Brandenburg (Nordita, Stockholm)

  2. Similar physics on different scales Earth: radius 60 Mm (=6x108 m), 0.5 G Sun: radius 700 Mm (=7x108 m), 20-2000 G Galaxies: radius 10 kpc (=3x1020 m), 2-20 mG Galaxy cluster: radius 1 Mpc (=3x1022 m), 0.1-1 mG

  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 butterfly diagram Poleward branch or poleward drift?

  6. Karlsruhe dynamo experiment (1999)

  7. Cadarache experiment (2007)

  8. Dynamos: kinetic  magnetic energy surface radiation viscous heat Ohmic heat magnetic energy thermal energy kinetic 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=curlA, advantage: divB=0 • J=curlB=curl(curlA) =curl2A • Not a disadvantage: consider Alfven waves B-formulation A-formulation 2nd der once is better than 1st der twice!

  13. Comparison of A and B methods

  14. Kolmogorov spectrum nonlinearity constant flux e [cm2/s3] [cm3/s2] E(k) a=2/3, b= -5/3 e e k

  15. Hyperviscous, Smagorinsky, normal height of bottleneck increased Haugen & Brandenburg (PRE, astro-ph/0402301) 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 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) Cyclonic convection; Buoyant flux tubes Equatorward migration  a-effect ?need meridional circulation

  20. Revised theory for a-effect 1st aspect: replace triple correlation by quadradatic 2nd aspect: do not neglect triple correlation 3rd 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)

  21. Implications of tau approximation • MTA does not a priori break down at large Rm. (Strong fluctuations of b are possible!) • Extra time derivative of emf •  hyperbolic eqn, oscillatory behavior possible! • t is not correlation time, but relaxation time with

  22. Kinetic and magnetic contributions

  23. a2-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 • 1980: magnetic buoyancy (Spiegel & Weiss) overshoot layer dynamos • 1985: helioseismology: dW/dr > 0  dynamo dilema, flux transport dynamos • 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)

  27. (ii) Before helioseismology • Angular velocity (at 4o 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 dW/dr<0: equatorward migr Brandenburg et al. (1992) Thompson et al. (1975) Yoshimura (1975)

  28. Near-surface shear layer:spots rooted at r/R=0.95? Benevolenskaya, Hoeksema, Kosovichev, Scherrer (1999) Pulkkinen & Tuominen (1998) • Df=tAZDW=(180/p) (1.5x107) (2p 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 • 1980: magnetic buoyancy  counteracted by pumping • 1985: helioseismology: dW/dr > 0  negative gradient in near-surface shear layer • 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 (6th order in space, 3rd 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 10243 , 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

  33. Increase in # of auto tests

  34. Evolution of code size

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

  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. Effect of helicity Brandenburg (2005, ApJ) 1046Mx2/cycle

  41. Conclusion • 11 yr cycle • Dyamo (SS vs LS) • Problems • 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 Mx2/cycle

More Related