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Self-assembly of shallow magnetic spots through strongly stratified turbulence

Self-assembly of shallow magnetic spots through strongly stratified turbulence. Axel Brandenburg (Nordita/Stockholm). Kemel+12. K äpylä +12. Warnecke+11. Brandenburg+13. The thin flux tube paradigm. Caligari et al. (1995). Charbonneau & Dikpati (1999).

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Self-assembly of shallow magnetic spots through strongly stratified turbulence

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  1. Self-assembly of shallow magnetic spots through strongly stratified turbulence Axel Brandenburg (Nordita/Stockholm) Kemel+12 Käpylä+12 Warnecke+11 Brandenburg+13

  2. The thin flux tube paradigm Caligari et al. (1995) Charbonneau & Dikpati (1999)

  3. Helioseismology vs current thinking Zhao, Kosovichev, et al (2010)

  4. B05

  5. Sunspots simulated realistically • Appearance of sunspot when coupled to radiation and confined by imposed inflows Rempel et al. (2009) Swedish Solar 1-m Telescope

  6. Examples of self-assembly • Can be result of self-assembly when ~1000 G field below surface Stein & Nordlund (2012)

  7. Turbulent sunspot origins?

  8. A possible mechanism ReM here based on forcing k Here 15 eddies per box scale ReM=70 means 70x15x2p=7000 based on box scale Brandenburg (2011,ApJ 740, L50) Breakdown of quasi-linear theory

  9. Negative effective magnetic pressure instability Kleeorin, Rogachevskii, Ruzmaikin (1989, 1990) • Gas+turbulent+magnetic pressure; in pressure equil. • B increases  turbulence is suppressed •  turbulent pressure decreases • Net effect?

  10. Setup • 3-D box, size (2p)3, isothermal MHD • Random, nonhelical forcing at kf/k1=5, 15 or 30 • Stratified in z, r~exp(-z/H), H=1, Dr=535 • Periodic in x and y • stress-free, perfect conductor in z • Weak imposed field B0 in y • Run for long times: what happens? • Turnover time tto=(urmskf)-1, turb diff ttd=(htk12)-1 • Is longer by factor 3(kf/k1)2 = 3 152 = 675 • Average By over y and Dt=80tto

  11. Basic mechanism Anelastic: descending structure  compression B amplifies B amplifies Growth rate

  12. Magnetic helicity spectra

  13. Much stronger with vertical fields • Gas+turb. press equil. • B increases • Turb. press. Decreases • Net effect?

  14. Self-assembly of a magnetic spot • Minimalistic model • 2 ingredients: • Stratification & turbulence • Extensions • Coupled to dynamo • Compete with rotation • Radiation/ionization

  15. Sunspot decay

  16. Some new type of inverse cascade/transfer? Finite cross helicity: Analogy with A.B? cross helicity production: Stratification + B-field Rudiger et al (2011)

  17. Sunspot formation that sucks Mean-field simulation: Neg pressure parameterized Typical downflow speeds Ma=0.2…0.3

  18. Bi-polar regions in simulations with corona Warnecke et al. (2013, ApJL 777, L37)

  19. Coronal loops? Warnecke et al. (2013, ApJL 777, L37)

  20. Bi-polar regions in simulations with corona Warnecke et al. (2013, 777, L37)

  21. Next level in mean-field concept a effect, turbulent diffusivity, Yoshizawa effect, etc Turbulent viscosity and other effects in momentum equation

  22. How about tilt angles? Tilt here from latitudinal shear Hindman et al. (2009, ApJ) Brandenburg (2005, ApJ)

  23. Thanks to Astrophysics group at Nordita and …

  24. Conclusions • No evidence for deeply rooted spots • Local confinement of spots required •  negative effective magnetic pressure instability • Further concentration from downflow

  25. Dynamo wave from simulations Kapyla et al (2012)

  26. Type of dynamo? • Use phase relation • Closer to a2 dynamo • Wrong for aW dyn. Oscillatory a2 dynamo Mitra et al. (2010)

  27. # of cells • Multi-cellular Kapyla et al. (2012)

  28. How deep are sunspots rooted? • Solar activity may not be so deeply rooted • The dynamo may be a distributed one • Near-surface shear important Hindman et al. (2009, ApJ)

  29. Larger scale separation: 30 instead of 15

  30. Alternative sunspot origins Kosovichev et al. (2000) Theories for shallow spots: (i) Collapse by suppression of turbulent heat flux (ii) Negative pressure effects from <uiuj> vs BiBj

  31. Pencilcode • 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 ~80 people (SVN) • Automatic validation (over night or any time) • 0.0013 ms/pt/step at 10243 , 2048 procs • http://pencil-code.googlecode.com • 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 • Chemistry, combustion • Spherical coordinates

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