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Magnetized stellar envelopes and buoyant flux ropes II: 3-d simulations

Magnetized stellar envelopes and buoyant flux ropes II: 3-d simulations. Bertil F. Dorch (1, 2) Copenhagen University Library, The Royal Library The Niels Bohr Institute, Copenhagen University. Menu. The general idea Summary of last years results (2-d)… 3-d low resolution, toy model

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Magnetized stellar envelopes and buoyant flux ropes II: 3-d simulations

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  1. Magnetized stellar envelopes and buoyant flux ropes II: 3-d simulations • Bertil F. Dorch (1, 2) • Copenhagen University Library, The Royal Library The Niels Bohr Institute, Copenhagen University Session III, DFS Årsmøde 2007, Nyborg

  2. Menu • The general idea • Summary of last years results (2-d)… • 3-d low resolution,toy model work-in-progress • Conclusions • Todo… Session III, DFS Årsmøde 2007, Nyborg

  3. The general idea: Buoyant flux rope • The current solar-like dynamo paradigm •  - type: poloidal fields ↔ toroidal fields via the -effect, -loops and the so called -effect • Flux tube dynamos • R-T instability  buoyant magnetic flux tubes = twisted flux ropes (done this 12 years ago) • Ropes work well within this framework… … but there are many questions – and skeptisism is healthy • How is the twist generated ? • How much twist is necessary ? • Is this picture at all correct ? • Here: How will a poloidal field affect the rise of toroidal ropes? And what about the twist ? Session III, DFS Årsmøde 2007, Nyborg

  4. Back of the envelope • “Poloidal” layer in convection zone: • Define fundamental parameters χ Brope / Bcz ε Bcz / Bφ • So that χε = f(Ψ) constant for varying Bcz • Primary parameters are χ and sign of twist • The Sun has χ๏ > 100 kG / Beq ≈ 10 • Toy rope • Textbook buoyant rope making dent in transverse layer χ > χc = √ (γ 2 Hp0/R) …for the rope to ascend… Session III, DFS Årsmøde 2007, Nyborg

  5. Making a simple model • Numerical full MHD simulations: Idealized model • 2.5-d (last year): For higher resolution (2048² points) and for simplicity + speed • 3-d: For low resolution (200100200) toy experiments with long rope: λ = 25 Hp • Idealized “convection zone” (2.3 Hp) • Polytrop, stable stratification • High buoyancy for speed: β ~ 100 « solar large scale • Textbook twist pitch angle ~35°  ÷kink ÷R-T • R ~ 0.14 Hp0 χc = 5 and χε ~ 4 Session III, DFS Årsmøde 2007, Nyborg

  6. 2-d: Bz in reference model and χ ~ 20 Reference modelanti-twist (-) χ ~ 20 The qualitative differences are clear ! Session III, DFS Årsmøde 2007, Nyborg

  7. 2-d: Magnetic field vectors (anti-twisted rope) Current sheet  Current sheet can carve away twisted field (flux)… Session III, DFS Årsmøde 2007, Nyborg

  8. 3-d: Buoyant loop ascending into magnetic layer Anti-parallel twist (-) χ = 9 Similarities to photospheric and coronal flux emergence B² Qualitatively rope is naturally influenced by the magnetic CZ! Session III, DFS Årsmøde 2007, Nyborg

  9. 3-d: Bz in reference model and χ ~ 9 Apex No CZ field: Reference model Anti-parallel twist (-) χ = 9 Parallel CZ field (+) χ = 9 Feet The rope’s apex is skewed for both signs: More so when anti-twisted Session III, DFS Årsmøde 2007, Nyborg

  10. 3-d: Flux rope height as a function of time 2-d ref. model 3-d ref. model 3-d non- magnetic • Stronger anti-parallel twist are ascending more efficiently… … below a certain limit (too strong CZ field damp rise anyway) Session III, DFS Årsmøde 2007, Nyborg

  11. Conclusions Flux rope dynamics • Rise speed and amplitude depend on strength and sign of the poloidal field: • Anti-parallel twisted ropes reach higher, faster • χ > χc = √ (γ 2 Hp0/R) holds approximately, but slightly better for 3-d Flux rope topology • The geometrical shape of ropes depends on the poloidal field: • Anti-parallel twisted ropes are flatter • Skewness of rope shape (depending on sign) Flux rope twist • Reconnection reduces twist of anti-parallel ropes • i.e. effect should vary if alternating cycles… Other 3-d effects • Draining • Buoyant acceleration • Motion of CZ field along the rope (parting of field lines) • Horizontal tension • Resolution effects ? 2048³ is currently impossible ! Session III, DFS Årsmøde 2007, Nyborg

  12. TODO: What will the future bring? • Todo • 3-d with Klaus Galsgaard & Vasilis Archontis ! • Higer resolution: Possibly with the AN-MHD code.. ? • With deep stratified convection ! • With self-consistent poloidal field (dynamo) ! Session III, DFS Årsmøde 2007, Nyborg

  13. Reklame… www.scholarpedia.org Session III, DFS Årsmøde 2007, Nyborg

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