Rethinking basic concepts of solar convection and sunspot
Rethinking basic concepts of solar convection and sunspot formation Axel Brandenburg (Nordita, Stockholm)
Spaceweather. com Space. Weather. com
Movie of the Sun
X-ray corona Triggers geomagnetic storms Aviation: affects communication & GPS Harmful proton radiation (~m. Sv)
Structure of the Sun Surface: granulation (~1 Mm) Radius of the Sun: 700 Mm Convection zone: 200 Mm 5
Agreement: simulations & observations Simulation: Stein & Nordlund, observation Swedish Solar Telescope What about deeper down?
Structure of convection zone mixing length theory vs simulations
Hanasoge
Results challenged • Ring diagram analysis by Greer et al. (2015) • One difference: no “noise” removed • Kernels
Basic concept of helioseismology Top: reflection when wavenlength ~ density scale height Deeper down: Sound speed large 10
Travel time differences • Contrib. from whole path • Esp. top layers (cs small) • averaging over rays through same point
Deep-focusing geometry • Removes strong contributions from top layers • Could they be right?
Other reasons for concern • Simulations predict giant cells • But are not observed
Do we need to rethink? • In mixing length theory: l=Hp only hypothesis • Simulations: subgrid scale diffusion, viscosity • Envisage reasons for (i) smaller scale flows and/or (ii) deeper parts subadiabatic? • Convection zone still 200 Mm
Helioseismology: change at 0. 7 R
Spruit 97 A changing paradigm
Entropy rain
Stein & Nordlund (1998) simulations Filamentary, nonlocal shown: entropy fluctuations pos neg
Entropy & convection Adiabatic changes: S=const P equilibrium: S+ buoyant S pert overshoot z S pert unstable z
Tau approximation Closure hypothesis
Deardorff 1
Deardorff 2
Physical meaning? S pert coasting… z
Why should only the top be unstable e. g. if Power law Polytropic index n
Deeper parts intrinsically stable Kramers opacity (interior): a=1, b=-7/2 n=3. 25 Polytropic index n Entropy gradient positive (stable) for n > 3/2
Early work in the 1930 s
Why should only the top be unstable
Hydrostatic reference solutions Thickness only ~1 Mm
Revised mixing length theory Entropy gradient old new
New solutions with Deardorff flux
Consequences of small scales • • • Larger kf less turb. Diffusion: ht=urms/3 kf Applications to dynamos: stronger, less turb diffusive Two other important effect: Lambda effect differential rotation Negative effective magnetic pressure spots 31
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? 32
Setup • • • 3 -D box, size (2 p)3, isothermal MHD Random, nonhelical forcing at kf/k 1=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 B 0 in y Run for long times: what happens? Turnover time tto=(urms kf)-1, turb diff ttd=(ht k 12)-1 Is longer by factor 3(kf/k 1)2 = 3 152 = 675 Average By over y and Dt=80 tto 33
Basic mechanism Anelastic: descending structure compression B amplifies Growth rate 34
Self-assembly of a magnetic spot • Minimalistic model • 2 ingredients: – Stratification & turbulence • Extensions – Coupled to dynamo – Compete with rotation – Radiation/ionization 35
Sunspot formation that sucks Mean-field simulation: Neg pressure parameterized Typical downflow speeds Ma=0. 2… 0. 3 Brandenbur et al (2014) 36
Flux tubes in global simulations Nelson, Brown, Brun, Miesch, Toomre (2014) 37
Other proposals • Rising flux tubes? • Hierachical convection? • Self-organization as part of the dynamo g. B u. B g. W u. w A. B 38
Bi-polar regions in simulations with corona Warnecke et al. (2013, Ap. JL 777, L 37) 39
First dynamo-generated bi-polar regions Mitra et al. (2014, ar. Xiv) 40
Jabbari et al. (2015, ar. Xiv) Global models 41
Conclusions • • • Sun: active & exciting Some basic questions worth rethinking Possibly Deardorff flux (Entropy rain) slightly subadiabatic: no giant cells Other interesting possibilities: dynamos, differential rotation, spotformation, …
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