Simulations and understanding large-scale dynamos

Transcription

1 Simulations and understanding large-scale dynamos Issues with global models Possibility of smaller scales Consequences of this Magnetic flux concentrations Unusual dynamo effects Axel randenburg (Nordita, Stockholm CU oulder) 1

2 Global models suggest Distributed dynamo action Difference to flux transport dynamos Would require smaller turb. diff. h t =u rms /3k f =u rms l/3 Surface flux from upper layers Difference to deeply rooted tube picture Surface flux reamplification needed NEMPI: works best for large k f H p Mostly cylindrical W-contours Anti-solar differential rotation 2

3 Hanasoge

4 Do we need to rethink? In mixing length theory: l=h p only hypothesis cf. Nick Featherstone s talk Simulations: subgrid scale diffusion, viscosity Envisage reasons for (i) smaller scale flows and/or (ii) deeper parts subadiabatic? ut depth of convection zone still 200 Mm

5 Spruit97 A changing paradigm

6 Entropy rain

7 Stein & Nordlund (1998) simulations Filamentary, nonlocal shown: entropy fluctuations pos neg

8 Tau approximation u p i i s j j N c s g u N S u s / su p i j j i i i i N c s g S u u u s u s t F / 2 i su F N Closure hypothesis

9 Deardorff1

10 Deardorff2

11 Physical meaning? s / c 1 ln p ln p S pert coasting z s 0, u 0 u s z z 0

12 Physical meaning? s / c 1 ln p ln p S pert z s 0, u 0 u s z z 0

13 Why should only the top be unstable dt F K const rad dz e.g. if dt dz const K 3 16T 3 const Power law 0 a T b Polytropic index n T ab T 1 3 n

14 Deeper parts intrinsically stable Kramers opacity n=3.25 (interior): a=1, b=-7/2 Polytropic index n T ab T 1 3 n Entropy gradient positive (stable) for n > 3/2

15 Solar opacities n << -1 n = 3.25

16 Hydrostatic reference solutions Double Kramers-like H Kr Thickness only ~1Mm

17 Early work in the 1930s

18 Original mixing length model stable unstable weakly unstable stable surface assume interior F conv u S 1 3 rms

19 New solutions with Deardorff flux Entropy gradient d ln T d ln p d / ( S / cp) / dz ( ad ) H p old F conv ( ) ad new F conv ad ) ( D arxiv: v2

20 Consequences of small scales Larger k f less turb. Diffusion: h t =u rms /3k f Applications to dynamos: stronger, less turb diffusive Helps flux transport dynamos Two other important effect: Lambda effect differential rotation (Co smaller, Ta larger) aroclinic term stronger? Negative effective magnetic pressure spots 20

21 Flux emergence in global simulations Nelson, rown, run, Miesch, Toomre (2014) 21

22 3 scenarios Rising flux tubes? Hierachical convection? Self-organization as part of the dynamo g. u. g.w u.w A. 22

23 Sunspot decay 23

24 Self-assembly of a magnetic spot Minimalistic model 2 ingredients: Stratification & turbulence Extensions Coupled to dynamo Compete with rotation Radiation/ionization 24

25 A possible mechanism U i U j i j ij 3 ij U ij U 2 const Re M here based on forcing k Here 15 eddies per box scale Re M =70 means 70x15x2p=7000 based on box scale reakdown of quasi-linear theory randenburg et al (2011,ApJ 740, L50) 25

26 Negative effective magnetic pressure instability Kleeorin, Rogachevskii, Ruzmaikin (1989, 1990) Gas+turbulent+magnetic pressure; in pressure equil. increases turbulence is suppressed turbulent pressure decreases Net effect? 26

27 Sunspot formation that sucks Mean-field simulation: Neg pressure parameterized Typical downflow speeds Ma= randenbur et al (2014) 27

28 i-polar regions in simulations with corona Warnecke et al. (2013, ApJL 777, L37) 28

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

30 First dynamo-generated bi-polar regions Mitra et al. (2014, arxiv) 30

31 Still negative effective magnetic pressure? Or something new? Mitra et al. (2014, arxiv) 31

32 Jabbari et al. (2015, arxiv) Global models 32

33 33 New aspects in mean-field concept b u U E J t... J b u p 2 1 s,, t q q U U u u ij j i i j j i j i Ohm s law Theory and simulations: a effect and turbulent diffusivity Turbulent viscosity and other effects in momentum equation

34 Calculate full ij and ij tensors A t U ε J effect and turbulent magnetic diffusivity turbulent emf j ij j ε J ub * ij j Imposed-field method Convection (randenburg et al. 1990) Correlation method MRI accretion discs (randenburg & Sokoloff 2002) Galactic turbulence (Kowal et al. 2005, 2006) Test field method Stationary geodynamo (Schrinner et al. 2005, 2007) 34

35 35 Calculate full ij and ij tensors J U A t J b u U A t j b u b u u b U a t pq pq pq pq pq pq t j b u b u u b U a Original equation (uncurled) Mean-field equation fluctuations Response to arbitrary mean fields

36 36 Test fields 0 sin 0, 0 cos sin, 0 0 cos kz kz kz kz pq k j ijk pq j ij pq j, kz k kz kz k kz cos sin sin cos cos sin sin cos kz kz kz kz k * 22 * 21 * 12 * 11 Example:

37 Kinematic and t independent of Rm (2 200) ω u u 2 u k 1 rms f u u rms rms k 1 f Sur et al. (2008, MNRAS) 37

38 Nonlocality: convolution Multiplication convolution abcock-leighton effect is an example Sharp structures in mean-field dynamos artifacts Convolution in x-space multiplication in k 38

39 The 4 Roberts flows IV flow: negative eddy diffusivity dynamo ut positive diffusion at small scales Devlen et al. (2013) 39

40 40 Time-delay dynamo for Roberts II and III flows x z x z x t 2 2 ik k decay oscillatory With time delay x z x z x t t 2 ) ( x z x t x z x t 2

41 Time-delay dynamo for Roberts II and III flows t x z 2 x t x zx 2 ( k) k Re 2 [1 ( k) ] Growth when / 2 2 u rms k f 1 3 Rheinhardt et al. (2014) 41

42 Conclusions Small scale deep convection Deep convective flux: Deardorff Thus marginally stable (not unstable) Such flows yield weaker turb diffusion Favor spot formation by NEMPI Dynamo effect from time delay 42