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

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

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

B05 4

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

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

Turbulent sunspot origins?

8 A possible mechanism Breakdown of quasi-linear theory Re M here based on forcing k Here 15 eddies per box scale Re M =70 means 70x15x2  =7000 based on box scale Brandenburg (2011,ApJ 740, L50)

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

10 Setup 3-D box, size (2  ) 3, isothermal MHD Random, nonhelical forcing at k f /k 1 =5, 15 or 30 Stratified in z,  ~exp(-z/H), H=1,  =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  to =(u rms k f ) -1, turb diff  td =(  t k 1 2 ) -1 Is longer by factor 3(k f /k 1 ) 2 = = 675 Average B y over y and  t=80  to

11 Basic mechanism Anelastic: descending structure  compression 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?

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

Sunspot decay 15

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

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

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

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

Bi-polar regions in simulations with corona 20 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? Hindman et al. (2009, ApJ) Brandenburg (2005, ApJ) Tilt here from latitudinal shear

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)

Type of dynamo? 26 Use phase relation Closer to  2 dynamo Wrong for  dyn. Mitra et al. (2010) Oscillatory  2 dynamo

# of cells 27 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 Theories for shallow spots: (i) Collapse by suppression of turbulent heat flux (ii) Negative pressure effects from vs B i B j Kosovichev et al. (2000)

Pencil code Started in Sept with Wolfgang Dobler High order (6 th order in space, 3 rd 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)  s/pt/step at , 2048 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 –Chemistry, combustion –Spherical coordinates