Rising-flux-tube mechanism: Many points of disagreement with observations

1. Mesoscale convective dynamo and sunspot formationA. V. GetlingSkobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University,Moscow, Russia V. V. Kolmychkov and O. S. MazhorovaKeldysh Institute of Applied Mathematics, Moscow, Russia

2. Rising-flux-tube mechanism: Many points of disagreement with observations No longer a paradigm! Alternative:formation of active regions in situ Different views of local dynamo Convection is frequently attributed to the production of only small-scale, highlyintermittentmagneticfields (e.g., Cattaneo 1999) In contrast, we consider a local mechanism whose action should be an inherent property of the topology of cellular convective flows on various scales

3. “Sweeping”of magnetic field lines by convective flow “Winding”of magnetic field lines:Tverskoi’storoidal eddy, the earliest local-convective-dynamo model B.A. Tverskoi, Geomagn. Aeron. 6 (1), 11–18, 1966

4. Previous simulationswith periodic boundary conditions at side boundaries (a strong stabilisung effect) W. DoblerandA.V. Getling, IAUS No. 223, St. Petersburg, 2004 Ra = 5 × 103, Pr = 1, Prm = 30, Q = 1 The u and B fields in the horizontal midplane

5. Rayleigh number: Prandtl number: Magnetic Prandtlnumber: Hartmann number: Heat-source/sink density: Present study: formulation of the problem Computation domain Units of measure Physical parameters Boundary conditions 1 Lx = 8 B0 Ly = 8 Boussinesq approximation is used

6. T = 1 – 2z + z2 Artificialstatic temperature profile(needed to obtainthree-dimensionalcells) The density ofheat sinksis specified so as to obtain a static temperature profile of the form (heating from below, volumetricheat removal) A modification of theSIMPLEalgorithm(Semi-Implicit Method for Pressure-Linked Equations) A predictor–corrector method of the first order in time and second order in spatial coordinates (ensures conservation of kinetic energy and heat balance): • C.A.J. Fletcher (1991) • V.V. Kolmychkov, O.S. Mazhorova and Yu.P. Popov (2006)

7. Ra~ 50 Rac, Pr=30,Prm= 60, На = 0.01 B (top) and Bzat z = 0.5 (bottom) vzatz = 0.5 Bz range is given for the whole volume in the upper right plot and for the midplane in the lower right plot

8. Ra~ 50 Rac, Pr=30,Prm= 60, На = 0.01 vzatz = 0.5 B (top) and Bzat z = 0.5 (bottom) Bz range is given for the whole volume in the upper right plot and for the midplane in the lower right plot

9. Ra~ 50 Rac, Pr=30,Prm= 60, На = 0.01

10. Ra~ 50 Rac, Pr=30,Prm= 60, На = 0.01 B (top) and Bzat z = 0.5 (bottom) vzatz = 0.5 Bz colour scales with saturation levels are given in the upper right plot; Bz range for the midplane, in the lower right plot. For the whole layer, Bz = [–460, 200 ]

11. Ra~ 50 Rac, Pr=30,Prm= 60, На = 0.01 Time variation of the extremum Bz values

12. Ra~ 100 Rac, Pr=30,Prm= 300, На = 0.01 Bz colour scales with saturation levels are given in the left-hand plots; Bz ranges for the whole layer, in the right-hand plots

13. Ra~ 100 Rac, Pr=30,Prm= 300, На = 0.01 Time variation of the extremum Bz values

14. Rising-flux-tube model:points of disagreemet with observations • In reality, thegrowingmagneticfield “seeps” throughthephotospherewithoutbreakingdowntheexistingsupergranularandmesogranularvelocityfield. • A stronghorizontalmagneticfieldattheapexoftherising-tube loopwoulddominateonthescaleoftheentireactiveregionbeforetheoriginof a sunspotgroup and impart a roll-typestructuretotheconvectiveflow. • Nospreadingflowsareobservedonthescaleoftheentirecomplexmagneticconfigurationofthedevelopingsunspotgroup. Instead, flowsarelocallyassociatedwitheachsmall-scalemagneticisland. • Thepresenceof “parasitic” polaritieswithintheareafilledwith a predominantmagneticpolarity. • Thecoexistenceofdifferentlydirectedverticalvelocitiesinsidetheregionsof a givenmagneticpolarity. See poster by Getling, Ishikawa & Bucnev

15. Convectivemechanism:betteragreement with observations • Theobservedconsistencyofthedevelopingmagneticfieldwiththeconvectivevelocityfieldisaninherentpropertyofthismechanism. • Sincetheamplifiedmagneticfieldshouldlargelybecollinearwiththestreamlines, nostronghorizontalfieldshouldconnectdifferentpolarities. • Ifconvectionformslocalmagneticfields, spreadingflowsshouldactuallybeassociatedwithdevelopingmagneticislandsratherthanwiththeentirecomplex. • Diversecomplexpatternswithmixedpolaritiescanbeaccountedforin a naturalwaybythepresenceof a finestructureoftheconvectiveflow. • Theconvectivemechanismcaninprincipleoperateonvariousspatialscales, beingcontrolledsolelybythetopologyoftheflow.

16. Summary • This simplified model demonstrates the ability of quasi-regular convective flowsto produce diverse magnetic-field configurations, which typically resemble those observed in the photosphere. • Local magnetic-field concentrations develop in both the intercellular network and inside the cells. Bipolar configurations form an important class of developing structures. • More complex initial magnetic fields would produce more complex configurations of the amplified field. • The flow topology is of primary importance for the magnetic-field amplification and structuring process. The regularities of the process can manifest themselves on different spatial scales. • Magnetic buoyancy should play a certain role in the further evolution of the magnetic structure formed. • The convective mechanism seems to better agree with the observations than the rising-tube mechanism does.

17. Thank you for your attention