Mesoscale convective dynamo and sunspot formation A. V. Getling Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia V. V. Kolmychkov and O. S. Mazhorova Keldysh Institute of Applied Mathematics, Moscow, Russia

Rising-flux-tube mechanism: Many points of disagreement with observations observations No longer a paradigm! Alternativeformation of active regions in situ Alternative: formation of active regions in situ Convection is frequently attributed to the production of only small-scalehighlyintermittentmagnetic fields (e.g., Cattaneo 1999) Convection is frequently attributed to the production of only small-scale, highly intermittent magnetic fields (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 Different views of local dynamo

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

Previous simulations with periodic boundary conditions at side boundaries (a strong stabilisung effect) W. Dobler and A.V. Getling, IAUS No. 223, St. Petersburg, 2004 W. Dobler and A.V. Getling, IAUS No. 223, St. Petersburg, 2004 Ra = 5 × 10 3, Pr = 1, Pr m = 30, Q = 1 The u and B fields in the horizontal midplane

Computation domain Units of measure L y = 8 L x = 8 1 B0B0 Boundary conditions Rayleigh number: Prandtl number: Magnetic Prandtl number: Hartmann number: Heat-source/sink density: Physical parameters Boussinesq approximation is used Present study: formulation of the problem

Artificial static temperature profile (needed to obtain three-dimensional cells) T = 1 – 2z + z 2 The density of heat sinks is specified so as to obtain a static temperature profile of the form (heating from below, volumetric heat removal) A modification of the SIMPLE algorithm (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)

Ra ~ 50 Ra c Pr = 30, Pr m = 60, На = 0.01 Ra ~ 50 Ra c, Pr = 30, Pr m = 60, На = 0.01 v z at z = 0.5 B (top) and B z at z = 0.5 (bottom) B z range is given for the whole volume in the upper right plot and for the midplane in the lower right plot

Ra ~ 50 Ra c Pr = 30, Pr m = 60, На = 0.01 Ra ~ 50 Ra c, Pr = 30, Pr m = 60, На = 0.01 v z at z = 0.5 B (top) and B z at z = 0.5 (bottom) B z range is given for the whole volume in the upper right plot and for the midplane in the lower right plot

Ra ~ 50 Ra c Pr = 30, Pr m = 60, На = 0.01 Ra ~ 50 Ra c, Pr = 30, Pr m = 60, На = 0.01

v z at z = 0.5 B (top) and B z at z = 0.5 (bottom) B z colour scales with saturation levels are given in the upper right plot; B z range for the midplane, in the lower right plot. For the whole layer, B z = [–460, 200 ]

Ra ~ 50 Ra c Pr = 30, Pr m = 60, На = 0.01 Ra ~ 50 Ra c, Pr = 30, Pr m = 60, На = 0.01 Time variation of the extremum B z values

Ra ~ 100 Ra c Pr = 30, Pr m = 300, На = 0.01 Ra ~ 100 Ra c, Pr = 30, Pr m = 300, На = 0.01 B z colour scales with saturation levels are given in the left-hand plots; B z ranges for the whole layer, in the right-hand plots

Ra ~ 100 Ra c Pr = 30, Pr m = 300, На = 0.01 Ra ~ 100 Ra c, Pr = 30, Pr m = 300, На = 0.01

Time variation of the extremum B z values

Rising-flux-tube model: points of disagreemet with observations In reality, the growing magnetic field “seeps” through the photosphere without breaking down the existing supergranular and mesogranular velocity field. In reality, the growing magnetic field “seeps” through the photosphere without breaking down the existing supergranular and mesogranular velocity field. A strong horizontal magnetic field at the apex of the rising-tube loop would dominate on the scale of the entire active region before the origin of a sunspot group and impart a roll-type structure to the convective flow. A strong horizontal magnetic field at the apex of the rising-tube loop would dominate on the scale of the entire active region before the origin of a sunspot group and impart a roll-type structure to the convective flow. No spreading flows are observed on the scale of the entire complex magnetic configuration of the developing sunspot group. Instead, flows are locally associated with each small-scale magnetic island. No spreading flows are observed on the scale of the entire complex magnetic configuration of the developing sunspot group. Instead, flows are locally associated with each small-scale magnetic island. The presence of “parasitic” polarities within the area filled with a predominant magnetic polarity. The presence of “parasitic” polarities within the area filled with a predominant magnetic polarity. The coexistence of differently directed vertical velocities inside the regions of a given magnetic polarity. The coexistence of differently directed vertical velocities inside the regions of a given magnetic polarity. See poster by Getling, Ishikawa & Bucnev See poster by Getling, Ishikawa & Bucnev

Convective mechanism: better agreement with observations The observed consistency of the developing magnetic field with the convective velocity field is an inherent property of this mechanism. The observed consistency of the developing magnetic field with the convective velocity field is an inherent property of this mechanism. Since the amplified magnetic field should largely be collinear with the streamlines, no strong horizontal field should connect different polarities. Since the amplified magnetic field should largely be collinear with the streamlines, no strong horizontal field should connect different polarities. If convection forms local magnetic fields, spreading flows should actually be associated with developing magnetic islands rather than with the entire complex. If convection forms local magnetic fields, spreading flows should actually be associated with developing magnetic islands rather than with the entire complex. Diverse complex patterns with mixed polarities can be accounted for in a natural way by the presence of a fine structure of the convective flow. Diverse complex patterns with mixed polarities can be accounted for in a natural way by the presence of a fine structure of the convective flow. The convective mechanism can in principle operate on various spatial scales, being controlled solely by the topology of the flow. The convective mechanism can in principle operate on various spatial scales, being controlled solely by the topology of the flow.

Summary This simplified model demonstrates the ability of quasi- regular convective flows to produce diverse magnetic- field configurations, which typically resemble those observed in the photosphere. This simplified model demonstrates the ability of quasi- regular convective flows to 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. 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. 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. 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. 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. The convective mechanism seems to better agree with the observations than the rising-tube mechanism does.

Thank you for your attention

Well known: Strong photospheric magnetic fields originate in the intercellular network Alternative: Bipolar and multipolar structures may develop inside supergranules A. Title, lecture at the IAU GA XXVI, Prague, 2006  Convection is frequently attributed to the production of only Cattaneo 1999) Convection is frequently attributed to the production of only small-scale, highly intermittent magnetic fields (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 Different views of local dynamo

Ra ~ 50 Ra c Pr = 30, Pr m = 300, На = 1 Ra ~ 50 Ra c, Pr = 30, Pr m = 300, На = 1

Basically roll convection: Ra ~ 50 Ra c Pr = 30, Pr m = 300, На = 100 Basically roll convection: Ra ~ 50 Ra c, Pr = 30, Pr m = 300, На = 100