Mesoscale convective Mesoscale convective dynamo and sunspot dynamo and sunspot

formationformation

A. V. GetlingA. V. Getling

Skobeltsyn Institute of Nuclear Physics, Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University,Lomonosov Moscow State University,

Moscow, RussiaMoscow, Russia

V. V. Kolmychkov and O. S. Mazhorova V. V. Kolmychkov and O. S. Mazhorova

Keldysh Institute of Applied Mathematics, Keldysh Institute of Applied Mathematics, Moscow, RussiaMoscow, Russia

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

observationsobservations

No longer a paradigm!No longer a paradigm!AlternativeAlternative: formation of active regions formation of active regions in situin situ

Convection is frequently attributed to the production Convection is frequently attributed to the production of only of only small-scalesmall-scale, highlyhighly intermittentintermittent magnmagneetictic fieldsfields (e.g., Cattaneo 1999) (e.g., Cattaneo 1999)

In contrast, we consider a local mechanism whose In contrast, we consider a local mechanism whose action should be an inherent property of the action should be an inherent property of the topologytopology of cellular convective flows on of cellular convective flows on variousvarious scalesscales

Different views of local dynamoDifferent views of local dynamo

““Sweeping”Sweeping” of of magnetic field magnetic field lines by lines by convective convective flowflow

““Winding”Winding” of magnetic field linesof magnetic field lines:: Tverskoi’s toroidal eddy, Tverskoi’s toroidal eddy, the earliest local-convective-dynamo modelthe earliest local-convective-dynamo model

B.A. TverskoB.A. Tverskoii, , Geomagn. AeronGeomagn. Aeron. . 66 (1), 11–18, 1966 (1), 11–18, 1966

Previous simulationsPrevious simulations with periodic with periodic boundary conditions at side boundariesboundary conditions at side boundaries

(a strong stabilisung effect)(a strong stabilisung effect)

W. DoblerW. Dobler andand A.V. Getling, IAUS No. 223, St. Petersburg, 2004A.V. Getling, IAUS No. 223, St. Petersburg, 2004

Ra = 5 Ra = 5 × 10× 1033, Pr = 1, Pr, Pr = 1, Prmm = 30, = 30, QQ = 1 = 1

The u and B fields in the horizontal midplane

Computation domain Units of measure Computation domain Units of measure

0

10

2

:field Magnetic

:eTemperatur

/ :Time

:Length

B

TTT

Ht

H

Ly = 8Lx = 8

1

B0

0 :boundaries side At

0,1 :surfaces horizontal At

,0 :boundaries all At

Swn

10

S0SS

T

z

TT

V

zz

BB

Boundary conditionsBoundary conditions

Pr

12

Ha

4Pr

Pr

Ra

2

0

2m

3

HTc

Qq

c

HB

c

HTg

p

Rayleigh number:

Prandtl number:

Magnetic Prandtl number:

Hartmann number:

Heat-source/sink density:

Physical parametersPhysical parameters

Boussinesq approximationBoussinesq approximationis usedis used

Present study: formulation of the problem

ArtificialArtificial static temperature profilestatic temperature profile(needed to obtain(needed to obtain three-dimensionalthree-dimensional cells)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 theA modification of the SIMPLESIMPLE algorithmalgorithm ((SSemi-emi-IImplicit mplicit MMethod for ethod for PPressure-ressure-LLinked inked EEquationsquations))

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)

RaRa ~ 50 Ra~ 50 Racc, PrPr == 3030,, Pr Prmm = 60= 60,, На = На = 0.010.01

vz at z = 0.5 B (top) and Bz at 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

RaRa ~ 50 Ra~ 50 Racc, PrPr == 3030,, Pr Prmm = 60= 60,, На = На = 0.010.01

vz at z = 0.5 B (top) and Bz at 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

RaRa ~ 50 Ra~ 50 Racc, PrPr == 3030,, Pr Prmm = 60= 60,, На = На = 0.010.01

RaRa ~ 50 Ra~ 50 Racc, PrPr == 3030,, Pr Prmm = 60= 60,, На = На = 0.010.01

vz at z = 0.5 B (top) and Bz at z = 0.5 (bottom)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 ]

RaRa ~ 50 Ra~ 50 Racc, PrPr == 3030,, Pr Prmm = 60= 60,, На = На = 0.010.01

Time variation of the extremum Bz values

RaRa ~ 100 Ra~ 100 Racc, PrPr == 3030,, Pr Prmm = = 303000,, На = На = 0.010.01

Bz colour scales with saturation levels are given in the left-hand plots; Bz ranges for the whole layer, in the right-hand plots

RaRa ~ 100 Ra~ 100 Racc, PrPr == 3030,, Pr Prmm = = 303000,, На = На = 0.010.01

Time variation of the extremum Bz values

Rising-flux-tube model:Rising-flux-tube model: points of disagreemet with observationspoints of disagreemet with observations

In reality, In reality, the the growgrowing magnetic field “seeping magnetic field “seepss” through ” through the photosphere withoutthe photosphere without breaking down the existing breaking down the existing supergranular and mesogranular velocity field.supergranular and mesogranular velocity field.

A strong horizontalA strong horizontal magnetic fieldmagnetic field at the apex of the at the apex of the risingrising-tube -tube looploop would dominawould dominate te on the scale of the on the scale of the entire active region before theentire active region before the origin of a sunspot origin of a sunspot groupgroup and and impart a roll-type structureimpart a roll-type structure to the to the convective flow.convective flow.

No spreading flows are observed on the scale of the No spreading flows are observed on the scale of the entire complex magnetic configurationentire complex magnetic configuration of the of the developing sunspot groupdeveloping sunspot group. . Instead, flows are locally Instead, flows are locally associated with each small-scale magnetic islandassociated with each small-scale magnetic island..

The presence of “parasitic” polarities within the area The presence of “parasitic” polarities within the area filled with a predominant magneticfilled with a predominant magnetic polarity.polarity.

The coexistence of differently directed vertical The coexistence of differently directed vertical velocities inside the regions of a givenvelocities inside the regions of a given magnetic magnetic polarity.polarity.

See poster by Getling, Ishikawa & BucnevSee poster by Getling, Ishikawa & Bucnev

Convective mechanismConvective mechanism::better agreebetter agreement with ment with observationobservationss

The observed consistency of the developing magnetic field The observed consistency of the developing magnetic field with the convective velocitywith the convective velocity field is an inherent property of field is an inherent property of this mechanism.this mechanism.

Since the amplified magnetic field should largely be Since the amplified magnetic field should largely be collinear with the streamlines, nocollinear with the streamlines, no strong horizontal field strong horizontal field should connect different polarities.should connect different polarities.

If convection forms local magnetic fields, spreading flows If convection forms local magnetic fields, spreading flows should actually be associatedshould actually be associated with developing magnetic with developing magnetic islands rather than with the entire complex.islands rather than with the entire complex.

Diverse complex patterns with mixed polarities can be Diverse complex patterns with mixed polarities can be accounted for in a natural way byaccounted for in a natural way by the presence of a fine the presence of a fine structure of the convective flow.structure of the convective flow.

The convective mechanism can in principle operate on The convective mechanism can in principle operate on various spatial scales, being controlledvarious spatial scales, being controlled solely by the solely by the topology of the flow.topology of the flow.

Summary This simplified model demonstrates the ability of This simplified model demonstrates the ability of quasi-quasi-

regular convective flowsregular convective flows to produce diverse magnetic-field to produce diverse magnetic-field configurations, which typically resemble those observed in configurations, which typically resemble those observed in the photospherethe photosphere..

Local magnetic-field concentrations develop in both the Local magnetic-field concentrations develop in both the intercellular network and inside the cells. Bipolar intercellular network and inside the cells. Bipolar configurations form an important class of developing configurations form an important class of developing structures.structures.

More complex initial magnetic fields would produce more More complex initial magnetic fields would produce more complex configurations of the amplified field.complex configurations of the amplified field.

The flow topology is of primary importance for the The flow topology is of primary importance for the magnetic-field amplification and structuring process. The magnetic-field amplification and structuring process. The regularities of the process can manifest themselves on regularities of the process can manifest themselves on different spatial scales.different spatial scales.

Magnetic buoyancy should play a certain role in the further Magnetic buoyancy should play a certain role in the further evolution of the magnetic structure formed.evolution of the magnetic structure formed.

The convective mechanism seems to better agree with the The convective mechanism seems to better agree with the observations than the rising-tube mechanism does.observations than the rising-tube mechanism does.

Thank you for your Thank you for your attentionattention