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cattaneo@flash.uchicago.edu The solar dynamo(s) Fausto Cattaneo Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas Chicago 2003

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The solar dynamo problem Chicago 2003 Wide range of spatial scales. From global scale to limit of resolution Wide range of temporal scales. From centuries to minutes Solar activity is extremely well documented The solar dynamo is invoked to explain the origin magnetic activity Three important features: Models are strongly observationally constrained

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Observations Chicago 2003 Hales polarity law suggests organization on global scale. Typical size of active regions approx 200,000Km Typical size of a sunspot 50,000Km Small magnetic elements show structure down to limit of resolution (approx 0.3")

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Observations: large scale Chicago 2003 Active regions migrate from mid- latitudes to the equator Sunspot polarity opposite in two hemispheres Polarity reversal every 11 years

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PROXY DATA OF SOLAR MAGNETIC ACTIVITY AVAILABLE : stored in ice cores after 2 years in atmosphere : stored in tree rings after ~30 yrs in atmosphere 10 Be C 14 Beer (2000) Wagner et al (2001) Cycle persists through Maunder Minimum (Beer et al 1998 ) Observations: large scale Chicago 2003

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Observations: small scale Chicago 2003 Two distinct scales of convection (maybe more) Supergranules: –not visible in intensity –20,000 km typical size –20 hrs lifetime –weak dependence on latitude Granules: –strong contrast –1,000km typical size –5 mins lifetime –homogeneous in latitude

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Observations: small scale Chicago 2003 Quiet photospheric flux Network fields –emerge as ephemeral regions (possibly) –reprocessing time approx 40hrs –weak dependence on solar cycle Intra-network magnetic elements –possibly unresolved –typical lifetime few mins

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General dynamo principle Chicago 2003 Any three-dimensional, turbulent (chaotic) flow with high magnetic Reynolds number is (extremely) likely to be a dynamo. Reflectionally symmetric flows: –Small-scale dynamo action –Disordered fields; same correlation length/time as turbulence –Generate but not Non-reflectionally symmetric flows: –Large-scale dynamo; inverse cascade of magnetic helicity –Organized fields; correlation length/time longer than that of turbulence –Possibility of

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In astrophysics lack of reflectional symmetry associated with (kinetic) helicity Coriolis force Rotation Rotational constraints Introduce Rossby radius Ro (in analogy with geophysical flows) Motions or instabilities on scales Ro feel the rotation. –Coriolis force important helical motions –Inverse cascades large-scale dynamo action Motions or instabilities on scales < Ro do not feel the rotation. –Coriolis force negligible non helical turbulence –Small-scale dynamo action Chicago 2003

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Modeling: large-scale generation Chicago 2003 Dynamical ingredients Helical motions: Drive the α-effect. Regenerate poloidal fields from toroidal Differential rotation: (with radius and/or latitude) Regenerate toroidal fields from poloidal. Probably confined to the tachocline Magnetic buoyancy: Removes strong toroidal field from region of shear. Responsible for emergence of active regions Turbulence: Provides effective transport

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Modeling: helical motions Chicago 2003 Laminar vs turbulent α-effect: –Babcock-Leighton models. α-effect driven by rise and twist of large scale loops and subsequent decay of active regions. Coriolis-force acting on rising loops is crucial. Helical turbulence is irrelevant. Dynamo works because of magnetic buoyancy. –Turbulent models. α-effect driven by helical turbulence. Dynamo works in spite of magnetic buoyancy. Nonlinear effects: –Turbulent α-effect strongly nonlinearly suppressed –Interface dynamos? –α-effect is not turbulent (see above) Cattaneo & Hughes

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Modeling: differential rotation Chicago 2003 Latitudinal differential rotation: –Surface differential rotation persists throughout the convection zone –Radiative interior in solid body rotation Radial shear: –Concentrated in the tachocline; a thin layer at the bottom of the convection zone –Whys is the tachocline so thin? What controls the local dynamics? No self-consistent model for the solar differential rotation Schou et al.

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Modeling: magnetic buoyancy Chicago 2003 Wissink et al. What is the role of magnetic buoyancy? Babcock-Leighton models: –Magnetic buoyancy drives the dynamo –Twisting of rising loops under the action of the Coriolis force generates poloidal field from toroidal field –Dynamo is essentially non-linear Turbulent models: –Magnetic buoyancy limits the growth of the magnetic field –Dynamo can operate in a kinematic regime Do both dynamos coexist? Recovery from Maunder minima?

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Modeling: turbulence Chicago 2003 How efficiently is turbulent transport? Babcock-Leighton models: Turbulent diffusion causes the dispersal of active regions. Transport of poloidal flux to the poles. Interface models: Turbulent diffusion couples the layers of toroidal and poloidal generation All models: –Turbulent pumping helps to keep the flux in the shear region –Turbulence redistributes angular momentum –Etc. etc. etc. Tobias et al.

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Modeling: challenges Chicago 2003 No fully self-consistent model exists. Self-consistent model must capture all dynamical ingredients (MHD, anelastic) Geometry is important (sphericity) Operate in nonlinear regime Resolution issues. Smallest resolvable scales are –in the inertial range –rotationally constrained –stratified Need sophisticated sub-grid models

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temperature g hot cold time evolution Plane parallel layer of fluid Boussinesq approximation Ra=500,000; P=1; Pm=5 Modeling: small-scale generation Chicago 2003 Simulations by Lenz & Cattaneo

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Modeling: physical parameters Chicago 2003 Re Rm Pm =1 Stars Liquid metal experiments simulations IM P m =1 10 2 10 3 10 7 Dynamo must operate in the inertial range of the turbulence Driving velocity is rough How do we model MHD behaviour with Pm <<1

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Pm= 1 Pm=0.5 Re=1100, Rm=550 Re=550, Rm=550 yes no Does the dynamo still operate? (kinematic issue) Dynamo may operate but become extremely inefficient (dynamical issue) Modeling: kinematic and dynamical issues Chicago 2003

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Relax requirement that magnetic field be self sustaining (i.e. impose a uniform vertical field) Construct sequence of simulations with externally imposed field, 8 Pm 1/8, and S = = 0.25 Adjust Ra so that Rm remains constant Pm8.04.02.01.00.50.250.125 Ra9.20E+041.40E+052.00E+053.50E+057.04E+051.40E+062.80E+06 Nx, Ny256 512 768 Modeling: magneto-convection Chicago 2003 Simulations by Emonet & Cattaneo

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Chicago 2003 B-field (vertical)vorticity (vertical) Pm = 8.0 Pm = 0.125 Modeling: magneto-convection

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Chicago 2003 Energy ratio flattens out for Pm < 1 PDFs possibly accumulate for Pm < 1 Evidence of regime change in cumulative PDF across Pm=1 Possible emergence of Pm independent regime Modeling: magneto-convection

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Summary Chicago 2003 Two related but distinct dynamo problems. Large-scale dynamo –Reproduce cyclic activity –Reproduce migration pattern –Reproduce angular momentum distribution (CV and tachocline) –Needs substantial advances in computational capabilities Small scale dynamo –Non helical generation –Small Pm turbulent dynamo

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