Magnetic helicity fluxes in interface and flux transport dynamos

Dynamos in the Sun and other bodies tend to produce magnetic fields that possess magnetic helicity of opposite sign at large and small scales, respectively. The build-up of magnetic helicity at small scales provides an important saturation mechanism. In order to understand the nature of the solar dynamo we need to understand the details of the saturation mechanism in spherical geometry. In particular, we want to understand the effects of magnetic helicity fluxes from turbulence and meridional circulation. We consider a model with just radial shear confined to a thin layer (tachocline) at the bottom of the convection zone. The kinetic alpha owing to helical turbulence is assumed to be localized in a region above the convection zone. The dynamical quenching formalism is used to describe the build-up of mean magnetic helicity in the model, which results in a magnetic alpha effect that feeds back on the kinetic alpha effect. In some cases we compare with results obtained using a simple algebraic alpha quenching formula. In agreement with earlier findings, the magnetic alpha effect in the dynamical alpha quenching formalism has the opposite sign compared with the kinetic alpha effect and leads to a catastrophic decrease of the saturation field strength with increasing magnetic Reynolds numbers. However, at high latitudes this quenching effect can lead to secondary dynamo waves that propagate poleward due to the opposite sign of alpha. Magnetic helicity fluxes both from turbulent mixing and from meridional circulation alleviate catastrophic quenching.Comment: 9 pages, 14 figures, submitted to A &

Extracting scaling laws from numerical dynamo models

Earth's magnetic field is generated by processes in the electrically conducting, liquid outer core, subsumed under the term `geodynamo'. In the last decades, great effort has been put into the numerical simulation of core dynamics following from the magnetohydrodynamic (MHD) equations. However, the numerical simulations are far from Earth's core in terms of several control parameters. Different scaling analyses found simple scaling laws for quantities like heat transport, flow velocity, magnetic field strength and magnetic dissipation time. We use an extensive dataset of 116 numerical dynamo models compiled by Christensen and co-workers to analyse these scalings from a rigorous model selection point of view. Our method of choice is leave-one-out cross-validation which rates models according to their predictive abilities. In contrast to earlier results, we find that diffusive processes are not negligible for the flow velocity and magnetic field strength in the numerical dynamos. Also the scaling of the magnetic dissipation time turns out to be more complex than previously suggested. Assuming that the processes relevant in the numerical models are the same as in Earth's core, we use this scaling to estimate an Ohmic dissipation of 3-8 TW for the core. This appears to be consistent with recent high CMB heat flux scenarios.Comment: 21 pages, 11 figure

The Magnetic Sun: Reversals and Long-Term Variations

A didactic introduction to current thinking on some aspects of the solar dynamo is given for geophysicists and planetary scientists.Comment: 17 pages, 9 figures; Space Science Rev., in pres

Accretion Disks and Dynamos: Toward a Unified Mean Field Theory

Conversion of gravitational energy into radiation in accretion discs and the origin of large scale magnetic fields in astrophysical rotators have often been distinct topics of research. In semi-analytic work on both problems it has been useful to presume large scale symmetries, necessarily resulting in mean field theories. MHD turbulence makes the underlying systems locally asymmetric and nonlinear. Synergy between theory and simulations should aim for the development of practical mean field models that capture essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion theory exemplify such ongoing pursuits. 21st century MFD theory has more nonlinear predictive power compared to 20th century MFD theory, whereas accretion theory is still in a 20th century state. In fact, insights from MFD theory are applicable to accretion theory and the two are artificially separated pieces of what should be a single theory. I discuss pieces of progress that provide clues toward a unified theory. A key concept is that large scale magnetic fields can be sustained via local or global magnetic helicity fluxes or via relaxation of small scale magnetic fluctuations, without the kinetic helicity driver of 20th century textbooks. These concepts may help explain the formation of large scale fields that supply non-local angular momentum transport via coronae and jets in a unified theory of accretion and dynamos. In diagnosing the role of helicities and helicity fluxes in disk simulations, each disk hemisphere should be studied separately to avoid being misled by cancelation that occurs as a result of reflection asymmetry. The fraction of helical field energy in disks is expected to be small compared to the total field in each hemisphere as a result of shear, but can still be essential for large scale dynamo action.Comment: For the Proceedings of the Third International Conference and Advanced School "Turbulent Mixing and Beyond," TMB-2011 held on 21 - 28 August 2011 at the Abdus Salam International Centre for Theoretical Physics, Trieste, http://users.ictp.it/~tmb/index2011.html Italy, To Appear in Physica Scripta (corrected small items to match version in print

Polar Field Puzzle: Solutions from Flux-Transport Dynamo and Surface Transport Models

Polar fields in solar cycle 23 were about 50% weaker than those in cycle 22. The only theoretical models which have addressed this puzzle are surface transport models and flux-transport dynamo models. Comparing polar fields obtained from numerical simulations using surface flux transport models and flux-transport dynamo models, we show that both classes of models can explain the polar field features within the scope of the physics included in the respective models. In both models, how polar fields change as a result of changes in meridional circulation depends on the details of meridional circulation profile used. Using physical reasoning and schematics as well as numerical solutions from a flux-transport dynamo model, we demonstrate that polar fields are determined mostly by the strength of surface poloidal source provided by the decay of tilted, bipolar active regions. Profile of meridional flow with latitude and its changes with time have much less effect in flux-transport dynamo models than in surface transport models.Comment: ApJ (accepted