An Introduction to Magnetohydrodynamics

The Sun's magnetic field is the engine and energy source driving all phenomena collectively defining solar activity, which in turn structures the whole heliosphere and significantly impacts Earth's atmosphere down at least to the stratosphere. The solar magnetic field is believed to originate through the action of a hydromagnetic dynamo process operating in the Sun's interior, where the strongly turbulent environment of the convection zone leads to flow-field interactions taking place on an extremely wide range of spatial and temporal scales. Following a necessarily brief observational overview of the solar magnetic field and its cycle, this review on solar dynamo theory is structured around three areas in which significant advances have been made in recent years: (a) global magnetohydrodynamical simulations of convection and magnetic cycles, (b) the turbulent electromotive force and the dynamo saturation problem, and (c) flux transport dynamos, and their application to model cycle fluctuations and grand ...

https://www.leif.org/EOS/Solar-Dynamo-Theory-Charbonneau.pdf

Solar Dynamo Theory

The Sun and other stars are magnetic: magnetism pervades their interiors and affects their evolution in a variety of ways In the Sun, both the fields themselves and their influence on other phenomena can be uncovered in exquisite detail, but these observations sample only a moment in a single star's life By turning to observations of other stars, and to theory and simulation, we may infer other aspects of the magnetism-eg, its dependence on stellar age, mass, or rotation rate-that would be invisible from close study of the Sun alone Here, we review observations and theory of magnetism in the Sun and other stars, with a partial focus on the "Solar-stellar connection": ie, ways in which studies of other stars have influenced our understanding of the Sun and vice versa We briefly review techniques by which magnetic fields can be measured (or their presence otherwise inferred) in stars, and then highlight some key observational findings uncovered by such measurements, focusing (in many cases) on those that offer particularly direct constraints on theories of how the fields are built and maintained We turn then to a discussion of how the fields arise in different objects: first, we summarize some essential elements of convection and dynamo theory, including a very brief discussion of mean-field theory and related concepts Next we turn to simulations of convection and magnetism in stellar interiors, highlighting both some peculiarities of field generation in different types of stars and some unifying physical processes that likely influence dynamo action in general We conclude with a brief summary of what we have learned, and a sampling of issues that remain uncertain or unsolved

Magnetism, dynamo action and the solar-stellar connection

Young solar-type stars rotate rapidly and many are magnetically active. Some appear to undergo magnetic cycles similar to the 22 yr solar activity cycle. We conduct simulations of dynamo action in rapidly rotating suns with the three-dimensional magnetohydrodynamic anelastic spherical harmonic (ASH) code to explore dynamo action achieved in the convective envelope of a solar-type star rotating at five times the current solar rotation rate. We find that dynamo action builds substantial organized global-scale magnetic fields in the midst of the convection zone. Striking magnetic wreaths span the convection zone and coexist with the turbulent convection. A surprising feature of this wreath-building dynamo is its rich time dependence. The dynamo exhibits cyclic activity and undergoes quasi-periodic polarity reversals where both the global-scale poloidal and toroidal fields change in sense on a roughly 1500 day timescale. These magnetic activity patterns emerge spontaneously from the turbulent flow and are more organized temporally and spatially than those realized in our previous simulations of the solar dynamo. We assess in detail the competing processes of magnetic field creation and destruction within our simulations that contribute to the global-scale reversals. We find that the mean toroidal fields are built primarily through an Ω-effect, while the mean poloidal fields are built by turbulent correlations which are not well represented by a simple α-effect. During a reversal the magnetic wreaths propagate toward the polar regions, and this appears to arise from a poleward propagating dynamo wave. As the magnetic fields wax and wane in strength and flip in polarity, the primary response in the convective flows involves the axisymmetric differential rotation which varies on similar timescales. Bands of relatively fast and slow fluid propagate toward the poles on timescales of roughly 500 days and are associated with the magnetic structures that propagate in the same fashion. In the Sun, similar patterns are observed in the poleward branch of the torsional oscillations, and these may represent poleward propagating magnetic fields deep below the solar surface.

/pdf/magnetic-cycles-in-a-convective-dynamo-simulation-of-a-young-1lrntjc5rv.pdf

Magnetic cycles in a convective dynamo simulation of a young solar-type star

A review of solar cycle prediction methods and their performance is given, including forecasts for cycle 24. The review focuses on those aspects of the solar cycle prediction problem that have a bearing on dynamo theory. The scope of the review is further restricted to the issue of predicting the amplitude (and optionally the epoch) of an upcoming solar maximum no later than right after the start of the given cycle. Prediction methods form three main groups. Precursor methods rely on the value of some measure of solar activity or magnetism at a specified time to predict the amplitude of the following solar maximum. Their implicit assumption is that each numbered solar cycle is a consistent unit in itself, while solar activity seems to consist of a series of much less tightly intercorrelated individual cycles. Extrapolation methods, in contrast, are based on the premise that the physical process giving rise to the sunspot number record is statistically homogeneous, i.e., the mathematical regularities underlying its variations are the same at any point of time and, therefore, it lends itself to analysis and forecasting by time series methods. Finally, instead of an analysis of observational data alone, model based predictions use physically (more or less) consistent dynamo models in their attempts to predict solar activity. In their overall performance during the course of the last few solar cycles, precursor methods have clearly been superior to extrapolation methods. Nevertheless, most precursor methods overpredicted cycle 23, while some extrapolation methods may still be worth further study. Model based forecasts have not yet had a chance to prove their skills. One method that has yielded predictions consistently in the right range during the past few solar cycles is that of K. Schatten et al., whose approach is mainly based on the polar field precursor. The incipient cycle 24 will probably mark the end of the Modern Maximum, with the Sun switching to a state of less strong activity. It will therefore be an important testbed for cycle prediction methods and, by inference, for our understanding of the solar dynamo.

/pdf/solar-cycle-prediction-5bvnpcjbaw.pdf

Solar cycle prediction

We report on a global magnetohydrodynamical simulation of the solar convection zone, which succeeds in generating a large-scale axisymmetric magnetic component, antisymmetric about the equatorial plane and undergoing regular polarity reversals on decadal timescales. We focus on a specific simulation run covering 255 years, during which 8 polarity reversals are observed, with a mean period of 30 years. Time-latitude slices of the zonally averaged toroidal magnetic component at the base of the convecting envelope show a well-organized toroidal flux system building up in each solar hemisphere, peaking at mid-latitudes and migrating toward the equator in the course of each cycle, in remarkable agreement with inferences based on the sunspot butterfly diagram. The simulation also produces a large-scale dipole moment, varying in phase with the internal toroidal component, suggesting that the simulation may be operating as what is known in mean-field theory as an αΩ dynamo.

/pdf/magnetic-cycles-in-global-large-eddy-simulations-of-solar-4aapphu326.pdf

Magnetic Cycles in Global Large-eddy Simulations of Solar Convection

In this paper, we examine the mode of dynamo action in the implicit large-eddy magnetohydrodynamical simulation of solar convection reported upon in Ghizaru et al. Motivated by the presence of a strong and well-defined large-scale axisymmetric magnetic component undergoing regular polarity reversals, we define the fluctuating component of the magnetic field as the difference between the total field and its zonal average. The subsequent analysis follows the physical logic and mathematical formulation of mean-field electrodynamics, whereby a turbulent electromotive force (EMF) is computed by the suitable averaging of cross-correlations between fluctuating flow and field components and expressed in terms of the mean field via a linear truncated tensorial expansion. We use singular value decomposition to perform a linear least-squares fit of the temporal variation of the EMF to that of the large-scale magnetic component, which yields the components of the full α-tensor. Its antisymmetric component, describing general turbulent pumping, is also extracted. The α-tensor so calculated reproduces a number of features already identified in local, Cartesian simulations of magnetohydrodynamical rotating convection, including an α component positive in the northern solar hemisphere, peaking at high latitudes, and reversing sign near the bottom of the convection zone; downward turbulent pumping throughout the convecting layer; and significant equatorward turbulent pumping at mid latitudes, and poleward at high latitudes in subsurface layers. We also find that the EMF contributes significantly to the regeneration of the large-scale toroidal magnetic component, which from the point of view of mean-field dynamo models would imply that the simulation operates as an α2Ω dynamo. We find little significant evidence of α-quenching by the large-scale magnetic field. The amplitude of the magnetic cycle appears instead to be regulated primarily by a magnetically driven reduction of the differential rotation.

Mihai Ghizaru

Papers

Magnetic Cycles in Global Large-eddy Simulations of Solar Convection

On the mode of dynamo action in a global large-eddy simulation of solar convection