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

Turbulent rotating convection is an important dynamical process occurring on nearly all planetary and stellar bodies, influencing many observed features such as magnetic fields, atmospheric jets and emitted heat flux patterns. For decades, it has been thought that the importance of rotation's influence on convection depends on the competition between the two relevant forces in the system: buoyancy (non-rotating) and Coriolis (rotating). The force balance argument does not, however, accurately predict the transition from rotationally controlled to non-rotating heat transfer behaviour. New results from laboratory and numerical experiments suggest that the transition is in fact controlled by the relative thicknesses of the thermal (non-rotating) and Ekman (rotating) boundary layers. Turbulent rotating convection controls many observed features in stars and planets, such as magnetic fields. It has been argued that the influence of rotation on turbulent convection dynamics is governed by the ratio of the relevant global-scale forces: the Coriolis force and the buoyancy force. This paper presents results from laboratory and numerical experiments which exhibit transitions between rotationally dominated and non-rotating behaviour that are not determined by this global force balance. Instead, the transition is controlled by the relative thicknesses of the thermal (non-rotating) and Ekman (rotating) boundary layers. Turbulent rotating convection controls many observed features of stars and planets, such as magnetic fields, atmospheric jets and emitted heat flux patterns1,2,3,4,5,6. It has long been argued that the influence of rotation on turbulent convection dynamics is governed by the ratio of the relevant global-scale forces: the Coriolis force and the buoyancy force7,8,9,10,11,12. Here, however, we present results from laboratory and numerical experiments which exhibit transitions between rotationally dominated and non-rotating behaviour that are not determined by this global force balance. Instead, the transition is controlled by the relative thicknesses of the thermal (non-rotating) and Ekman (rotating) boundary layers. We formulate a predictive description of the transition between the two regimes on the basis of the competition between these two boundary layers. This transition scaling theory unifies the disparate results of an extensive array of previous experiments8,9,10,11,12,13,14,15, and is broadly applicable to natural convection systems.

Boundary Layer Control of Rotating Convection Systems

Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a uni-dimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state. These simulations are shown to be in good agreement with direct simulations in the range where both are feasible, and can be computed for control parameter values far beyond the current state of the art, such as an Ekman number . We obtain strong-field convective dynamos approaching the MAC balance and a Taylor state to an unprecedented degree of accuracy. The physical connection between classical models and asymptotic conditions is shown to be devoid of abrupt transitions, demonstrating the asymptotic relevance of classical numerical dynamo mechanisms. The fields of the system are confirmed to follow diffusivity-free, power-based scaling laws along the path.

Spherical convective dynamos in the rapidly rotating asymptotic regime

Rayleigh–Benard convection in rotating spherical shells can be considered as a simplified analogue of many astrophysical and geophysical fluid flows. Here, we use three-dimensional direct numerical simulations to study this physical process. We construct a dataset of more than 200 numerical models that cover a broad parameter range with Ekman numbers spanning , Rayleigh numbers within the range and a Prandtl number of unity. The radius ratio is 0.6 in all cases and gravity is assumed to be proportional to . We investigate the scaling behaviours of both local (length scales, boundary layers) and global (Nusselt and Reynolds numbers) properties across various physical regimes from onset of rotating convection to weakly rotating convection. Close to critical, the convective flow is dominated by a triple force balance between viscosity, Coriolis force and buoyancy. For larger supercriticalities, a small subset of our numerical data approach the asymptotic diffusivity-free scaling of rotating convection in a narrow fraction of the parameter space delimited by . Using a decomposition of the viscous dissipation rate into bulk and boundary layer contributions, we establish a theoretical scaling of the flow velocity that accurately describes the numerical data. In rapidly rotating turbulent convection, the fluid bulk is controlled by a triple force balance between Coriolis, inertia and buoyancy, while the remaining fraction of the dissipation can be attributed to the viscous friction in the Ekman layers. Beyond , the rotational constraint on the convective flow is gradually lost and the flow properties continuously vary to match the regime changes between rotation-dominated and non-rotating convection. We show that the quantity provides an accurate transition parameter to separate rotating and non-rotating convection.

Scaling regimes in spherical shell rotating convection

Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a unidimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state. These simulations are shown to be in good agreement with direct simulations in the range where both are feasible, and can be computed for control parameter values far beyond the current state of the art, such as an Ekman number $E=10^{-8}$. We obtain strong-field convective dynamos approaching the MAC balance and a Taylor state to an unprecedented degree of accuracy. The physical connection between classical models and asymptotic conditions is shown to be devoid of abrupt transitions, demonstrating the asymptotic relevance of classical numerical dynamo mechanisms. The fields of the system are confirmed to follow diffusivity-free, power-based scaling laws along the path.

https://escholarship.org/content/qt97s3x12h/qt97s3x12h.pdf?t=nvfp71

E.M. King

Papers

Rotating convective turbulence in Earth and planetary cores