Living Rev. Sol. Phys. (2017) 14:4 DOI 10.1007/s41116-017-0007-8 REVIEW ARTICLE Magnetism, dynamo action and the solar-stellar connection Allan Sacha Brun1 · Matthew K. Browning2 Received: 23 August 2016 / Accepted: 28 July 2017 © The Author(s) 2017. This article is an open access publication Abstract 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 observa- tions of other stars, and to theory and simulation, we may infer other aspects of the magnetism—e.g., 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 connec- tion”: i.e., 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, includ- ing 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 B Allan Sacha Brun [email protected] Matthew K. Browning [email protected] 1 Laboratoire AIM, DRF/IRFU/Département d’Astrophysique, CEA-Saclay 91191, Gif-sur-Yvette, France 2 Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, UK 123 4 Page 2 of 133 Living Rev. Sol. Phys. (2017) 14:4 summary of what we have learned, and a sampling of issues that remain uncertain or unsolved. Keywords Stellar magnetism · Dynamo · Sun: magnetic fields, rotation · Stars: magnetism, rotation, wind · Convection · Magnetohydrodynamics (MHD) · Methods: numerical Contents 1 Introduction ............................................... 2 The Sun: dynamics and magnetism over time .............................. 3 Aspects of stellar evolution ....................................... 3.1 Mass loss .............................................. 3.2 Rotational evolution ......................................... 4 Diversity of stellar dynamics and magnetism .............................. 4.1 Main observational techniques ................................... 4.2 Pre main sequence stars ....................................... 4.3 Main sequence solar-like stars ................................... 4.4 Lower-mass stars .......................................... 4.4.1 Introduction .......................................... 4.4.2 Observational challenges and summary ........................... Many fully convective stars are very active ............................. Some correlations between rotation and activity persist ...................... 4.4.3 Spatial structure of the fields ................................. 4.4.4 Possible impact of magnetism on structure .......................... 4.5 More massive main-sequence stars ................................. 4.5.1 Convective cores, radiative envelopes and the presence of coronae ............. 4.5.2 The Ap/Bp phenomenon ................................... 5 Origins of stellar activity ......................................... 5.1 Basics of convection and rotation .................................. 5.2 Basics of dynamo theory ...................................... 5.2.1 Dynamos in principle: equations, limits, and energetics ................... When do we expect a dynamo? ................................... Estimates of field strength ...................................... 5.2.2 Mean field theory ....................................... 5.3 Applications to solar and stellar dynamos ............................. 5.3.1 Overview of mean field models ............................... 5.3.2 Babcock–Leighton effects and flux transport ........................ 5.3.3 Open issues and overview .................................. 5.3.4 Application to stars other than the Sun ............................ 5.3.5 Summary of models and their observational attributes .................... 5.4 Fossil fields ............................................. 5.4.1 How strong should fossil fields be? ............................. 5.4.2 Evolution and stability of fields ............................... 5.5 Flux emergence and stellar spots .................................. 5.6 Magnetic effects on coronal activity and winds ........................... 6 Simulations of stellar magnetism and rotation .............................. Unifying physics and methods ...................................... Overview of computational approaches ................................. 6.1 The Sun ............................................... 6.1.1 Historical survey of simulations and codes .......................... 6.1.2 The development of large-scale fields and magnetic cycles ................. 6.1.3 Some recent developments and general principles ...................... 6.2 Young stars ............................................. 6.3 Solar-like stars ............................................ 123 Living Rev. Sol. Phys. (2017) 14:4 Page 3 of 133 4 6.4 Low-mass stars ........................................... Parallels with planetary dynamo simulations ............................ 6.5 More massive stars ......................................... 6.5.1 Core convection simulations: aspects of flows and fields .................. 6.5.2 Evolution of magnetism in stable layers ........................... 6.5.3 Waves in the stable envelope ................................. 6.5.4 Summary and possible implications ............................. 7 Perspectives ............................................... References .................................................. 1 Introduction A star’s life is shaped partly by its magnetism. In its infancy and youth, magnetic fields help mediate the collapse of molecular clouds and, later, the accretion of mate- rial through a protoplanetary disk; during its main-sequence lifetime, they regulate spindown through a stellar wind; as it approaches the end stages of its evolution, they may transport angular momentum, influencing the spin rate of the interior and in turn its ultimate fate. Throughout the star’s life, its surface and interior may crackle with activity induced by the magnetic fields. Like gravity, magnetism can sculpt pro- cesses on the largest of scales; but whereas the gravitational force exerted by a star depends mainly on one parameter (its mass), its magnetism depends on a host of fac- tors (including mass, rotation rate, stratification, and in some cases the past history of the object). In many cases the magnetism is built by the action of a dynamo, a process that converts kinetic energy into magnetic and sustains it against resistive decay. In some others, observed fields are probably inherited from earlier stages of the star’s life, encoding (in principle) information about the interaction of various magnetohydro- dynamic (MHD) instabilities acting cumulatively over aeons. In neither case do we yet have a truly comprehensive theory of the magnetism—i.e., one that would allow us to predict the magnetic field strength and geometry of a given star at a given point in its evolution. But we have many clues, derived from observation, basic theory, and numerical simulations. This paper seeks partly to review those clues. Many of the strongest constraints on stellar magnetism have come from close study of the Sun. Our nearest star has a cyclical large-scale magnetic field, pervasive and variable smaller-scale fields, sunspots that exhibit remarkable spatial and temporal organization—and also exhibits flares, coronal mass ejections, and mass loss that are all ultimately linked to the magnetism. These features, now being probed in exquisite detail by a variety of space-based and ground-based instruments, are described in Sect. 2. Some aspects of the Sun’s magnetism can be traced (albeit indirectly) for millennia, and sunspots have been observed directly for centuries, so observational constraints abound. In this sense, the Sun is an extraordinary laboratory for plasma astrophysics—but it is a laboratory with no accessible controls. To describe how the dynamo process depends on basic parameters like stellar rotation rate or mass, we must also turn to observations (and theory) of other stars. Observations of magnetism on other stars (described mainly in Sect. 4)alsohave a long history, but have lately been revolutionized by new observational instruments and techniques. Extraordinarily precise photometry has allowed fine probing of sur- 123 4 Page 4 of 133 Living Rev. Sol. Phys. (2017) 14:4 face activity and even (through asteroseismology) provided some windows into interior dynamics as well; spectropolarimetry has begun to enable inferences of the field mor- phology; large surveys increasingly constrain the prevalence of