Magnetic fields in the solar convection zone

It has been a prevailing picture that active regions on the solar surface originate from a strong toroidal magnetic field stored in the overshoot region at the base of the solar convection zone, generated by a deep seated solar dynamo mechanism. This article reviews the studies in regard to how the toroidal magnetic field can destabilize and rise through the convection zone to form the observed solar active regions at the surface. Furthermore, new results from the global simulations of the convective dynamos, and from the near-surface layer simulations of active region formation, together with helioseismic investigations of the pre-emergence active regions, are calling into question the picture of active regions as buoyantly rising flux tubes originating from the bottom of the convection zone. This article also gives a review on these new developments.

Space weather: the solar perspective

The Sun, as an active star, is the driver of energetic phenomena that structure interplanetary space and affect planetary atmospheres. The effects of Space Weather on Earth and the solar system is of increasing importance as human spaceflight is preparing for lunar and Mars missions. This review is focusing on the solar perspective of the Space Weather relevant phenomena, coronal mass ejections (CMEs), flares, solar energetic particles (SEPs), and solar wind stream interaction regions (SIR). With the advent of the STEREO mission (launched in 2006), literally, new perspectives were provided that enabled for the first time to study coronal structures and the evolution of activity phenomena in three dimensions. New imaging capabilities, covering the entire Sun-Earth distance range, allowed to seamlessly connect CMEs and their interplanetary counterparts measured in-situ (so called ICMEs). This vastly increased our knowledge and understanding of the dynamics of interplanetary space due to solar activity and fostered the development of Space Weather forecasting models. Moreover, we are facing challenging times gathering new data from two extraordinary missions, NASA’s Parker Solar Probe (launched in 2018) and ESA’s Solar Orbiter (launched in 2020), that will in the near future provide more detailed insight into the solar wind evolution and image CMEs from view points never approached before. The current review builds upon the Living Reviews article by Schwenn from 2006, updating on the Space Weather relevant CME-flare-SEP phenomena from the solar perspective, as observed from multiple viewpoints and their concomitant solar surface signatures.

Solar structure and evolution

The Sun provides a critical benchmark for the general study of stellar structure and evolution. Also, knowledge about the internal properties of the Sun is important for the understanding of solar atmospheric phenomena, including the solar magnetic cycle. Here I provide a brief overview of the theory of stellar structure and evolution, including the physical processes and parameters that are involved. This is followed by a discussion of solar evolution, extending from the birth to the latest stages. As a background for the interpretation of observations related to the solar interior I provide a rather extensive analysis of the sensitivity of solar models to the assumptions underlying their calculation. I then discuss the detailed information about the solar interior that has become available through helioseismic investigations and the detection of solar neutrinos, with further constraints provided by the observed abundances of the lightest elements. Revisions in the determination of the solar surface abundances have led to increased discrepancies, discussed in some detail, between the observational inferences and solar models. I finally briefly address the relation of the Sun to other similar stars and the prospects for asteroseismic investigations of stellar structure and evolution.

The evolution of the solar wind

How has the solar wind evolved to reach what it is today? In this review, I discuss the long-term evolution of the solar wind, including the evolution of observed properties that are intimately linked to the solar wind: rotation, magnetism and activity. Given that we cannot access data from the solar wind 4 billion years ago, this review relies on stellar data, in an effort to better place the Sun and the solar wind in a stellar context. I overview some clever detection methods of winds of solar-like stars, and derive from these an observed evolutionary sequence of solar wind mass-loss rates. I then link these observational properties (including, rotation, magnetism and activity) with stellar wind models. I conclude this review then by discussing implications of the evolution of the solar wind on the evolving Earth and other solar system planets. I argue that studying exoplanetary systems could open up new avenues for progress to be made in our understanding of the evolution of the solar wind.

Solar force-free magnetic fields

The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces such as plasma pressure gradients and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relationship between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently a large area of research, as accurate measurements of the photospheric field are available from ground-based observatories such as the Synoptic Optical Long-term Investigations of the Sun and the Daniel K. Inouye Solar Telescope (DKIST) and space-born, e.g., from Hinode and the Solar Dynamics Observatory. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma.

The Parker problem: existence of smooth force-free fields and coronal heating

Parker (Astrophys J 174:499, 1972) put forward a hypothesis regarding the fundamental nature of equilibrium magnetic fields in astrophysical plasmas. He proposed that if an equilibrium magnetic field is subjected to an arbitrary, small perturbation, then—under ideal plasma dynamics—the resulting magnetic field will in general not relax towards a smooth equilibrium, but rather, towards a state containing tangential magnetic field discontinuities. Even at astrophysical plasma parameters, as the singular state is approached dissipation must eventually become important, leading to the onset of rapid magnetic reconnection and energy dissipation. This topological dissipation mechanism remains a matter of debate, and is a key ingredient in the nanoflare model for coronal heating. We review the various theoretical and computational approaches that have sought to prove or disprove Parker’s hypothesis. We describe the hypothesis in the context of coronal heating, and discuss different approaches that have been taken to investigating whether braiding of magnetic field lines is responsible for maintaining the observed coronal temperatures. We discuss the many advances that have been made, and highlight outstanding open questions.

Dynamo models of the solar cycle

This paper reviews recent advances and current debates in modeling the solar cycle as a hydromagnetic dynamo process. Emphasis is placed on (relatively) simple dynamo models that are nonetheless detailed enough to be comparable to solar cycle observations. After a brief overview of the dynamo problem and of key observational constraints, I begin by reviewing the various magnetic field regeneration mechanisms that have been proposed in the solar context. I move on to a presentation and critical discussion of extant solar cycle models based on these mechanisms, followed by a discussion of recent magnetohydrodynamical simulations of solar convection generating solar-like large-scale magnetic cycles. I then turn to the origin and consequences of fluctuations in these models and simulations, including amplitude and parity modulation, chaotic behavior, and intermittency. The paper concludes with a discussion of our current state of ignorance regarding various key questions relating to the explanatory framework offered by dynamo models of the solar cycle.

Radiation hydrodynamics in simulations of the solar atmosphere

Nearly all energy generated by fusion in the solar core is ultimately radiated away into space in the solar atmosphere, while the remaining energy is carried away in the form of neutrinos. The exchange of energy between the solar gas and the radiation field is thus an essential ingredient of atmospheric modeling. The equations describing these interactions are known, but their solution is so computationally expensive that they can only be solved in approximate form in multi-dimensional radiation-MHD modeling. In this review, I discuss the most commonly used approximations for energy exchange between gas and radiation in the photosphere, chromosphere, and corona.

Solar cycle prediction

A review of solar cycle prediction methods and their performance is given, including early forecasts for Cycle 25. 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. The choice of a good precursor often implies considerable physical insight: indeed, it has become increasingly clear that the transition from purely empirical precursors to model-based methods is continuous. Model-based approaches can be further divided into two groups: predictions based on surface flux transport models and on consistent dynamo models. The implicit assumption of precursor methods 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. In their overall performance during the course of the last few solar cycles, precursor methods have clearly been superior to extrapolation methods. One method that has yielded predictions consistently in the right range during the past few solar cycles is the polar field precursor. Nevertheless, some extrapolation methods may still be worth further study. Model based forecasts are quickly coming into their own, and, despite not having a long proven record, their predictions are received with increasing confidence by the community.

Historical sunspot records

Sunspot observations are available in fairly good numbers since 1610, after the invention of the telescope. This review is concerned with those sunspot observations of which longer records and drawings in particular are available. Those records bear information beyond the classical sunspot numbers or group sunspot numbers. We begin with a brief summary on naked-eye sunspot observations, in particular those with drawings. They are followed by the records of drawings from 1610 to about 1900. The review is not a compilation of all known historical sunspot information. Some records contributing substantially to the sunspot number time series may therefore be absent. We also glance at the evolution of the understanding of what sunspots actually are, from 1610 to the 19th century. The final part of the review illuminates the physical quantities that can be derived from historical drawings.