In this review, our present day understanding of the Sun's global photospheric and coronal magnetic fields is discussed from both observational and theoretical viewpoints. Firstly, the large-scale properties of photospheric magnetic fields are described, along with recent advances in photospheric magnetic flux transport models. Following this, the wide variety of theoretical models used to simulate global coronal magnetic fields are described. From this, the combined application of both magnetic flux transport simulations and coronal modeling techniques to describe the phenomena of coronal holes, the Sun's open magnetic flux and the hemispheric pattern of solar filaments is discussed. Finally, recent advances in non-eruptive global MHD models are described. While the review focuses mainly on solar magnetic fields, recent advances in measuring and modeling stellar magnetic fields are described where appropriate. In the final section key areas of future research are identified.
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 like plasma pressure gradient 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 relation 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 of large interests, as accurate measurements of the photospheric field become available from ground-based (for example SOLIS) and space-born (for example Hinode and SDO) instruments. 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.
We review the properties of solar magneto-convection in the top half of the convection zones scale heights (from 20 Mm below the visible surface to the surface, and then through the photosphere to the temperature minimum). Convection is a highly non-linear and non-local process, so it is best studied by numerical simulations. We focus on simulations that include sufficient detailed physics so that their results can be quantitatively compared with observations.
The solar surface is covered with magnetic features with spatial sizes ranging from unobservably small to hundreds of megameters. Three orders of magnitude more magnetic flux emerges in the quiet Sun than emerges in active regions. In this review we focus mainly on the properties of the quiet Sun magnetic field.
The Sun’s magnetic field is produced by dynamo action throughout the convection zone, primarily by stretching and twisting in the turbulent downflows. Diverging convective upflows and magnetic buoyancy carry magnetic flux toward the surface and sweep the field into the surrounding downflow lanes where the field is dragged downward. The result is a hierarchy of undulating magnetic Ω- and U-loops of different sizes. New magnetic flux first appears at the surface in a mixed polarity random pattern and then collects into isolated unipolar regions due to underlying larger scale magnetic structures. Rising magnetic structures are not coherent, but develop a filamentary structure. Emerging magnetic flux alters the convection properties, producing larger, darker granules.
Strong field concentrations inhibit transverse plasma motions and, as a result, reduce convective heat transport toward the surface which cools. Being cooler, these magnetic field concentrations have a shorter scale height and become evacuated. The field becomes further compressed and can reach strengths in balance with the surrounding gas pressure. Because of their small internal density, photons escape from deeper in the atmosphere. Narrow evacuated field concentrations get heated from their hot sidewalls and become brighter than their surroundings. Wider magnetic concentrations are not heated so they become darker, forming pores and sunspots.
Prominences are intriguing, but poorly understood, magnetic structures of the solar corona. The dynamics of solar prominences has been the subject of a large number of studies, and of particular interest is the study of prominence oscillations. Ground- and space-based observations have confirmed the presence of oscillatory motions in prominences and they have been interpreted in terms of magnetohydrodynamic (MHD) waves. This interpretation opens the door to perform prominence seismology, whose main aim is to determine physical parameters in magnetic and plasma structures (prominences) that are difficult to measure by direct means. Here, we review the observational information gathered about prominence oscillations as well as the theoretical models developed to interpret small amplitude oscillations and their temporal and spatial attenuation. Finally, several prominence seismology applications are presented.
In this review we give an overview about the current state-of-knowledge of the magnetic field in sunspots from an observational point of view. We start by offering a brief description of tools that are most commonly employed to infer the magnetic field in the solar atmosphere with emphasis in the photosphere of sunspots. We then address separately the global and local magnetic structure of sunspots, focusing on the implications of the current observations for the different sunspots models, energy transport mechanisms, extrapolations of the magnetic field towards the Corona, and other issues.
We review our current understanding of sunspots from the scales of their fine structure to their large scale (global) structure including the processes of their formation and decay. Recently, sunspot models have undergone a dramatic change. In the past, several aspects of sunspot structure have been addressed by static MHD models with parametrized energy transport. Models of sunspot fine structure have been relying heavily on strong assumptions about flow and field geometry (e.g., flux-tubes, "gaps", convective rolls), which were motivated in part by the observed filamentary structure of penumbrae or the necessity of explaining the substantial energy transport required to maintain the penumbral brightness. However, none of these models could self-consistently explain all aspects of penumbral structure (energy transport, filamentation, Evershed flow). In recent years, 3D radiative MHD simulations have been advanced dramatically to the point at which models of complete sunspots with sufficient resolution to capture sunspot fine structure are feasible. Here overturning convection is the central element responsible for energy transport, filamentation leading to fine-structure and the driving of strong outflows. On the larger scale these models are also in the progress of addressing the subsurface structure of sunspots as well as sunspot formation. With this shift in modeling capabilities and the recent advances in high resolution observations, the future research will be guided by comparing observation and theory.
Coronal loops are the building blocks of the X-ray bright solar corona. They owe their brightness to the dense confined plasma, and this review focuses on loops mostly as structures confining plasma. After a brief historical overview, the review is divided into two separate but not independent parts: the first illustrates the observational framework, the second reviews the theoretical knowledge. Quiescent loops and their confined plasma are considered, and therefore topics such as loop oscillations and flaring loops (except for non-solar ones which provide information on stellar loops) are not specifically addressed here. The observational section discusses loop classification and populations, and then describes the morphology of coronal loops, its relationship with the magnetic field, and the concept of loops as multi-stranded structures. The following part of this section is devoted to the characteristics of the loop plasma and of its thermal structure in particular, according to the classification into hot, warm, and cool loops. Then, temporal analyses of loops and the observations of plasma dynamics and flows are illustrated. In the modeling section some basics of loop physics are provided, supplying some fundamental scaling laws and timescales, a useful tool for consultation. The concept of loop modeling is introduced and models are distinguished between those treating loops as monolithic and static, and those resolving loops into thin and dynamic strands. Then, more specific discussions address modeling the loop fine structure and the plasma flowing along the loops. Special attention is devoted to the question of loop heating, with separate discussion of wave (AC) and impulsive (DC) heating. Finally, a brief discussion about stellar X-ray emitting structures related to coronal loops is included and followed by conclusions and open questions.
The Sun’s supergranulation refers to a physical pattern covering the surface of the quiet Sun with a typical horizontal scale of approximately 30,000 km and a lifetime of around 1.8 d. Its most noticeable observable signature is as a fluctuating velocity field of 360 m s–1 rms whose components are mostly horizontal. Supergranulation was discovered more than fifty years ago, however explaining why and how it originates still represents one of the main challenges of modern solar physics.
A lot of work has been devoted to the subject over the years, but observational constraints, conceptual difficulties and numerical limitations have all concurred to prevent a detailed understanding of the supergranulation phenomenon so far. With the advent of 21st century supercomputing resources and the availability of unprecedented high-resolution observations of the Sun, a stage at which key progress can be made has now been reached. A unifying strategy between observations and modelling is more than ever required for this to be possible.
The primary aim of this review is therefore to provide readers with a detailed interdisciplinary description of past and current research on the problem, from the most elaborate observational strategies to recent theoretical and numerical modelling efforts that have all taken up the challenge of uncovering the origins of supergranulation. Throughout the text, we attempt to pick up the most robust findings so far, but we also outline the difficulties, limitations and open questions that the community has been confronted with over the years.
In the light of the current understanding of the multiscale dynamics of the quiet photosphere, we finally suggest a tentative picture of supergranulation as a dynamical feature of turbulent magnetohydrodynamic convection in an extended spatial domain, with the aim of stimulating future research and discussions.
Coronal holes are the darkest and least active regions of the Sun, as observed both on the solar disk and above the solar limb. Coronal holes are associated with rapidly expanding open magnetic fields and the acceleration of the high-speed solar wind. This paper reviews measurements of the plasma properties in coronal holes and how these measurements are used to reveal details about the physical processes that heat the solar corona and accelerate the solar wind. It is still unknown to what extent the solar wind is fed by flux tubes that remain open (and are energized by footpoint-driven wave-like fluctuations), and to what extent much of the mass and energy is input intermittently from closed loops into the open-field regions. Evidence for both paradigms is summarized in this paper. Special emphasis is also given to spectroscopic and coronagraphic measurements that allow the highly dynamic non-equilibrium evolution of the plasma to be followed as the asymptotic conditions in interplanetary space are established in the extended corona. For example, the importance of kinetic plasma physics and turbulence in coronal holes has been affirmed by surprising measurements from the UVCS instrument on SOHO that heavy ions are heated to hundreds of times the temperatures of protons and electrons. These observations point to specific kinds of collisionless Alfvén wave damping (i.e., ion cyclotron resonance), but complete theoretical models do not yet exist. Despite our incomplete knowledge of the complex multi-scale plasma physics, however, much progress has been made toward the goal of understanding the mechanisms ultimately responsible for producing the observed properties of coronal holes.
We review the properties of solar convection that are directly observable at the solar surface, and discuss the relevant underlying physics, concentrating mostly on a range of depths from the temperature minimum down to about 20 Mm below the visible solar surface.
The properties of convection at the main energy carrying (granular) scales are tightly constrained by observations, in particular by the detailed shapes of photospheric spectral lines and the topology (time- and length-scales, flow velocities, etc.) of the up- and downflows. Current supercomputer models match these constraints very closely, which lends credence to the models, and allows robust conclusions to be drawn from analysis of the model properties.
At larger scales the properties of the convective velocity field at the solar surface are strongly influenced by constraints from mass conservation, with amplitudes of larger scale horizontal motions decreasing roughly in inverse proportion to the scale of the motion. To a large extent, the apparent presence of distinct (meso- and supergranulation) scales is a result of the folding of this spectrum with the effective "filters" corresponding to various observational techniques. Convective motions on successively larger scales advect patterns created by convection on smaller scales; this includes patterns of magnetic field, which thus have an approximately self-similar structure at scales larger than granulation.
Radiative-hydrodynamical simulations of solar surface convection can be used as 2D/3D time-dependent models of the solar atmosphere to predict the emergent spectrum. In general, the resulting detailed spectral line profiles agree spectacularly well with observations without invoking any micro- and macroturbulence parameters due to the presence of convective velocities and atmosphere inhomogeneities. One of the most noteworthy results has been a significant reduction in recent years in the derived solar C, N, and O abundances with far-reaching consequences, not the least for helioseismology.
Convection in the solar surface layers is also of great importance for helioseismology in other ways; excitation of the wave spectrum occurs primarily in these layers, and convection influences the size of global wave cavity and, hence, the mode frequencies. On local scales convection modulates wave propagation, and supercomputer convection simulations may thus be used to test and calibrate local helioseismic methods.
We also discuss the importance of near solar surface convection for the structure and evolution of magnetic patterns: faculae, pores, and sunspots, and briefly address the question of the importance or not of local dynamo action near the solar surface. Finally, we discuss the importance of near solar surface convection as a driver for chromospheric and coronal heating.
Kinetic plasma physics of the solar corona and solar wind are reviewed with emphasis on the theoretical understanding of the in situ measurements of solar wind particles and waves, as well as on the remote-sensing observations of the solar corona made by means of ultraviolet spectroscopy and imaging. In order to explain coronal and interplanetary heating, the microphysics of the dissipation of various forms of mechanical, electric and magnetic energy at small scales (e.g., contained in plasma waves, turbulences or non-uniform flows) must be addressed. We therefore scrutinise the basic assumptions underlying the classical transport theory and the related collisional heating rates, and also describe alternatives associated with wave-particle interactions. We elucidate the kinetic aspects of heating the solar corona and interplanetary plasma through Landau- and cyclotron-resonant damping of plasma waves, and analyse in detail wave absorption and micro instabilities. Important aspects (virtues and limitations) of fluid models, either single- and multi-species or magnetohydrodynamic and multi-moment models, for coronal heating and solar wind acceleration are critically discussed. Also, kinetic model results which were recently obtained by numerically solving the Vlasov–Boltzmann equation in a coronal funnel and hole are presented. Promising areas and perspectives for future research are outlined finally.
This paper reviews our attempts to understand the transport of magnetic flux on the Sun from the Babcock and Leighton models to the recent revisions that are being used to simulate the field over many sunspot cycles. In these models, the flux originates in sunspot groups and spreads outward on the surface via supergranular diffusion; the expanding patterns become sheared by differential rotation, and the remnants are carried poleward by meridional flow. The net result of all of the flux eruptions during a sunspot cycle is to replace the initial polar fields with new fields of opposite polarity. A central issue in this process is the role of meridional flow, whose relatively low speed is near the limit of detection with Doppler techniques. A compelling feature of Leighton’s original model was that it reversed the polar fields without the need for meridional flow. Now, we think that meridional flow is central to the reversal and to the dynamo itself.
Wave and oscillatory activity of the solar corona is confidently observed with modern imaging and spectral instruments in the visible light, EUV, X-ray and radio bands, and interpreted in terms of magnetohydrodynamic (MHD) wave theory. The review reflects the current trends in the observational study of coronal waves and oscillations (standing kink, sausage and longitudinal modes, propagating slow waves and fast wave trains, the search for torsional waves), theoretical modelling of interaction of MHD waves with plasma structures, and implementation of the theoretical results for the mode identification. Also the use of MHD waves for remote diagnostics of coronal plasma - MHD coronal seismology - is discussed and the applicability of this method for the estimation of coronal magnetic field, transport coefficients, fine structuring and heating function is demonstrated.