Abstract We review major achievements in our understanding of multiphase coronal plasma, where cool-dense and hot-tenuous matter coexists, brought about by advances in modeling and theory, inspired by observations. We give an overview of models that self-consistently form solar (or stellar) prominences and filaments, or (postflare) coronal rain, and clarify how these different phenomena share a common physical origin, relating radiative losses and coronal heating. While we do not fully understand the coronal heating, multi-dimensional models of solar prominence and rain formation demonstrate how thermal instability triggers condensations, and how their morphology may reveal aspects of the applied heating at play. We emphasize how the many pathways to linear instability due to combined ingredients of heat-loss, gravity, flows, and magnetic topologies are all involved in the resulting nonlinear magnetohydrodynamics. We provide some challenges to future model efforts, especially concerning prominence fine structure, internal dynamics, and their overall lifecycle.

Abstract Mean-field dynamo theory, describing the evolution of large-scale magnetic fields, has been the mainstay of theoretical interpretation of magnetism in astrophysical objects such as the Sun for several decades. More recently, three-dimensional magnetohydrodynamic simulations have reached a level of fidelity where they capture dynamo action self-consistently on local and global scales without resorting to parametrization of unresolved scales. Recent global simulations also capture many of the observed characteristics of solar and stellar large-scale magnetic fields and cycles. Successful explanation of the results of such simulations with corresponding mean-field models is a crucial validation step for mean-field dynamo theory. Here the connections between mean-field theory and current dynamo simulations are reviewed. These connections range from the numerical computation of turbulent transport coefficients to mean-field models of simulations, and their relevance to the solar dynamo. Finally, the most notable successes and current challenges in mean-field theoretical interpretations of simulations are summarized.

Coronal dimmings associated with coronal mass ejections (CMEs) from the Sun have gained much attention since the late 1990s when they were first observed in high-cadence imagery of the SOHO/EIT and Yohkoh/SXT instruments. They appear as localized sudden decreases of the coronal emission at extreme ultraviolet (EUV) and soft X-ray (SXR) wavelengths, that evolve impulsively during the lift-off and early expansion phase of a CME. Coronal dimmings have been interpreted as “footprints” of the erupting flux rope and also as indicators of the coronal mass loss by CMEs. However, these are only some aspects of coronal dimmings and how they relate to the overall CME/flare process. The goal of this review is to summarize our current understanding and observational findings on coronal dimmings, how they relate to CME simulations, and to discuss how they can be used to provide us with a deeper insight and diagnostics of the triggering of CMEs, the magnetic connectivities and coronal reconfigurations due to the CME as well as the replenishment of the corona after an eruption. In addition, we go beyond a pure review by introducing a new, physics-driven categorization of coronal dimmings based on the magnetic flux systems involved in the eruption process. Finally, we discuss the recent progress in studying coronal dimmings on solar-like and late-type stars, and how to use them as a diagnostics for stellar coronal mass ejections and their properties.Supplementary InformationThe online version contains supplementary material available at 10.1007/s41116-025-00041-4.

The Sun provides nearly all the energy powering the Earth’s climate system, far exceeding all other energy sources combined. The incident radiant energy, the “total solar irradiance,” has been measured by an uninterrupted series of temporally overlapping precision space-borne radiometric instruments since 1978, giving a record spanning more than four 11-year solar cycles. Short-term total-irradiance variations exceeding 0.1% can occur over a few days while variations of ~ 0.1% in-phase with the solar cycle are typical. Knowledge of solar variability on timescales longer than the current multi-decadal space-borne record relies on solar-activity proxies and models, which indicate similar-magnitude changes over centuries. Spectrally resolved space-borne irradiance measurements in the ultraviolet have been acquired continuously since 1979, while measurements contiguously spanning the near-ultraviolet to the near-infrared began in 2003. The combination of long-term total- and spectral-irradiance measurements helps determine both the solar causes of irradiance variability, which are primarily due to solar-surface magnetic-activity regions such as sunspots and faculae, and the mechanisms by which solar variability affects the Earth’s climate system, with global and regional temperatures responding to variability at solar-cycle and longer timescales. To better understand these solar influences, the most modern total-irradiance instruments are approaching the needed climate-driven measurement accuracy and stability requirements for detection of potential long-term solar-variability trends, while the latest spectral-irradiance instruments are beginning to be able to discern solar-cycle variability. Focusing on the space-borne era where such measurements are the most accurate and stable, this article describes solar-irradiance instrument designs, capabilities, and operational methodologies. It summarizes the many total- and spectral-irradiance measurements available and the measured solar variabilities on timescales from minutes to solar cycles and discusses extrapolations via models to longer timescales. Measurement composites and reference spectra are reviewed. Current capabilities and future directions are described along with the climate-driven solar-irradiance measurement requirements.

Magnetic storms on stars manifest as remarkable, randomly occurring changes of the luminosity over durations that are tiny in comparison to the normal evolution of stars. These stellar flares are bursts of electromagnetic radiation from X-ray to radio wavelengths, and they occur on most stars with outer convection zones. They are analogous to the events on the Sun known as solar flares, which impact our everyday life and modern technological society. Stellar flares, however, can attain much greater energies than those on the Sun. Despite this, we think that these phenomena are rather similar in origin to solar flares, which result from a catastrophic conversion of latent magnetic field energy into atmospheric heating within a region that is relatively small in comparison to normal stellar sizes. We review the last several decades of stellar flare research. We summarize multi-wavelength observational results and the associated thermal and nonthermal processes in flaring stellar atmospheres. Static and hydrodynamic models are reviewed with an emphasis on recent progress in radiation-hydrodynamics and the physical diagnostics in flare spectra. Thanks to their effects on the space weather of exoplanetary systems (and thus in our search for life elsewhere in the universe) and their preponderance in Kepler mission data, white-light stellar flares have re-emerged in the last decade as a widely-impactful area of study within astrophysics. Yet, there is still much we do not understand, both empirically and theoretically, about the spectrum of flare radiation, its origin, and its time evolution. We conclude with several big-picture questions that are fundamental in our pursuit toward a greater understanding of these enigmatic stellar phenomena and, by extension, those on the Sun.

The application of machine learning in solar physics has the potential to greatly enhance our understanding of the complex processes that take place in the atmosphere of the Sun. By using techniques such as deep learning, we are now in the position to analyze large amounts of data from solar observations and identify patterns and trends that may not have been apparent using traditional methods. This can help us improve our understanding of explosive events like solar flares, which can have a strong effect on the Earth environment. Predicting hazardous events on Earth becomes crucial for our technological society. Machine learning can also improve our understanding of the inner workings of the sun itself by allowing us to go deeper into the data and to propose more complex models to explain them. Additionally, the use of machine learning can help to automate the analysis of solar data, reducing the need for manual labor and increasing the efficiency of research in this field.

One obvious feature of the solar cycle is its variation from one cycle to another. In this article, we review the dynamo models for the long-term variations of the solar cycle. By long-term variations, we mean the cycle modulations beyond the 11-year periodicity and these include, the Gnevyshev–Ohl/Even–Odd rule, grand minima, grand maxima, Gleissberg cycle, and Suess cycles. After a brief review of the observed data, we present the dynamo models for the solar cycle. By carefully analyzing the dynamo models and the observed data, we identify the following broad causes for the modulation: (1) magnetic feedback on the flow, (2) stochastic forcing, and (3) time delays in various processes of the dynamo. To demonstrate each of these causes, we present the results from some illustrative models for the cycle modulations and discuss their strengths and weakness. We also discuss a few critical issues and their current trends. The article ends with a discussion of our current state of ignorance about comparing detailed features of the magnetic cycle and the large-scale velocity from the dynamo models with robust observations.

Here we review present knowledge of the long-term behaviour of solar activity on a multi-millennial timescale, as reconstructed using the indirect proxy method. The concept of solar activity is discussed along with an overview of the dedicated indices used to quantify different aspects of variable solar activity, with special emphasis on sunspot numbers. Over long timescales, quantitative information about past solar activity is historically obtained using a method based on indirect proxies, such as cosmogenic isotopes 14\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{14}$$\\end{document}C and 10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{10}$$\\end{document}Be in natural stratified archives (e.g., tree rings or ice cores). We give a historical overview of the development of the proxy-based method for past solar-activity reconstruction over millennia, as well as a description of the modern state of the art. Special attention is paid to the verification and cross-calibration of reconstructions. It is argued that the method of cosmogenic isotopes makes a solid basis for studies of solar variability in the past on a long timescale (centuries to millennia) during the Holocene (the past ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document}12 millennia). A separate section is devoted to reconstructions of extremely rare solar eruptive events in the past, based on both cosmogenic-proxy data in terrestrial and lunar natural archives, as well as statistics of sun-like stars. Finally, the main features of the long-term evolution of solar magnetic activity, including the statistics of grand minima and maxima occurrence, are summarized and their possible implications, especially for solar/stellar dynamo theory, are discussed.

Waves and oscillations have been observed in the Sun’s atmosphere for over half a century. While such phenomena have readily been observed across the entire electromagnetic spectrum, spanning radio to gamma-ray sources, the underlying role of waves in the supply of energy to the outermost extremities of the Sun’s corona has yet to be uncovered. Of particular interest is the lower solar atmosphere, including the photosphere and chromosphere, since these regions harbor the footpoints of powerful magnetic flux bundles that are able to guide oscillatory motion upwards from the solar surface. As a result, many of the current- and next-generation ground-based and space-borne observing facilities are focusing their attention on these tenuous layers of the lower solar atmosphere in an attempt to study, at the highest spatial and temporal scales possible, the mechanisms responsible for the generation, propagation, and ultimate dissipation of energetic wave phenomena. Here, we present a two-fold review that is designed to overview both the wave analyses techniques the solar physics community currently have at their disposal, as well as highlight scientific advancements made over the last decade. Importantly, while many ground-breaking studies will address and answer key problems in solar physics, the cutting-edge nature of their investigations will naturally pose yet more outstanding observational and/or theoretical questions that require subsequent follow-up work. This is not only to be expected, but should be embraced as a reminder of the era of rapid discovery we currently find ourselves in. We will highlight these open questions and suggest ways in which the solar physics community can address these in the years and decades to come.

Solar meridional circulation is an axisymmetric flow system, extending from the equator to the poles (sim 20 m/s at the surface, approx 1% of the mean solar rotation rate), plunging inwards and subsequently completing the circuit in the interior through an equatorward return flow and a radially outward flow back up to the surface. This article reviews the profound role that meridional circulation plays in maintaining global dynamics and regulating large-scale solar magnetism. Because it is relatively weak in comparison to differential rotation (sim 300 m/s, approx 7% of the mean solar rotation rate) and owing to numerous systematical errors, accurate surface measurements were only first made in 1978 and initial inferences of interior meridional circulation were obtained using helioseismology two decades later. However, systematical biases have made it very challenging to reliably recover flow in the deep interior. Despite numerous advances that have served to improve the accuracy of inferences, the location of the return flow and the full extent of the circulation are still open problems. This article follows the historical developments and summarises contemporary advances that have led to modern inferences of surface and interior meridional flow.