Solar flares result from explosive magnetic energy release in the solar atmosphere, often linked to magnetic reconnection. While the underlying physical mechanisms are generally understood, the specific conditions that make an active region (AR) flare at a particular moment remain poorly understood. We aim to investigate the role of magnetic vortices in the flare activity of solar ARs, and to assess whether the presence and evolution of such structures can serve as precursors to major flares. We applied the Integrated Averaged Current Deviation (IACD) method to vector magnetic field data from Helioseismic and Magnetic Imager (HMI)/SHARP for three ARs—AR 11157 (nonflaring), AR 11158, and AR 12673 (both flaring). Time series of IACD values were analyzed using the power spectral density, zeta function scaling, kurtosis, and current helicity to characterize the temporal variability and energy distribution of the vortices. Long-lived magnetic vortices were observed to form and intensify before X-class flare events, followed by abrupt changes and collapse near flare onset. The IACD method isolated these structures more effectively than standard diagnostics, such as magnetograms, current density, or helicity maps. Flaring ARs exhibited flatter power spectra, lower kurtosis, and linear zeta scaling, suggesting more continuous energy accumulation. In contrast, the nonflaring AR displayed steeper spectral slopes, higher kurtosis, and nonlinear zeta scaling, indicative of intermittent and less coherent magnetic activity. Magnetic vortices detected via IACD are promising indicators of flare-productive conditions and may reflect topological changes in the magnetic field. Their temporal evolution provides a potential basis for improving flare forecasting tools.

The spatiotemporal inhomogeneous-homogeneous transition in the dynamics and structures of solar photospheric turbulence is studied by applying the complexity-entropy analysis to Hinode images of a vortical region of supergranular junctions in the quiet Sun. During a period of supergranular vortex expansion of 37.5 min, the spatiotemporal dynamics of the line-of-sight magnetic field and the horizontal electromagnetic energy flux display the characteristics of inverse turbulent cascade, evidenced by the formation of a large magnetic coherent structure via the merger of two small magnetic elements trapped by a long-duration vortex. Both magnetic and Poynting fluxes exhibit an admixture of chaos and stochasticity in the complexity-entropy plane, involving a temporal transition from low to high complexity and a temporal transition from high to low entropy during the period of vortex expansion, consistent with Hinode observations.

In the week including Mother’s Day 2024, active region (AR) 13664 became superactive when AR 13668 emerged nearby, causing multiple X-class flares and coronal mass ejections, and an increase in activity level similar to that inferred from geomagnetic storms associated with the historic 1859 events. By analyzing both global warped toroids on which the active regions are strung, and active-region-scale magnetic flux and helicity, we find (i) the north and south toroids have nearly identical warped patterns, with mostly longitudinal wave numbers m = 1–3; (ii) in three longitude intervals the north and south toroids were tipped away from each other in latitude, with a longitude phase shift between them, creating locations most prone to AR eruptions; (iii) on an active region scale, vector magnetic fields deviate far from potential fields, and therefore contain large amounts of magnetic “free energy” available for conversion into kinetic energy and high-temperature radiation; (iv) the positive and negative polarities converge toward each other, facilitating reconnection and magnetic energy release; and (v) rapid changes in magnetic helicity, caused by helicity injection from below that creates helicity imbalances. Despite the coarser resolution of GONG magnetograms, the derived global toroids are strikingly similar to those derived from the Solar Dynamics Observatory's Helioseismic and Magnetic Imager. We conclude that the Mother’s Day superstorms were caused by enhanced magnetic complexity occurring due to intricate interactions among multiple active regions emerging at nearly the same locations. This suggests that predicting the locations of magnetically complex active regions, and studying and tracking their eruptive states using different proxy parameters can greatly improve our ability to forecast intense storms, not only hours but potentially weeks in advance.

Context. The configuration of the longitudinally elongated region that active regions (ARs) cluster around, known as a toroid belt, has been shown to be an indicator of intense activity. In particular, complex ARs at locations in the north and/or south toroids tend to appear "tipped-away" with respect to each other. On the other hand, magnetic helicity has been used as an indicator of flare activity in ARs. Aims. As solar cycle (SC) 25 approaches its peak, a number of significant (X-class) flares have been produced. Here, we investigate the circumstances surrounding two of the most flare-prolific ARs of solar cycle 25, namely, ARs 13590 and 13514. Two aspects of the evolution of these ARs are investigated in this work: the global-scale magnetic toroid configuration and small-scale magnetic field morphology and topology - before, during, and after the onset of major flares. Methods. We studied the global morphology of the solar magnetic fields near intense flares in terms of the spatial distribution of ARs on magnetic fields synoptic maps. On AR scales, we analyzed the magnetic helicity accumulation, as well as its current-carrying and potential components. Results. Our results are consistent with major flare-prolific ARs from solar cycles 23 and 24. In particular, we observe a consistent dominance of current-carrying magnetic helicity at the time of major flares. The evolution of global magnetic toroids, indicating the occurrence of flare-prolific ARs in the tipped-away portion of the toroid, together with the local dynamics of complex ARs, could offer a few weeks of lead time to prepare for upcoming space weather hazards.

Context. Rossby waves, large-scale meandering patterns drifting in longitude, detected in the Sun, were recently shown to a play a crucial role in understanding "seasons" of space weather. Unlike Earth's purely classical atmospheric Rossby waves, the solar counterparts are strongly magnetized and most likely originate in the tachocline. Because of their deeper origin, detecting these magnetized Rossby waves is a challenging task that relies on careful observations of long-lived longitudinally drifting magnetic patterns at the surface and above. Aims. Here, we have utilized 3 years of global, synchronous observations of coronal bright point densities to obtain empirical signatures of dispersion relations that can be attributed to the simulated waves in the tachocline. By tracking the bright point densities at selected latitudes, we computed their wave-number x frequency spectra. Methods. Wave-number x frequency spectra were computed utilizing the Wheeler-Kiladis method. This method has been extensively used in the identification of equatorial waves in Earth's atmosphere by highlighting spectral peaks in the wave-number x frequency space. Results. Our results are compatible with the predictions of magneto-Rossby waves with typical periods of several months and inertio-gravity waves with typical periods of a few weeks, depending on the background magnetic field's strength and stratification at the convection zone base. Our analysis suggests that magnetized Rossby waves originate from the tachocline toroidal field of less than or similar to 15 kG. Global observations of bright points over extended periods will allow us to better constrain the stratification and magnetic field strength in the tachocline.

The “extended solar cycle” indicates that there are two deeply seated toroidal magnetic field bands in each hemisphere. Both bands migrate equatorward as a sunspot cycle progresses. Here, we examine the consequences of global MHD instability of this migrating double-band system in tachocline on the latitudinal structure of unstable modes, which are essentially MHD Rossby waves. We find that latitude-location, latitude-separation, and the amplitude of the bands strongly influence the latitudinal structure and growth rates of the unstable modes of both symmetries about the equator. These properties can lead to “teleconnections” between low- and high-latitudes in each hemisphere and across the equator. High-latitude bands can destabilize low-latitude bands that would otherwise be stable. Stronger high-latitude bands lead to strong interactions between low and high latitude in each hemisphere, but inhibit cross-equatorial band-interaction. Strong cross-equatorial interactions of modes can synchronize cycle minima in north and south. Symmetric and antisymmetric modes of similar amplitudes can lead to substantial asymmetries between north and south. As a solar cycle progresses, excited MHD Rossby waves go through a sequence of changes in latitude structure and growth rate, while maintaining strong links in latitude. These changes and links are theoretical evidence of teleconnections between widely separated latitudes and longitudes in the Sun, which may explain many of the evolving surface magnetic patterns observed as a solar cycle progresses. The wider the separation between high- and low-latitude bands, the earlier the cross-equatorial teleconnection starts in a cycle, and hence the earlier the cycle starts declining.

Instead of using the traditional space-time Fourier analysis of filtered specific atmospheric fields, a normal-mode decomposition method was used to analyze South American intraseasonal variability (ISV). Intraseasonal variability was examined separately in the 30–90-day band, 20–30-day band, and 10–20-day band. The most characteristic structure in the intraseasonal time-scale, in the three bands, was the dipole-like convection between the South Atlantic Convergence Zone (SACZ) and the central-east South America (CESA) region. In the 30–90-day band, the convective and circulation patterns were modulated by the large-scale Madden–Julian oscillation (MJO). In the 20–30-day and 10–20-day bands, the convection structures were primarily controlled by extratropical Rossby wave trains. The normal-mode decomposition of reanalysis data based on 30–90-day, 20–30-day, and 10–20-day ISV showed that the tropospheric circulation and CESA–SACZ convective structure observed over South America were dominated by rotational modes (i.e., Rossby waves, mixed Rossby-gravity waves). A considerable portion of the 30–90-day ISV was also associated with the inertio-gravity (IGW) modes (e.g., Kelvin waves), mainly prevailing during the austral rainy season. The proposed decomposition methodology demonstrated that a realistic circulation can be reproduced, giving a powerful tool for diagnosing and studying the dynamics of waves and the interactions between them in terms of their ability to provide causal accounts of the features seen in observations.

Polar vortices are ubiquitous features of planetary atmospheric flows, from the Earth-like rocky planets to Jupiter- and Saturn-like gas giant planets. Very little is known about their existence or dynamics on the Sun. What should be expected near the Sun’s pole for the upcoming solar multi-viewpoint and polar missions? Here, we report the magnetohydrodynamic (MHD) nonlinear simulations for the formation and evolution of solar polar vortices using a near-surface MHD shallow-water model. Our findings indicate that the rush to the poles, the migration of magnetic fields toward the pole following the Sun’s magnetic cycle, can positively contribute to the formation of polar vortices. The mechanism proposed here for the formation of polar vortices involves the role of magnetic fields and may be relevant to any star with a magnetic cycle. The Sun’s polar vortices resulting from this mechanism are predominantly MHD, consisting of a tight pair of cyclonic and anticyclonic swirls. This mechanism is likely to operate during all solar cycle phases except the peak, when the polar field reverses. Polar vortices can impact dynamical evolution of global flows and polar fields, which seed the next activity cycle, hence better knowledge of physics of polar regions may lead to improved solar cycle and space weather forecasts.

Physics of magnetohydrodynamic (MHD) Rossby waves in the tachocline-layer were studied by Dikpati et al., using a fluid-particle-trajectory approach along with solving vorticity and induction equations. By extending that model to include a hydrodynamic turbulent convection zone (CZ), we examine how MHD Rossby waves generated in the tachocline might diffuse upward through the CZ to solar surface. We find that pure hydrodynamic Rossby wave amplitudes decline with height due to viscous diffusion at a rate that is independent of viscosity and increases with longitude wavenumber. Fast MHD Rossby waves amplitude declines faster with height for increasing toroidal field, due to their longitude-phase shifting with height, which increases dissipation of kinetic energy in the wave velocities. Slow MHD Rossby waves decline even faster with height because their longitude-phase shifts more rapidly with height, due to their slow phase speed. We conclude that low wavenumber HD and fast MHD Rossby waves, originating in the tachocline, might be detected at the photosphere, but slow MHD Rossby waves should be virtually impossible to detect. We infer from fluid particle trajectories that wave amplitudes declining with height and longitude phase shifting with height associated with decline, implies a powerful mechanism for tangling of magnetic fields, distinct from convective turbulence effects. This could cause a sustained or dissipative local dynamo action triggered by Rossby waves.

The equatorial region of the Earth's atmosphere serves as both a significant locus for phenomena, including the Madden-Julian Oscillation (MJO), and a source of formidable complexity. This complexity arises from the intricate interplay between nonlinearity and thermodynamic processes, particularly those involving moisture. In this study, we employ a normal mode decomposition of atmospheric reanalysis ERA-5 datasets to investigate the influence of nonlinearity and moisture on amplitude growth, propagation speed, and mode coupling associated with equatorially trapped waves. We focus our analysis on global-scale baroclinic Kelvin and Rossby waves, recognized as crucial components contributing to the variability of the MJO. We examine the dependence of wave amplitudes on the background moisture field in the equatorial region, as measured by total column water vapor. Our analysis demonstrates the crucial role of moisture in exciting these waves. We further investigate the dependence of the propagation speed of the waves on their amplitudes and the background moisture field. Our analysis reveals a robust correlation between the phase speed of the normal modes and their corresponding amplitude, whereas a weaker correlation is found between the eigenmodes' phase speed and the moisture field. Hence, our findings suggest that moisture plays a role in exciting the global-scale Rossby-Kelvin structure of the MJO. In this context, the propagation speed of the eigenmodes is mainly influenced by their amplitudes, underscoring the significant role of nonlinearity in wave propagation.

Much of the research on the magnetic activity of the Sun has been focused on its axisymmetric component. However, the longitudinal complexity plays a fundamental role in the solar magnetic activity. Rossby waves have recently been proposed as a fundamental mechanism regarding the nonaxisymmetric nature of the solar magnetic fields. Here, we use HMI and MDI magnetic field synoptic maps to evaluate the magnetic field structures’ (mainly active regions) organization and propagation as a function of time and latitude. We demonstrate, using information theory, that the organization of longitudinal structures observed on synoptic maps is proportional to the level of activity at a given latitude. We further show that this organization on the longitudinal structures is persistent and due to long-lived features. The drift velocity of these long-lived photospheric features is inferred and is shown to significantly vary with latitude, and is compatible with the phase speed of tachocline magnetic Rossby waves with a toroidal field in the range of 5–10 kG. Our results suggest that Rossby waves contribute to the organization and propagation of photospheric magnetic features on the timescale of several months and beyond.

The importance of measuring topological quantities, such as magnetic helicity, in solar observations has long been recognized. In particular, topological quantities play an important role in both understanding and predicting solar eruptions. In this paper, we present ARTop (Active Region Topology), an open-source and end-to-end software tool that allows researchers to calculate the fluxes of topological quantities based on solar magnetograms. In addition to this, ARTop also allows for the efficient analysis of these quantities in both 2D maps and time series. ARTop calculates the fluxes of magnetic helicity and magnetic winding, together with particular decompositions of these quantities. To perform these calculations, SHARP magnetograms are downloaded and velocity maps are created using the DAVE4VM method. Visualization tools, written in Python, are provided to aid in the selection of appropriate output variables and for the straightforward creation of maps and time series. Additionally, other analysis functions are included to facilitate and aid solar flare investigations. This software offers researchers a powerful tool for investigating the behaviour of active regions and the origins of space weather.

Much of solar activity within a sunspot cycle occurs as bursts, or 'seasons' of strong activity over several months, separated by periods of much less activity.The most important space weather effects occur during these bursty periods.Previous modeling and forecasting efforts have focused on time-scales of hours-to-days and decades-to-centuries.The recent discovery of Rossby waves in the Sun, together with recently developed global models of solar MHD Rossby waves and their interactions with differential rotation and spot-producing magnetic fields, reveal the opportunity to simulate and predict the occurrence, strength and location of enhanced activity bursts a few weeks up to several months in advance.We now have a golden opportunity to fill in this gap in forecasting space weather in these time scales.This requires a) continuous observations of solar Rossby waves by various techniques; b) development of coupled nonlinear MHD models that simulate both global Rossby waves and the much smaller spatial scale emergence of new active regions; c) application of advanced data assimilation techniques to couple surface observations to update the model-system to integrate forward in time for creating forecasts months ahead.Then it will be possible to build operational space weather prediction models to meet the needs of customers and stakeholders, including support of future NASA missions, on a time scale of a few weeks to several months ahead.

Magnetic fields in stars and planets are generated by a dynamo process that results from multi-scale interactions of the flows in conducting fluids. On the large scales, these flows are dominated by a strong zonal component, while the magnetic fields exhibit a strong toroidal/zonal character. Although dissipation certainly acts on these flows, the kinematic and magnetic viscosities associated with these large-scale flows are small, so that, over the timescale of several years and beyond, the system may be modelled as a conservative one. In this context, the Hamiltonian formulation may give several insights, providing a systematic way to relate the symmetries of the system with conservation laws. In the present article, we introduce the Hamiltonian formulation for a model that reasonably describes the dynamics of large-scale flows in stars and planets: the two-dimensional magnetohydrodynamic quasi-geostrophic equations. In this context, we find the invariants of the system, which are of two kinds: the Casimirs, related to the particle relabelling symmetry, and the zonal momentum, which is related to the translational invariance in the zonal direction. We then use these invariants to study the stability of some stationary solutions that are relevant for geophysical and astrophysical applications.

The study of tropical tropospheric disturbances has led to important challenges from both observational and theoretical points of view. In particular, the observed wavenumber-frequency spectrum of tropical oscillations has helped bridge the gap between observations and the linear theory of equatorial waves. In this study, we obtained a similar wavenumber-frequency spectrum for each equatorial wave type by performing a normal mode function (NMF) decomposition of global Era–Interim reanalysis data. The NMF basis used here is provided by the eigensolutions of the primitive equations in spherical coordinates as linearized around a resting background state. In this methodology, the global multi-level horizontal velocity and geopotential height fields are projected onto the normal mode functions, characterized by a vertical mode, a zonal wavenumber, a meridional quantum index, and a mode type, namely, Rossby, Kelvin, mixed Rossby-gravity, and westward/eastward propagating inertio-gravity modes. The horizontal velocity and geopotential height fields associated with each mode type are then reconstructed in the physical space, as well as their corresponding filtered versions defined according to the vertical mode classes that exhibit barotropic and baroclinic structures within the troposphere. The results reveal expected structures, such as the dominant global-scale Rossby and Kelvin waves constituting the intraseasonal frequency associated with the Madden–Julian Oscillation. On the other hand, a number of unexpected features, such as eastward propagating westward inertio-gravity waves, are revealed by our observed 200 hPa zonal wind spectrum. Among all possible nonlinear processes, we focus on the analysis of the interaction between Kelvin and westward inertio-gravity waves, providing evidence for their coupling. Apart from the nonlinearity, we discuss the potential roles of a vertically/meridionally varying background state as well as the coupling with moist convection in explaining the departures of the observed spectra from the corresponding linear equatorial wave theory.

We investigate whether global toroid patterns and the local magnetic field topology of solar active region (AR) 12673 together can hindcast the occurrence of the biggest X-flares of solar cycle (SC)-24. Magnetic toroid patterns (narrow latitude belts warped in longitude, in which ARs are tightly bound) derived from the surface distributions of ARs, prior and during AR 12673 emergence, reveal that the portions of the south toroid containing AR 12673 was not tipped away from its north-toroid counterpart at that longitude, unlike the 2003 Halloween storms scenario. During the minimum phase there were too few emergences to determine multimode longitudinal toroid patterns. A new emergence within AR 12673 produced a complex nonpotential structure, which led to the rapid buildup of helicity and winding that triggered the biggest X-flare of SC-24, suggesting that this minimum-phase storm can be anticipated several hours before its occurrence. However, global patterns and local dynamics for a peak-phase storm, such as that from AR 11263, behaved like the 2003 Halloween storms, producing the third biggest X-flare of SC-24. AR 11263 was present at the longitude where the north and south toroids tipped away from each other. While global toroid patterns indicate that prestorm features can be forecast with a lead time of a few months, their application to observational data can be complicated by complex interactions with turbulent flows. Complex nonpotential field structure development hours before the storm are necessary for short-term prediction. We infer that minimum-phase storms cannot be forecast accurately more than a few hours ahead, while flare-prone ARs in the peak phase may be anticipated much earlier, possibly months ahead from global toroid patterns.

The dynamics of the Earth's atmosphere is characterized by a wide spectrum of oscillations, ranging from hourly to interdecadal and beyond. The low-frequency component of the atmospheric variability cannot be understood solely in terms of linear atmospheric waves that have shorter timescales. A newly proposed mechanism, the precession resonance mechanism, is a regime of highly efficient energy transfer in the spectral space in turbulent systems. Here, we investigate the role of the precession resonance, and the alignment of dynamical phases, in the generation of low-frequency oscillations and the redistribution of energy/enstrophy in the spectral space using the barotropic vorticity equation. First, the mechanism and its ability to generate low-frequency oscillations are demonstrated in low-order models consisting of four and five nonlinearly interacting Rossby–Haurwitz waves. The precession resonance onset is also investigated in the full barotropic vorticity equation, and the results are in agreement with the reduced models. Efficiency peaks in the energy/enstrophy transfer also correspond to regimes of strong excitation of low-frequency oscillations. The results suggest that the organization of the dynamical phases plays a key role in the redistribution of energy in the spectral space, as well as the generation of low frequencies in the barotropic vorticity equation.

Rossby waves have been recently recognised for their role in the large-scale spatio-temporal organisation of the solar magnetic activity. Here, we study the propagation of magnetohydrodynamic Rossby waves in a thin layer, representing the solar tachocline. We consider the waves embedded in a meridionally varying background state characterised by a mean zonal flow, which mimics the differential rotation profile of the Sun, and a toroidal magnetic field. Two anti-symmetric toroidal magnetic fields are utilised: one having a global structure with the maximum at around 50 o and the other characterised by a narrow band centered at around 20 o . We show that for a global structure toroidal magnetic field, the MHD Rossby modes undergo significant meridional propagation, either equatorward or poleward. In addition, the latitude where the waves exhibit a stationary behaviour is sensitive to the strength of the background magnetic field. On the other hand, a narrow band toroidal magnetic field is shown to work as a waveguide for the fast branch of MHD Rossby waves.

Magnetic helicity is a measure of the entanglement of magnetic field lines used to characterize the complexity of solar active region (AR) magnetic fields. Previous attempts to use helicity-based indicators to predict solar eruptive/flaring events have shown promise but not been universally successful. Here we investigate the use of a quantity associated with the magnetic helicity, the magnetic winding, as a means to predict flaring activity. This quantity represents the fundamental entanglement of magnetic field lines and is independent of the magnetic field strength. We use vector magnetogram data derived from the Helioseismic Magnetic Imager (HMI) to calculate the evolution and distribution of the magnetic winding flux associated with five different ARs, three of them with little flaring activity/nonflaring (AR 11318, AR 12119, AR 12285) and two highly active with X-class flares (AR 11158, AR 12673). We decompose these quantities into “current-carrying” and “potential” parts. It is shown that the ARs that show flaring/eruptive activity have significant contributions to the winding input from the current-carrying part of the field. A significant and rapid input of current-carrying winding is found to be a precursor of flaring/eruptive activity, and, in conjunction with the helicity, sharp inputs of both quantities are found to precede individual flaring events by several hours. This suggests that the emergence/submergence of topologically complex current-carrying field is an important element for the ignition of AR flaring.

The magnetic nature of the formation of solar active regions lies at the heart of understanding solar activity and, in particular, solar eruptions. A widespread model, used in many theoretical studies, simulations and the interpretation of observations, is that the basic structure of an active region is created by the emergence of a large tube of pre-twisted magnetic field. Despite plausible reasons and the availability of various proxies suggesting the accuracy of this model, there has not yet been a methodology that can clearly and directly identify the emergence of large pre-twisted magnetic flux tubes. Here, we present a clear signature of the emergence of pre-twisted magnetic flux tubes by investigating a robust topological quantity, called magnetic winding, in solar observations. This quantity detects the emerging magnetic topology despite the significant deformation experienced by the emerging magnetic field. Magnetic winding complements existing measures, such as magnetic helicity, by providing distinct information about field line topology, thus allowing for the direct identification of emerging twisted magnetic flux tubes.