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Magnetic helicity has been used widely in the analysis and modelling of solar active regions. However, it is difficult to evaluate and interpret helicity in spherical geometry since coronal magnetic fields are rooted in the photosphere and helicity is susceptible to gauge choices. Recent work extended a geometrical definition of helicity from Cartesian to spherical domains, by interpreting helicity as the average, flux-weighted pairwise winding of magnetic-field lines. In this paper, by adopting the winding-based definition of helicity, we compute helicity and winding in spherical coordinates for SHARP (Spaceweather HMI Active Region Patches) magnetograms. This is compared with results obtained in Cartesian coordinates to quantitatively investigate the effect of spherical geometry. We find that the Cartesian approximations remain mostly valid, but for active regions with large spatial extents or strong field strengths (usually leading to flares and coronal mass ejections) there are significant deviations due to surface curvature that must be accounted for. [ABSTRACT FROM AUTHOR]

We review the surface flux transport model for the evolution of magnetic flux patterns on the Sun's surface. Our underlying motivation is to understand the model's prediction of the polar field (or axial dipole) strength at the end of the solar cycle. The main focus is on the "classical" model: namely, steady axisymmetric profiles for differential rotation and meridional flow, and uniform supergranular diffusion. Nevertheless, the review concentrates on recent advances, notably in understanding the roles of transport parameters and – in particular – the source term. We also discuss the physical justification for the surface flux transport model, along with efforts to incorporate radial diffusion, and conclude by summarizing the main directions where researchers have moved beyond the classical model. [ABSTRACT FROM AUTHOR]

In ideal magnetohydrodynamics, magnetic helicity is a conserved dynamical quantity and a topological invariant closely related to Gauss linking numbers. However, for open magnetic fields with non-zero boundary components, the latter geometrical interpretation is complicated by the fact that helicity varies with non-unique choices of a field's vector potential or gauge. Evaluated in a particular gauge called the winding gauge, open-field helicity in Cartesian slab domains has been shown to be the average flux-weighted pairwise winding numbers of field lines, a measure constructed solely from field configurations that manifest its topological origin. In this paper, we derive the spherical analogue of the winding gauge and the corresponding winding interpretation of helicity, in which we formally define the concept of spherical winding of curves. Using a series of examples, we demonstrate novel properties of spherical winding and the validity of spherical winding helicity. We further argue for the canonical status of the winding gauge choice among all vector potentials for magnetic helicity by exhibiting equivalences between local coordinate changes and gauge transformations. [ABSTRACT FROM AUTHOR]

We describe a new automated technique for active region emergence in coronal magnetic field models, based on the inversion of the electric field locally from a single line-of-sight magnetogram for each region. The technique preserves the arbitrary shapes of magnetic field distribution associated with individual active regions and incorporates emerging magnetic helicity (twist) in a parametrized manner through a noninductive electric field component. We test the technique with global magnetofrictional simulations of the coronal magnetic field during Solar Cycle 24 Maximum from 2011 June 1 to 2011 December 31. The active regions are determined in a fully automated and objective way using Spaceweather HMI Active Region Patch (SHARP) data. Our primary aim is to constrain two free parameters in the emergence algorithm: the duration of emergence and the twist parameter for each individual active region. While the duration has a limited effect on the resulting coronal magnetic field, changing the sign and amplitude of the twist parameters profoundly influences the amount of nonpotentiality generated in the global coronal magnetic field. We explore the possibility of constraining both the magnitude and sign of the twist parameter using estimates of the current helicity derived from vector magnetograms and supplied in the SHARP metadata for each region. Using the observed sign of twist for each region reduces the overall nonpotentiality in the corona, highlighting the importance of scatter in the emerging active region helicities. [ABSTRACT FROM AUTHOR]

An important element of 3D data-driven simulations of solar magnetic fields is the determination of the horizontal electric field at the solar photosphere. This electric field is used to drive the 3D simulations and inject energy and helicity into the solar corona. One outstanding problem is the localisation of the horizontal electric field such that it is consistent with Ohm's law. Yeates (Astrophys. J.836(1), 131, 2017) put forward a new "sparse" technique for computing the horizontal electric field from normal-component magnetograms that minimises the number of non-zero values. This aims to produce a better representation of Ohm's law compared to previously used "non-sparse" techniques. To test this new approach we apply it to active region (AR) 10977, along with the previously developed non-sparse technique of Mackay, Green, and van Ballegooijen (Astrophys. J.729(2), 97, 2011). A detailed comparison of the two techniques with coronal observations is used to determine which is the most successful. Results show that the non-sparse technique of Mackay, Green, and van Ballegooijen (2011) produces the best representation for the formation and structure of the sigmoid above AR 10977. In contrast, the Yeates (2017) approach injects strong horizontal fields between spatially separated, evolving magnetic polarities. This injection produces highly twisted unphysical field lines with significantly higher magnetic energy and helicity. It is also demonstrated that the Yeates (2017) approach produces significantly different results that can be inconsistent with the observations depending on whether the horizontal electric field is solved directly or indirectly through the magnetic vector potential. In contrast, the Mackay, Green, and van Ballegooijen (2011) method produces consistent results using either approach. The sparse technique of Yeates (2017) has significant pitfalls when applied to spatially resolved solar data, where future studies need to investigate why these problems arise. [ABSTRACT FROM AUTHOR]

We discuss the potential use of an algebraic method to compute the value of the solar axial dipole moment at solar minimum, widely considered to be the most reliable precursor of the activity level in the next solar cycle. The method consists of summing up the ultimate contributions of individual active regions to the solar axial dipole moment at the end of the cycle. A potential limitation of the approach is its dependence on the underlying surface flux transport (SFT) model details. We demonstrate by both analytical and numerical methods that the factor relating the initial and ultimate dipole moment contributions of an active region displays a Gaussian dependence on latitude with parameters that only depend on details of the SFT model through the parameter η/Δu where η is supergranular diffusivity and Δu is the divergence of the meridional flow on the equator. In a comparison with cycles simulated in the 2 × 2D dynamo model we further demonstrate that the inaccuracies associated with the algebraic method are minor and the method may be able to reproduce the dipole moment values in a large majority of cycles. [ABSTRACT FROM AUTHOR]

Seven different models are applied to the same problem of simulating the Sun's coronal magnetic field during the solar eclipse on 2015 March 20. All of the models are non-potential, allowing for free magnetic energy, but the associated electric currents are developed in significantly different ways. This is not a direct comparison of the coronal modelling techniques, in that the different models also use different photospheric boundary conditions, reflecting the range of approaches currently used in the community. Despite the significant differences, the results show broad agreement in the overall magnetic topology. Among those models with significant volume currents in much of the corona, there is general agreement that the ratio of total to potential magnetic energy should be approximately 1.4. However, there are significant differences in the electric current distributions; while static extrapolations are best able to reproduce active regions, they are unable to recover sheared magnetic fields in filament channels using currently available vector magnetogram data. By contrast, time-evolving simulations can recover the filament channel fields at the expense of not matching the observed vector magnetic fields within active regions. We suggest that, at present, the best approach may be a hybrid model using static extrapolations but with additional energization informed by simplified evolution models. This is demonstrated by one of the models. [ABSTRACT FROM AUTHOR]

We study coherent structures in solar photospheric flows in a plage in the vicinity of the active region AR 10930 using the horizontal velocity data derived from Hinode/Solar Optical Telescope magnetograms. Eulerian and Lagrangian coherent structures (LCSs) are detected by computing the Q-criterion and the finite-time Lyapunov exponents of the velocity field, respectively. Our analysis indicates that, on average, the deformation Eulerian coherent structures dominate over the vortical Eulerian coherent structures in the plage region. We demonstrate the correspondence of the network of high magnetic flux concentration to the attracting Lagrangian coherent structures (aLCSs) in the photospheric velocity based on both observations and numerical simulations. In addition, the computation of aLCS provides a measure of the local rate of contraction/expansion of the flow. [ABSTRACT FROM AUTHOR]

The high-cadence, comprehensive view of the solar corona by SDO/AIA shows many events that are widely separated in space while occurring close together in time. In some cases, sets of coronal events are evidently causally related, while in many other instances indirect evidence can be found. We present case studies to highlight a variety of coupling processes involved in coronal events. We find that physical linkages between events do occur, but concur with earlier studies that these couplings appear to be crucial to understanding the initiation of major eruptive or explosive phenomena relatively infrequently. We note that the post-eruption reconfiguration timescale of the large-scale corona, estimated from the extreme-ultraviolet afterglow, is on average longer than the mean time between coronal mass ejections (CMEs), so that many CMEs originate from a corona that is still adjusting from a previous event. We argue that the coronal field is intrinsically global: current systems build up over days to months, the relaxation after eruptions continues over many hours, and evolving connections easily span much of a hemisphere. This needs to be reflected in our modeling of the connections from the solar surface into the heliosphere to properly model the solar wind, its perturbations, and the generation and propagation of solar energetic particles. However, the large-scale field cannot be constructed reliably by currently available observational resources. We assess the potential of high-quality observations from beyond Earth's perspective and advanced global modeling to understand the couplings between coronal events in the context of CMEs and solar energetic particle events. [ABSTRACT FROM AUTHOR]

Solar filaments are known to exhibit a hemispheric pattern in their chirality, where dextral/sinistral filaments dominate in the northern/southern hemisphere. We show that this pattern may be explained through data driven 3D global magnetic field simulations of the Sun's large-scale magnetic field. Through a detailed comparison with 109 filaments over a 6 month period, the model correctly reproduces the filament chirality and helicity with a 96% agreement. The data driven simulation is extended to run over a full solar cycle, where predictions are made for the spatial and temporal dependence of the hemispheric pattern over the solar cycle. [ABSTRACT FROM PUBLISHER]

The motivation for our research was to study the correlation between the chirality of filaments and the handedness (S- or Z-shape) of sigmoids. It was assumed that sigmoids would mostly coincide with filaments and that the S-shaped sigmoids would correlate well with filaments of sinistral chirality, which we found that to be at best a very weak relation. Since we had a full solar cycle of filament metadata at hand it was easy to verify the supposedly known hemispheric preference of filament chirality. We discovered that the hemispheric chirality rule was confirmed for the epoch where a thorough manual study had been performed, but that at other phases of the solar cycle the rule seems to disappear and sometimes even reverse. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

This paper examines the locations where large, stable solar filaments form relative to magnetic bipoles lying underneath them. The study extends the earlier work of F. Tang to include two additional classification categories for stable filaments and to consider their population during four distinct phases of the solar cycle. With this new classification scheme, results show that over 92% of filaments form in flux distributions that are nonbipolar in nature where the filament lies either fully (79%) or partially (13%) above a polarity inversion line (PIL) external to any single bipole. Filaments that form within a single bipole (traditionally called Type A) are not as common as previously thought. These results are a significant departure from those of F. Tang. Consistency with the earlier work is shown when our data are regrouped to conform to the two-category classification scheme for filaments adopted by F. Tang. We also demonstrate that only filaments that form along the external PIL lying between two bipoles (62% of the full sample, traditionally called Type B) show any form of solar cycle dependence, where their number significantly increases with magnetic activity over the solar cycle. Finally, current observations and theoretical models for the formation of filaments are discussed in the context of the present results. We conclude that key elements in the formation of the majority of filaments considered within this study must be the convergence of magnetic flux resulting in either flux cancellation or coronal reconnection. [ABSTRACT FROM AUTHOR]

We investigate how representing active regions with bipolar magnetic regions (BMRs) affects the end-of-cycle polar field predicted by the surface flux transport model. Our study is based on a new database of BMRs derived from the SDO/HMI active region patch data between 2010 and 2020. An automated code is developed for fitting each active region patch with a BMR, matching both the magnetic flux and axial dipole moment of the region and removing repeat observations of the same region. By comparing the predicted evolution of each of the 1090 BMRs with the predicted evolution of their original active region patches, we show that the bipolar approximation leads to a 24% overestimate of the net axial dipole moment, given the same flow parameters. This is caused by neglecting the more complex multipolar and/or asymmetric magnetic structures of many of the real active regions, and may explain why previous flux transport models had to reduce BMR tilt angles to obtain realistic polar fields. Our BMR database and the Python code to extract it are freely available. [ABSTRACT FROM AUTHOR]

In the present study, we consider where large, stable solar filaments form relative to underlying magnetic polarities. We find that 92% of all large stable filaments form in magnetic configurations involving the interaction of two or more bipoles. Only 7% form above the Polarity Inversion Line (PIL) of a single bipole. This indicates that a key element in the formation of large-scale stable filaments is the convergence of magnetic flux, resulting in either flux cancellation or coronal reconnection. [ABSTRACT FROM PUBLISHER]

In this work, we take advantage of 11 different sunspot group, sunspot, and active region databases to characterize the area and flux distributions of photospheric magnetic structures. We find that, when taken separately, different databases are better fitted by different distributions (as has been reported previously in the literature). However, we find that all our databases can be reconciled by the simple application of a proportionality constant, and that, in reality, different databases are sampling different parts of a composite distribution. This composite distribution is made up by linear combination of Weibull and log-normal distributions—where a pure Weibull (log-normal) characterizes the distribution of structures with fluxes below (above) 1021Mx (1022Mx). Additionally, we demonstrate that the Weibull distribution shows the expected linear behavior of a power-law distribution (when extended to smaller fluxes), making our results compatible with the results of Parnell et al. We propose that this is evidence of two separate mechanisms giving rise to visible structures on the photosphere: one directly connected to the global component of the dynamo (and the generation of bipolar active regions), and the other with the small-scale component of the dynamo (and the fragmentation of magnetic structures due to their interaction with turbulent convection). [ABSTRACT FROM AUTHOR]