Julia K. Thalmann

Aims. We examine the relation between solar eruptivity and the relative helicity that is contained around the polarity-inversion line (PIL) of the magnetic field, along with its current-carrying component. Methods. To this end, we analysed the evolution of the PIL helicities in a sample of ∼40 solar active regions that exhibited more than 200 flares of class M or higher. We computed the PIL helicities with the help of the relative field line helicity, the recently developed proxy for the density of relative helicity, following the extrapolation of the 3D coronal magnetic field with a non-linear force-free method. Results. The relative helicity of the PIL decreases significantly on average by more than 10% during stronger eruptive flares (M5.0 class and above), while smaller changes are observed for confined and/or weaker flares. The PIL current-carrying helicity shows higher-magnitude decreases in strong and weak flares and reaches an average of 20% of changes during the stronger eruptive flares. Notably, the PIL current-carrying helicity differs most between eruptive and confined flares, which indicates its strong potential as a diagnostic of solar eruptivity. We discuss the implications of these findings for solar flare forecasting.

Aims. We aim to better characterize the conditions of the solar corona, especially with respect to the occurrence of confined and eruptive flares. In this work, we model the coronal evolution around 231 large flares observed during solar cycle 24. Methods. Using Helioseismic and Magnetic Imager vector magnetic field data around each event, we employed nonlinear force-free field extrapolations to approximate the coronal energy and helicity budgets of the solar source regions. A superposed epoch analysis and dynamical time warping applied to the time series of selected photospheric and coronal quantities were used to pin down the characteristics of the pre- and postflare time evolution, as well as to assess flare-related changes. Results. During the 24 hours leading up to a major flare, the total magnetic energy and unsigned magnetic flux were seen to evolve closely with respect to each other, irrespective of the flare type. Prior to confined flares, the free energy evolves in a way that exhibits more of a similarity with the unsigned flux than the helicity of the current-carrying field, while the opposite trend is seen prior to eruptive flares. Furthermore, the flare type can be predicted correctly in more than 90% of major flares when combining measures of the active regions nonpotentiality and local stability. The coronal energy and helicity budgets return to preflare levels within ≈6 to 12 hours after eruptive major M-class flares, while the impact of eruptive X-flares lasts considerably longer. Finally, the postflare replenishment times of ≳12 hours after eruptive X-class flares may serve as a partial explanation for the rare observation of eruptive X-class flares within a time frame of a few hours.

Context.The coronal magnetic field, which overlies the current-carrying field of solar active regions, straps the magnetic configuration below. The characteristics of this overlying field are crucial in determining if a flare will be eruptive and accompanied by a coronal mass ejection (CME), or if it will remain confined without a CME.Aims.In order to improve our understanding of the pre-requisites of eruptive solar flares, we study and compare different measures that characterize the eruptive potential of solar active regions – the critical height of the torus instability (TI) as a local measure and the helicity ratio as a global measure – with the structural properties of the underlying magnetic field, namely the altitude of the center of the current-carrying magnetic structure.Methods.Using time series of 3D optimization-based nonlinear force-free magnetic field models of ten different active regions (ARs) around the time of large solar flares, we determined the altitudes of the current-weighted centers of the non-potential model structures. Based on the potential magnetic field, we inspected the decay index,n, in multiple vertical planes oriented alongside or perpendicular to the flare-relevant polarity inversion line, and estimated the critical height (h_crit) of TI using different thresholds ofn. The critical heights were interpreted with respect to the altitudes of the current-weighted centers of the associated non-potential structures, as well as the eruptive character of the associated flares, and the eruptive potential of the host AR, as characterized by the helicity ratio.Results.Our most important findings are that (i)h_critis more segregated in terms of the flare type than the helicity ratio, and (ii) coronal field configurations with a higher eruptive potential (in terms of the helicity ratio) also appear to be more prone to TI. Furthermore, we find no pronounced differences in the altitudes of the non-potential structures prior to confined and eruptive flares. An aspect that requires further investigation is that, generally, the modeled non-potential structures do not really reside in a torus-instable regime, so the applicability of the chosen nonlinear force-free modeling approach when targeting the structural properties of the coronal magnetic field is unclear.

Nonlinear force-free extrapolations are a common approach to estimate the 3D topology of coronal magnetic fields based on photospheric vector magnetograms. The force-free assumption is a valid approximation at coronal heights, but for the dense plasma conditions in the lower atmosphere, this assumption is not satisfied. In this study, we utilize multiheight magnetic field measurements in combination with physics-informed neural networks to advance solar magnetic field extrapolations. We include a flexible height-mapping, which allows us to account for the different formation heights of the observed magnetic field measurements. The comparison to analytical and simulated magnetic fields demonstrates that including chromospheric magnetic field measurements leads to a significant improvement of our magnetic field extrapolations. We also apply our method to chromospheric line-of-sight magnetograms from the Vector Spectromagnetograph (VSM) on the Synoptic Optical Long-term Investigations of the Sun (SOLIS) observatory, in combination with photospheric vector magnetograms from the Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). The comparison to observations in extreme-ultraviolet wavelengths shows that the additional chromospheric information leads to a better agreement with the observed coronal structures. In addition, our method intrinsically provides an estimate of the corrugation of the observed magnetograms. With this new approach, we make efficient use of multiheight magnetic field measurements and advance the realism of coronal magnetic field simulations.

Magnetic free energy powers solar flares and coronal mass ejections, and the buildup of magnetic helicity might play a role in the development of unstable structures that subsequently erupt. To better understand the roles of energy and helicity in large flares and eruptions, we have characterized the evolution of magnetic energy and helicity associated with 21 X-class flares from 2010 to 2017. Our sample includes both confined and eruptive events, with 6 and 15 in each category, respectively. Using the Helioseismic and Magnetic Imager vector magnetic field observations from several hours before to several hours after each event, we employ (a) the Differential Affine Velocity Estimator for Vector Magnetograms to determine the photospheric fluxes of energy and helicity, and (b) nonlinear force-free field extrapolations to estimate the coronal content of energy and helicity in source-region fields. Using superposed epoch analysis, we find, on average, the following: (1) decreases in both magnetic energy and helicity, in both photospheric fluxes and coronal content, that persist for a few hours after eruptions, but no clear changes, notably in relative helicity, for confined events; (2) significant increases in the twist of photospheric fields in eruptive events, with twist uncertainties too large in confined events to constrain twist changes (and lower overall twist in confined events); and (3) on longer timescales (event time +12 hr), replenishment of free magnetic energy and helicity content to near preevent levels for eruptive events. For eruptive events, magnetic helicity and free energy in coronal models clearly decrease after flares, with the amounts of decrease proportional to each region’s pre-flare content.

Coronal mass ejections are among the Sun’s most energetic activity events yet the physical mechanisms that lead to their occurrence are not yet fully understood. They can drive major space weather impacts at Earth, so knowing why and when these ejections will occur is required for accurate space weather forecasts. In this study we use a 4 day time series of a quantity known as the helicity ratio, ∣H _J ∣/∣H _V ∣ (helicity of the current-carrying part of the active region field to the total relative magnetic helicity within the volume), which has been computed from nonlinear force-free field extrapolations of NOAA active region 11158. We compare the evolution of ∣H _J ∣/∣H _V ∣ with the activity produced in the corona of the active region and show this ratio can be used to indicate when the active region is prone to eruption. This occurs when ∣H _J ∣/∣H _V ∣ exceeds a value of 0.1, as suggested by previous studies. We find the helicity ratio variations to be more pronounced during times of strong flux emergence, collision and reconnection between fields of different bipoles, shearing motions, and reconfiguration of the corona through failed and successful eruptions. When flux emergence, collision, and shearing motions have lessened, the changes in helicity ratio are somewhat subtle despite the occurrence of significant eruptive activity during this time.

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Nonlinear force-free (NLFF) modeling is regularly used in order to indirectly infer the 3D geometry of the coronal magnetic field, not accessible on a regular basis by means of direct measurements otherwise. We study the effect of binning in time series NLFF modeling of individual active regions (ARs) in order to quantify the effect of a different underlying spatial sampling on the quality of modeling as well as on the derived physical parameters. We apply an optimization method to sequences of SDO/HMI vector magnetogram data at three different plate scales for three solar ARs to obtain nine NLFF model time series. From the NLFF models, we deduce active-region magnetic fluxes, electric currents, magnetic energies and relative helicities, and analyze those with respect to the underlying spatial sampling. We calculate various metrics to quantify the quality of the derived NLFF models and apply a Helmholtz decomposition to characterize solenoidal errors. At a given spatial sampling, the quality of NLFF modeling is different for different ARs, as well as varies along of the individual model time series. For a given AR, modeling at a given spatial sampling is not necessarily of superior quality compared to that performed with a different plate scale. Generally, the NLFF model quality tends to be higher for larger pixel sizes with the solenoidal quality being the ultimate cause for systematic variations in model-deduced physical quantities. Optimization-based modeling based on binned SDO/HMI vector data delivers magnetic energies and helicity estimates different by $\lesssim$30\%, given that concise checks ensure the physical plausibility and high solenoidal quality of the tested model. Thus, spatial-sampling-induced differences are relatively small compared to that arising from other sources of uncertainty.

In this ISSI-supported series of studies on magnetic helicity in the Sun, we systematically implement different magnetic helicity calculation methods on high-quality solar magnetogram observations. We apply finite-volume, discrete flux tube (in particular, connectivity-based) and flux-integration methods to data from Hinode’s Solar Optical Telescope. The target is NOAA Active Region 10930 during a 1.5-day interval in 2006 December that included a major eruptive flare (SOL2006-12-13T02:14X3.4). Finite-volume and connectivity-based methods yield instantaneous budgets of the coronal magnetic helicity, while the flux-integration methods allow an estimate of the accumulated helicity injected through the photosphere. The objectives of our work are twofold: a cross-validation of methods, as well as an interpretation of the complex events leading to the eruption. To the first objective, we find (i) strong agreement among the finite-volume methods, (ii) a moderate agreement between the connectivity-based and finite-volume methods, (iii) an excellent agreement between the flux-integration methods, and (iv) an overall agreement between finite-volume- and flux-integration-based estimates regarding the predominant sign and magnitude of the helicity. To the second objective, we are confident that the photospheric helicity flux significantly contributed to the coronal helicity budget and that a right-handed structure erupted from a predominantly left-handed corona during the X-class flare. Overall, we find that the use of different methods to estimate the (accumulated) coronal helicity may be necessary in order to draw a complete picture of an active region corona, given the careful handling of identified data (preparation) issues, which otherwise would mislead the event analysis and interpretation.

Sunspot light bridges are known to exhibit a variety of dynamic and persistent phenomena such as surges, small-scale jets, etc., in the chromosphere and transition region. While it has generally been proposed that magnetic reconnection is responsible for this small-scale dynamism, persistent flaring activity lasting several hours from the same spatial location on a sunspot light bridge has rarely been reported. We combine observations from the Atmospheric Imaging Assembly and the Helioseismic Magnetic Imager on board the Solar Dynamics Observatory to investigate homologous flaring activity over a small sunspot light bridge in an emerging flux region. The homologous flares all produced broad, collimated jets including a B6.4 class flare. The jets rise at a speed of about 200 km s⁻¹, reach projected heights of about 98 Mm, and emerge from the same spatial location for nearly 14 hrs, after which they cease completely. A nonlinear force-free extrapolation of the photospheric magnetic field shows a low-lying flux rope connecting the light bridge to a remote opposite-polarity network. The persistent flares occur as a result of the rapid horizontal motion of the leading sunspot that causes the relatively vertical magnetic fields in the adjacent umbra to reconnect with the low-lying flux rope in the light bridge. Our results indicate that the flaring ceases once the flux rope has lost sufficient twist through repeated reconnections.