A clear understanding of the nature of the pre-eruptive magnetic field configurations of Coronal Mass Ejections (CMEs) is required for understanding and eventually predicting solar eruptions. Only ...two, but seemingly disparate, magnetic configurations are considered viable; namely, sheared magnetic arcades (SMA) and magnetic flux ropes (MFR). They can form via three physical mechanisms (flux emergence, flux cancellation, helicity condensation). Whether the CME culprit is an SMA or an MFR, however, has been strongly debated for thirty years. We formed an International Space Science Institute (ISSI) team to address and resolve this issue and report the outcome here. We review the status of the field across modeling and observations, identify the open and closed issues, compile lists of SMA and MFR observables to be tested against observations and outline research activities to close the gaps in our current understanding. We propose that the combination of multi-viewpoint multi-thermal coronal observations and multi-height vector magnetic field measurements is the optimal approach for resolving the issue conclusively. We demonstrate the approach using MHD simulations and synthetic coronal images.
Our key conclusion is that the differentiation of pre-eruptive configurations in terms of SMAs and MFRs seems artificial. Both observations and modeling can be made consistent if the pre-eruptive configuration exists in a hybrid state that is continuously evolving from an SMA to an MFR. Thus, the ‘dominant’ nature of a given configuration will largely depend on its evolutionary stage (SMA-like early-on, MFR-like near the eruption).
ABSTRACT Solar flares produce radiation that can have an almost immediate effect on the near-Earth environment, making it crucial to forecast flares in order to mitigate their negative effects. The ...number of published approaches to flare forecasting using photospheric magnetic field observations has proliferated, with varying claims about how well each works. Because of the different analysis techniques and data sets used, it is essentially impossible to compare the results from the literature. This problem is exacerbated by the low event rates of large solar flares. The challenges of forecasting rare events have long been recognized in the meteorology community, but have yet to be fully acknowledged by the space weather community. During the interagency workshop on "all clear" forecasts held in Boulder, CO in 2009, the performance of a number of existing algorithms was compared on common data sets, specifically line-of-sight magnetic field and continuum intensity images from the Michelson Doppler Imager, with consistent definitions of what constitutes an event. We demonstrate the importance of making such systematic comparisons, and of using standard verification statistics to determine what constitutes a good prediction scheme. When a comparison was made in this fashion, no one method clearly outperformed all others, which may in part be due to the strong correlations among the parameters used by different methods to characterize an active region. For M-class flares and above, the set of methods tends toward a weakly positive skill score (as measured with several distinct metrics), with no participating method proving substantially better than climatological forecasts.
Abstract
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.
In earlier works we introduced and tested a nonlinear force-free (NLFF) method designed to self-consistently calculate the coronal free magnetic energy and the relative magnetic helicity budgets of ...observed solar magnetic structures. In principle, the method requires only a single, photospheric or low-chromospheric, vector magnetogram of a quiet-Sun patch or an active region and performs calculations without three-dimensional magnetic and velocity-field information. In this work we strictly validate this method using three-dimensional coronal magnetic fields. Benchmarking employs both synthetic, three-dimensional magnetohydrodynamic simulations and nonlinear force-free field extrapolations of the active-region solar corona. Our time-efficient NLFF method provides budgets that differ from those of more demanding semi-analytical methods by a factor of approximately three, at most. This difference is expected to come from the physical concept and the construction of the method. Temporal correlations show more discrepancies that are, however, soundly improved for more complex, massive active regions, reaching correlation coefficients on the order of, or exceeding, 0.9. In conclusion, we argue that our NLFF method can be reliably used for a routine and fast calculation of the free magnetic energy and relative magnetic helicity budgets in targeted parts of the solar magnetized corona. As explained in this article and in previous works, this is an asset that can lead to valuable insight into the physics and triggering of solar eruptions.
We study the writhe, twist, and magnetic helicity of different magnetic flux ropes, based on models of the solar coronal magnetic field structure. These include an analytical force-free ...Titov-Démoulin equilibrium solution, non-force-free magnetohydrodynamic simulations, and nonlinear force-free magnetic field models. The geometrical boundary of the magnetic flux rope is determined by the quasi-separatrix layer and the bottom surface, and the axis curve of the flux rope is determined by its overall orientation. The twist is computed by the Berger-Prior formula, which is suitable for arbitrary geometry and both force-free and non-force-free models. The magnetic helicity is estimated by the twist multiplied by the square of the axial magnetic flux. We compare the obtained values with those derived by a finite volume helicity estimation method. We find that the magnetic helicity obtained with the twist method agrees with the helicity carried by the purely current-carrying part of the field within uncertainties for most test cases. It is also found that the current-carrying part of the model field is relatively significant at the very location of the magnetic flux rope. This qualitatively explains the agreement between the magnetic helicity computed by the twist method and the helicity contributed purely by the current-carrying magnetic field.
Aims.
We study the role of magnetic helicity and free magnetic energy in the initiation of eruptions in two differently evolving solar active regions (ARs).
Methods.
Using vector magnetograms from ...the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory and a magnetic connectivity-based method, we calculate the instantaneous relative magnetic helicity and free magnetic energy budgets for several days in two ARs, AR11890 and AR11618, both with complex photospheric magnetic field configurations.
Results.
The ARs produced several major eruptive flares while their photospheric magnetic field exhibited different evolutionary patterns: primarily flux decay in AR11890 and primarily flux emergence in AR11618. Throughout much of their evolution, both ARs featured substantial budgets of free magnetic energy and of both positive (right-handed) and negative (left-handed) helicity. In fact, the imbalance between the signed components of their helicity was as low as in the quiet Sun and their net helicity eventually changed sign 14−19 h after their last major flare. Despite this incoherence, the eruptions occurred at times of net helicity peaks that were co-temporal with peaks in the free magnetic energy. The percentage losses, associated with the eruptive flares, in the normalized free magnetic energy were significant, in the range of ∼10−60%. For the magnetic helicity, changes ranged from ∼25% to the removal of the entire excess helicity of the prevailing sign, leading a roughly zero net helicity, but with significant equal and opposite budgets of both helicity senses. Respective values ranged from (0.3 − 2)×10
32
erg and (1.3 − 20)×10
42
Mx
2
for energy and helicity losses. The removal of the slowly varying background component of the free energy and helicity (either the net helicity or the prevailing signed component of helicity) time series revealed that all eruption-related peaks of both quantities exceeded the 2
σ
levels of their detrended time series above the removed background. There was no eruption when only one or none of these quantities exceeded its 2
σ
level.
Conclusions.
Our results indicate that differently evolving ARs may produce major eruptive flares even when, in addition to the accumulation of significant free magnetic energy budgets, they accumulate large amounts of both left- and right-handed helicity without a strong dominance of one handedness over the other. In most cases, these excess budgets appear as localized peaks, co-temporal with the flare peaks, in the time series of free magnetic energy and helicity (and normalized values thereof). The corresponding normalized free magnetic energy and helicity losses can be very significant at certain times.
In this article, we present the application of the weighted horizontal gradient of magnetic field (WGM) flare prediction method to three-dimensional (3D) extrapolated magnetic configurations of 13 ...flaring solar active regions (ARs). The main aim is to identify an optimal height range, if any, in the interface region between the photosphere and lower corona, where the flare onset time prediction capability of WGM is best exploited. The optimal height is where flare prediction, by means of the WGM method, is achieved earlier than at the photospheric level. 3D magnetic structures, based on potential and nonlinear force-free field extrapolations, are constructed to study a vertical range from the photosphere up to the low corona with a 45 km step size. The WGM method is applied as a function of height to all 13 flaring AR cases that are subject to certain selection criteria. We found that applying the WGM method between 1000 and 1800 km above the solar surface would improve the prediction of the flare onset time by around 2-8 hr. Certain caveats and an outlook for future work along these lines are also discussed.
During its 2000 January flight, the Flare Genesis Experiment observed the gradual emergence of a bipolar active region, by recording a series of high-resolution photospheric vector magnetograms and ...images in the blue wing of the Ha line. Previous analyses of these data revealed the occurrence of many small-scale, transient Ha brightenings identified as Ellerman bombs (EBs). They occur during the flux emergence, and many of them are located near moving magnetic dipoles in which the vector magnetic field is nearly tangential to the photosphere. A linear force-free field extrapolation of one of the magnetograms was performed to study the magnetic topology of small-scale EBs and their possible role in the flux emergence process. We found that 23 out of 47 EBs are cospatial with bald patches (BPs), while 15 are located at the footpoints of very flat separatrix field lines passing through distant BPs. We conclude that EBs can be due to magnetic reconnection, not only at BP locations, but also along their separatrices, occurring in the low chromosphere. The topological analysis reveals, for the first time, that many EBs and BPs are linked by a hierarchy of elongated flux tubes showing aperiodic spatial undulations, whose wavelengths are typically above the threshold of the Parker instability. These findings suggest that arch filament systems and coronal loops do not result from the smooth emergence of large-scale -loops from below the photosphere, but rather from the rise of undulatory flux tubes whose upper parts emerge because of the Parker instability and whose dipped lower parts emerge because of magnetic reconnection. EBs are then the signature of this resistive emergence of undulatory flux tubes.
Virtually all X-class flares produce a coronal mass ejection (CME), and each CME carries magnetic helicity into the heliosphere. Using magnetograms from the Michelson Doppler Imager on the Solar and ...Hellospheric Observatory, we surveyed magnetic helicity injection into 48 X-flare-producing active regions recorded by the MDI between 1996 July and 2005 July. Magnetic helicity flux was calculated according to the method of Chae for the 48 X-flaring regions and for 345 non-X-flaring regions. Our survey revealed that a necessary condition for the occurrence of an X-flare is that the peak helicity flux has a magnitude > 6 x 10 super(36) Mx super(2) s super(-1). X-flaring regions also consistently had a higher net helicity change during the similar to 6 day measurement intervals than nonflaring regions. We find that the weak hemispherical preference of helicity injection, positive in the south and negative in the north, is caused by the solar differential rotation, but it tends to be obscured by the intrinsic helicity injection, which is more disorganized and tends to be of opposite sign. An empirical fit to the data shows that the injected helicity over the range 10 super(39)-10 super(43) Mx super(2) s super(-1) is proportional to magnetic flux squared. Similarly, over a range of 0.3-3000 days, the time required to generate the helicity in a CME is inversely proportional to the magnetic flux squared. Most of the X-flare regions generated the helicity needed for a CME in a few days to a few hours.
We introduce a nonpotential magnetic field calculation (NPFC) technique to perform azimuth disambiguation in solar vector magnetograms. It is shown that resolving the 180 ambiguity would be a ...numerically fully determined problem if the vertical electric current density was known a priori. Since this is not the case, we enforce a minimum-magnitude current density solution. The NPFC disambiguation is otherwise assumption-free, with the quality of the results depending on the quality of the measurements. The NPFC method first infers the nonpotential magnetic field component responsible for the assumed vertical currents and then determines the vertical magnetic field whose potential extrapolation, added to the nonpotential field, best reproduces the observationally inferred horizontal magnetic field. The technique is fast, effective, and physically sound, so it may be instrumental in a routine, real-time, disambiguation of future space-borne solar vector magnetograms.
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