Context.
In order to better understand the underlying processes and prerequisites for solar activity, it is essential to study the time evolution of the coronal magnetic field of solar active regions ...(ARs) associated with flare activity.
Aims.
We investigate the coronal magnetic energy and helicity budgets of ten solar ARs around the times of large flares. In particular, we are interested in a possible relation of the derived quantities to the particular type of the flares that the AR produces, namely, whether they are associated with a CME or whether they are confined (i.e., not accompanied by a CME).
Methods.
Using an optimization approach, we employed time series of 3D nonlinear force-free magnetic field models of ten ARs, covering a time span of several hours around the time of occurrence of large solar flares (GOES class M1.0 and larger). We subsequently computed the 3D magnetic vector potentials associated to the model 3D coronal magnetic field using a finite-volume method. This allows us to correspondingly compute the coronal magnetic energy and helicity budgets, as well as related (intensive) quantities such as the relative contribution of free magnetic energy,
E
F
/
E
(energy ratio), the fraction of non-potential (current-carrying) helicity, |
H
J
|/|
H
V
| (helicity ratio), and the normalized current-carrying helicity, |
H
J
|/
ϕ
′
2
.
Results.
The total energy and helicity budgets of flare-productive ARs (extensive parameters) cover a broad range of magnitudes, with no obvious relation to the eruptive potential of the individual ARs, that is, whether or not a CME is produced in association with the flare. The intensive eruptivity proxies,
E
F
/
E
and |
H
J
|/|
H
V
|, and |
H
J
|/
ϕ
′
2
, however, seem to be distinctly different for ARs that produce CME-associated large flares compared to those which produce confined flares. For the majority of ARs in our sample, we are able to identify characteristic pre-flare magnitudes of the intensive quantities that are clearly associated with subsequent CME-productivity.
Conclusions.
If the corona of an AR exhibits characteristic values of ⟨|
H
J
|/|
H
V
|⟩ > 0.1, ⟨
E
F
/
E
⟩ > 0.2, and ⟨|
H
J
|/
ϕ
′
2
⟩ > 0.005, then the AR is likely to produce large CME-associated flares. Conversely, confined large flares tend to originate from ARs that exhibit coronal values of ⟨|
H
J
|/|
H
V
|⟩ ≲ 0.1, ⟨
E
F
/
E
⟩ ≲ 0.1, and ⟨|
H
J
|/
ϕ
′
2
⟩ ≲ 0.002.
Aims.
We study the relative helicity of active region (AR) NOAA 12673 during a ten-hour time interval centered around a preceding X2.2 flare (SOL2017-09-06T08:57) and also including an eruptive X9.3 ...flare that occurred three hours later (SOL2017-09-06T11:53). In particular, we aim for a reliable estimate of the normalized self-helicity of the current-carrying magnetic field, the so-called helicity ratio, |
H
J
|/|
H
|, a promising candidate to quantity the eruptive potential of solar ARs.
Methods.
Using Solar Dynamics Observatory Helioseismic and Magnetic Imager vector magnetic field data as an input, we employ nonlinear force-free (NLFF) coronal magnetic field models using an optimization approach. The corresponding relative helicity, and related quantities, are computed using a finite-volume method. From multiple time series of NLFF models based on different choices of free model parameters, we are able to assess the spread of |
H
J
|/|
H
|, and to estimate its uncertainty.
Results.
In comparison to earlier works, which identified the non-solenoidal contribution to the total magnetic energy,
E
div
/
E
, as selection criterion regarding the required solenoidal quality of magnetic field models for subsequent relative helicity analysis, we propose to use in addition the non-solenoidal contribution to the free magnetic energy, |
E
mix
|/
E
J
, s
. As a recipe for a reliable estimate of the relative magnetic helicity (and related quantities), we recommend to employ multiple NLFF models based on different combinations of free model parameters, to retain only those that exhibit smallest values of both
E
div
/
E
and |
E
mix
|/
E
J
, s
at a certain time instant, to subsequently compute mean estimates, and to use the spread of the individually contributing values as an indication for the uncertainty.
ABSTRACT The unusually large active region (AR) NOAA 2192, observed in 2014 October, was outstanding in its productivity of major two-ribbon flares without coronal mass ejections. On a large scale, a ...predominantly north-south oriented magnetic system of arcade fields served as a strong top and lateral confinement for a series of large two-ribbon flares originating from the core of the AR. The large initial separation of the flare ribbons, together with an almost absent growth in ribbon separation, suggests a confined reconnection site high up in the corona. Based on a detailed analysis of the confined X1.6 flare on October 22, we show how exceptional the flaring of this AR was. We provide evidence for repeated energy release, indicating that the same magnetic field structures were repeatedly involved in magnetic reconnection. We find that a large number of electrons was accelerated to non-thermal energies, revealing a steep power-law spectrum, but that only a small fraction was accelerated to high energies. The total non-thermal energy in electrons derived (on the order of 1025 J) is considerably higher than that in eruptive flares of class X1, and corresponds to about 10% of the excess magnetic energy present in the active-region corona.
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.
Aims. A broad jet was observed in a weak magnetic field area at the edge of active region NOAA 11106 that also produced other nearby recurring and narrow jets. The peculiar shape and magnetic ...environment of the broad jet raised the question of whether it was created by the same physical processes of previously studied jets with reconnection occurring high in the corona. Methods. We carried out a multi-wavelength analysis using the EUV images from the Atmospheric Imaging Assembly (AIA) and magnetic fields from the Helioseismic and Magnetic Imager (HMI) both on-board the Solar Dynamics Observatory, which we coupled to a high-resolution, nonlinear force-free field extrapolation. Local correlation tracking was used to identify the photospheric motions that triggered the jet, and time-slices were extracted along and across the jet to unveil its complex nature. A topological analysis of the extrapolated field was performed and was related to the observed features. Results. The jet consisted of many different threads that expanded in around 10 minutes to about 100 Mm in length, with the bright features in later threads moving faster than in the early ones, reaching a maximum speed of about 200 km s-1. Time-slice analysis revealed a striped pattern of dark and bright strands propagating along the jet, along with apparent damped oscillations across the jet. This is suggestive of a (un)twisting motion in the jet, possibly an Alfvén wave. Bald patches in field lines, low-altitude flux ropes, diverging flow patterns, and a null point were identified at the basis of the jet. Conclusions. Unlike classical λ or Eiffel-tower-shaped jets that appear to be caused by reconnection in current sheets containing null points, reconnection in regions containing bald patches seems to be crucial in triggering the present jet. There is no observational evidence that the flux ropes detected in the topological analysis were actually being ejected themselves, as occurs in the violent phase of blowout jets; instead, the jet itself may have gained the twist of the flux rope(s) through reconnection. This event may represent a class of jets different from the classical quiescent or blowout jets, but to reach that conclusion, more observational and theoretical work is necessary.
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 of n . 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 crit is 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.
The
Helioseismic and Magnetic Imager
(HMI) on board the
Solar Dynamics Observatory
(SDO) provides photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to ...model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation code. Our code is based on an optimization principle and has been tested extensively with semianalytic and numeric equilibria and applied to vector magnetograms from
Hinode
and ground-based observations. Recently we implemented a new version which takes into account measurement errors in photospheric vector magnetograms. Photospheric field measurements are often affected by measurement errors and finite nonmagnetic forces inconsistent for use as a boundary for a force-free field in the corona. To deal with these uncertainties, we developed two improvements: i) preprocessing of the surface measurements to make them compatible with a force-free field, and ii) new code which keeps a balance between the force-free constraint and deviation from the photospheric field measurements. Both methods contain free parameters, which must be optimized for use with data from SDO/HMI. In this work we describe the corresponding analysis method and evaluate the force-free equilibria by how well force-freeness and solenoidal conditions are fulfilled, by the angle between magnetic field and electric current, and by comparing projections of magnetic field lines with coronal images from the
Atmospheric Imaging Assembly
(SDO/AIA). We also compute the available free magnetic energy and discuss the potential influence of control parameters.
Solar flares and coronal mass ejections are associated with rapid changes in field connectivity and are powered by the partial dissipation of electrical currents in the solar atmosphere. A critical ...unanswered question is whether the currents involved are induced by the motion of preexisting atmospheric magnetic flux subject to surface plasma flows or whether these currents are associated with the emergence of flux from within the solar convective zone. We address this problem by applying state-of-the-art nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA AR 10930 around the time of a powerful X3.4 flare. We compute 14 NLFFF models with four different codes and a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We discuss the relative merits of these models in a general critique of present abilities to model the coronal magnetic field based on surface vector field measurements. For our application in particular, we find a fair agreement of the best-fit model field with the observed coronal configuration, and argue (1) that strong electrical currents emerge together with magnetic flux preceding the flare, (2) that these currents are carried in an ensemble of thin strands, (3) that the global pattern of these currents and of field lines are compatible with a large-scale twisted flux rope topology, and (4) that the image10 super(32) erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection.
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.
A statistical study of the chromospheric ribbon evolution in H
α
two-ribbon flares was performed. The data set consists of 50 confined (62%) and eruptive (38%) flares that occurred from June 2000 to ...June 2015. The flares were selected homogeneously over the H
α
and
Geostationary Operational Environmental Satellite
(GOES) classes, with an emphasis on including powerful confined flares and weak eruptive flares. H
α
filtergrams from the Kanzelhöhe Observatory in combination with
Michelson Doppler Imager
(MDI) and
Helioseismic and Magnetic Imager
(HMI) magnetograms were used to derive the ribbon separation, the ribbon-separation velocity, the magnetic-field strength, and the reconnection electric field. We find that eruptive flares reveal statistically larger ribbon separation and higher ribbon-separation velocities than confined flares. In addition, the ribbon separation of eruptive flares correlates with the GOES SXR flux, whereas no clear dependence was found for confined flares. The maximum ribbon-separation velocity is not correlated with the GOES flux, but eruptive flares reveal on average a higher ribbon-separation velocity (by ≈ 10 km s
−1
). The local reconnection electric field of confined (
c
c
=
0.50
±
0.02
) and eruptive (
c
c
=
0.77
±
0.03
) flares correlates with the GOES flux, indicating that more powerful flares involve stronger reconnection electric fields. In addition, eruptive flares with higher electric-field strengths tend to be accompanied by faster coronal mass ejections.
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