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Register a new userA Study of Pre-Flare Solar Coronal Magnetic Fields: Magnetic Flux Ropes
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Magnetic flux ropes (MFRs) are thought to be the central structure of solar eruptions, and their ideal MHD instabilities can trigger the eruption. Here we performed a study of all the MFR configurations that lead to major solar flares, either eruptive or confined, from 2011 to 2017 near the solar disk center. The coronal magnetic field is reconstructed from observed magnetograms, and based on magnetic twist distribution, we identified the MFR, which is defined as a coherent group of magnetic field lines winding an axis with more than one turn. It is found that 90% of the events possess pre-flare MFRs, and their three-dimensional structures are much more complex in details than theoretical MFR models. We further constructed a diagram based on two parameters, the magnetic twist number which controls the kink instability (KI), and the decay index which controls the torus instability (TI). It clearly shows lower limits for TI and KI thresholds, which are $n_{rm crit} = 1.3$ and $|T_w|_{rm crit} = 2$, respectively, as all the events above $n_{rm crit}$ and nearly 90% of the events above $|T_w|_{rm crit}$ erupted. Furthermore, by such criterion, over 70% of the events can be discriminated between eruptive and confined flares, and KI seems to play a nearly equally important role as TI in discriminating between the two types of flare. There are more than half of events with both parameters below the lower limits, and 29% are eruptive. These events might be triggered by magnetic reconnection rather than MHD instabilities.
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It remains unclear how solar flares are triggered and in what conditions they can be eruptive with coronal mass ejections. Magnetic flux ropes (MFRs) has been suggested as the central magnetic structure of solar eruptions, and their ideal instabilities including mainly the kink instability (KI) and torus instability (TI) provide important candidates for triggering mechanisms. Here using magnetic field extrapolations from observed photospheric magnetograms, we systematically studied the variation of coronal magnetic fields, focusing on MFRs, through major flares including 29 eruptive and 16 confined events. We found that nearly 90% events possess MFR before flare and 70% have MFR even after flare. We calculated the controlling parameters of KI and TI, including the MFRs maximum twist number and the decay index of its strapping field. Using the KI and TI thresholds empirically derived from solely the pre-flare MFRs, two distinct different regimes are shown in the variation of the MFR controlling parameters through flares. For the events with both parameters below their thresholds before flare, we found no systematic change of the parameters after the flares, in either the eruptive or confined events. In contrast, for the events with any of the two parameters exceeding their threshold before flare (most of them are eruptive), there is systematic decrease in the parameters to below their thresholds after flares. These results provide a strong constraint for the values of the instability thresholds and also stress the necessity of exploring other eruption mechanisms in addition to the ideal instabilities.
We investigate the formation times of eruptive magnetic flux ropes relative to the onset of solar eruptions, which is important for constraining models of coronal mass ejection (CME) initiation. We inspected uninterrupted sequences of 131 AA images that spanned more than eight hours and were obtained by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) to identify the formation times of hot flux ropes that erupted in CMEs from locations close to the limb. The appearance of the flux ropes as well as their evolution toward eruptions were determined using morphological criteria. Two-thirds (20/30) of the flux ropes were formed well before the onset of the eruption (from 51 minutes to more than eight hours), and their formation was associated with the occurrence of a confined flare. We also found four events with preexisting hot flux ropes whose formations occurred a matter of minutes (from three to 39) prior to the eruptions without any association with distinct confined flare activity. Six flux ropes were formed once the eruptions were underway. However, in three of them, prominence material could be seen in 131 AA images, which may indicate the presence of preexisting flux ropes that were not hot. The formation patterns of the last three groups of hot flux ropes did not show significant differences. For the whole population of events, the mean and median values of the time difference between the onset of the eruptive flare and the appearance of the hot flux rope were 151 and 98 minutes, respectively. Our results provide, on average, indirect support for CME models that involve preexisting flux ropes; on the other hand, for a third of the events, models in which the ejected flux rope is formed during the eruption appear more appropriate.
Coronal mass ejections (CME) occur when long-lived magnetic flux ropes (MFR) anchored to the solar surface destabilize and erupt away from the Sun. This destabilization is often described in terms of an ideal magnetohydrodynamic (MHD) instability called the torus instability. It occurs when the external magnetic field decreases sufficiently fast such that its decay index, $n=-z,partial,(ln B)/partial z$ is larger than a critical value, $n>n_{rm cr}$, where $n_{rm cr}=1.5$ for a full, large aspect ratio torus. However, when this is applied to solar MFRs, a range of conflicting values for $n_{rm cr}$ is found in the literature. To investigate this discrepancy, we have conducted laboratory experiments on arched, line-tied flux ropes and have applied a theoretical model of the torus instability. Our model describes an MFR as a partial torus with footpoints anchored in a conducting surface and numerically calculates various magnetic forces on it. This calculation yields a better prediction of $n_{rm cr}$ which takes into account the specific parameters of the MFR. We describe a systematic methodology to properly translate laboratory results to their solar counterparts, provided that the MFRs have sufficiently small edge safety factor, or equivalently, large enough twist. After this translation, our model predicts that $n_{rm cr}$ in solar conditions often falls near $n_{rm cr}^{rm Sol}sim0.9$ and within a larger range of $n_{rm cr}^{rm Sol}sim(0.7,1.2)$ depending on the parameters. The methodology of translating laboratory MFRs to their solar counterparts enables quantitative investigations of the initiation of CMEs through laboratory experiments. These experiments allow for new physics insights that are required for better predictions of space weather events but are difficult to obtain otherwise.
Potential field extrapolations are widely used as minimum-energy models for the Suns coronal magnetic field. As the reference to which other magnetic fields are compared, they have -- by any reasonable definition -- no global (signed) magnetic helicity. Here we investigate the internal topological structure that is not captured by the global helicity integral, by splitting it into individual field line helicities. These are computed using potential field extrapolations from magnetogram observations over Solar Cycle 24, as well as for a simple illustrative model of a single bipolar region in a dipolar background. We find that localised patches of field line helicity arise primarily from linking between strong active regions and their overlying field, so that the total unsigned helicity correlates with the product of photospheric and open fluxes. Within each active region, positive and negative helicity may be unbalanced, but the signed helicity is only around a tenth of the unsigned helicity. Interestingly, in Cycle 24, there is a notable peak in unsigned helicity caused by a single large active region. On average, the total unsigned helicity at the resolution considered is approximately twice the typical signed helicity of a single real active region, according to non-potential models in the literature.
This paper is the second in a series of studies working towards constructing a realistic, evolving, non-potential coronal model for the solar magnetic carpet. In the present study, the interaction of two magnetic elements is considered. Our objectives are to study magnetic energy build up, storage and dissipation as a result of emergence, cancellation, and flyby of these magnetic elements. In the future these interactions will be the basic building blocks of more complicated simulations involving hundreds of elements. Each interaction is simulated in the presence of an overlying uniform magnetic field, which lies at various orientations with respect to the evolving magnetic elements. For these three small-scale interactions, the free energy stored in the field at the end of the simulation ranges from $0.2-2.1times 10^{26}$ ergs, while the total energy dissipated ranges from $1.3-6.3times 10^{26}$ ergs. For all cases, a stronger overlying field results in higher energy storage and dissipation. For the cancellation and emergence simulations, motion perpendicular to the overlying field results in the highest values. For the flyby simulations, motion parallel to the overlying field gives the highest values. In all cases, the free energy built up is sufficient to explain small-scale phenomena such as X-ray bright points or nanoflares. In addition, if scaled for the correct number of magnetic elements for the volume considered, the energy continually dissipated provides a significant fraction of the quiet Sun coronal heating budget.
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