Issue
J. Space Weather Space Clim.
Volume 9, 2019
Developing New Space Weather Tools: Transitioning fundamental science to operational prediction systems
Article Number A6
Number of page(s) 12
DOI https://doi.org/10.1051/swsc/2019002
Published online 01 February 2019

© M.B. Korsœs et al., Published by EDP Sciences 2019

Licence Creative Commons
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1 Introduction

A clear understanding of the dynamics and energetics of magnetic reconnection remains an important goal of solar flare research. A key aspect of this research area is to determine the dynamics of an active region (AR) before flare occurrence. Reliably identifying flare precursors also has practical significance for flare predictions (see, e.g., Georgoulis, 2012, 2013; Barnes et al., 2016, and references therein). The aim of finding such precursors was achieved by, e.g., Korsós et al. (2014) and Korsós et al. (2015) (K14 and K15 thereafter, respectively), developing a new type of proxy measure of magnetic non-potentiality in an AR.

K14 and K15 analysed the horizontal gradient of the line of sight (LOS) component of the magnetic field in the vicinity of polarity inversion lines (PILs), and found indicative features of the imminent flaring behaviour up to two-three days prior to the actual flare occurrance. The pre-flare dynamics and the related physical processes at the solar surface were investigated using data with an hourly temporal resolution from joint SDD ground- (Debrecen Heliophysical Observatory, DHO) and space-based (Solar and Heliospheric Observatory, SOHO) sunspot data catalogues (see, e.g., Baranyi et al., 2016) from 1996 to 2010. Furthermore, K14 and K15 focused solely on the largest intensity flare-class during the investigated AR’s disk passage. Based on the Geostationary Operational Environmental Satellite (GOES) flare classification system, the 61 investigated flare cases were all stronger than M5 flare-class in those two papers.

K14 introduced the horizontal gradient of the magnetic field (GM), a proxy which measures the magnetic non-potentiality at the photosphere. The GM is applied between umbrae with opposite polarities at the PIL of ARs and provides key information about the most important properties of an imminent flare: its intensity and occurrence time. K14 identified pre-flare patterns of this proxy quantity: increasing phase, high maximum and gradual decrease prior to flaring. A linear relationship was found between the pre-flare GM maximum and the largest flare intensity class of the AR. Next, the occurrence time estimation was found to be somewhat less precise, for the most probable time of flare occurrence being between 2–10 h after the GM maximum.

In K15, the authors generalised the GM method and presented the concept of the weighted horizontal gradient of the magnetic field, WGM. The introduction of the WGM has enhanced the application capability by indicating a second flare precursor. Namely, the barycenters (the area-weighted centers of the positive and negative polarities) display a pattern of approach and recession prior to the flare. We found that the flare occurs when the distance between the barycenters is approximately equal to the corresponding distance at the beginning of the convergence phase. This precursor has the capability for a more accurate flare occurrence time prediction, which is based on the relationship between the durations of the divergence (T D+F) and convergence phase (T C) of the barycenters of the opposite polarity regions. Next, K15 also found a linear relationship between the values of the maxima of the WGM () and the highest flare intensity of an AR(s). They reported that if one can identify concurrently the two pre-flare behaviours discussed above, then flare(s) do occur in their sample. They have also shown that if one of the required pre-flare patterns is absent then a flare may not be expected (Korsós et al., 2014; Korsós & Ruderman, 2016).

Also, K15 investigated separately the single-flare case when only one energetic flare took place after and cases when multiple flares erupted after reaching . In the 61 flare cases, the longest study period was 48 h from the moment of reaching to the moment of first flare. The percentage difference () was calculated between the value of and the first value of the WGM after the flare peak time (). In brief, they found the following: if is over 54%, no further flare of the same class or above would be expected; but, if is less than: 42%, further flare(s) of the same class is probable within about an 18-hour window. The longest time interval of a subsequent flare to occur was 18 h in the study samples. K15 suggested that these latter features may serve as practical additional flare alert tools.

In this study, we have generalised the application of the WGM method in two main ways. First, we have expanded the number of investigated ARs by taking into account not only ARs observed by the SOHO satellite but also those detected by the higher spatial and temporal resolution SDO (Solar Dynamics Observatory) mission. Second, we have extended the analysis to encompass GOES flare classes from as low as B-class to as high as X-class flares. In Section 2, we briefly introduce and apply the WGM method to lower energetic flares, i.e., between B and M5 flares. In Section 3, we present an extended statistical analysis of these higher number of AR cases and summarise our findings. In Section 4, we introduce a simple visualisation of our observational experience of the pre-flare behaviour of distance. Finally, we provide discussions of our results and draw conclusions in Section 5.

2 Applying the WGM method

2.1 Implementation of the WGM Method

In 61 flare cases, K15 demonstrated that WGM could be successfully applied to help identify features preceding flares with classes above M5. Later, in Zheng et al. (2015) and Korsós and Ruderman (2016), the WGM method was applied to case studies of lower than M5 flare cases employing the SDO/HMI-Debrecen Data (also known as HMIDD, the continuation of the SDD) catalogue. In the present paper, we go further by enlarging the observational sample to include 6 ARs with B-class flares, 21 with C-class flares, 13 with M1–M5, and 30 additional ARs with flare events above M5 (see Appendix A).

The main reasons of the small number of the weaker than M5 flaring AR in the sample are as follows: (i) When the investigated strongest energetic flare class becomes lower and lower (e.g., it is below M5 or less) then there is an associated decreased chance of having this low-energy flare class to be the largest flare class of an AR. (ii) In principle, the HMIDD (2011–2014) database would be slightly more suitable to investigate the lower than M5-class flares because the temporal and spatial resolutions of this catalogue are better than that of the SDD. However, in case of these weaker flares, often, we simply cannot identify the two nearby opposite polarities of the AR in the HMIDD catalogue, so, the WGM method is not applicable.

By considering lower-energy flares, this expansion of the investigation of flare classes explores whether there could be a “common” physical mechanism underlying the flare process across all energy scales. However, it must be noted that our method does not give insight into which of the wide range of proposed flare models available in the literature is applicable. Our method points merely towards the idea that, regardless of model, there could be a “common” pre-flare features identified at photospheric level.

The method is based on tracking changes of the solar surface magnetic configuration in ARs with the following five steps:

  1. During the entire investigated period it is required that the AR is located between −70° and +70° (occasionally, when the data permit +75°, but not further) from the central meridian of the Sun.

  2. During the AR’s disk passage, the largest intensity flare-class event of the AR is selected from the GOES flare catalog.

  3. In order to acquire enough preceding data to identify the precursors, the occurrence of the associated strongest flare class could be no further than: 40° east of the central meridian.

  4. The WGM method is applied in a selected area of the AR. As an initial approach, the selected area is an entire δ-spot of the AR where all umbrae are now taken into account for analysis. This assumption is based on the idea that the δ-type sunspots themselves are observed and identified as the most probable places for the flare onset. A δ-type spot contains opposite polarity umbrae surrounded by a common penumbra, therefore it has polarity inversion line(s) (PIL). It is also well known that solar flares often are related to PILs (Schrijver, 2007; Louis et al., 2015). Furthermore, the umbrae are loci of high flux densities, so they are presumably the dominant components of the flare processes. However, it should be noted that the Debrecen sunspot catalogue does not always indicate the two close opposite magnetic polarities as a δ-type spot. In this case, the selected area is a circle with a radius of 1.5° ± 0.5° around the barycentrum of the two closest opposite polarity umbrae. We introduced the circle in the studied samples of K15. The diameter of the circle is derived from the common amorphous shape penumbra of the opposite polarity umbrae approximated by a circle with a radius of 1.5° ± 0.5° in Carrington heliographic coordinates. Finally, the selected area is tracked and the evolution (e.g., emergence of new flux or flux cancellation) of umbrae are monitored.

  5. At the end, the WGM method is applied to the selected area. The evolution of the unsigned magnetic flux, the distance between the area-weighted barycenters of opposite polarities and the WGM are followed as outlined below:

  1. To establish that a behaviour is related to the upcoming flare rather than merely an insignificant fluctuation, (i) the relative gradient of the rising phase of WGM is 30% and (ii) the relative gradient of the distance parameter of the converging motion is greater than 10% for a period of at least 4 h. Furthermore, a maximum of 10% deviation is allowed as the distance increases back to its original value that it had at the moment when the convergence phase started.

  2. When the relevant pre-flare behaviour of the WGM proxy is identified as given in point a) above, then and can also be determined.

  3. Next, the relevant pre-flare behaviour of the distance parameter is marked with a parabolic curve. The parabolic curve is fitted from the starting time of convergence to the end of the divergence phase, where its minimum is the moment of reaching the closest position of the two barycenters.

Let us comment on the errors and uncertainties of the WGM methods: The uncertainty in obtaining the distance parameter originates from the error of position measurements that is 0.1 heliographic degree, while measuring the area has 10% error (Győri et al., 2011). The mean error of the unsigned magnetic flux is 15%. The magnetic field used here to calculate WGM is estimated from the values of umbral area and mean field strength recorded in the Debrecen (SDD and HMIDD) catalogues through the application of equation (1) in Korsós et al. (2014). Therefore, the total calculated uncertainty of WGM is 20%.

2.2 Applying the WGM method to M-, C- and microflare cases

First, let us now demonstrate the technique of applying the WGM method to three representative examples where the flare classes are all lower than M5. The examples for analysis discussed here are: AR 11504 produced two low M-class flares; AR 11281 generated 3 C-class flares as the largest-class flare. Finally, AR 11967 is interesting because it hosted a known and identified microflare (Yang et al., 2015). In Yang et al. (2015), observational evidence of X-shape magnetic reconnection before a microflare was introduced. The magnetic reconnection occurred at the topside edge of AR 11967 on February 3, 2014 07:15 UT. There, Yang et al. (2015) found that the X-shape reconnection process builds up of two types of reconnection: (i) First, two anti-parallel loops slowly reconnect, and, after the new loops were formed, they became stacked. This slow reconnection continued for several tens of minutes. (ii) The second type of reconnection, the rapid reconnection, took only about three minutes. During the rapid reconnection, the anti-parallel loops very quickly approached each other and reconnected. After the rapid reconnection, the former anti-parallel loops disappeared and new loops formed separately.

The resulting diagrams of the WGM analysis of ARs 11504, 11281, and 11967 are shown in Figures 1a, 2a and 3, respectively. In Figures 1a3, we depict the pre- and post-flare evolution of WGM (top panel) and we also plot the distance between the barycentres of opposite polarities as a function of time (middle panel). In the middle panels of Figures 1a3, the relevant pre-flare behaviour of the distance parameter is marked with red parabolic curves. In the bottom panels of Figures 1a3, we show the temporal variation of the unsigned magnetic flux in selected area. Figures 1b2b visualise the investigated area by red ellipses in their white-light appearance (upper panel), the corresponding magnetogram (middle panel) and the corresponding synthetic polarity drawing from the Debrecen sunspot data catalogue (bottom panel) from which umbral area and mean field strength are taken to calculate WGM.

thumbnail Fig. 1

(a) Example for applying the WGM method to two smaller (M1.2 and M1.9) GOES M-class flares in AR 11504. The top panel shows the WGM, the middle panel plots the distance between the barycentres, and the bottom panel is a plot of the associated unsigned magnetic flux as a function of time. The M1.2 and M1.9 flares are indicated by (blue) vertical lines where the value of the is taken. Note the U-shapes (red parabolae) in the middle panel that are key flare precursors of the WGM method. The error is marked with shaded grey. (b) Top/middle and bottom panels are the related intensity/magnetogram maps and the associated Debrecen data catalogue representation of synthetic polarity drawing of AR at 01:59 on 13 June 2012. The red circle shows which umbral area and mean field strength are taken to calculate WGM.

thumbnail Fig. 2

(a) Representative example for applying the WGM method to GOES C-class flares in AR 11281. (b) Top/middle and bottom panels are the associated intensity/magnetogram maps and the Debrecen catalogue representation of the associated synthetic polarity drawing at 00:59 on 03 September 2011.

thumbnail Fig. 3

Evolution of the pre-flare indicators of the WGM method, similar to those of Figure 2 but for a B-class flaring event in AR 11967. The estimated error is marked by the shaded grey envelope.

Let us first investigate the case where the largest intensity flare class was a weak M-class. AR 11504 produced an M1.2 flare on June 13, 2012 13:17 UT and a further M1.9 flare on June 14, 2012 14:35 UT. In Figure 1a, we see that the WGM increases to a maximum value (= 0.55 × 106 Wb/m), followed by a less steep decrease which ends with an M1.2 ( = 0.35 × 106 Wb/m) flare and is succeeded by another M1.9 ( = 0.23 × 106 Wb/m) energetic flare (top panel). The conditions specified by step 5a are satisfied by the pre-flare behaviour of the WGM, therefore we can dismiss the idea that this behaviour is unconnected to the flare. Moreover, the percentage difference () is only 34% in the first flare case, which is less than 42% (as defined by the criterion given by K15), therefore we expected more flares to follow, which did indeed happen. After the second flare, the is 61%, so further flares were not expected. Regarding the distance parameter, the two convergence-divergence phases are evident. The first one is before the M1.2 flare where the T C is 9 h and T D+F is 34 h. The second one occurred before the M1.9 flare where T C is 14 h and T D+F is 19 h. It is worth mentioning that the two convergence phases of the barycenters had a duration longer than 4 h; the relative gradient of the first decreasing phase is 56% and for the second one it is 54%.

Let us now introduce a representative example of the analysis of a C-class flare of this by investigating, AR 11281. This AR was the cradle to the following 3 C-class flares: C1.8 on September 2, 2011 15:16 UT, C2.4 and C1.2 on September 3, 2011 07:56 and 20:10 UT, respectively. In Figure 2a, we recognise the following pre-flare properties of the WGM and the distance: (i) The rising phase and a maximum value of the WGM ( = 0.78 × 106 Wb/m) is followed by a less steep decrease which ends with C1.8 ( = 0.45 × 106 Wb/m), C2.4 ( = 0.51 × 106 Wb/m) and after that with the C1.2 ( = 0.36 × 106 Wb/m) energetic flares. The conditions of point 5a are satisfied, therefore the pre-flare behaviour can be confidently attributed to the flare. (ii) The convergence-divergence feature of the barycentric distance prior to the first C-class flare are also evident. The duration of the convergence phase of the distance is 13 h and the gradient is 26%. The first flare occurred 30 h later, measured from the moment of the closest position of the two opposite polarity barycenters. The second C-class flare occurred approximately 17 h after the first C-class flare. The final C1.2 flare occurred 12 h after the second C2.4 flare. Let us now briefly investigate the percentage differences of the three flares. The is 42% after the first C-class flare (C1.8). The is 35% after the C2.4 and 54% after the last C-class occurrence from the previous . We conclude that one should indeed expect flare(s) after the first C1.8 flare, and that one should not expect further same class flare(s) after the last C-class, which is what happened. Because there was only one clear U-shape flare precursor, we could not say anything about how many same-class flares will follow the first C flare.

In Figure 3, for AR 11967 we analysed the same area in the HMIDD catalogue as was analysed from HMI line-of-sight magnetograms in Figure 1 of Yang et al. (2015).

One can indeed recognise the increasing and decreasing phase of the WGM before the microflare. The maximum value of the WGM is 0.65 × 106 Wb/m and the value of the is 0.38 × 106 Wb/m. The is 42% after the maximum of the WGM. Unfortunately, we cannot say whether a further flare occurred because we do not have any later observations from this area. Next, the convergence and divergence phases of the distance are also identifiable: we emphasise this with a red parabola in the middle panel of Figure 3. Here, the duration of the observed TC is 7 h, with 40% decreasing of the distance and TD+F is 6 h. Based on the required conditions and steps outlined in 1–5 above, these two pre-flare behaviours can be classified as true precursors of the microflare. Note that there may be another typical pre-flare behaviour of the WGM and distance between 02/02 08:00 and 02/02 18:00. Although, based on 5(a), the pre-flare behaviour of the WGM could be a precursor, but, the pre-flare behaviour of distance does not qualify as a precursor because the decreasing time is only one hour. In summary, as Figure 3 demonstrates, it is clear that even microflares seem to show the precursors of flaring identified by the horizontal magnetic gradient method.

From these three sample studies presented (Figs. 13) and, supported by analyses of the entire ensemble data, we propose that the pre-flare behaviour of WGM and the distance of the area-weighted barycentre of opposite polarities may be present widely and may be indispensable before the associated reconnection and/or flaring process. If the conjecture of pre-flare behaviour is proven to even more solar data than the current ensemble of 127 AR cases, this will certainly give us a greater statistical significance for understanding the underlying physics.

3 Statistical analyses of WGM method on the extended data

Our aim is to analyse the photospheric precursors of flares of a 127 strong set of AR from SDD and HMIDD. First, let us focus on the relationship between the log value of largest intensity flare of an AR (log(I)) and the preceding maximum of the WGM (see Fig. 4). We have found a logarithmic dependence between the log(I) and the . The correlation coefficient of the fitted logarithmic function is R 2 = 0.54 and is an indicator for a reasonable functional fit to the data. The root mean square error (RMSE) of log(I[W/m2]) is 0.51.

thumbnail Fig. 4

The log value of GOES flare intensity (log(I)) as function of the maximum WGM (). The estimated errors are also given in the lower right corner.

Next, the WGM method reveals further important connections between the proposed precursors and the associated flare properties. K15 showed that, for large flares, there is a relationship between the duration of the converging motion (T C) and the sum of the duration of the diverging motion of the barycenters of opposite polarities together with the remaining time until flare peak (T D+F). The question is then whether this relationship is also valid in the extended data studied here. In other words, it is of interest to establish whether this relationship found for flares above M5 remains for less energetic flares, i.e., below M5 down to C-class or microflares.

Figure 5 (left panel) gives a further insight into the relation between these physical quantities by plotting the elapsed time between the start of the divergence phase and the flare peak as a function of the duration of converging motion. The linear relationship found may possess the capability to estimate an approximate occurrence time of the associated flare. R 2 of the fitted linear function is 0.60 indicating a moderate correlation. By identifying the start of the divergence phase of the barycenters of opposite polarity, one may predict the time of first flare occurrance with an estimated error of 7.2 h. We also investigated whether there is a correlation between the duration of converging-diverging motion and the flare intensity, but we were unable to conclude any statistically significant relationship.

thumbnail Fig. 5

Left: Relationship between the durations of converging motion and the duration from the moment of time of closest position up to the first flare occurrences. Right: Relationship between difference of the distances between the barycenters at the start of the convergence phases and at the closest approach (D C) and the distance between the point of closest approach to the position of first flare occurrence (D FM) at photospheric level. The estimated errors are given in the lower right corner.

thumbnail Fig. 6

Figure demonstrating the process (1) when two opposite polarities of initial barycenter separation distance D 0 are convergence; (2) the two opposite polarities are at their closest and a current sheet starts forming, where D min is the minimum distance, with D 0 > D min; (3) the two opposite polarities are divergence from their closest distance, D min, back to D 0, and the associated current sheet is still developing above the photosphere; (4) reconnection takes place and a flare occurs above the polarity inversion line (PIL). After the distance between the polarity barycentres returns to the initial separation, D 0, during a further evolution, this distance can now either decrease or increase (i.e., D 1 < D 0 or D 1 > D 0). D C = D 0D min in Figure 5 (right panel).

Figure 5 (right panel) shows the linear correlation between the distance from the starting point of the converging phase to the point of the closest approach (D C) and the distance between the point of closest approach to the position of the first flare occurrences (D FM). The linear fit between D C and D FM may provide another practical tool for estimating the spatial location of the flare. Here, the R 2 of the linear regression is only 0.42 which means that the correlation is moderate. The RMSE is 3.6 Mm. Again, we cannot report any statistically significant relationship between the distance values and flare intensity. However, it is worth mentioning that the expected occurrence time and estimated location could both reinforce the search for a more reliable flare prediction.

Last, but not least, we carried out an analysis similar to that of K15 to estimate the corresponding probability thresholds and have found reassuring results confirming the earlier findings. Namely, if the is over 55%, no further energetic flares are expected; but, if the is less than: 40%, a further flare is probable within approximately 18 h. If the is between 40% and 55%, one cannot make a reliable prediction of whether additional flares will/will not take place. In summary, therefore, these properties of the WGM method may serve as practical flare watch alert tools across a wide range of the flare energies, subject of course to the conditions outlined in Section 2.

4 Visualisation of pre-flare behaviour of the distance parameter

In this section, inspired by laboratory experiments, we introduce a simple visual interpretation of the observed pre-flare behaviour of the area-weighted barycenters of opposite polarities prior to the reconnection process. The process of magnetic reconnection in the solar atmosphere is mostly studied either using space-based observations or theoretical (e.g., numerical or analytical) modelling. However, laboratory experiments may also yield some interesting insight and impetus. A good example is the series of experimental studies by e.g., Yamada (1999) and Yamada et al. (2010). Yamada (1999) investigating the physics of magnetic reconnection in a controlled laboratory environment. In these experiments, reconnection is driven by torus-shaped flux cores which contain toroidal and poloidal coil windings. Two types of reconnection modes were found, according to whether the poloidal field coil current increased or decreased. When the poloidal coil current increased then the poloidal fluxes increased as well and plasma was pushed toward the X-point. This reconnection process is called the push mode. On the other hand, when the poloidal current decreased, the associated decreasing poloidal flux in the common plasma was pulled back toward the X-point, a reconnection process known as the pull mode. They found that the push mode occurs more rapidly than the pull mode.

Besides the extensive modelling in the literature, the experiments by Yamada et al. (2010) have been a direct drive to solar observational studies of the process of magnetic reconnection. For example, in K15, it was found that the area-weighted barycentres of two opposite magnetic polarities of an AR in the investigated area first approach each other, reach their minimum distance followed by a divergence phase. Most surprisingly, the flare occurrence(s) take place when the growth of the distance becomes large enough and it approaches the value it had at the beginning of the convergence phase (for the actual details see their middle panel of Figures 1a3). K15 have shown, using 61 samples from the SOHO (Solar and Heliospheric Observatory) era, that there is never a large flare occurrence when the barycenters are closest. Occasionally, though, smaller so-called precursor flares may take place. The divergence phase was found to continue until the distance increased back to about its original value, i.e., to the level of separation when the convergence phase started. The most energetic flares were found to happen after the divergence phase, and for the flare occurrence time a statistical relationship was established in terms of the duration of the convergence/divergence phases (see left-hand side of Fig. 5).

In Figure 5, we introduce a simple visualisation of the pre-flare behaviour. First, the two opposite magnetic polarities start convergence (panel 1), with an initial barycentric distance of D 0. When the barycentres reach their closest position (i.e., the separation is D min), a thin current sheet begins to form between the opposite polarity field lines (or sheets) but there is no reconnection yet (see panel 2). After the minimum distance stage, the two opposite polarities begin to recede from each other and the separation at photospheric level increases back to the about the same level of separation when the converging process started (see panel 3), with barycentric separation distance of: D 0. The current sheet is still forming during the divergence phase above the photosphere. Finally, reconnection takes place, however, well after the moment when the photospheric distance between the area-weighted centres of polarity is at its about the same value of what it had at the beginning of the convergence phase (see panel 4), with a barycentric distance D 1. During the process of magnetic reconnection, the magnetic field lines rearrange according to the yet unknown key principles of reconnection in the highly stratified lower solar atmosphere. This rearrangement is accompanied with a sudden energy release, e.g., flare eruption, where the energy of eruption was stored in the stressed magnetic fields.

A further possible explanation of our empirical finding may be that the actual convergence phase is caused by bipolar flux emergence between the two barycenters at the area of the PIL that eventually brings the barycenters closer. Next, the divergence may be caused by the strong shearing motion between the opposite polarities (Ye et al., 2018).

5 Conclusions

Most flare forecasting models attempt to predict flare probability (see, e.g., Georgoulis, 2012, 2013; Barnes et al., 2016, and references therein). Many of these flare forecast studies focus on a predictive time window of 6, 12, 24 and 48 h (see, e.g., Al-Ghraibah et al., 2015; Benz, 2017, and references therein). In K15, the concept of the weighted horizontal gradient of the magnetic field, WGM, was introduced where all umbrae were taken into account in the selected δ-spot for analysis. Initially, the WGM method was tested on data available from the SOHO era only.

Here, we carry out an extended statistical analysis of these photospheric precursors of pre-flare dynamics on a larger sample of δ-spots observed, including not only those contained by SDD but also by those found in HMIDD. The main motivation is to further develop, improve and confirm the applicability of two parameters (the WGM and barycentric distance parameters) introduced. Inspired by the results of Zheng et al. (2015) and Korsós and Ruderman (2016), we expanded the statistical sample of flares to be investigated below the M5-class down to B-class microflares, therefore offering an over-arching view of the applicability of the WGM method for a wider energy spectrum of flares. An answer is searched for to the question, do smaller flares display the same predictive pre-flare features as their stronger cousins. In the present work, we have outlined the case for the affirmative answer.

In Section 2, we introduced three representative δ-type ARs, AR 11504, AR 11281 and AR 11967 for presenting characteristic sample studies from our extended dataset. These are typical ARs for less significant GOES energetic flare classes. Based on Debrecen Heliophysical Observatory catalogues, in all of the observed δ-spot of the 127 ARs, we have identified the two pre-flare patterns established earlier in K15: (i) the pre-flare behaviour pattern of WGM: a rising phase, a maximum and a gradual decrease prior to flaring and (ii) the pre-flare evolutionary pattern of the distance of the area-weighted barycentres during the converging and diverging motion from the minimum distance value of the area-weighted barycenters of opposite polarities until the flare occurrence. Furthermore, we have set out empirical conditions that the WGM and the barycenter distance parameters have to satisfy to qualify as being precursive of a flare rather than an unrelated fluctuation.

After identifying the pre-conditions, we have also investigated the relationship between the intensity of flares from δ-spots in terms of the (see Fig. 4). We have always focussed on the largest intensity flare (I) which has occurred in the given AR after reaching . By extending the flare samples down to B-class, we found a logarithmic relationship between the log(I) of the investigated ARs and . This relationship may provide a tool to estimate the log(I) of the expected flare with ±0.51 uncertainty from the measured .

In K15, we found a linear relationship between the duration of the converging motion and the time elapsed from the moment of minimum distance until the flare peak. Our extended statistical sample from SDD and HMIDD data from B-class to X-class flares, again, confirms this linear relationship. Therefore, we propose that if one can reliably identify the moment when the barycenter distance in a δ-spot begins to grow again then one is able to estimate the occurrance time of the flare with ±7.2 h of uncertainty. Furthermore, we also investigated the connection between the length of distance from the starting point of the converging phase to the point of closest approach (D C) and the distance between the point of closest approach to the position of the first flare (D FM) between the area-weighted barycentres. The linear relationship, with an estimated error of 3.6 Mm, found between D C and D FM may help to identify the region where the flare occurrence may be expected. So, the expected time of flare occurrence and its predicted location could serve as combined tools for flare warning.

We have also searched for phenomenological clues for differences for predicting the number of flares expected from δ-spots after the horizontal magnetic gradient reaches , during its decreasing phase. In K15, for flares stronger than M5, the conclusion was: if the percentage difference () between the value of the and the first value of the WGM after the flare peak () is over 54%, no further energetic flare(s) may be expected; but, if the percentage difference is less than about: 42%, further flaring is likely within the following 18 h. In the present study, we have revisited the estimated probability of further flares during the descending phase of the WGM after its maximum. We found encouraging results extending the initial findings of K15 to a wider flare energy range, namely: if the percentage difference () is over 55%, no further energetic flare(s) may be expected; but, if is less than: 40%, further flaring is probable within about 18 h. The importance of this empirical result is that it could be a further auxiliary tool for indicating the properties of imminent flares from δ-spots.

Acknowledgments

MBK is grateful to the University of Sheffield and the Hungarian Academy of Sciences for the supports received. MBK also acknowledges the open research program of CAS Key Laboratory of Solar Activity, National Astronomical Observatories, No. KLSA201610. MBK and RE acknowledge the CAS Key Laboratory of Solar Activity, National Astronomical Observatories Commission for Collaborating Research Program for support received to carry out part of this work. RE acknowledges the CAS Presidents International Fellowship Initiative, Grant No. 2016VMA045. RE is also grateful to Science and Technology Facilities Council (STFC, grant number ST/M000826/1) UK and the Royal Society for enabling this research. SY is supported by the National Natural Science Foundations of China (11673035, 11790304). All authors thank Christopher Nelson and Matthew Allcock for fruitful discussions. Last but not least, the authors also would like to thank the two anonymous referees and the Guest Editor for their helpful comments received during the peer-review evaluation process. The editor thanks two anonymous referees for their assistance in evaluating this paper.

Appendix A

List of investigated ARs

The first column is the NOAA AR number. The second column is the largest flare-class during the AR’s disk passage (M5< denotes classes between M5–M9.9 and M1< stands for M1–M4.9). The third and fourth columns include the starting and finishing moments and the corresponding locations of the AR analysis.

1997
8088 M5< 22/09 00:00 S28E53 24/09 23:59 S28E10
8100 X 03/11 00:00 S19W12 04/11 23:59 S21W39
1998
8210 1X< 01/05 00:00 S17W03 03/05 23:00 S17W36
1999
8485 M5< 14/03 00:00 N23E00 16/03 23:59 S14W43
8647 X 01/08 17:00 S18W18 04/08 14:00 S18W63
8771 X 23/11 16:00 S15W20 27/11 13:00 S14W71
8806 M5< 20/12 00:00 N24E48 25/12 00:00 N24W18
2000
8882 X 01/03 00:00 S18W31 02/03 23:59 S16W60
8910 X 19/03 00:00 N11W10 22/06 23:59 N13W61
9026 X 04/06 00:00 N20E48 08/06 23:59 N22W17
9077 X 10/07 00:00 N18E55 14/07 23:59 N18W09
9090 M5< 20/07 00:00 N11E32 21/07 10:00 N12E05
9087 M5< 18/07 00:00 S12E28 19/07 23:59 S12E13
9097 M5< 23/07 00:00 N06E25 25/07 23:59 N08W15
9165 M5< 15/09 00:00 N13E14 19/09 10:00 N14W40
2001
9368 M5< 07/03 12:00 N25W15 08/03 23:59 N26W33
9393 X 26/03 00:00 N20E39 02/04 23:59 N16W70
9415 X 05/04 00:00 S21E60 14/04 23:59 S22W72
9433 M5< 23/04 00:00 N17E26 29/04 23:59 N17W50
9503 M5< 21/06 00:00 N16W20 22/06 23:59 N17W46
9511 X 22/06 14:00 N10E30 23/06 23:59 N10E00
9601 M5< 04/09 00:00 N14W06 05/09 23:59 N14W38
9608 M5< 14/09 00:00 S25W33 17/09 23:59 S28W75
9628 M5< 23/09 00:00 S17E25 27/09 23:59 S18W01
9632 X 22/09 00:00 S17E56 24/09 23:59 S19E06
9661 X 13/10 00:00 N14E55 19/10 23:59 N16W35
9672 X 23/10 00:00 S18E13 25/10 23:59 S18W27
9684 X 01/11 00:00 N06E29 04/11 23:59 N05W28
9704 X 17/11 00:00 S18E41 22/10 23:59 S18W38
9727 M5< 09/12 00:00 S22E03 12/12 23:59 S21W52
9733 X 10/12 00:00 N14E58 18/12 23:59 N13W65
9742 M5< 22/12 00:00 N10W03 26/12 23:59 N12W68
2002
9773 M5< 08/01 14:00 N12E17 09/01 23:59 N14W05
9866 M5< 12/03 00:00 S10E43 14/03 23:59 S10E07
10017 X 02/07 00:00 S19W37 03/07 23:59 S18W63
10044 M5< 25/07 17:00 S20E34 26/07 23:59 S21E17
10069 X 14/08 00:00 S07E50 21/08 06:00 S08W50
10226 M5< 16/12 00:00 S28E25 20/12 23:59 S28W41
2003
10314 X 15/03 11:00 S14W05 18/03 23:59 S16W52
10338 M5< 22/04 11:00 N18W10 26/04 22:00 N18W70
10365 X 25/05 00:00 S08E11 30/05 23:59 S07W59
10375 X 06/06 00:00 N12E24 11/06 23:59 N12W62
10484 X 20/10 00:00 N06E53 28/10 23:59 N03W68
10486 X 25/10 00:00 N06E53 02/11 23:59 N03W68
10488 X 28/10 00:00 N09E09 03/11 12:00 N08W74
10501 M5< 15/11 00:00 N04E61 21/11 23:59 N02W18
2004
10564 X 23/02 00:00 N13E26 26/02 23:59 N14W27
10649 X 14/07 00:00 S10E64 19/07 23:59 S10E00
10652 M5< 21/07 00:00 N10E32 22/07 23:59 N08E06
10691 X 29/10 14:00 N15W02 30/10 23:59 N14W25
10696 X 04/11 00:00 N09E32 10/11 23:59 N08W62
10715 X 30/12 00:00 N04E61 31/12 23:59 N04E34
2005
10720 X 12/01 00:00 N13E52 20/01 23:59 N14W70
10759 M5< 11/05 00:00 N12E50 13/05 23:59 N12E06
2006
10875 M5< 25/04 00:00 S10E62 27/04 23:59 S11E20
10930 X 11/12 00:00 S05E06 15/12 23:59 S06W59
2010
11045 M5< 06/02 04:00 N24E20 08/02 23:59 N23W17
11046 M5< 10/02 00:00 N24E42 12/02 23:59 N24E00
11066 B 03/05 00:00 S27E16 03/05 23:59 S27E04
11069 M1< 05/05 00:00 N40W20 07/05 23:59 N40W63
11078 B 08/06 08:00 S21W40 09/06 23:59 S21W61
11081 C 12/07 00:00 N23W45 13/07 10:00 N23W66
11092 C 31/07 18:00 N13E50 01/08 23:59 N13E20
11099 C 13/08 11:00 N19W42 14/08 23:59 N19W60
11109 C 13/08 11:00 N19W42 14/08 23:59 N19W60
11117 C 24/10 00:00 S22E24 11/10 12:00 S22W70
11123 C 11/10 12:00 N20E23 11/10 12:00 N20W16
11130 C 30/11 00:00 N13W54 02/12 23:59 N13W54
2011
11142 C 03/01 18:00 S14E11 03/01 23:35 S14E08
11158 X 12/02 00:00 S19E25 15/02 23:59 S21W27
11164 M1< 05/03 00:00 N2319 07/03 23:59 N23W58
11166 X 07/03 00:00 N11E27 11/03 17:00 N09W36
11169 M1< 12/03 00:00 N17W11 15/03 23:59 N17W65
11176 M1< 24/03 00:00 S15E56 25/03 23:59 S15E30
11190 M1< 14/04 08:00 N13W05 17/03 23:59 N13W55
11204 B 09/05 00:00 N17W43 11/05 03:00 N17W60
11210 C 09/05 00:00 N20E20 10/05 23:59 N20W08
11224 C 28/05 00:00 N21W15 30/05 00:00 N21W55
11226 M1< 05/06 06:00 S22W27 07/06 07:00 S22W55
11227 C 31/05 18:00 S20E66 02/06 08:00 S20E27
11236 C 20/06 18:00 N17E23 21/06 23:59 N17W60
11241 B 25/06 04:00 N20W05 27/06 12:00 N20W40
11244 C 03/07 00:00 N16W25 03/07 23:59 N16W40
11249 C 09/07 19:00 S19E01 11/07 12:00 S19W22
11260 M1< 26/07 16:00 N19E50 28/07 19:00 N19E20
11261 M5< 29/07 00:00 N16E48 05/08 23:59 N16W64
11281 C 31/08 19:00 S20E30 04/09 23:59 S20W12
11283 X 04/09 00:00 N13E22 10/09 22:00 N13W70
11363 C 02/12 17:00 S21E35 06/12 20:00 S21W20
11387 M1< 25/12 04:00 S21E36 27/12 23:59 S21W57
2012
11402 M5< 20/01 00:00 N24E16 23/01 23:59 N30W24
11429 X 04/03 00:00 N17E67 11/03 12:00 N17W31
11430 X 05/03 00:00 N20E38 07/03 23:59 N17E12
11455 B 13/04 00:00 N06E06 14/04 08:00 N14W24
11465 C 21/04 00:00 S18E40 27/04 23:59 S18W55
11476 M5< 07/05 00:00 N10E60 13/05 23:59 N10W37
11490 B 28/05 00:00 S12E17 28/05 15:00 S12E08
11494 M1< 05/06 18:00 S17E20 08/06 23:59 S17W32
11504 M1< 12/06 00:00 S17E40 14/06 19:00 S17E03
11512 C 26/06 00:00 S16E40 29/06 18:00 S16W14
11515 X 01/07 00:00 S17E30 07/07 23:59 S17W65
11520 X 09/07 00:00 S16E46 13/07 00:00 S17W60
11542 C 08/08 09:00 S14E63 12/08 08:00 S14W05
11553 C 30/08 09:00 S20W16 02/09 23:59 S20W68
11613 M5< 12/11 00:00 S22E57 13/11 23:59 S22E31
11618 M1< 19/11 00:00 S12E40 26/11 23:59 N06W66
2013
11719 M5< 08/04 17:00 N10E53 11/04 23:59 N11W14
11776 C 18/06 08:00 N11E11 19/06 18:00 N11W07
11818 M1< 16/08 04:00 S07W04 17/08 23:59 S07W35
11865 M1< 09/10 16:00 S22E60 15/10 15:00 S22W22
11875 X 19/10 00:00 N06E16 28/10 03:00 N06W68
11877 M5< 23/10 00:00 S12W08 24/10 10:00 S12W15
11884 M5< 29/10 04:00 S12E52 03/11 17:00 S12W21
11890 X 04/11 00:00 S11E63 12/11 23:59 S11W58
11936 M5< 30/12 00:00 S16W09 02/01 23:59 S16W67
2014
11944 X 05/01 00:00 S09E40 10/01 09:00 S09W33
11966 M5< 10/03 10:00 N14W41 12/03 22:00 N14W72
11967 M5< 31/01 00:00 S12E44 08/02 23:59 S12W63
12017 X 28/03 00:00 N10W08 30/03 23:59 N10W50
12036 M5< 15/04 00:00 S17E13 18/04 23:59 S17W40
12146 M1< 22/08 19:00 N09W01 25/08 23:59 N09W43
12158 X 07/09 15:00 N15E54 11/09 23:59 N15W12
12192 X 18/10 09:00 S13E70 27/10 15:00 S13W52
12205 X 05/11 12:00 N15E66 12 /11 23:59 N15W35
12241 M5< 18/12 00:00 S09E20 21/12 23:59 S09W34
12246 M5< 18/12 00:00 S09E20 21/12 23:59 S09W34
12242 X 15/12 15:00 S17W33 20/12 23:59 S17W33

References

Cite this article as: Korsós M.B, Yang S & Erdélyi R 2019. Investigation of pre-flare dynamics using the weighted horizontal magnetic gradient method: From small to major flare classes. J. Space Weather Space Clim. 9, A6.

All Figures

thumbnail Fig. 1

(a) Example for applying the WGM method to two smaller (M1.2 and M1.9) GOES M-class flares in AR 11504. The top panel shows the WGM, the middle panel plots the distance between the barycentres, and the bottom panel is a plot of the associated unsigned magnetic flux as a function of time. The M1.2 and M1.9 flares are indicated by (blue) vertical lines where the value of the is taken. Note the U-shapes (red parabolae) in the middle panel that are key flare precursors of the WGM method. The error is marked with shaded grey. (b) Top/middle and bottom panels are the related intensity/magnetogram maps and the associated Debrecen data catalogue representation of synthetic polarity drawing of AR at 01:59 on 13 June 2012. The red circle shows which umbral area and mean field strength are taken to calculate WGM.

In the text
thumbnail Fig. 2

(a) Representative example for applying the WGM method to GOES C-class flares in AR 11281. (b) Top/middle and bottom panels are the associated intensity/magnetogram maps and the Debrecen catalogue representation of the associated synthetic polarity drawing at 00:59 on 03 September 2011.

In the text
thumbnail Fig. 3

Evolution of the pre-flare indicators of the WGM method, similar to those of Figure 2 but for a B-class flaring event in AR 11967. The estimated error is marked by the shaded grey envelope.

In the text
thumbnail Fig. 4

The log value of GOES flare intensity (log(I)) as function of the maximum WGM (). The estimated errors are also given in the lower right corner.

In the text
thumbnail Fig. 5

Left: Relationship between the durations of converging motion and the duration from the moment of time of closest position up to the first flare occurrences. Right: Relationship between difference of the distances between the barycenters at the start of the convergence phases and at the closest approach (D C) and the distance between the point of closest approach to the position of first flare occurrence (D FM) at photospheric level. The estimated errors are given in the lower right corner.

In the text
thumbnail Fig. 6

Figure demonstrating the process (1) when two opposite polarities of initial barycenter separation distance D 0 are convergence; (2) the two opposite polarities are at their closest and a current sheet starts forming, where D min is the minimum distance, with D 0 > D min; (3) the two opposite polarities are divergence from their closest distance, D min, back to D 0, and the associated current sheet is still developing above the photosphere; (4) reconnection takes place and a flare occurs above the polarity inversion line (PIL). After the distance between the polarity barycentres returns to the initial separation, D 0, during a further evolution, this distance can now either decrease or increase (i.e., D 1 < D 0 or D 1 > D 0). D C = D 0D min in Figure 5 (right panel).

In the text

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