Unsupervised Machine Learning for the Identification of Preflare Spectroscopic Signatures

This work primarily utilizes spectroscopic observations made by IRIS, a NASA Small Explorer Mission that was launched in 2013 June as a single instrument mission designed to investigate the dynamics of the chromosphere and transition region with high spatial, temporal, and spectral resolution.

The IRIS spectrograph observes two wavelength windows, one in the far-ultraviolet (split into FUV 1; 1332–1358 Å and FUV 2; 1389–1407 Å) and one in the near-ultraviolet (NUV; 2783–2835 Å). In the FUV, the IRIS spectrograph can achieve a spectral resolution of 26 mÅ, along with a spatial sampling of 033, while the NUV window spectral sampling is 53 mÅ with a spatial sampling of 04. To achieve larger fields of view, IRIS, like many solar spectrographs, makes use of a technique called rastering, i.e., an image having spectral information in one direction and spatial information along the slit (I_λ , Y) in the orthogonal direction on the detector. These individual observations are then combined to make a 3D data cube (Y(t), X(t), I_λ (t)), with t indicating the frame taken at time t. A raster is, therefore, a set of spectral images taken at any step the slit moves in the direction perpendicular to its largest axis (X(t)), scanning the Sun with the slit (Y) in the X direction. If the slit remains in the same position in the X direction at all times during the acquisition, the set of spectral images is referred to as a sit-and-stare data set. The downside of raster imaging is that by increasing the field of view in the x direction, the temporal coherence of the image is reduced. Utilizing rastering, the spectrograph can cover a maximum field of view of 130'' × 175''. IRIS also obtains slit-jaw images (SJIs) to provide contextual information in a 175'' × 175'' field of view around the slit in four passbands (C ii doublet centered at 1335 Å, Si iv 1394/1403 Å, Mg ii k 2796 Å, and Mg ii wing emission around 2830 Å, respectively).

In this work we also make use of the photospheric line-of-sight magnetograms created by the Helioseismic and Magnetic Imager (HMI; Scherrer et al. 2012), an instrument on board NASA's Solar Dynamics Observatory (SDO; Pesnell et al.2012).

2.1.1. Data Selection

Machine learning can be broadly divided into two disciplines: supervised and unsupervised. In terms of categorization problems, of which our study is one, supervised machine-learning techniques make use of data in which the outcome is known as a ground truth to train an algorithm to categorize unseen data. For data where there is no known categorization, and hence no ability to produce a training data set, unsupervised machine-learning techniques can be used. One such technique, which we make use of in this paper, is called k-means clustering (MacQueen 1967). k-means clustering is a technique that is used to take a data set of N observations and split the data into K discrete clusters. Each of these K clusters has a centroid μ_j , which is defined by the mean Euclidean distance to the data points in the given cluster. To find the best fit of these centroids to the data, the algorithm aims to minimize a property called inertia, or within-cluster variance:

$$\begin{eqnarray}&&\sum _{j=1}^{K}\sum _{i=0}^{N}\mathop{\min }\limits_{{\mu }_{j}\in C}(| | {x}_{i}-{\mu }_{j}| {| }^{2}),\end{eqnarray} \tag{ 1 }$$

where C is a cluster and x_i is an individual data point. The first step of the algorithm is to assign the initial location of the centroids. The number of the clusters, and therefore of the resulting centroids, is defined by the user. Several initialization procedures are available to avoid the impact of randomly selecting the initial centroids (as the original k-means clustering technique was implemented). This is important as by simply randomly assigning one set of initial centroids, the algorithm may identify local, rather than global, minima of the inertia. The algorithm then proceeds to define new centroids through the mean of all the data points assigned to each of the original centroids. This process is then repeated until the difference between the old and updated centroids is deemed to be negligible. When this point is reached, the k-means process is finished and the data have been clustered according to the final centroids.

The aim of this work is to apply k-means clustering to the problem of identifying spectral profiles that occur prior to flaring. In the previous section we have described how the basic k-means algorithm works, and we shall now outline how we apply k-means in this work for our purposes.

the A multistage approach to identifying possible unique preflare spectra is employed. We wish to identify not only whether unique clusters of preflare spectra exist within the chosen data sets, but investigate how these evolve in time if they are present. To be able to determine whether spectra are seen only during the preflare period, we need to also include data from AR and quiet Sun QS observations. For each flare data set, the start time of the flare was identified from the GOES flare catalog. The data were then gathered and preprocessed between the flare start time and a given preflare time period. Preprocessing is an important step in all machine-learning techniques. This can be done for numerous reasons, but chief among them is to standardize the data sets used. The preprocessing carried out is as follows:

• 1.  
  each data set used was normalized by exposure time to correct for the difference in the observing program used.
• 2.  
  the wavelength range of each spectral line was truncated to be the same for each data set. For the spectral range including the Mg ii lines, the initial and final considered wavelengths are 2794.5–2805 Å.
• 3.  
  All spectra had their wavelength dimension interpolated to have 200 data points.

The cumulative effect of this preprocessing is that it allows the direct comparison of all of the spectra, no matter their original data set.

Principal component analysis (PCA; Hotelling 1933) was then run on the preprocessed data set. PCA is a common technique used in many machine-learning settings, which allows the reduction of the dimensionality of data in a data set while still maintaining the key information of each individual data point. The dimensionality of the data set is the number of features or variables that it has. PCA therefore is essentially projecting a data set with n features into one that has a number of features < n. This reduction in dimensionality has two important effects: to mitigate the effect of high-dimensional data during the computation of the Euclidean distance and to reduce the computational requirements required when running the k-means clustering.

After several tests, we also decided to utilize a feature scaler, in this case, the MinMaxScaler included in the Python package scikit-learn (Pedregosa et al. 2011). This scaler sets the data in each feature to be between a set maximum and minimum value. In the case of our data, a feature is the intensity at each wavelength point in the spectra. The use of this MinMaxScaler is advantageous as without it variations in small-scale features, e.g., the Mg ii UV triplet line and nearby wavelength region, can be swamped by variations in the larger-scale Mg ii k & h lines. This therefore improves the accuracy of the clusters, as a more equal weighting between the features is achieved.

The next step in the analysis process is to determine the number of clusters that will be used. For this we used the elbow method to determine the minimum number of clusters that is appropriate for the data. This involves testing numerous numbers of clusters and plotting the numerical value of the inertia for the tested cluster number. The resultant plot should ideally show a steep decrease and a break, or elbow, before reaching a plateau. The point at which this break occurs, and therefore the number of clusters it pertains to, is generally agreed to be the minimum number of clusters that could describe the data.

We then move onto clustering for each time step under consideration. For every given flare data set, the first time step was chosen to be 40 minutes prior to the flare start time. This value was chosen due to previous work (Woods et al. 2017; Panos & Kleint 2020), which has identified preflare spectral signatures up to 40 minutes prior to flare onset. For each time step, the closest raster to that time is selected for clustering. In the case of the nonflaring and quiet Sun data sets, all available data are clustered, rather than the single rasters of the preflare case. This is to maximize the number of spectra to compare to the preflare spectra. The spectra in each data set are then clustered into the desired number of clusters. As a result, we obtain a representative profile (RP), i.e., the centroid, for each cluster found by the k-means algorithm. This is done for every cluster, resulting in the total number of RPs being n_rp = n_clusters × n_{data sets}. We then group these RPs and run k-means clustering on them all together. This second round of clustering allows us to identify groups of RPs with similar shape across all data sets. As with the results of the first round of clustering, we then determine the second-round representative profiles. A cartoon of this process is shown in Figure 1 to help with visualization. This same two-step process is carried out for each time step up to the flare start time.

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The results of our Mg ii clustering, as discussed in the preceding section, revealed the presence of preflare clusters. We find that in the nine time steps that are studied in this work, preflare clusters are identified in all of them. In Figure 3 we show examples of the eight broad categories of preflare clusters identified. We can see that these eight broad categories are profiles that exhibit single-peaked Mg ii k and h lines, with single-peaked emission in the Mg ii UV triplet lines; double-peaked k and h lines, with emission in the Mg ii triplet line; single-peaked Mg ii k and h lines; double-peaked Mg ii k and h lines; broad-shouldered Mg ii k and h; broad Mg ii k and h; cosmic-ray hits; and the final group is of clusters that are irregular profiles with broad wings. From Table 5 we see that the majority of these spectral exhibit single-peaked Mg ii k and h lines, with single-peaked emission in the Mg ii triplet line. Representative profiles of this type make up a median of 66% of the preflare clusters at each time step. When we consider the number of individual spectra that compose each of these representative profiles, the median percentage occurrence rises to 76%. These profiles that show single-peaked Mg ii k I and h lines, with single-peaked emission in the Mg ii triplet line, are the most abundant and consistent of the preflare clusters that we have identified. It is important therefore to understand how these profiles are distributed among the preflare data sets. To this end, Table 6 shows the number of this type of spectrum in each preflare data set at each time step. The distribution of all the types of preflare clusters across the data sets can be found in the additional tables in Appendix A. These are provided both in terms of the number of spectra and the proportion of the raster field of view. What we can see from Table 6 is that the spread of these spectra across the flares studied is not even. We find that these spectra are less likely to be found in X-class flare data sets (data sets 0–3), with only one X-class flare (data set 3) and all the M-class flares (data set 4–7) consistently showing these spectra to occur.

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Figure 4 shows the locations of preflare clusters for data set 3, which is the X2.1 flare that occurred on 2015 March 11. This event is chosen as a representative example of the preflare cluster locations seen across the other flare data sets used. Preflare cluster locations are shown overlaid on the SJI images taken during the raster. Also overlaid (as black contours) are the locations of the flare ribbons as measured at the flare peak time. We can clearly see that the majority of the preflare clusters are located in regions in which the flare ribbons are later seen during the course of the flare event or are related to transient bright points within the center of the ARs under study. Figure 5 shows the location of the preflare clusters overlaid on the corresponding SDO HMI line-of-sight magnetogram images. From these we can see that the location for most of the preflare clusters broadly aligns with regions of intersection between the positive and negative magnetic fields (the white and black areas in the images, respectively). This behavior is seen in all of the flare events studied.

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While the observational evidence suggests that these profiles could result from heating, we perform further investigation to better determine the thermodynamic conditions that give rise to the spectra observed in these locations. This would allow us to infer the conditions that give rise to these particular spectra.

As a first effort to investigate the atmosphere that produced these spectra, we turned to IRIS² (Sainz Dalda et al. 2019). IRIS² (Inversion based on Representative profiles Inverted by STiC) is a code that aims to provide fast recovery of model atmospheres for input spectra. The returned thermodynamic parameters of the model atmosphere are temperature, the logarithm of electron density, line-of-sight velocity, and microturbulence—all as a function of optical depth. It does this by utilizing a database of synthetic RPs and their associated representative model atmospheres, resulting from the inversion of observed IRIS Mg ii h and k RPs using the STiC inversion code (de la Cruz Rodríguez et al. 2019). We used IRIS² to investigate whether we can recover the model atmosphere for the spectra that exhibit single-peaked Mg ii k and h lines along with single-peaked emission in the Mg ii triplet. It was found that while IRIS² is able to identify some of these profiles, the error bars on the returned thermodynamic parameters of the model atmosphere were large. We therefore decided to produce a dedicated inversion of this type of spectra in order to discern the atmospheric properties with better accuracy.

We produced new inversions for the 2015 March 11 data set, from the time step 2400 s prior to flare occurrence. From Table 5 we see that at this time step there are five clusters identified that show the single-peaked form we are interested in investigating. From Table 6 we can see that four are present in the 2015 March 11 data set, with a total of 93 individual spectra. In addition to these spectra, a selection of non-preflare spectra was chosen to be inverted. These spectra were of the following types: far from the flare site in the quietest region of the raster; the penumbra of the active region's sunspot; the umbra of the sunspot (both single- and double-peaked profiles); and finally, nonflaring spectra close to the flare site. These spectra were then inverted considering both the Mg ii h and k lines—including two of the lines belonging to the Mg ii UV triplet located at wavelengths of 2797.9 and 2798.0 Å—and the C ii 1334 and 1335 lines. We have performed simultaneous inversions of the Mg ii h and k lines because the Mg ii h and k lines and the C ii 1334 and 1335 lines are sensitive to variations in the thermodynamics in roughly the same region of the solar atmosphere (see Figure 17 of Rathore et al. 2015). By inverting all of these lines simultaneously, we aim to untangle the contributions of the temperature and microturbulent motions to the width of the observed lines (da Silva Santos et al. 2018, 2020). Therefore, the values of T and v_turb corresponding to the mid-chromosphere obtained in this paper are likely more realistic than in previous works that consider only one line to derive these quantities. We have inverted these profiles with the STiC code. We used the FALC model (Fontenla et al. 1993) as the initial model guess for the first cycle of the inversions, while v_los and v_turb are introduced ad hoc as these variables were not included in the available FALC model. For more technical details about the inversions, see A. Sainz Dalda (2021, in preparation).

Figures 7 and 8 show a selection of results from the inversions. For each of the panels in these figures, the upper panel shows the observed C ii 1334 and 1335 Å line spectra (purple) with the best-fitted inverted synthetic profile (black). The middle panel shows the observed Mg ii spectra (purple), the model fit (black), and those corresponding to the FALC (dashed line). The two panels below this show the parameters of the inverted model atmospheres from the observed profiles (solid lines) and those corresponding to the FALC (dashed line). The temperature (T, orange) and electron density ($\mathrm{log}({n}_{e})$, blue) are shown on the left, while microturbulence (v_turb, purple) and line-of-sight velocity (v_LOS, green) are shown on the right. This adapted FALC model was used as the initial model guess during the first cycle of the inversion. We find that the lines are well fit. Figure 7, panel (a), shows an example inversion of one of the preflare spectrum, and panel (b) shows a single-peaked umbral spectrum. Figure 8 panel (a) shows a non-preflare spectrum, and panel (b) shows a penumbral spectrum. From comparing the preflare spectra to the other model atmospheres we can see clear differences. In the preflare model atmospheres, when considering the electron density, we see a single rise moving from larger to smaller $\mathrm{log}(\tau )$, e.g., moving higher in the atmosphere. We then see a plateau that is increased compared to the FALC model between $-5\leqslant \mathrm{log}(\tau )\leqslant -4$, followed by a dropoff in value. Within this same region, for the double-peaked profiles (Figure 8, panels (a) and (b)) the electron density shows a propensity to drop in value at $\mathrm{log}(\tau )\approx -5$.

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Figure 9 a shows the observed spectra and associated model atmospheres for all 93 preflare spectra that were inverted. We can see that there is a broad similarity in distributions. This is particularly true in terms of temperature, where the temperature minimum is observed at $\mathrm{log}(\tau )\approx -3$ and then rises to a plateau (above the FALC atmosphere, dashed line) between $-5\leqslant \mathrm{log}(\tau )\leqslant -4$, followed by a continued rise in temperature at greater heights in the atmosphere. However, from the Mg ii spectra, it is clear that there are in fact three distributions present among these spectra. Panel (b) in Figure 9 and panels (a) and (b) in Figure 10 show these three populations separately. These three distributions, while all exhibiting single peaks in the Mg ii h, k, and triplet lines, differ in the width of the h and k lines and in the intensity of the triplet line. The widest population is shown in panel (b) of Figure 9. We see that the associated model atmospheres show a temperature minimum at $\mathrm{log}(\tau )\approx -2.75$, followed by a temperature increase with height. Temperatures are enhanced above the values of the FALC atmosphere and continue to rise with height until they reach a stable value of approximately 8 kK between $-5\leqslant \mathrm{log}(\tau )\leqslant -4$. The electron density also has its minimum at around a height of $\mathrm{log}(\tau )\approx -2.75$, after which it rises to values above those of the FALC. For the population in panel (a) of Figure 10, we see that the minima of temperature and electron density are closer to $\mathrm{log}(\tau )\approx -3$. For this population the temperature increases with height from its minimum, again achieving values higher than the FALC. Unlike the population in Figure 9 panel (b), in the region $-5\leqslant \mathrm{log}(\tau )\leqslant -4$ the temperatures do not reach a stable plateau; instead, they show a gradual increase with height. The electron density increases above the values of the FALC and stays enhanced with respect to the FALC as height in the atmosphere increases. The population in Figure 10, panel (b), shows the narrowest line widths, as well as the least intense triplet emission. We can see that the temperature increase starts from just above $\mathrm{log}(\tau )\approx -3$. The temperatures in this population increase with height from the minimum, but unlike the previous two populations, the temperature profile is very similar to that of the FALC atmosphere, i.e., rising gradually. This continues until $\mathrm{log}(\tau )\approx -5$ when there is a large increase in temperature above that of the FALC. Electron density is also seen to have its minimum just above $\mathrm{log}(\tau )\approx -3$. At higher heights, the electron density is somewhat increased with respect to the FALC in this population, but when compared to the populations in Figure 9, panel (b), and Figure 10, panel (a), it is the most similar to the FALC. In all three of the populations, there are clearly discernible patterns in the temperature and electron density; the distributions of microturbulence and line-of-sight velocity are less clear. In the line-of-sight velocity, there seems to be a partition of velocity that occurs around the temperature minimum with larger downward velocities seen in the lower atmosphere. Looking at the distributions of microturbulence, there is a large variance, both within and across the three populations. Despite these differences in the populations, the overall trend for the model atmospheres derived from our inversion of the preflare profiles is that above $\mathrm{log}(\tau )\approx -3$ we see increased temperatures and increased electron densities. This result is derived directly from inversions. It is compatible with forward modeling (e.g., Carlsson et al. 2015; Rubio da Costa & Kleint 2017; Zhu et al. 2019 and Pereira et al. 2015), which suggests that single-peaked Mg ii h and k profiles and single-peaked Mg ii triplet emission can be caused by heating (and resulting temperature and density increase) in the chromosphere.

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We have established that our observations and retrieved models are consistent with a scenario in which preflare signals seem to be associated with heating events in the chromosphere. Our results suggest that such heating may be occurring across a wide range of heights, from the low to upper chromosphere. The locations of these events have a clear association with sites of the ribbons. We also find a somewhat weaker association with neutral lines in active regions, i.e., locations where the magnetic flux of opposite polarities is in close proximity to one another. These results suggest the possibility that these heating events could be driven by magnetic reconnection. These reconnection events could be linked to preflare phenomena such as tether-cutting reconnection building up a magnetic flux rope, or possibly could be related to flare trigger scenarios such as outlined in Bamba et al. (2017), where small-scale flux emergence at polarity inversion lines leads to reconnection, which could trigger the onset of flaring. Our results suggest that more detailed follow-up studies of the complex preflare atmosphere, including the magnetic field evolution and distribution, are needed to shed further light on the exact nature of these preflare signals.