Identifying, from IRIS observations, the “typical” response to flare

heating of the upper chromosphere and lower transition region

Description of data processing and clustering algorithms

• Statistical moments of line profiles. The zeroth moment will represent the maximumor the integrated line intensity. The first (Doppler shift), second (line width), third (lineasymmetry), and higher statistical moments can be computed as:

𝑆𝑘 =𝑘න 𝜆 − 𝜆 𝑘𝐼 𝜆 𝑑𝜆 /න 𝐼 𝜆 𝑑𝜆 , 𝜆 = නλ𝐼 𝜆 𝑑𝜆 /න 𝐼 𝜆 𝑑𝜆

• K-Means clustering. The K-Means method takes the number of clusters as an inputparameter and initially seeds the cluster centers randomly among the data points. Theneach point is labeled with its nearest cluster center, the cluster centers are recomputedas the means among points of the same label, and the procedure is repeated until thereare no changes in labeling.

• Average silhouette width. The silhouette is defined for data i point as 𝑠 𝑖 =𝑏 𝑖 −𝑎(𝑖)

max{𝑎 𝑖 ,𝑏(𝑖)}, where a(i) is the average distance from point i to points of the same

cluster, and b(i) is the average distance from point i to points of the closest neighboringcluster. The average s(i) across all points indicates how well the points lie within theirclusters.

• The optimal number of clusters can be estimated by maximizing s(i).

• When s(i) < 0, point i no longer “belongs” to its current cluster.

• The Interface Region Imaging Spectrograph (IRIS, De Pontieu et al. 2014) hasobserved hundreds of flares of ≥ C1.0, but statistical studies are hard to performbecause of the complexity of imaging spectroscopy data.

• Finding “typical” responses to flare heating using unsupervised machine learning(clustering) techniques can simplify the analysis of spectroscopic data.

Plans and ideas for the future

• Recognition of typical line profiles and dynamical responses of the atmosphereto flare heating from IRIS data based on large statistics of flare events.

• Correlation of the appearance of certain line profile shapes and dynamicalbehavior with properties of hard X-rays (from RHESSI, Fermi GBM, andKonus-WIND) and soft X-rays (from GOES/XRS).

• Understanding the evolution of the quiet Sun EUV emission observed bySDO/AIA and spectral lines observed by IRIS based on clusterization(quantization) of the data. Analysis of the timescales of underlying processes.

• More detailed analysis of IRIS line profiles (Mg II, C II) for the consideredStellarBox run and development of automatic recognition of shocks fromsynthesized spectra.

• Connection between simulations and observations via comparison of thestatistical properties (timescales and patterns) of emission.

References.

1. De Pontieu, B., Title, A.M., Lemen, J.R. et al. 2014, Solar Physics, 289, 2733

2. Panos, B., Kleint, L., Huwyler, C. et al. 2018, ApJ, 861, 62.

3. Pereira, T.M.D., and Uitenbroek, H. 2015, A&A, 574, A3

4. Sainz Dalda, A., de la Cruz Rodríguez, J., De Pontieu, B., and Gošić, M. 2019, ApJL,875 L18.

5. Vernazza, J.E., Avrett, E.H., Loeser, R. 1981, ApJSS, 45, 635

6. Wray A.A., Bensassi K., Kitiashvili I.N. et al. 2018a, In Book: "Variability of the Sunand Sun-like Stars: from Asteroseismology to Space Weather". Eds: J.-P. Rozelot, E.S.Babaev, EDP Sciences, p.39-62.

7. Wray, A.A., Bensassi K., Kitiashvili I.N. et al. 2015, eprint arXiv:1507.07999

This research is funded by the NASA Heliophysics Supporting Research Program

Cluster Analysis of IRIS Spectroscopic Line Profiles and SDO/AIA EUV Emission in

Observations and RMHD Simulations of the Solar AtmosphereViacheslav Sadykov1,2, Irina Kitiashvili1,2, Alexander Kosovichev1,3

Spatially-resolved observations from the IRIS and SDO/AIA satellites, especially when coupled with realistic 3D RMHD simulations, are a powerful tool for analysis of processes in the solar chromosphere, transition region, and corona. However, the complexity

of the data makes understanding the observations and modeling results difficult. In this work, we apply unsupervised clustering algorithms for analysis of observational and synthetic chromospheric Mg II h&k 2796Å&2803Å and transition region C II

1334Å&1335Å line profiles observed by IRIS, and extreme ultraviolet (EUV) emission observed by SDO/AIA, for various types of problems. The synthetic line profiles are computed for simulations of the quiescent solar atmosphere (using the StellarBox and

RH1.5 codes). The K-Means clustering algorithm is applied, and the selection of an optimal number of clusters is supported by the average silhouette width technique. We discuss applications of the line profile clustering method to 1) visualization of

computational and observational spectroscopic imaging data; 2) understanding of evolutionary trends and behavior patterns of quiet Sun emission and during solar flares; and 3) recognition of heating events and shock waves.

1NASA ARC, 2BAERI, 3NJIT

Clustering of synthetic Mg II spectraRecognition of shocks and heating events from synthetic AIA emissionsQuantizing SDO/AIA EUV emission of the quiet Sun

▲ An example of clustering of C II 1334.5 Å line profiles for the M1.0 flare of June 12,2014. The clustering is done in I(λ) space. The maps of line profile representatives(panels d-g) inform by encoding the evolution of the line in time. Such clustering waspreviously used by Panos et al. (2018) and Sainz Dalda et al. (2019).

▲ Typical evolution of statistical moments of Mg II k 2796 Å during the M1.8 classsolar flare of February 13, 2014. K-Means clustering was performed simultaneously forthe evolutions of line intensity, Doppler shift, and line width, with equal contributionfrom each considered statistical moment. The color map in panel (d), supported bypanels (a-c), illustrates the Mg II k line evolution during the entire flare. The red, blue,and black clusters are of special interest: the red cluster behaves as expected during“explosive” chromospheric evaporation, while the blue and black clusters reveal slightredshifts followed by strong blueshifts of the spectral lines.

Color = Cluster

• The “StellarBox” code solves the fully compressible MHD equations with radiativetransfer solved by ray-tracing and opacity binning techniques and uses a large-eddysimulation (LES) treatment of subgrid turbulent transport (Wray et al. 2015, 2018). Formore details see poster SH31E-3350.

• The computational domain of 12.8 x 12.8 x 15.2 Mm includes a 10-Mm layer from thephotosphere to the low corona. The horizontal resolution is 25km, and the lateralboundary conditions are periodic. 176 simulation time moments with 2s temporalcadence are analyzed.

• A Synthetic top-view AIA emission is computed for each time moment for eachcolumn separately, using SDO/AIA temperature response functions from SSW IDL.Strong impacts (“shocks” hereafter) are observed in AIA running difference images.

• K-Means clustering is performed for sparse selection of columns and snapshots for allAIA channels together. The contribution of each channel is normalized. Seven clustersare used.

Shock signature Shock signature Shock signature

Shock signature Shock signature Shock signature

Shock signatures Shock signaturesShock signatures

▲ Illustration of the distribution of physical parameters (temperature, vertical velocity,magnetic field) at 4 Mm above the photosphere for the StellarBox setup, and thesynthesized 171 Å emission, running differences, and label maps for times t=62s, t=188s,and t=226s. The cyan cluster correlates well with the shock signatures, demonstrating thatshocks have distinguishable fingerprints in SDO/AIA emission.

Why is it important to identify shockwaves?

Shocks are among the possible mechanisms contributing to coronal heating. Ourpreliminary study indicates that the properties of synthesized emission are wellcorrelated with the energy transported by the shock to the corona. Examples ofthese correlations are shown below.

• Synthetic Mg II spectra are computed for the previously-described StellarBoxsimulation, with 2s temporal cadence, for the last 176 simulation time moments. Non-LTE calculations are done with the RH1.5 radiative transfer code (Pereira andUitenbroek 2015)

• We reduced the original spectral resolution to match the IRIS resolution.

• The clustering of Mg II k line profiles is done in I(λ) space. Results for the originalresolution and for the IRIS-compatible spectral resolution are demonstrated below forthe last time moment of the analyzed time sequence.

Original

spectral

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IRIS

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One can see that the reduction of spectral resolution to the IRIS-compatible onesignificantly smooths the lines. Asymmetry of the line peaks, as well as the line dip(central reversal), almost vanish across the domain. Clustering helps us tounderstand how resolution reduction affects the line profiles not simply at a singlepoint but across the entire domain.

Color

=

Cluster

We selected the 10-minute series of SDO/AIA quiet Sun observations restricted to 200arcseconds from the disc center on July 12, 2019, 18:00 pm. Examples of the default non-aligned maps are illustrated below. Notice the offset between the images.

P(m|k) State 1(193A, 1.2MK)

State 2 (94A, 6.3MK)

State 3(335A, 2.5MK)

State 4(211A, 2.0MK)

State 5(131A, 0.4MK)

State 6(171A, 0.63MK)

State 7(background)

State 1 0.034 0.130 0.133 0.151 0.134 0.141 0.146

State 2 0.149 0.038 0.175 0.158 0.171 0.158 0.166

State 3 0.152 0.174 0.037 0.159 0.169 0.156 0.165

State 4 0.163 0.144 0.147 0.031 0.149 0.150 0.146

State 5 0.144 0.159 0.158 0.150 0.029 0.149 0.153

State 6 0.149 0.149 0.148 0.152 0.150 0.042 0.154

State 7 0.208 0.206 0.203 0.198 0.198 0.204 0.070

As one can see, the temporal behavior of RRD clusters is stochastic, and the system “doesnot like” to be in one state for a long time (the diagonal elements of the matrix aresignificantly lower than the off-diagonal).

• Six EUV channels (all except the 304 Å channel) were aligned using the cross-correlation technique and averaged over 3x3 pixel areas, then Relative RunningDifferences were computed for the series: RRD(t) = I(t)/I(t-1) - 1

• The RRDs were clustered at each 12 s time moment at each pixel, and the contributionsfrom RRDs of different channels were normalized. 7 clusters were selected for the k-Means algorithm. The distribution of clusters at the initial time is shown below.

Important: we now consider evolution of the EUV emission “quantum state” (a numberranging from 1 to 7 to indicate the cluster the point belongs to), which significantlysimplifies the analysis and enhances understanding. Hereafter we will say that the RRD“is in state k” instead of “belongs to cluster k”.

Let P(nt+1=m|nt=k) = P(m|k) be the conditional probability of a point now in state k tojump to state m after 12 s. For our system, we have the very important property thatP(nt+1=m|nt=k, nt-1=l) ≈ P(nt+1=m|nt=k) for any m, k, l.

This tells us that the evolution of RRD states behaves as a Markov chain: the propagationto the next time step depends only on the current state. Markov chain dynamics is fullydescribed by its transition matrix Tmk = P(nt+1=m|nt=k) = P(m|k):

This plot shows the Frobenius norm ofthe matrix (T)nt-(T)∞. The matricesbecome identical after 2-3 transitions(36-48 s), i.e., the system quickly“forgets” its initial state.

So one can write:

P(nt > t0+3=m|nt0=k) = P(nt0=k),

where P(nt0=k) is simply theprobability to find the state k across thedomain.

Timescales of processes. For a Markov process, the transition matrix for nt time steps isthe nt-th power of the single-step transition matrix. The difference between (T)nt and (T)∞

illustrates how strongly the system “remembers” its initial state after nt transitions.

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