Non-flaring Active Region Research Articles

Three Types of Solar Coronal Rain during Magnetic Reconnection between Open and Closed Magnetic Structures

Coronal rain (CR) is a crucial part of the mass cycle between the corona and chromosphere. It includes flare-driven CR and two types of quiescent CR, along nonflaring active region closed loops and along open structures, separately, labeled as type I, type II, and type III CR, respectively. Among them, type I and type III CR are generally associated with magnetic reconnection. In this study, employing data taken by the Solar Dynamics Observatory and the Solar Upper Transition Region Imager on 2022 October 11, we report three types of CR during an interchange reconnection between open and closed magnetic field structures above the southeastern solar limb. The open and closed structures converge, with the formation of the current sheet at the interface, and reconnect. The newly formed closed and open structures then recede from the reconnection region. During the reconnection, coronal condensation occurs along the reconnecting closed loops and falls toward the solar surface along both loop legs, as type II CR. Subsequently, condensation happens in the newly formed closed loops and moves down toward the solar surface along both loop legs, as type I CR. Magnetic dips of the reconnecting open structures form during the reconnection. In the dips, condensation occurs and propagates along the open structures toward the solar surface as type III CR. Our results suggest that the reconnection rate may be crucial for the formation of type I and type III CR during reconnection.

Identifying preflare spectral features using explainable artificial intelligence

The prediction of solar flares is of practical and scientific interest; however, many machine learning methods used for this prediction task do not provide the physical explanations behind a model’s performance. We made use of two recently developed explainable artificial intelligence techniques called gradient-weighted class activation mapping (Grad-CAM) and expected gradients (EG) to reveal the decision-making process behind a high-performance neural network that has been trained to distinguish between Mg II spectra derived from flaring and nonflaring active regions, a fact that can be applied to the task of short timescale flare forecasting. The two techniques generate visual explanations (heatmaps) that can be projected back onto the spectra, allowing for the identification of features that are strongly associated with precursory flare activity. We automated the search for explainable interpretations on the level of individual wavelengths, and provide multiple examples of flare prediction using IRIS spectral data, finding that prediction scores in general increase before flare onset. Large IRIS rasters that cover a significant portion of the active region and coincide with small preflare brightenings both in IRIS and SDO/AIA images tend to lead to better forecasts. The models reveal that Mg II triplet emission, flows, as well as broad and highly asymmetric spectra are all important for the task of flare prediction. Additionally, we find that intensity is only weakly correlated to a spectrum’s prediction score, meaning that low intensity spectra can still be of great importance for the flare prediction task, and that 78% of the time, the position of the model’s maximum attention along the slit during the preflare phase is predictive of the location of the flare’s maximum UV emission.

The faintest solar coronal hard X-rays observed with FOXSI

Context. Solar nanoflares are small impulsive events releasing magnetic energy in the corona. If nanoflares follow the same physics as their larger counterparts, they should emit hard X-rays (HXRs) but with a rather faint intensity. A copious and continuous presence of nanoflares would result in a sustained HXR emission. These nanoflares could deliver enormous amounts of energy into the solar corona, possibly accounting for its high temperatures. To date, there has not been any direct observation of such persistent HXRs from the quiescent Sun. However, the quiet-Sun HXR emission was constrained in 2010 using almost 12 days of quiescent solar off-pointing observations by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). These observations set 2σ upper limits at 3.4 × 10−2 photons s−1 cm−2 keV−1 and 9.5 × 10−4 photons s−1 cm−2 keV−1 for the 3–6 keV and 6–12 keV energy ranges, respectively. Aims. Observing faint HXR emission is challenging because it demands high sensitivity and dynamic range instruments. The Focusing Optics X-ray Solar Imager (FOXSI) sounding rocket experiment excels in these two attributes when compared with RHESSI. FOXSI completed its second and third successful flights (FOXSI-2 and -3) on December 11, 2014, and September 7, 2018, respectively. This paper aims to constrain the quiet-Sun emission in the 5–10 keV energy range using FOXSI-2 and -3 observations. Methods. To fully characterize the sensitivity of FOXSI, we assessed ghost ray backgrounds generated by sources outside of the field of view via a ray-tracing algorithm. We used a Bayesian approach to provide upper thresholds of quiet-Sun HXR emission and probability distributions for the expected flux when a quiet-Sun HXR source is assumed to exist. Results. We found a FOXSI-2 upper limit of 4.5 × 10−2 photons s−1 cm−2 keV−1 with a 2σ confidence level in the 5–10 keV energy range. This limit is the first-ever quiet-Sun upper threshold in HXR reported using ∼1 min observations during a period of high solar activity. RHESSI was unable to measure the quiet-Sun emission during active times due to its limited dynamic range. During the FOXSI-3 flight, the Sun exhibited a fairly quiet configuration, displaying only one aged nonflaring active region. Using the entire ∼6.5 min of FOXSI-3 data, we report a 2σ upper limit of ∼10−4 photons s−1 cm−2 keV−1 for the 5–10 keV energy range. Conclusions. The FOXSI-3 upper limits on quiet-Sun emission are similar to that previously reported, but FOXSI-3 achieved these results with only 5 min of observations or about 1/2600 less time than RHESSI. A possible future spacecraft using hard X-ray focusing optics like those in the FOXSI concept would allow enough observation time to constrain the current HXR quiet-Sun limits further, or perhaps even make direct detections. This is the first report of quiet-Sun HXR limits from FOXSI and the first science paper using FOXSI-3 observations.

Magnetic Helicity Flux Oscillations in the Atmospheres of Flaring and Nonflaring Active Regions

Analyzing the evolution of magnetic helicity flux at different atmospheric heights is key for identifying its role in the dynamics of active regions (ARs). The three-dimensional (3D) magnetic field of both flaring and nonflaring ARs is constructed using potential field extrapolations, enabling the derivation of emergence, shearing, and total magnetic helicity components at a range of atmospheric heights. An analysis of temporal oscillations of the derived components shows that the largest significant period of the three helicity fluxes are common (within ±2 hr) from the photosphere up to at least 1 Mm for flaring ARs—being consistent with the presence of a coupled oscillatory behavior that is absent in the nonflaring ARs. We suggest that large, energetic solar eruptions may have been produced in ARs when the vertical and horizontal helicity flux components became a coupled oscillatory system in the low solar atmosphere.

Temperature Analysis of Flaring (AR 11283) and Non-flaring (AR 12194) Coronal Loops

Here, we study the temperature structure of flaring and non-flaring coronal loops, using extracted loops from images taken in six extreme ultraviolet channels recorded by Atmospheric Imaging Assembly/Solar Dynamics Observatory. We use data for loops of an X2.1-class-flaring active region (AR 11283) during 22:10 UT until 23:00 UT, on 2011 September 6; and a non-flaring active region (AR 12194) during 08:00:00 UT until 09:00:00 UT on 2014 October 26. By using the spatially synthesized Gaussian differential emission measure (DEM) forward-fitting method, we calculate the peak temperatures for each strip of the loops. We apply the Lomb–Scargle method to compute the oscillation periods for the temperature series of each strip. The periods of the temperature oscillations for the flaring loops ranged from 7 to 28.4 minutes. These temperature oscillations show very close behavior to the slow-mode oscillation. We observe that the temperature oscillations in the flaring loops started at least around 10 minutes before the transverse oscillations and continue for a long time duration even after the transverse oscillations ended. The temperature amplitudes increased during the flaring time (20 minutes) in the flaring loops. The periods of the temperatures obtained for the non-flaring loops ranged from 8.5 to 30 minutes, but their significances are less (below 0.5) in comparison with the flaring ones (near to one). Hence the detected temperature periods for the non-flaring loops’ strips are less probable in comparison with the flaring ones, and maybe they are just fluctuations. Based on our confined observations, it seems that the flaring loops’ periods show more diversity and their temperatures have wider ranges of variation than the non-flaring ones. More accurate commentary in this respect requires more extensive statistical research and broader observations.

On the Differences in the Periodic Behavior of Magnetic Helicity Flux in Flaring Active Regions with and without X-class Events

Abstract Observational precursors of large solar flares provide a basis for future operational systems for forecasting. Here, we study the evolution of the normalized emergence (EM), shearing (SH), and total (T) magnetic helicity flux components for 14 flaring (with at least one X-class flare) and 14 nonflaring (<M5-class flares) active regions (ARs) using the Space-weather Helioseismic Magnetic Imager Active Region Patches vector magnetic field data. Each of the selected ARs contain a δ-type spot. The three helicity components of these ARs were analyzed using wavelet analysis. Localized peaks of the wavelet power spectrum (WPS) were identified and statistically investigated. We find that (i) the probability density function of the identified WPS peaks for all the EM/SH/T profiles can be fitted with a set of Gaussian functions centered at distinct periods between ∼3 and 20 hr. (ii) There is a noticeable difference in the distribution of periods found in the EM profiles between the flaring and nonflaring ARs, while no significant difference is found in the SH and T profiles. (iii) In flaring ARs, the distributions of the shorter EM/SH/T periods (<10 hr) split up into two groups after flares, while the longer periods (>10 hr) do not change. (iv) When the EM periodicity does not contain harmonics, the ARs do not host a large energetic flare. (v) Finally, significant power at long periods (∼20 hr) in the T and EM components may serve as a precursor for large energetic flares.

Empirical Scaling Relations for the Photospheric Magnetic Elements of the Flaring and Non-Flaring Active Regions

Here, we analyzed magnetic elements of the solar active regions (ARs) observed in the line-of-sight magnetograms (the 6173 \AA~Fe \small{I} line) recorded with the Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI). The Yet Another Feature Tracking Algorithm (\textsf{YAFTA}) was employed to extract the statistical properties of these features (\textit{e.g.} filling factor, magnetic flux, and lifetime) within the areas of $180{\small^{\prime\prime}} \times 180{\small^{\prime\prime}}$ inside the flaring AR (NOAA 12443) and the non-flaring AR (NOAA 12446) for 3 to 5 November 2015 and for 4 to 6 November 2015, respectively. The mean filling factor of polarities was obtained to be about 0.49 for the flaring AR; this value was 0.08 for the non-flaring AR. Time series of the filling factors of the negative and positive polarities for the flaring AR showed anti-correlation (with the Pearson value of -0.80); while for the non-flaring AR, there was the strong positive correlation (with the Pearson value of 0.95). A power-law function was fitted to the frequency distributions of flux ($F$), size ($S$), and lifetime ($T$). Power exponents of the distributions of flux, size, and lifetime for the flaring AR were obtained to be about -2.36, -3.11, and -1.70, respectively; these values of exponents for the non-flaring AR were found to be about -2.53, -3.42, and -1.61, respectively. ...

Supervised Convolutional Neural Networks for Classification of Flaring and Nonflaring Active Regions Using Line-of-sight Magnetograms

Abstract Solar flares are explosions in the solar atmosphere that release intense bursts of short-wavelength radiation and are capable of producing severe space-weather. Flares release free energy built up in coronal fields, which are rooted in active regions (ARs) on the photosphere, via magnetic reconnection. The exact processes that lead to reconnection are not fully known and therefore reliable forecasting of flares is challenging. Recently, photospheric magnetic-field data has been extensively analyzed using machine learning (ML) and these studies suggest that flare-forecasting accuracy does not strongly depend on how long in advance flares are predicted. Here, we use ML to understand the evolution of AR magnetic fields before and after flares. We explicitly train convolutional neural networks (CNNs) to classify Solar Dynamics Observatory/Helioseismic and Magnetic Imager line-of-sight magnetograms into ARs producing at least one M- or X-class flare or as nonflaring. We find that flaring ARs remain in flare-productive states—marked by recall > 60% with a peak of ∼80%—days before and after flares. We use occlusion maps and statistical analysis to show that the CNN pays attention to regions between the opposite polarities from ARs and the CNN output is dominantly decided by the total unsigned line-of-sight flux of ARs. Using synthetic bipole magnetograms, we find spurious dependencies of the CNN output on magnetogram dimensions for a given bipole size. Our results suggest that it is important to use CNN designs that eliminate such artifacts in CNN applications for processing magnetograms and, in general, solar image data.

Differences in Periodic Magnetic Helicity Injection Behavior between Flaring and Non-flaring Active Regions: Case Study

Abstract The evolution of magnetic helicity has a close relationship with solar eruptions and is of interest as a predictive diagnostic. In this case study, we analyze the evolution of the normalized emergence, shearing, and total magnetic helicity components in the case of three flaring and three non-flaring active regions (ARs) using Spaceweather Helioseismic Magnetic Imager Active Region Patches vector magnetic field data. The evolution of the three magnetic helicity components is analyzed with wavelet transforms, revealing significant common periodicities of the normalized emergence, shearing, and total helicity fluxes before flares in the flaring ARs. The three non-flaring ARs do not show such common periodic behavior. This case study suggests that the presence of significant periodicities in the power spectrum of magnetic helicity components could serve as a valuable precursor for flares.

Distinguishing between flaring and nonflaring active regions

Context.Large-scale solar eruptions significantly affect space weather and damage space-based human infrastructures. It is necessary to predict large-scale solar eruptions; it will enable us to protect the vulnerable infrastructures of our modern society.Aims.We investigate the difference between flaring and nonflaring active regions. We also investigate whether it is possible to forecast a solar flare.Methods.We used photospheric vector magnetogram data from the Solar Dynamic Observatory’s Helioseismic Magnetic Imager to study the time evolution of photospheric magnetic parameters on the solar surface. We built a database of flaring and nonflaring active regions observed on the solar surface from 2010 to 2017. We trained a machine-learning algorithm with the time evolution of these active region parameters. Finally, we estimated the performance obtained from the machine-learning algorithm.Results.The strength of some magnetic parameters such as the total unsigned magnetic flux, the total unsigned magnetic helicity, the total unsigned vertical current, and the total photospheric magnetic energy density in flaring active regions are much higher than those of the non-flaring regions. These magnetic parameters in a flaring active region evolve fast and are complex. We are able to obtain a good forecasting capability with a relatively high value of true skill statistic. We also find that time evolution of the total unsigned magnetic helicity and the total unsigned magnetic flux provides a very high ability of distinguishing flaring and nonflaring active regions.Conclusions.We can distinguish a flaring active region from a nonflaring region with good accuracy. We confirm that there is no single common parameter that can distinguish all flaring active regions from the nonflaring regions. However, the time evolution of the top two magnetic parameters, the total unsigned magnetic flux and the total unsigned magnetic helicity, have a very high distinguishing capability.

Ultraviolet solar flare signatures in the framework of complex network.

Studying natural phenomena via the complex network approach makes it possible to quantify the time-evolving structures with too many elements and achieve a deeper understanding of interactions among the components of a system. In this sense, solar flare as a complex system with the chaotic behavior could be better characterized by the network parameters. Here, we employed an unsupervised network-based method to recognize the position and occurrence time of the solar flares by using the ultraviolet emission (1600 Å) recorded by the Atmospheric Imaging Assembly on board Solar Dynamics Observatory. Three different regions, the flaring active regions, the non-flaring active regions, and the quiet-Sun regions, were considered to study the variations of the network parameters in the presence and absence of flaring phases in various datasets over time intervals of several hours. The whole parts of the selected datasets were partitioned into sub-windows to construct networks based on computing the Pearson correlation between time series of the region of interest and intensities. Analyzing the network parameters such as the clustering coefficient, degree centrality, characteristic length, and PageRank verified that flare triggering has an influence on the network parameters around the flare occurrence time and close to the location of flaring. It was found that the values of the clustering coefficient and characteristic length approach those obtained for the corresponding random network in the flaring phase. These findings could be used for detecting the occurrence times and locations of the region at ultraviolet images.

Real-time Flare Prediction Based on Distinctions between Flaring and Non-flaring Active Region Spectra

Abstract With machine learning entering into the awareness of the heliophysics community, solar flare prediction has become a topic of increased interest. Although machine-learning models have advanced with each successive publication, the input data has remained largely fixed on magnetic features. Despite this increased model complexity, results seem to indicate that photospheric magnetic field data alone may not be a wholly sufficient source of data for flare prediction. For the first time, we have extended the study of flare prediction to spectral data. In this work, we use Deep Neural Networks to monitor the changes of several features derived from the strong resonant Mg II h and k lines observed by the Interface Region Imaging Spectrograph. The features in descending order of predictive capability are: the triplet emission at 2798.77 Å, line core intensity, total continuum emission between the h and k line cores, the k/h ratio, line width, followed by several other line features such as asymmetry and line center. Regions that are about to flare generate spectra that are distinguishable from non-flaring active region spectra. Our algorithm can correctly identify pre-flare spectra approximately 35 minutes before the start of the flare, with an AUC of 86% and an accuracy, precision, and recall of 80%. The accuracy and AUC monotonically increase to 90% and 97%, respectively, as we move closer in time to the start of the flare. Our study indicates that spectral data alone can lead to good predictive models and should be considered an additional source of information alongside photospheric magnetograms.

Impulsive Coronal Heating from Large-scale Magnetic Rearrangements: From IRIS to SDO/AIA

Abstract The Interface Region Imaging Spectrograph (IRIS) has observed bright spots at the transition region footpoints associated with heating in the overlying loops, as observed by coronal imagers. Some of these brightenings show significant blueshifts in the Si iv line at 1402.77 Å ( ). Such blueshifts cannot be reproduced by coronal loop models assuming heating by thermal conduction only, but are consistent with electron beam heating, highlighting for the first time the possible importance of nonthermal electrons in the heating of nonflaring active regions. Here we report on the coronal counterparts of these brightenings observed in the hot channels of the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. We show that the IRIS bright spots are the footpoints of very hot and transient coronal loops that clearly experience strong magnetic interactions and rearrangements, thus confirming the impulsive nature of the heating and providing important constraints for their physical interpretation.

Machine learning reveals systematic accumulation of electric current in lead-up to solar flares

Solar flares-bursts of high-energy radiation responsible for severe space weather effects-are a consequence of the occasional destabilization of magnetic fields rooted in active regions (ARs). The complexity of AR evolution is a barrier to a comprehensive understanding of flaring processes and accurate prediction. Although machine learning (ML) has been used to improve flare predictions, the potential for revealing precursors and associated physics has been underexploited. Here, we train ML algorithms to classify between vector-magnetic-field observations from flaring ARs, producing at least one M-/X-class flare, and nonflaring ARs. Analysis of magnetic-field observations accurately classified by the machine presents statistical evidence for (i) ARs persisting in flare-productive states-characterized by AR area-for days, before and after M- and X-class flare events; (ii) systematic preflare buildup of free energy in the form of electric currents, suggesting that the associated subsurface magnetic field is twisted; and (iii) intensification of Maxwell stresses in the corona above newly emerging ARs, days before first flares. These results provide insights into flare physics and improving flare forecasting.

Estimate of the Upper Limit on Hot Plasma Differential Emission Measure (DEM) in Non-Flaring Active Regions and Nanoflare Frequency Based on the Mg xii Spectroheliograph Data from CORONAS-F/SPIRIT

The nanoflare-heating theory predicts steady hot plasma emission in the non-flaring active regions. It is hard to find this emission with conventional non-monochromatic imagers (such as Atmospheric Imaging Assembly or X-Ray Telescope), because their images contain a cool temperature background. In this work, we search for hot plasma in non-flaring active regions using the Mg XII spectroheliograph onboard Complex Orbital Observations Near-Earth of Activity on the Sun (CORONAS)-F/SPectroheliographIc X-ray Imaging Telescope (SPIRIT). This instrument acquired monochromatic images of the solar corona in the Mg XII 8.42 \AA line, which emits only at temperatures higher than 4 MK. The Mg XII images contain the signal only from hot plasma without any low-temperature background. We studied the hot plasma in active regions using the SPIRIT data from 18-28 February 2002. During this period, the Mg XII spectroheliograph worked with a 105-second cadence almost without data gaps. The hot plasma was observed only in the flaring active regions. We do not observe any hot plasma in non-flaring active regions. The hot plasma column emission measure in the non-flaring active region should not exceed $3 \times 10^{24}$ cm$^{-5}$. The hot Differential Emission Measure (DEM) is less than 0.01 % of the DEM of the main temperature component. Absence of Mg XII emission in the non-flaring active regions can be explained by weak and frequent nanoflares (delay less than 500 seconds) or by very short and intense nanoflares that lead to non-equilibrium ionization.

The evolution of flaring and non-flaring active regions

The evolution of flaring and non-flaring active regions

Temporal and Periodic Variations of Sunspot Counts in Flaring and Non-Flaring Active Regions

We analyzed temporal and periodic behavior of sunspot counts (SSCs) in flaring (C, M, or X class flares), and non-flaring active regions (ARs) for the almost two solar cycles (1996 through 2016). Our main findings are as follows: i) The temporal variation of monthly means of daily total SSCs in flaring and non-flaring ARs are different and these differences are also varying from cycle to cycle; temporal profile of non-flaring ARs are wider than the flaring ones during the solar cycle 23, while they are almost the same during the current cycle 24. The second peak (second maximum) of flaring ARs are strongly dominate during current cycle 24, while this difference is not such a remarkable during cycle 23. The amplitude of SSCs in the non-flaring ARs are comparable during the first and second peaks (maxima) of the current solar cycle, while the first peak is almost not existent in case of the flaring ARs. ii) Periodic variations observed in SSCs of flaring and non-flaring ARs are quite different in both MTM spectrum and wavelet scalograms and these variations are also different from one cycle to another; the largest detected period in the flaring ARs is 113 days, while there are much higher periodicities (327, 312, and 256 days) in non-flaring ARs. There are no meaningful periodicities in MTM spectrum of flaring ARs exceeding 45 days during solar cycle 24, while a 113 days periodicity detected from flaring ARs of solar cycle 23. For the non-flaring ARs the largest period is 72 days during solar cycle 24, while the largest period is 327 days during current cycle.

PREDICTION OF SOLAR FLARES USING UNIQUE SIGNATURES OF MAGNETIC FIELD IMAGES

ABSTRACT Prediction of solar flares is an important task in solar physics. The occurrence of solar flares is highly dependent on the structure and topology of solar magnetic fields. A new method for predicting large (M- and X-class) flares is presented, which uses machine learning methods applied to the Zernike moments (ZM) of magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory for a period of six years from 2010 June 2 to 2016 August 1. Magnetic field images consisting of the radial component of the magnetic field are converted to finite sets of ZMs and fed to the support vector machine classifier. ZMs have the capability to elicit unique features from any 2D image, which may allow more accurate classification. The results indicate whether an arbitrary active region has the potential to produce at least one large flare. We show that the majority of large flares can be predicted within 48 hr before their occurrence, with only 10 false negatives out of 385 flaring active region magnetograms and 21 false positives out of 179 non-flaring active region magnetograms. Our method may provide a useful tool for the prediction of solar flares, which can be employed alongside other forecasting methods.

INFERENCE OF HEATING PROPERTIES FROM “HOT” NON-FLARING PLASMAS IN ACTIVE REGION CORES. II. NANOFLARE TRAINS

ABSTRACT Despite its prediction over two decades ago, the detection of faint, high-temperature (“hot”) emission due to nanoflare heating in non-flaring active region cores has proved challenging. Using an efficient two-fluid hydrodynamic model, this paper investigates the properties of the emission expected from repeating nanoflares (a nanoflare train) of varying frequency as well as the separate heating of electrons and ions. If the emission measure distribution (EM(T)) peaks at T = T m , we find that EM(T m ) is independent of details of the nanoflare train, and EM(T) above and below T m reflects different aspects of the heating. Below T m , the main influence is the relationship of the waiting time between successive nanoflares to the nanoflare energy. Above T m , power-law nanoflare distributions lead to an extensive plasma population not present in a mono-energetic train. Furthermore, in some cases, characteristic features are present in EM(T). Such details may be detectable given adequate spectral resolution and a good knowledge of the relevant atomic physics. In the absence of such resolution we propose some metrics that can be used to infer the presence of “hot” plasma.

Motion Magnification in Coronal Seismology

We introduce a new method for the investigation of low-amplitude transverse oscillations of solar plasma non-uniformities, such as coronal loops, individual strands in coronal arcades, jets, prominence fibrils, polar plumes, and other contrast features, observed with imaging instruments. The method is based on the two-dimensional dual tree complex wavelet transform (DT$\mathbb{C}$WT). It allows us to magnify transverse, in the plane-of-the-sky, quasi-periodic motions of contrast features in image sequences. The tests performed on the artificial data cubes imitating exponentially decaying, multi-periodic and frequency-modulated kink oscillations of coronal loops showed the effectiveness, reliability and robustness of this technique. The algorithm was found to give linear scaling of the magnified amplitudes with the original amplitudes provided they are sufficiently small. Also, the magnification is independent of the oscillation period in a broad range of the periods. The application of this technique to SDO/AIA EUV data cubes of a non-flaring active region allowed for the improved detection of low-amplitude decay-less oscillations in the majority of loops.