Oscillations Above Sunspots and Faculae: Height Stratification and Relation to Coronal Fan Structure
Oscillation properties in two sunspots and two facular regions are studied using Solar Dynamics Observatory (SDO) data and ground-based observations in the Si i 10827Å and He i 10830Å lines. The aim is to study different-frequency spatial distribution characteristics above sunspots and faculae and their dependence on magnetic-field features and to detect the oscillations that reach the corona from the deep photosphere most effectively. We used Fast-Fourier-Transform and frequency filtration of the intensity and Doppler-velocity variations with Morlet wavelet to trace the wave propagating from the photosphere to the chromosphere and corona. Spatial distribution of low-frequency (1 – 2 mHz) oscillations outlines well the fan-loop structures in the corona (the Fe ix 171 Å line) above sunspots and faculae. High-frequency oscillations (5 – 7 mHz) are concentrated in fragments inside the photospheric umbra boundaries and close to facular-region centers. This implies that the upper parts of most coronal loops, which transfer low-frequency oscillations from the photosphere, sit in the Fe ix 171 Å line-formation layer. We used dominant frequency vs. distance from barycenter relations to estimate magnetic-tube inclination angle in the higher layers, which poses difficulties for direct magnetic-field measurements. According to our calculations, this angle is 40 in the transition region around umbra borders. Phase velocities measured in the coronal loops’ upper parts in the Fe ix 171 Å line-formation layer reach 100 – 150 km s for sunspots and 50 – 100 km s for faculae.
The intensive study of oscillations observed in the solar atmosphere has lasted half a century. Many new facts about the origin and properties of oscillations have been obtained. One of the relevant problems is the interaction mechanism between the solar magnetic field and oscillations. According to early studies, the oscillation properties in the magnetic-field regions differ significantly from those observed in non-magnetic ones (Howard, Tanenbaum, and Wilcox, 1968; Balthasar and Wiehr, 1984; Lites, 1984; Kobanov, 1985).
The most noticeable magnetic-field regions on the Sun are sunspots and faculae. Magnetic structure of a single regularly formed sunspot has circular symmetry. Magnetic field is vertical in the center of a sunspot. The inclination increases with distance from the barycenter, and the field becomes almost horizontal in the outer penumbra. This feature makes sunspots the most attractive objects to study the relationship between the oscillatory-wave process properties and the magnetic field topology.
The study of oscillations in the lower layers of the solar atmosphere has revealed the decrease in dominant frequency with distance from the sunspot center (Rimmele, 1995; Sigwarth and Mattig, 1997; Kobanov, 2000; Kobanov and Makarchik, 2004). A peculiar property of sunspots is the existence of running penumbral waves (RPW), which are readily detected in the sunspot chromosphere (Beckers and Tallant, 1969; Giovanelli, 1972; Zirin and Stein, 1972). Two scenarios were proposed to interpret RPWs. According to the first one – the trans-sunspot wave scenario – the waves propagate from sunspot umbrae to penumbrae along an almost horizontal trajectory (Alissandrakis, Georgakilas, and Dialetis, 1992; Tsiropoula, Alissandrakis, and Mein, 2000; Tziotziou et al., 2004, 2006). According to the second one – the visual pattern scenario – the waves propagate from the lower layers to the upper ones along a path with different angles. When observing the chromosphere, one sees an illusion of horizontal propagation (Rouppe van der Voort et al., 2003; Bogdan and Judge, 2006; Bloomfield, Lagg, and Solanki, 2007; Kobanov et al., 2009).
Oscillations in sunspots and faculae have combined and individual properties. For example, studies of the line-of-sight (LOS) velocity showed that five-minute band oscillations dominate in the photosphere of sunspot umbrae (Howard, Tanenbaum, and Wilcox, 1968; Bhatnagar, 1971; Thomas, Cram, and Nye, 1982; Balthasar and Wiehr, 1984) and faculae (Orrall, 1965; Howard, 1967; Sheeley and Bhatnagar, 1971); the amplitude of the oscillations is suppressed relative to the undisturbed regions. Three-minute-band oscillations dominate in the chromosphere above spot umbrae (Beckers and Tallant, 1969; Kneer, Mattig, and von Uexkuell, 1981; Lites, 1984, 1986; Zhugzhda and Sych, 2014), while the facular chromosphere preserves five-minute oscillations and even reveals lower-frequency oscillations (Orrall, 1965; Howard, 1967; Teske, 1974; Blondel, 1971; Cram and Woods, 1980; Balthasar, 1990; Kobanov and Pulyaev, 2007).
The present opinion is that coronal five-minute oscillations are observed mainly above faculae and the chromospheric network (De Moortel, Ireland, and Walsh, 2000; Centeno, Collados, and Trujillo Bueno, 2006; Vecchio et al., 2007), while three-minute oscillations in the solar corona are related to sunspots (O’Shea, Muglach, and Fleck, 2002; Doyle, Dzifćáková, and Madjarska, 2003). Three-minute oscillations above sunspots in the microwave range were observed with a 50-second delay compared with the chromospheric oscillations(Abramov-Maximov et al., 2011).
Now excellent Solar Dynamics Observatory (SDO) data allow us to study mode properties in sunspots and faculae at different heights from the photosphere to the corona (Reznikova and Shibasaki, 2012; Reznikova et al., 2012; Kobanov and Chelpanov, 2014).
Altitudinal cuts of the frequency spatial localization allow us to trace the path of wave perturbations. In the future, this technique can be used to determine magnetic-field inclination in the transition zone and the low corona using an alternative method (Jess et al., 2013).
Fan structures are often observed in the corona above sunspot and faculae. These structures are seen especially clearly in the Fe ix 171Å line. It is possible to determine the frequency of the waves traveling along fan structures by comparing the spatial distribution (power localization) of selected frequency waves with the Fe ix 171Å line images of these regions. The relation between fan structures and waves is the subject of many studies. Marsh and Walsh (2006) found that three-minute umbral oscillations propagate directly into coronal loops. Similar conclusions have been made by Jess et al. (2012), who demonstrated that coronal loops are anchored in the photospheric umbral dots with enhanced intensity of three-minute oscillations. Earlier Brynildsen et al. (2004) showed that three-minute oscillations in the corona were confined to the narrow domain that corresponded to the sunspot umbra boundary at the photospheric level. These oscillations are suppressed in fan structures. Wang, Ofman, and Davila (2009) revealed 12- and 25-minute oscillations in coronal fans above sunspots and identified them as slow magnetoacoustic waves. Kobanov, Chelpanov, and Kolobov (2013) supported the conclusions made by Brynildsen et al. (2004) concerning three-minute oscillations, and detected waves with periods of 12 – 15 minutes propagating from the penumbral photosphere to the coronal fans.
We used both space- and ground-based telescope observations that cover the same active regions at the same temporal intervals. SDO has three instruments onboard: the Atmospheric Imaging Assembly (AIA), the Helioseismic and Magnetic Imager (HMI) and Extreme Ultraviolet Variability Experiment (EVE), more details can be found in Lemen et al. (2012); Scherrer et al. (2012); Woods et al. (2012). The first provides data in a wide range of UV spectral lines, which cover heights from the photosphere to the corona. The intensity image series have cadences of 12 seconds for all but two lines: the 1600 Å and 1700 Å bands’ cadence is 24 seconds. We chose four bands for the analysis. The coronal heights are represented by the Fe ix 171 Å and Fe xii, xxiv 193 Å lines. The other two are the continuum 1700 Å (the upper photosphere) and He ii 304 Å (the transition region) lines, whose formation heights are the closest to those of the Si i 10827 Å and He i 10830 Å lines, which we used in the ground-based observations.
The second instrument, HMI, provides intensity, Doppler velocity, and magnetic field data obtained using the Fe i 6173 Å line with a 45 second cadence. This line is formed in the photosphere at a height of 100 – 150 km (Fleck, Couvidat, and Straus, 2011; Parnell and Beckers, 1969).
The ground-based observations were obtained with the solar telescope at the Sayan Solar Observatory located at an altitude of 2000 m. The telescope is elevated six meters above the ground and is equipped with a special system to suppress atmospheric turbulence (Hammerschlag and Zwaan, 1973). The telescope contains a coelostat, with the effective diameter of its main mirrors being 800 mm and a guiding system that keeps the Sun’s image on the spectrograph slit with an accuracy of one arcsec. We used a Princeton Instruments RTE/CCD camera (2561024). One element corresponded to a spatial resolution of 0.23 arcsecs along the entrance slit of the spectrograph and to 7 mÅ in the direction of the spectrograph dispersion. The observations provided a series of spectrograms with a cadence of 3 seconds containing the He i 10830 Å and Si i 10827 Å spectral lines. For details, see Kobanov et al. (2013).
3.1 Oscillations and Fan Structures Above Sunspots
Active regions NOAA 11311 and 11479 are single, round, medium-sized sunspots (see Figure 1). We observed them near the central meridian, which allowed us to minimize the projection effect on the analysis of oscillations at different heights. The domains studied included sunspots and the neighboring regions up to 5 – 10 from the outer penumbra borders, since sunspots affect the oscillation characteristics of these regions (Kobanov, 2000).
Figure 2 shows the dominant frequency for every spatial element of the sunspots at several heights: Fe i 6173 Å, 1700 Å, He ii 304 Å, and Fe ix 171 Å bands. The frequency determination was performed as follows. Firstly, the FFT intensity spectrum for each 0.60.6domain was obtained. Preparing the signals for the FFT analysis, we subtracted an average intensity and applied a bell filter to minimize effects of abrupt endings. Then, the integral power in a 1 mHz rectangular window was calculated. The window was moved throughout the spectrum with a 0.02 mHz step giving a set of values. The frequency corresponding to the maximum value was taken as the dominant one for the particular spatial domain. This representation is a convenient way to obtain a picture of the spatial distribution of oscillation frequencies above the sunspots under study. Five-minute oscillations dominate in the lower photosphere (the Fe i 6173 Å line), forming typical fragmented structure in the umbrae and the neighboring outer penumbra regions. Photospheric three-minute oscillations in sunspot NOAA 11311 are located mainly along the umbra boundary instead of the umbral central part, where these oscillations are located in the 1700 Å, He ii 304 Å, and Fe ix 171 Å bands. This corresponds to our earlier results (Kobanov et al., 2011; Kobanov, Chelpanov, and Kolobov, 2013). Five-minute oscillations are located in an annular zone around the sunspot center, which expands beyond the umbra boundaries with increasing height in both sunspots. Low-frequency oscillations start in the lower photosphere of the penumbra (left panels in Figure 2). Such a topology of the frequency distribution height cuts supports the concept explaining RPW as a “visual pattern” (Rouppe van der Voort et al., 2003; Bloomfield, Lagg, and Solanki, 2007; Kobanov et al., 2009). In the upper layers of the solar atmosphere, the field of view is mostly occupied by the low-frequency oscillations marked in red (Figure 2), whereas the high-frequency oscillations marked with blue color reside within the inner-penumbra boundaries. The presence of the low-frequency inclusions inside the umbrae can probably be explained by fine-structure irregularities of the magnetic field. One should note that Figure 2 does not give the real picture of the oscillation power; it merely shows the spatial distribution of the frequencies instead. Circular-shaped frequency spatial localization allowed us to plot the frequency vs. distance from barycenter for three height levels: Fe i 6173 Å, 1700 Å, He ii 304 Å (see Figure 3). White-light images were used to find barycenters of the sunspots. Then, using the data in Figure 2, we calculated a mean frequency value  averaged over the points located at distance from the barycenter (Figure 3). Each point of the curves was determined as described. The radial spatial step was chosen to be 0.6. Similarly, the longitudinal magnetic field  in Figure 3 and the absolute value of the magnetic-field inclination in Figure 4 (solid lines) were plotted against the distance from the barycenter. Magnetic-field inclination angle  to the solar-surface normal was calculated using SDO/HMI data as described by Borrero et al. (2011) and converted following the formalism of Gary and Hagyard (1990). It is of interest to compare the derived dependencies with the cut-off frequency for the waves, using the slow magnetoacoustic wave approximation. For this purpose, we used the following equation (McIntosh and Jefferies, 2006; Botha et al., 2011):
where is the cut-off frequency; =274 is the gravitational constant; is the speed of sound; is the adiabatic index; is the dependence of inclination angle on the barycenter distance. Finally, we obtain the dashed curves in Figure 3 expressing the dependence of on the barycenter distance for both sunspots.
Analyzing the plots in Figure 3, one can see several features: curves of the lowest atmospheric layers (Fe i 6173 Å and 1700 Å) show a jump. This is typical for both sunspots and is thus unlikely to be an artifact. The curves expressing frequency vs. distance from the barycenter do not coincide with those for calculated using Equation (1). This is especially evident in the umbra, where the curve is almost horizontal. Note that more correspondence is found for the curve in Figure 3 (upper panels). All of the curves approach each other in the middle parts of the penumbrae. This implies that the 3 – 3.5 mHz oscillations observed in the corresponding penumbra regions prevail at these heights. Probably, this circular penumbral zone is the very place to search for the upwardly propagating five-minute waves.
As Jess et al. (2013) showed, the dominant frequency distribution can be used to study physical conditions at corresponding heights (e.g. the magnetic-field inclination). Substituting with measured at the He ii 304 Å line formation level in Equation (1), one can roughly estimate the magnetic-field inclination at this height:
Direct substitution of the dominant frequency  for cut-off frequency  results in the ratio in the parentheses being greater than 1 for the high frequencies, which is unacceptable. Following Yuan et al. (2014), we used an empirical ratio 0.81F(r) mHz mHz for the 304 Å line. The result is suitable for qualitative assessments. To acquire more precise quantitative assessments the empirical ratio between and should be determined based on greater statistics. The results of such an estimation are presented in Figure 4, where the solid lines denote the magnetic field inclination angles derived with SDO/HMI in the photospheric Fe i 6173 Å line, and the dashed lines denote those derived using Equation (2) for the He ii 304 Å line. The inclination reaches 40° at the inner penumbra boundary. Close values were obtained by other authors (Jess et al., 2012; Reznikova et al., 2012; Kobanov, Chelpanov, and Kolobov, 2013), who used different methods. In accordance with the derived plots, the magnetic-field inclination angle at the He ii 304 Å line formation level rapidly increases in the umbrae and the adjacent penumbrae, and this rate gradually decreases in the outer penumbrae. This dependence corresponds to the plot presented by Yuan et al. (2014) for the He ii 304 Å line.
As was noted above, the low-frequency oscillations occupy a greater area in the FOV with increasing height (Figure 2). At the same time, image fragments in the power maps become elongated in the radial direction. Frequency filtering provides clear visualization of spatial localization of different modes. Figure 5 presents 6 – 7 mHz filtered intensity signals corresponding to several heights. High-frequency oscillation locations at all levels are confined to the domains of the photospheric umbral boundaries. No fan structures are seen in this image. The situation is different for low-frequency oscillations of the 3–3.8 and 1–2 mHz bands. We refer to Figure 6, as we are most interested in finding the wave frequencies that penetrate into the corona and dominate in the fan structures at the Fe ix 171Å line level. Left and middle panels in this figure show spatial distribution of the oscillation power in the 3 – 4 and 1 – 2 mHz bands respectively; right panels show the Fe ix 171Å intensity images, averaged over the entire time series. The intensity images were inverted for the convenience of visual comparison. One can see that coronal-fan structures are best reproduced in the middle panels showing the 1–2 mHz band oscillation power. Joint analysis of Figures 6 and 2 leads to the following conclusions: i) the 10 – 15 minute oscillations dominate in the corona above sunspots; ii) these oscillations are observed along the loops; thus, one can trace changes in their properties along the horizontal part of the loops and try to measure the propagation speed.
The crosses in the middle panel of Figure 6 show the points that were analyzed in detail. The power spectra for these points are shown in Figure 7. A correspondence between the spectra indicates that both of them belong to the same loop. Contrary to our expectations, the time delay between the signals from two points of the same loop was ambiguous, with variations in amplitude and sign over the whole time series. One of the possible explanations implies the existence of several thin and highly transparent coronal loops contributing to the signal. In spite of such a phase difference, the oscillations with close frequencies have similar power spectra. The averaged estimations give the following phase velocities: 120 25 km s for NOAA 11479 and 130 30 km s for NOAA 11311. Similar values were obtained by Nightingale, Aschwanden, and Hurlburt (1999); Robbrecht et al. (2001); Marsh et al. (2003).
3.2 Characteristics of Facular Oscillations
The analysis was performed using two faculae. Facula No. 1 was observed on 6 October 2011 from 00:47 UT untill 02:42 UT, with center coordinates S12 E05. This facula is of special interest due to its proximity to sunspot NOAA 11311, which implies its direct connection through magnetic field arches. We observed facula region No. 2 with coordinates N13 W08 on 1 October 2011, from 03:41 UT untill 05:06 UT. We identified this facula as not being connected with sunspots. The ground-based observations are spectrogram time series in the Si i 10827Å and He i 10830Å lines. The temporal resolution was 3.3 seconds, and the spatial resolution along the slit was 1 – 1.5 on average. We chose the same SDO lines that we used for the sunspot analysis. Facular regions were confined by the 0.7 brightness isoline in the 1700 Å band, where the 100 % brightness was considered to be the maximum facula-core brightness. The faculae have arbitrary shapes and lack radial symmetry. We intended to determine the frequency bands which prevail in the fan structures observed at the 171 Å line formation level, and to reveal their source as far as possible. To this end, we needed to study facular oscillation properties from the deep photosphere to the corona.
Information about oscillation parameters in the upper atmosphere of faculae is controversial. Koutchmy, Zhugzhda, and Locans (1983) observed periodic displacements of the coronal 5303 Å line at a height of 25 000 – 30 000 km above a facula. They revealed 300 seconds, 80 seconds, and 40 seconds periods. Using high spatial resolution observations, de Wijn, McIntosh, and De Pontieu (2009) found that three-minute periods prevail in the chromosphere above the facula core, while five-minute periods dominate on its periphery. This configuration is similar to that observed in sunspots. When studying five-minute oscillations in the X-rays above faculae, Didkovsky et al. (2011) concluded that they were related to global solar surface oscillations (-modes) observed in the photosphere. Ofman, Nakariakov, and Deforest (1999) and Deforest and Gurman (1998) recorded 15-minute oscillations in the corona above polar faculae, which they explained as a manifestation of slow magnetoacoustic waves.
First, we analyzed characteristics of LOS-velocity oscillations observed at three heights: Fe i 6173Å – 200 km (Parnell and Beckers, 1969), Si i 10827Å – 540 km; He i 10830Å – 2000 km (Centeno, Collados, and Trujillo Bueno, 2009).
The observed LOS-velocity signals contain information about acoustic oscillations at these heights. Figure 8 shows the power spectra for the signals averaged over the area marked with a square in the middle part of Facula 2 in Figure 10 (first column, second panel). Both space (Fe i 6173Å) and ground-based (Si i 10827Å, He i 10830 Å) observations of LOS velocity show that the five-minute period is dominant in the photosphere and upper chromosphere (Figure 8, top row). The lower row in Figure 8 presents the intensity variation spectra in the same locations. All spectra are normalized to their maximum values. The five-minute oscillations are almost absent in the intensity spectra, while they dominate in the LOS-velocity spectra. The 0.7 – 1.2 mHz oscillations dominate in the intensity spectra of the lower photosphere. There have always been doubts about the solar origin of intensity oscillations in ground-based observations: are they a result of the Earth’s atmospheric turbulence? The photospheric spectra of space observations (Fe i 6173 Å) agree well with those of ground-based observations (Si i 10827 Å). The height difference between the formation levels (200 km and 540 km for the Fe i and Si i lines respectively) may explain the minor difference in details. At the same time, the photospheric and chromospheric ground-based spectra also differ, which should not be the case if they are affected by the same artifact. These arguments confirm the solar origin of the low-frequency peak shown in the lower panels in Figure 8. The absence of such peaks in the LOS-velocity variation spectra may signify that two different types of oscillations coexist in the observed volume. The five-minute variations in the LOS-velocity signals are undoubtedly acoustic oscillations, and the 0.7 – 1.2 mHz peaks are probably a sausage-mode manifestation.
Figure 9 shows how modes with different frequencies are distributed in the lower corona (the Fe ix 171 Å line). Spatial distributions of low-frequency oscillation power outlines fan-loop structures best. This similarity is less pronounced in the five-minute range and almost disappears in the three-minute range. The change in power spatial localization of these frequencies with height can be illustrated by the example of Facula 2 (Figure 10). At the lowest level (Fe i 6173 Å), the facula region is similar to the surrounding background at all frequencies (see Figure 10, upper row). At the temperature minimum level (the 1700 Å line) the decrease in oscillation power becomes evident, relative to the surrounding background. This is most apparent at high frequencies (Figure 10, the third panel in the second row). The oscillation-power distribution in the transition region (the He ii 304 Å line) shows the first signs of elongated elements, which become a clearly expressed fan structure in the lower corona (Fe ix 171 Å) in the frequency range of 0.9 – 1.5 mHz. This structure has reduced contrast at the Fe xii, xxiv 193 Å line formation height. At the level of the Fe xii, xxiv 193 Å line, the facula shows higher oscillation power relative to the adjacent regions at the highest level in the 2.8 – 3.8 mHz and 5.0 – 6.0 mHz ranges. Probably, this tendency is better developed higher above the Fe xii, xxiv 193 Å line formation height. This will be a subject for further research. The fact that spatial localization of low-frequency oscillations closely reproduces coronal-loop structures means that facular low-frequency oscillations penetrate to the corona through this very loop system. We observe the upper and, thus, the most horizontal parts of the loops at the Fe ix 171 Å line-formation level. Such a feature of the loop geometry gives an opportunity to analyze the oscillation spectral-phase characteristics in more detail. The marks in Figure 11 show points that we used to calculate the FFT power spectra. Figure 12 represents the spectra for each element pair (1.21.2 in size) located at individual loop. These spectra are convincing evidence of the fact that low frequencies dominate in loop structures at the 171 Å line formation height. May these oscillations exist outside loops as well? Figure 13 gives answers to this question, showing the spectra for two spatial elements, one inside the loop and the other one 2away from the loop. The oscillation inside the loop element is approximately five times higher than the background level. Spectral similarity for the loop elements gives hope that we are able to unambiguously measure the phase speed at the dominant frequency. However, the results of a similar analysis were ambiguous (Kobanov and Chelpanov, 2014). The phase speed based on the time-lag measurement varies from 50 km s to 100 km s with the average value of 60 km s.
We performed a similar analysis for a loop connecting Facula 1 and sunspot NOAA 11311 (Figure 14). Note that the oscillation spectra in the loop’s footpoints 1 and 2 differ noticeably (Figure 15, the upper row). The spectra of the elements located fairly close to each other in the middle part of the loop show differences as well (Figure 15, lower row). Phase-speed measurements based on the signals at points 3 and 4 in the middle part of the loop are also ambiguous and yield values of 100 – 120 km s. One can conclude that oscillation spectral-phase characteristics in the analyzed loop of Facula 1 considerably differ from those of Facula 2, which is caused by the NOAA 11311 influence. Figure 16 represents the maximum intensity variation values for three frequency bands at five heights. Both faculae show that the low frequencies dominate at all heights, and the largest intensity variation is detected in the transition region (the He ii 304 Å line).
Low-frequency oscillations (1 – 2 mHz) in sunspots are concentrated in penumbrae forming annular areas, which expand with height. High-frequency oscillations (5 -â 7 mHz) are concentrated in fragments located in areas confined to the photosphere umbra boundaries at all heights. Spatial distribution of low-frequency oscillations in the corona above sunspots and faculae reproduces the coronal fan structures well. This signifies that the upper parts of most coronal loops conducting 10 – 15 min oscillations are located within the Fe ix 171 Å line-formation layer, while three-minute and shorter-period oscillations possibly penetrate to higher coronal levels by other loops. The observation-based dominant frequency vs. distance from barycenter relations may be used to determine inclination of magnetic tubes in higher levels where it cannot be measured directly. The calculations show that this angle is close to 40 above the umbral borders in the transition region. Phase speeds measured in the coronal loops’ upper parts at the Fe ix 171 Å line formation height reach 100 – 150 km s for sunspots and 50 – 100 km s for faculae. Intensity and LOS-velosity oscillation power spectra differ significantly in the facular lower atmospheric layers: spectra of intensity oscillations show the prevalence of the 0.7 – 1.2 mHz frequency oscillations; in those of LOS-velocity, the dominant oscillations are five-minute oscillations. Such spectra are typical for both ground-based and space observations. The absence of low-frequency peaks in LOS-velocity spectra may signify that two oscillation types coexist in the region under study. Amplitude of intensity oscillations is maximum in the transition region (He ii 304 Å) above faculae.
Acknowledgements. The study was performed with partial support of the Projects No. 16.3.2, 16.3.3 of ISTP SB RAS. We acknowledge E. Korzhova for her help in preparing the English version of the article and the NASA/SDO science team for providing the data. We are grateful to an anonymous referee for the helpful remarks and suggestions.
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