Spatial Distributions of Sunspot Oscillation Modes at Different Temperatures
aa r X i v : . [ a s t r o - ph . S R ] A ug Research in Astronomy and Astrophysics manuscript no.(L A TEX: ms0172˙arxiv.tex; printed on August 15, 2019; 0:40)
Spatial Distributions of Sunspot Oscillation Modes at DifferentTemperatures ∗ Zhengkai WANG , Song FENG , , † , Linhua DENG , , , Yao MENG Faculty of Information Engineering and Automation, Kunming University of Science and Technology,Kunming 650500, China; [email protected] Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216, China College of Science, China Three Gorges University, Yichang 443002, China Chongqing University of Arts and Sciences, Chongqing 402160, China
Received 20XX Month Day; accepted 20XX Month Day
Abstract
Three- and five-minute oscillations of sunspots have different spatial distributionsin the solar atmospheric layers. The spatial distributions are crucial to reveal the physicalorigin of sunspot oscillations and to investigate their propagation. In this study, six sunspotsobserved by Solar Dynamics Observatory/Atmospheric Imaging Assembly were used to ob-tain the spatial distributions of three- and five-minute oscillations. The fast Fourier transformmethod is applied to represent the power spectra of oscillation modes. We find that, from thetemperature minimum to the lower corona, the powers of the five-minute oscillation exhibit acircle-shape distribution around its umbra, and the shapes gradually expand with temperatureincrease. However, the circle-shape is disappeared and the powers of the oscillations appearto be very disordered in the higher corona. This indicates that the five-minute oscillation canbe suppressed in the high-temperature region. For the three-minute oscillations, from the tem-perature minimum to the high corona, their powers mostly distribute within an umbra, andpart of them locate at the coronal fan loop structures. Moreover, those relative higher powersare mostly concentrated in the position of coronal loop footpoints.
Key words:
Sun: atmosphere — Sun: sunspots — Sun: oscillations ∗ Supported by the National Natural Science Foundation of China. † Corresponding author
WANG Z. et al.
Sunspot oscillations are crucial to explore structures of solar magnetic fields (Bogdan & Judge 2006;De Moortel & Nakariakov 2012). Two oscillation modes (one is a three-minute period, and the other five-minute) were initially found in the photosphere and chromosphere, respectively (Beckers & Schultz 1972;Bhatnagar et al. 1972; Bhatnagar & Tanaka 1972; Giovanelli 1972). Since the early 1970s, many authors(e.g., Lites 1992; Solanki 2003; Bogdan & Judge 2006; Jess et al. 2015) further studied the two modes andrevealed that the oscillations exhibit different spatial distributions in different atmospheric layers (Balthasar1990; Bogdan & Judge 2006; Kobanov et al. 2011). The spatial distributions are believed to be importantfor investigating the physical origin of the oscillation modes and their propagation in the solar atmosphere(O’Shea et al. 2002; Rouppe van der Voort et al. 2003).From the temperature minimum to the upper coronal layer, the three-minute oscillation mostly exists inan umbra (O’Shea et al. 2002). Nagashima et al. (2007) further stated that the three-minute oscillation canbe suppressed in the photosphere and enhanced in the chromosphere. High spatial and temporal resolutionobservations provided a chance to reveal spatial distributions of sunspot oscillations in different atmosphericlayers. Using data observed by Sayan Solar Observatory and Solar Dynamics Observatory/AtmosphericImaging Assembly (SDO/AIA; Lemen et al. 2012; Pesnell et al. 2012), Kobanov et al. (2013) found thatthe powers of the three-minute oscillation mainly concentrate within an umbra in the temperature minimumand chromosphere. Although the oscillation expands significantly in the transition region and lower corona,it is still limited within the umbra. In contrast, Reznikova & Shibasaki (2012) stated that the three-minuteoscillation leaks clearly along the coronal fan-structures in the lower corona.Although the findings of the spatial distributions of three-minute oscillations are controversial, the mainstandpoints about five-minute oscillations are roughly similar to each other (Lites et al. 1982; Balthasar1990; Marco et al. 1996; Sych & Nakariakov 2008; Reznikova & Shibasaki 2012; Kobanov et al. 2013;Yuan 2015). The powers of five-minute oscillations mostly distribute the umbra-penumbra boundary.Moreover, the distribution of the powers exhibits a nearly circle-shape structure. The structure continuouslyexpands from the chromosphere to the transition region, but part disappears in the lower corona.The results imply that the spatial distributions of three- and five-minute oscillations are closely related tothe solar atmospheric temperature (Fludra 2001; Reznikova & Shibasaki 2012). So, we randomly selectedsix sunspots observed by SDO/AIA to reveal the statistical features of sunspot oscillations at differenttemperatures. The selected observations cover different temperatures from the temperature minimum to thehigher corona.The paper is as follows. We first describe the observations and data reduction in Section 2, and thenthe oscillation modes of sunspots and their spatial distributions are given in Sections 3 and 4, respectively.Finally, our conclusion is presented in Section 5. patial Distributions of Sunspot Oscillation Modes at Different Temperatures 3
Table 1: Data series observed by SDO/AIA in our analysis
NOAA Date Location(arcsec) T start (UTC) T end (UTC)11176 27 Mar. 2011 [1, -136] 16:00 17:0011433 16 Mar. 2012 [-5, 285] 18:00 19:0011479 17 May 2012 [-7, 273] 00:00 01:0011896 15 Nov. 2013 [-191, 136] 18:00 19:0012036 17 Apr. 2014 [341, -66] 09:00 10:0012638 25 Feb. 2017 [3, 388] 22:00 23:00
All six sunspots were observed with SDO/AIA for one hour. Table 1 shows the details of these sunspots.We chose the observations of five channels, i.e., AIA 1700 ˚A (located in the temperature minimum), 304 ˚A(the transition region), 171 ˚A (the lower corona), 211 ˚A and 131 ˚A (the higher corona). The characteristictemperatures of the five channels are: 0.6 × , 5 × , 100 × , 200 × , and 1000 × K,respectively. The image series have cadences of 12 seconds for all, except for the AIA 1700 ˚A channel, itscadence is 24 seconds. We used the routine aia prep.pro to process level 1.0 data for obtaining level 1.5.Furthermore, all the data were truncated to a region with 48 ′′ × ′′ , which contains an entire sunspot. Due to different spatial distributions of three- and five-minute oscillations in umbrae and penumbrae(Balthasar 1990), we separately studied them at different temperatures. Using an intensity threshold toan AIA 1700 ˚A image of different sunspots, we obtained the umbral and penumbral boundaries of eachsunspot. The top of Figure 1 shows an image series observed by the AIA 1700 ˚A, 304 ˚A, 171 ˚A, 211 ˚A, and131 ˚A channels in NOAA 12638. The two white closed curves denote the umbral and penumbral bound-aries, respectively. In the following sections, we take the sunspot as an example to illustrate our analysisprocess.
The middle row of Figure 1 shows average intensity variations of the entire penumbra of the sunspot (AR12638) on each channel. Note that the linear trend of each curve is removed to reduce the disturbancecaused by its background intensities. The bottom of Figure 1 shows the corresponding power spectra ofthe curves obtained by fast Fourier transform (FFT). Note that the spectra are plotted using a log-log scale.Moreover, we normalized the power spectra using the variance of the intensity curve shown in middlefor easy comparison in different channels. We easily find that the spectra with the log-log scale nearlyexhibit a linear relationship between frequencies and powers, meaning that the powers follow a power-lawdistribution.
WANG Z. et al.
Fig. 1: Top: AIA intensity images observed in NOAA 12638. The two white closed curves denote the umbraland penumbral boundaries, respectively. Middle: the average intensity curves of the entire penumbra indifferent channels. Bottom: the corresponding power spectrum of the average intensity curves, but they area log-log scale. The red solid line denotes a goodness-of-fit of each power spectrum, and the blue dottedline the 95% confidence level. Only the peaks above the confidence level are considered as the oscillationmodes. The blue shadow of each spectrum denotes our region of interest whose period range from 2.5 to5.5 minutes.This is due to the FFT spectra of sunspot oscillations are dominated by red noise and present a power-law distribution (Vaughan 2005; Ireland et al. 2015). For extracting true oscillation modes from the powerspectra dominated by red noise, we used a similar method proposed by Vaughan (2005) to obtain goodness-of-fits of the spectra and further tested the significant peaks in the spectra. We used linear functions tofit the log-log power spectra for obtaining their goodness-of-fits, and their 95% confidence levels are alsocalculated with a chi-square test. Red solid and blue dotted lines shown in the bottom of Figure 1 indicatethe goodness-of-fits for the power spectra and their confidence levels. Here, only the peaks above the 95%confidence level are considered as the true oscillation modes. In our analysis, we only focus on the three-and five-minute oscillations, i.e., those peaks appearing between 2.5 and 5.5 minutes. The blue regions inthe bottom of Figure 1 denote the ranges between 2.5 and 5.5 minutes. Obviously, there are several signif-icant peaks above the confidence level in the blue shadow region of each power spectrum. The frequencycorresponding to the peaks are 3.9 ± ± ± patial Distributions of Sunspot Oscillation Modes at Different Temperatures 5 Fig. 2: The average intensities of the entire umbra and their corresponding power spectra with a log-logscale.304 ˚A, and 3.6 ± ± ± ± The same analysis method was used to study the oscillations in the umbra. The top and bottom of Figure 2show the average intensity curves of the umbra and its power spectra, respectively. To the umbra, we findthat the three- and five-minute oscillations can be found, but the three-minute oscillation exists in all AIAchannels, and further their powers are relatively high, expect for AIA 1700 ˚A channel. However, the five-minute oscillation only exists in the AIA 1700 ˚A channel, and the others did not. The result indicates that, inthe umbra, the three-minute oscillation distributes in different temperatures of the solar atmosphere from thetemperature minimum to the higher corona. But, the five-minute oscillation only exists in the temperatureminimum. Analyzing the sunspots of the other active regions, we also obtain similar results as above.Combined with the oscillations observed by the six sunspots, we conclude that, from the temperatureminimum to the corona, three-minute oscillations can by observed in penumbra and umbra. Meanwhile, wealso find that the powers of three-minute oscillations are higher in umbra than in penumbrae. To five-minute
WANG Z. et al. S o l a r- Y ( a r c s ec )
304 Å 171 Å 211 Å 131 Å-21 -9 3 15 27Solar-X (arcsec)364376388400412 S o l a r- Y ( a r c s ec ) -21 -9 3 15 27Solar-X (arcsec) -21 -9 3 15 27Solar-X (arcsec) -21 -9 3 15 27Solar-X (arcsec) -21 -9 3 15 27Solar-X (arcsec) 00.050.10.150.20.250.3 Fig. 3: Top: power maps of the five-minute oscillation centered at 3.3 with 1 mHz bandwidth to the sunspotin NOAA 12638. Bottom: the map of the three-minute oscillation centered at 5.6 with 1 mHz width. Thecolorbar is shown on the right. The white closed curves denote the umbral and penumbral boundaries,respectively.oscillations, the powers exist in penumbrae except for the temperature minimum. Moreover, the powers offive-minute oscillations are obviously higher than that of three-minute in the temperature minimum.
To further investigate the spatial positions of three- and five-minute oscillations in sunspots, we analyzedthe power spectrum of each pixel in every channel. Here, we used two frequency bands (centered at 3.3 and5.6 mHz with 1 mHz bandwidth) to construct their power maps. The constructed processes are as follows:(1) Remove a linear trend of the intensity curve of each pixel to remove the influence of the backgroundintensity variations.(2) Obtain the power spectrum of each intensity curve, and normalize them. The aim is to easily comparethe power spectra to different channel data.(3) Use a linear function to fit the power spectrum with a log-log scale, and extract the power above 95%confidence level. The process is similar to analyzing sunspot oscillations as above.(4) Accumulate those powers above the confidence level in a frequency band, and consider the sum as thevalue of the pixel position.The top and bottom of Figure 3 show power maps of the sunspot in NOAA 12638 in each channel forthe five- and three-minute oscillations, respectively. The colorbar is shown on the right, and the color fromred to black represents the power from high to low. patial Distributions of Sunspot Oscillation Modes at Different Temperatures 7
From the top of Figure 3 we can see that the powers of the five-minute oscillation mainly located at theumbral boundary in the AIA 1700 ˚A channel, and their distribution approximates a circle-shape structure.Moreover, part of spectra can also be found in the penumbra and umbra. This further explains the result,illustrated in the bottoms of Figures 1 and 2, that the five-minute oscillation appears in the penumbra andumbra in the AIA 1700 ˚A channel. In the AIA 304 ˚A channel, the diameter of the circle enlarges, meaningthat the oscillation propagates toward the penumbral boundary. In the 1700 ˚A and 304 ˚A channels, themaps of the other five sunspots are similar to that in NOAA 12638. The results have also been obtainedby Kolobov et al. (2016). They explained that five-minute oscillations propagate along inclined magneticfield lines. Our analysis further confirms their conclusion. Coincidentally, we used the same one of sunspotdata with them, i.e., the sunspot in NOAA 11479. To the AIA 171 ˚A, 211 ˚A, and 131 ˚A channels, withthe temperatures increase, it still expands outwards, but the oscillation becomes more disordered and theirpowers distinctly decrease. In particular, we are almost hard to find the circular shape in AIA 211 ˚A and 131˚A. This indicates that the five-minute oscillation is suppressed in high-temperature corona. We also mustpoint out that, to the two sunspots in NOAA 11433 and 12638, in 171 ˚A channel, only a semicircular shapeis found, and their powers are sporadic in the AIA 211 ˚A and 131 ˚A channels.
The bottom of Figure 3 shows the power maps of the three-minute oscillation. The powers mostly situate inthe umbral center in the 1700 ˚A channel. To the AIA 304 ˚A and 171 ˚A channels, the powers are obviouslyenhanced, and the oscillation gradually moves outward and until the umbral boundary. But, in the AIA 211˚A and 131 ˚A channels, the oscillation diffuses to the entire sunspot, and the powers also appear relativelyweak. This indicates that the three-minute oscillation is enhanced from the transition region to the lowercorona however its strength gradually decreases with the temperature increase.Other sunspots also have the same results that, from the AIA 1700 ˚A to 171 ˚A channels, the relativelyhigh powers gradually spread out from the umbral center to the boundary. Compared with the power maps ofNOAA 12638 in the AIA 171 ˚A, 211 ˚A, and 131 ˚A, the oscillations of the two sunspots in NOAA 11433 andNOAA 11479 have expended to their penumbral regions. The original images in the two active regions andthe corresponding power maps of the three-minute oscillations are shown in Figures 4 and 5, respectively.Here, the red asterisks mark the positions of the coronal loop footpoints. Combining the intensity images andpower maps, we can see that the oscillation powers outside the umbra locate at the coronal fan-structures.Furthermore, we note that the regions of the relatively high powers roughly coincide with loop footpoints.This meaning that three-minute oscillations may propagate along coronal fan-structures. The conclusionis also found by some authors (Reznikova & Shibasaki 2012; Yuan & Nakariakov 2012; De Moortel et al.2002; Jess et al. 2012).
WANG Z. et al.
171 Å16:00:12 UT-160-148-136-124-112 S o l a r- Y ( a r c s ec ) -23 -11 1 13 25Solar-X (arcsec)-160-148-136-124-112 S o l a r- Y ( a r c s ec )
211 Å16:00:12 UT-23 -11 1 13 25Solar-X (arcsec) 131 Å16:00:09 UT-23 -11 1 13 25Solar-X (arcsec) 00.050.10.150.20.250.3
Fig. 4: Top: images of the sunspot (NOAA 11176) observed in three channels: AIA 171 ˚A, 211 ˚A, and131 ˚A. Red asterisks denote loop footpoints. Bottom: the corresponding power maps of the three-minuteoscillation.
171 Å00:00:12 UT249261273285297 S o l a r- Y ( a r c s ec ) -31 -19 -7 5 17Solar-X (arcsec)249261273285297 S o l a r- Y ( a r c s ec )
211 Å00:00:12 UT-31 -19 -7 5 17Solar-X (arcsec) 131 Å00:00:09 UT-31 -19 -7 5 17Solar-X (arcsec) 00.050.10.150.20.250.3
Fig. 5: Same as Figure 4, but the sunspot in NOAA 11479. patial Distributions of Sunspot Oscillation Modes at Different Temperatures 9
By analyzing power spectra and power maps of three- and five-minute oscillations in randomly-chosen sixsunspots, we found that the three-minute oscillation is concentrated within an umbral area in the tempera-ture minimum, and the oscillation areas constantly increase in the transition region. With the temperaturesincrease, the power spectra of the three-minute oscillation are mostly concentrated in the position of theloop footpoints, and part of the power spectra are located at fan-loop structures. To the five-minute oscilla-tion, the power spectra exhibit a circle-shape structure at an umbra-penumbra boundary in the temperatureminimum. From the temperature minimum to the lower corona, the oscillations gradually move outward,and disappear in the higher corona.
Acknowledgements
The authors gratefully acknowledge the anonymous referee for his/her critical read-ing and invaluable comments and suggestions. We thank the use of
SDO/AIA image obtained courtesy ofNASA/SDO and the AIA science teams. This research is supported by the Joint Funds of the NationalNatural Science Foundation of China, and the Key Applied Basic Research Program of Yunnan Province(2018FA035), as well as the National Natural Science Foundation of China (11761141002, 11873089), theYouth Innovation Promotion Association CAS.
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