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# Proper Motions of Sunspots' Umbral Dots at High Temporal and Spatial Resolution

Hadis Goodarzi, Serge Koutchmy, Ali Adjabshirizadeh

► To cite this version:

Hadis Goodarzi, Serge Koutchmy, Ali Adjabshirizadeh. Proper Motions of Sunspots' Umbral Dots at High Temporal and Spatial Resolution. The Astrophysical Journal, 2018, 860, 10.3847/1538-4357/aac499. insu-03747696

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# Proper Motions of Sunspots' Umbral Dots at High Temporal and Spatial Resolution

Hadis Goodarzi<fnref n="1" />,<fnref n="2" /> ID, Serge Koutchmy<fnref n="3" />, and Ali Adjabshirizadeh<fnref n="4" />

Received 2017 December 31; revised 2018 May 5; accepted 2018 May 10; published 2018 June 25

## Abstract

To deepen the analysis of the photometric properties of the umbra of a sunspot, we study proper motions of small features such as umbral dots (UDs) inside a single sunspot observed by the Solar Optical Telescope of *Hinode* close to the disk center. We consider horizontal flows with high precision and details to study the transient motion behavior of UDs in short time intervals. Blue continuum images were first deconvolved with the point-spread function, such that the stray light is precisely removed and the original resolution is improved. Several images were co-added to improve the signal-to-noise ratio, keeping a reasonable temporal resolution and checking that the results are reproducible. The Fourier local correlation tracking technique is applied to the new corrected time sequence of images, and horizontal velocity maps were obtained both for the whole umbra (16" × 12") and for a high-resolution small region of the umbra (3'′5 × 3'′5) to study the smallest details of the velocity fields. We used two different Gaussian tracking windows (0.8 and 0.2′′), which reveals two types of horizontal motions for umbral features. First, a global inner penumbra and peripheral umbra inward motion directed to the central parts is revealed as an overall proper motion of bright peripheral fine structures. Second, motions matching small cells inside the darkest parts of the umbra with apparent sink and source areas are revealed, suggesting possible upflows and downflows appearing in different bright and dark locations without a definite answer regarding their brightness identification with a convective or a buoyant cell.

**Key words:** proper motions – Sun: photosphere – sunspots

**Supporting material:** animation

## 1. Introduction

Study of the sunspots and their fine structures is one the most important aspects of solar activity physics (Adjabshirizadeh & Koutchmy 1983). The velocity field inside a sunspot presents a significant amount of details presumably related to the origin of the sunspot. Methods like the local correlation tracking technique applied to images obtained in the deep continuum allow us to determine the proper motions in horizontal directions. The analysis of spectral shifts of photospheric absorption lines permits us to determine vertical or line-of-sight motions in higher levels where the lines are formed (Ortiz et al. 2010; Bharti et al. 2013; Riethmüller et al. 2013).

The existence of upflows and downflows in the umbra of a sunspot has been debated for several years (Deinzer 1965; Denker & Verma 2011; Riethmüller et al. 2013). For example, Deinzer (1965) concluded that convective motions should contribute to radiation, explaining the brightness of the umbra, and the question of the field-free or of the magnetized nature of these motions is open (Ortiz et al. 2010). The value of the plasma beta inside the umbra is close to unity, making both the mechanism of thermodynamical convection and the mechanism of buoyancy candidates for explaining up and down motions. Some evidence for upflows and downflows has been detected in sunspot structures as umbral dots (UDs) and light bridges (Rouppé van der Voort et al. 2010; Riethmüller et al. 2013). For instance, Watanabe et al. (2012) detected clear upflows for UDs using CRISP imaging spectropolarimeter data but could not detect systematic downflows associated with UDs. Also, Riethmüller et al. (2013) used the spectropolarization technique from *Hinode*/SP data by means of a 2D inversion method to

deduce line-of-sight velocity and managed to detect upflows and downflows for peripheral UDs; note that this is above the deepest layers forming the continuum radiation that we study here.

Because of the small size of the UDs and their varying size and velocity within a few minutes, studying motions of UDs requires high spatial and temporal resolution. Hence, we use the best available observations of the partial Sun free of turbulent Earth atmospheric effects from the Solar Optical Telescope (SOT) on board the *Hinode* spacecraft, after significantly enhancing the visibility and contrast by an optimum Maxlikelihood deconvolution with the point-spread function (PSF) deduced in a preceding paper (Goodarzi et al. 2015, hereafter Paper I) and improving the signal-to-noise ratio (S/N) by co-adding several images. The Fourier local correlation tracking (FLCT) technique has been used with different time intervals, fields of view, and FWHMs of the windowing Gaussian function for constructing a velocity map of the sunspot UDs with different resolutions to see any faint velocity changes in time. This technique was also applied to a granulation field of the nearby photosphere to demonstrate the correlation between converging (c) and diverging (d) proper motions in a cell pattern with downflows of intergranular parts and upflows of bright granular parts, respectively. Based on these results, horizontal velocity proper-motion maps can more convincingly also be used to consider vertical motion in the core of the sunspot by inferring sink (convergence) and source (divergence) area (November 1994; Sobotka et al. 1999), making the same assumption of mass continuity in a stratified medium as for granulation.

<footnote n="1">¹ School of Astronomy Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746, Tehran, Iran; goodarzi@ipm.ir, hadisgoodarzy@yahoo.com</footnote>

<footnote n="2">² Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha, Iran</footnote>

<footnote n="3">³ Institut d'Astrophysique de Paris UMR 7091 CNRS and UPMC (Sorbonne University) 98 Bis Bd Arago, F-75014, Paris, France</footnote>

<footnote n="4">⁴ Department of Astrophysics, Faculty of Physics Tabriz University, Tabriz, Iran</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Proper-motion (horizontal velocity component) map in the sunspot observed on 2007 March 1 as deduced from using the FLCT technique (the FWHM of the Gaussian windowing function is 0.′′8). The scale for velocity is inserted at the bottom left of the figure and corresponds to 2 km s⁻¹. Note the systematic inward proper motion of the inner penumbral features and dots; it is better to use a magnified image from the digital variant of the paper.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Histogram of horizontal velocities (in km s⁻¹) inside the sunspot for two different thresholds, 0.25 and 0.52 of the average photosphere intensity, revealing velocity values for only the central region of the umbra (left) and of the whole umbra (right), including the peripheral UD.</figcaption></figure>

## 2. Observations

We used well-focused images recorded with the broadband filter imager of the SOT on board the *Hinode* spacecraft (Suematsu et al. 2008; Tsuneta et al. 2008). Blue continuum images of the sunspot in NOAA AR 10944 that observed close to the disk center (heliocentric angle of 4°) on 2007 March 1 were selected. The blue filter has a central wavelength at 4504.5 Å and a bandwidth of 4 Å. Each pixel corresponds to 0.′′05448 on the surface of the Sun. Exposure time is 102 ms, the cadence is 6.4 s, and the field of view is approximately 56′′ × 28′′. All of the images are first corrected for dark current,

flat field, and bad pixels that are removed using the `fg_prep` routine and then co-aligned by means of the 2D cross-correlation algorithm involved in the `fg_rigidalign` routine (both of the codes are from the Solar Soft library) and then deconvolved with the PSF deduced in the previous paper (Goodarzi et al. 2015). Ninety successive blue continuum images taken between 00:19:51 and 00:29:20 with 6.4 s time intervals have been used to consider proper motions of fine structures inside sunspot umbra at high resolution, when adding images (at least three images averaging) to improve the S/N.
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Top: sunspot image observed on 2007 March 1 after correction with the deconvolution procedure. A red arrow shows the part of the umbra that is used to consider in detail the inward motion of the peripheral UDs. Bottom: velocity map for a partial frame of the umbra, including peripheral UDs (indicated with red arrows at the top of the image). The FWHM of the Gaussian windowing function is 0.′′2. Peripheral UDs show well inward motion to the umbra, but more details are revealed.</figcaption></figure>

## 2.1. FLCT Technique

In order to track proper motions of UDs, we used the FLCT method (Fisher & Welsch 2008). This technique permits us to map a 2D velocity field that connects two images that are taken at two different times, such that this flow field provides the scalar field in the first image, the result having the most similarity to the second image (Fisher & Welsch 2008). With this technique, it is possible to adjust a threshold value for intensities used to compute the flow field, so the algorithm will skip pixels with intensities lower than the threshold value (Fisher & Welsch 2008). Note that since the work from this

paper, a more advanced algorithm has appeared; see Asensio Ramos et al. (2017), where the possibility of computing the maps at three different levels is offered, using much more extended computations.

Up to now, the velocity field inside and around sunspots was described in several papers where ground-based images were used; see, e.g., Molowny-Horas (1994) and Ji et al. (2016). Space data have the great advantage of being free from the turbulent Earth atmosphere image effects, which is very important for a correlation-type analysis. In addition, effects due to scattered light should be corrected. This is especially important when fine and low-intensity structures are concerned, such as UDs. We described in our previous paper (Goodarzi et al. 2015) how important it is to take into account the far wings of the PSF, and only with this is it possible to remove stray light coming from far distances, indeed from the whole bright solar disk. We performed it by adding the Lorentzian function that has extended wings to the Gaussian function that describes the core of the PSF. We also use the limb of the Sun for modeling stray light quite far from the solar disk instead of the Mercury or Venus disk of limited diameter; this permitted us to go further and compute the coefficients of the Lorentzian and Gaussian functions more accurately.

After deducing the PSF precisely, a deconvolution procedure was performed using the iteration method (Goodarzi et al. 2015, 2016). Correction with this method leads to a higher contrast and a deeper evaluation of the images that are now free of stray light. In order to improve the S/N, several images (at least three images, up to 10 images) were co-added, and then the FLCT technique was applied to successive average images to deduce the velocity fields. We performed our analysis of sunspot umbra in two parts: an overall proper-motion mapping of the whole umbra (including the inward motion of peripheral UDs; see Figure 1), and a mapping of a small selected region, which represents a part of the sunspot umbra, to see the ultimate details of proper motions.

## 3. Overall Proper Motion of the Whole Umbra

To see the overall proper motions of umbral features, we applied the FLCT technique to the images of the sunspot observed on 2007 March 1 after deconvolution and co-adding images to improve the S/N. This part is specially done to demonstrate that the result of running the FLCT code is altogether in agreement with the results of other works (e.g., Molowny-Horas 1994; Sobotka et al. 2008), but in the details, there are a lot of new features. It is also in agreement with the impression given after watching the movie of our deconvolved images (see Paper I).

In order to analyze the overall proper motions of umbral features and UDs, we selected the entire field of view for running the FLCT code with a rather large FWHM of the windowing Gaussian function (0.′′8) used for the mapping. Figure 1 shows the velocity map of the whole sunspot region obtained using deconvolved images and averaging three successive images made with a 6.4 s interval between two successive images (19 s averaging) and shifting the averaging by 6 minutes after another three successive images were averaged (without overlapping) to see the motion of the umbral and the penumbral features during this 6-minute interval between two average images. Also, we imposed a threshold value equal to approximately 15% of the average photospheric intensity for using the FLCT code to select just the behavior of
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Detailed horizontal velocity map, including the darkest umbral parts of the sunspot observed on March 1, after significantly improving the S/N (see Section 5). The FWHM of the Gaussian windowing function is 0.2". The scale inserted at the bottom left corresponds to 200 m s⁻¹.</figcaption></figure>

the very bright features, so the code skips pixels with lower intensities dominated by the noise. For the corrected intensity values that we used, see our Paper II (Goodarzi et al. 2016). Inward motions of the peripheral UDs are well apparent in this velocity map. Note also in the granular region of the image that the downflow in the dark intergranular region and upflows in the bright parts are clearly seen all around the sunspot.

It can be seen from Figure 1 (it is better to use a magnified image from the digital variant of the paper) that our result of running the FLCT code on deeply deconvolved images is in overall agreement with Molowny-Horas (1994), Ji et al. (2016), and Sobotka et al. (2008). As Figure 1 suggests, peripheral UDs show higher horizontal velocities in comparison with central UDs. To compare this quantitatively, two histograms of the velocity values have been prepared: one of them includes both peripheral and central UDs, and one of them includes only velocities of the central part of the umbra. This is performed using two different threshold values, corresponding to approximately 50% and 25% of the average frontier intensities. As can be seen from the histograms in Figure 2 and the velocity map of Figure 1, when peripheral UDs are included, higher values of the horizontal velocities (between 400 and 700 m s⁻¹) are more likely to exist, which means that features faster than 400 m s⁻¹ are usually found in the peripheral part of the umbra, where magnetic field is weaker than inside the core and is more horizontal, which is consistent with the results of Sobotka & Puschmann (2009) and also Watanabe et al. (2009).

## 4. Inward Motion of Peripheral UDs

In velocity maps derived with different methods, peripheral UDs show the inward motion toward the umbra (Hamedivafa 2015). These motions can be clearly seen from Figure 1, but to consider them with more details and with a higher resolution, we made a velocity map for a small part of the umbra–penumbral border (also called the periphery of the umbra) and using a much smaller FWHM of the windowing Gaussian function (0.2"). This is made achievable since, by using accurately deconvolved images free of scattered light (Goodarzi et al. 2015) and after improving the S/N at an optimum level to guarantee the reproducibility of the results, the most significant intensity distributions (see the next part) are used. The selected part is shown with a red arrow in the top panel of Figure 3, using a deconvolved sunspot full image observed on 2007 March 1; this field includes several bright peripheral UDs. The bottom panel of Figure 3 shows the result of using the FLCT technique for this region (we have six consecutive images with 6.4 s cadence; averaging every three images leads to two average images, and Figure 3 is the result of an FLCT run from comparison of these two average images). As can be seen, peripheral UDs have inward motion to the umbra, but some more details are also revealed, like the small diverging and/or converging flows that accompany this inward motion.
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Top: deconvolved sunspot image, with the blue box showing a selected field of view for making proper-motion maps of the granulation part (Figure 6) and the red box showing a selected field of view for computing the horizontal flow field for 9.6 minutes in the small part of the umbra as illustrated in Figure 8. A mosaic of the averaged images of a selected part of the sunspot (red box at the top of image) evolving for 9.6 minutes is shown, with the isolated bright UD of a short lifetime shown in window “e.”</figcaption></figure>

**5. High-resolution Velocity Maps**

We presented in Figure 1 the global proper-motion map of the sunspot field, including the umbra, penumbra, and also the granulation part of the surrounding photosphere, by imposing a threshold value for using the FLCT code to follow only the very bright features while using a large FWHM of the windowing Gaussian function (0.8).

Now, to see the details in full resolution, a smaller FWHM of the windowing Gaussian function has been used for the whole umbra without any threshold value. Because we take into account all pixels, including pixels corresponding to low intensities (especially in the darkest parts of the umbra), we have to significantly improve the S/N by co-adding more images (10 images) to reduce the noise that would contribute in deriving velocity maps. Figure 4 shows the proper-motion map of the sunspot umbra that is obtained after deconvolution of 90 images (after making evaluation tests to optimize the procedure), an averaging of 10 successive images with a 6.4 s time interval between them (1-minute averaging), and shifting the averaging procedure to the next 10 images, with three images overlapping, and computing the velocity field from these average images. The averaging procedure continued up to

90 images, which led to 11 resulting velocity maps. Figure 4 is the average of these 11 velocity maps, corresponding to a duration of 9.6 minutes.

From Figure 4 the following can be seen: (i) Peripheral UD's show the inward motion to the umbra, with additional details revealing converging and diverging flows; the converging and diverging behavior happens more clearly in the endpoint of the penumbral filaments or peripheral UD's with higher S/N in comparison with central UD's, which is consistent with Riethmüller et al. (2013). (ii) In the penumbral part of the image (top left) we see flows that are perpendicular to the bright filament and that move across the bright filament going to the dark filament. (iii) In the umbra, there is evidence of both converging and diverging horizontal motions everywhere.

**6. Interpreting Upflows and Downflows from Converging and Diverging Horizontal Motions**

The FLCT technique has been used to deduce horizontal motions of different solar structures. However, some upflows and downflows can be inferred from the converging and diverging arrow distribution, as has been done for the granulation starting from the works on SOUP data (see Simon et al. 1989). In order to examine this technique to presumably infer vertical motions, we applied it to a granulation part of the adjacent photosphere surrounding the sunspot, indicated with a blue rectangle in the top panel of Figure 5. This field was submitted to exactly the same processing (cadence, corrections, deconvolution, and summing) that was done for the UD field (see below). We assume as usual that bright granules are convective cells. Accordingly, they correspond to upward motions, and conversely, intergranular space corresponds to downward motions. We also assume that for the small scales corresponding to our analysis, 5-minute oscillations do not perturb the results. Every 10 images with 6.4 s cadence have been added, with three images overlapping, and the proper motion between the first two average images (45 s time interval) has been computed and depicted in Figure 6. The Gaussian width used for weighting images equals 0.2. In this velocity map, we see converging flows in intergranular parts, and diverging flows also appear in several bright points of granular parts, which corresponds to downflows and upflows, respectively.

We notice that these apparent flows could also be due to brightness changes of coherent but unknown nature; however, it is not legitimate to ignore the presence of downflows and upflows contributing to these brightness changes in order to take into account the convective phenomena that are today well explained by impressive theoretical simulations (see, e.g., Stein & Nordlund 1998). The good correlation of lanes with downflow in the intergranular parts and the diverging pattern as cells with upflow in the bright granular parts show that the FLCT techniques permit a valuable evaluation of vertical motions using the parameters of our analysis.

**7. Proper Motions of UD's at Ultimate Resolution**

In the velocity maps of Figures 3 and 4 it was clear that using the high-quality deconvolved and averaged images reveals more details of proper motions and some diverging and converging areas appear in both the bright and dark regions. Also, some of the motions change their orientation in short time intervals (less than 1 minutes) that might be ignored in velocity
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Horizontal velocity field computed for the selected granulation part near the sunspot shown in the blue box in the top panel of Figure 5. The FWHM of the Gaussian windowing function is 0.2 arcsec.</figcaption></figure>

maps derived from images with longer time intervals (Figure 4, which is an average over 9.6 minutes). To see the maximum of details and the tiny variations of proper motions using the ultimate resolution from this analysis, a set of new velocity maps was evaluated on a small field of view (3.5 × 3.5) and short time interval (45 s) after corrections and improving the S/N.

For this purpose, we used 90 successive blue filter images with 6.4 s cadence after deconvolution that cover approximately 9.6 minutes. Each set of 10 images was co-added, with three images overlapping, in order to improve the S/N and also to preserve the continuity between images, so 12 average images were deduced with approximately a 45 s time interval between them. Then, a small field of view that includes a part of the inner penumbra and some peripheral UDs is selected from the sunspot image to see the tiny velocity field attributed to umbral features. This selected part (shown with a red box in the top panel of Figure 5) is specially chosen because of the very typical case of a well-observed isolated bright UD (see the red circle in panel (e) of Figure 5), which is approximately roundish and evolutionally appealing. The Gaussian width used for weighting images equals 0.2, which is almost the smallest reasonable width for a tracking window keeping a reasonable signal/noise ratio.

From the 12 average images, 11 velocity maps are prepared, and a mosaic of them is depicted in Figure 7; they are also shown in a short online video (made from 11 frames), which is available in the electronic version of the paper.

The bottom panels of Figure 5 show the time brightness evolution of the selected small part of the umbra with a cadence of 45 s (red box in the top panel of Figure 5), including the interesting case of a well-isolated UD indicated with a red circle in “e.” This UD first appears faintly (a), then becomes brighter (f, g), and finally fades after approximately 9.6 minutes when its direction of motion changes over time, which can be seen better with the high resolution in the velocity maps of Figure 7 (or in the movie).

From the velocity maps (Figure 7 and the movie) two kinds of motions can be distinguished at a short time interval (45 s) and for a small field of view with a much improved resolution: (i) Proper motions toward a preferred direction, for example, position (x, y) = (0.8, 1.4) in panel (a) of Figure 7. Some of these motions can change slightly their trajectory, by tracking the case of an isolated UD (position (x, y) = (1.5, 1.5) in panel (a) of Figure 7). It can be seen that the direction of its horizontal motion changes during a small time interval but there is a dominant movement toward the umbra. As noted before, the most dominant horizontal motion of the bright
<figure><img src="image_10.png" /><figcaption>**Figure 7.** Velocity field computed from the FLCT technique for a small field of view (red box in the top panel of Figure 5) and for short time intervals (45 s). The FWHM of the Gaussian windowing function is 0.2. Red arrows show the direction of velocity for each point, and its length shows the amplitude of the horizontal component of the velocity compared to the scale inserted in panel (j), which corresponds to 200 m s⁻¹.</figcaption></figure>

(An animation of this figure is available.)
<figure><img src="image_11.png" /><figcaption>**Figure 8.** Velocity field computed from the FLCT technique for a small field of view and for short time intervals (45 s), with labels showing converging (c) and diverging (D) flows. The FWHM of the Gaussian windowing function is $0.2''$.</figcaption></figure>

points (like the one marked with a red circle in the bottom panels of Figure 5) is toward the umbra, but some small-scale turbulent behavior may be seen also. (ii) Some flows in the form of converging (c) and diverging (d) cells that could correspond to possible inward and outward motions as deduced from considerations of continuity. Outward motions (source area, where red arrows tend to show up farther from each other; see, e.g., Figure 8) are sometimes seen near some bright points, while there are cases of outward motions in the dark area. The centers of several diverging velocity patterns ("d" cells) are rather side-on to the UDs' maximum intensity brightness.

Since the occurrence of vertical flows preferentially in deep photospheric layers was considered in theoretical works (e.g., Riethmüller et al. 2013), images taken in the blue continuum that we used correspond to the deepest layer of the photosphere, and they show suitable candidates for revealing these flows. Source fields associated with bright UDs are not always overlapping the maximum brightness of UDs, and some displacement can be seen, as also appears in other works (Ortiz et al. 2010). There are also some sink areas (or downflows) that mostly appear at the periphery of UDs or in the border region between bright features, and this is rather consistent with Riethmüller et al. (2013), which found downflows in 200–500 km distance from UD center, which are concentrated on one or two sides of UDs. Since we could not detect any dark lane inside UDs, it is not possible to follow their endpoints looking at downflows, as Schüssler & Vögler (2006) predicted from their most detailed magnetoconvective simulations, but we can say that they mostly appear only at the side of the bright features (see also Goodarzi et al. 2016). In addition, our observations show fast changes, over 1 minute of time, which are not seen in published magnetoconvection simulations.

## 8. Conclusion

We detected proper motion of umbral fine features from corrected (restored by deconvolution of the measured PSF) blue continuum images with different time intervals, and spatial scales show new features in the small-scale velocity maps. The most dominant motion of fine structures is toward the umbra, but when higher resolution is considered, more details can be seen, such as the complex cells of converging and diverging flows, which could be the sign of vertical motions of plasma. These possible upflows usually appear near bright features, while downflow evidences tend to exist at the periphery of bright features or in the border between them.

We could not see any dark lane inside of UDs predicted by numerical simulation (Schüssler & Vögler 2006; Bharti et al. 2010), but their prediction of upflows and downflows in and around UDs can still be consistent with our observational findings, taking into account (i) the limited resolution of our observations, (ii) the limitation of the interpretation of our flow map of horizontal velocities in term of upflows (source) and downflows (sink), and (iii) the approximations used in the simulations.

Our results are complementary to the results obtained from the analysis of spectral line shifts in the regions above the continuum layers (Ortiz et al. 2010; Riethmüller et al. 2013). Furthermore, we provide evidence for systematic fast motions inside the core of the probed sunspot.

When a time sequence is considered, the temporal variation of the velocity reveals a sort of turbulent behavior in the trajectory of the bright UDs that was analyzed in detail. Horizontal proper motions that are not reproduced in the recent numerical simulations that we know are evidenced. The example of a dark region of the core showing some diverging cells appearing to be temporary is pointed out. Accordingly, it is not inappropriate to remind about the umbral oscillatory convection theoretically studied in Weiss et al. (1990) in the frame of the magnetoconvection inside a sunspot. The analysis of a much longer time sequence taken at different formation heights is desirable to go in this direction. Given the improved S/N (Figures 4 and 7), a detailed and complete map of the entire umbra, including the darkest regions, has been obtained. We note that when we point to the systematic motions toward the umbra, it does not necessarily mean a direct movement, and some turbulent behavior also exists that is revealed by tracking a sequence of high-resolution velocity maps (see also the movie of Paper I).

Hinode is a Japanese mission developed and launched by ISAS/JAXA, collaborating with NAOJ as a domestic partner, NASA and STFC (UK) as international partners. Scientific operation of the Hinode mission is conducted by the Hinode science team organized at ISAS/JAXA. This team mainly consists of scientists from institutes in the partner countries. Support for the post-launch operation is provided by JAXA and NAOJ (Japan), STFC (U.K.), NASA, ESA, and NSC (Norway). We thank Habib Khosroshahi for providing a critical reading of the paper and our reviewer for meaningful remarks. This work has been supported financially by the Research Institute for Astronomy and Astrophysics of Maragha (RIAAM) under research project No. 1/5237-69.
ORCID iDs

Hadis Goodarzi https://orcid.org/0000-0001-9128-2012

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